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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1880

Last change on this file since 1880 was 1880, checked in by hoffmann, 8 years ago
Bugfix in lpm_collision_kernels
Property svn:keywords set to `Id`
File size: 38.8 KB

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[1873]	1	!> @file lpm_collision_kernels.f90
[1036]	2	!--------------------------------------------------------------------------------!
	3	! This file is part of PALM.
	4	!
	5	! PALM is free software: you can redistribute it and/or modify it under the terms
	6	! of the GNU General Public License as published by the Free Software Foundation,
	7	! either version 3 of the License, or (at your option) any later version.
	8	!
	9	! PALM is distributed in the hope that it will be useful, but WITHOUT ANY
	10	! WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR
	11	! A PARTICULAR PURPOSE. See the GNU General Public License for more details.
	12	!
	13	! You should have received a copy of the GNU General Public License along with
	14	! PALM. If not, see <http://www.gnu.org/licenses/>.
	15	!
[1818]	16	! Copyright 1997-2016 Leibniz Universitaet Hannover
[1036]	17	!--------------------------------------------------------------------------------!
	18	!
[790]	19	! Current revisions:
	20	! -----------------
[1880]	21	! Bugfix: The index of the larger particle has to be chosen for interpolation.
[1347]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: lpm_collision_kernels.f90 1880 2016-04-20 09:36:50Z hoffmann $
	26	!
[1874]	27	! 1873 2016-04-18 14:50:06Z maronga
	28	! Module renamed (removed _mod)
	29	!
[1859]	30	! 1858 2016-04-13 13:12:11Z hoffmann
	31	! Interpolation of collision kernels adjusted to more reasonable values.
	32	! Reformatting of the code.
	33	!
[1851]	34	! 1850 2016-04-08 13:29:27Z maronga
	35	! Module renamed
	36	!
[1823]	37	! 1822 2016-04-07 07:49:42Z hoffmann
	38	! PALM kernel has been deleted.
	39	! Bugfix in the calculation of the turbulent enhancement factor of the
	40	! collection efficiency.
	41	!
	42	! Unused variables removed.
	43	!
[1777]	44	! 1776 2016-03-02 17:54:58Z hoffmann
	45	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	46	!
[1683]	47	! 1682 2015-10-07 23:56:08Z knoop
	48	! Code annotations made doxygen readable
	49	!
[1520]	50	! 1519 2015-01-08 10:20:42Z hoffmann
	51	! Bugfix: Using the new particle structure, particles are not sorted by size.
	52	! Hence, computation of collision efficiencies must ensure that the ratio of
	53	! two colliding droplets is < 1.
	54	!
[1360]	55	! 1359 2014-04-11 17:15:14Z hoffmann
	56	! New particle structure integrated.
	57	! Kind definition added to all floating point numbers.
	58	!
[1347]	59	! 1346 2014-03-27 13:18:20Z heinze
	60	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	61	! intrinsic function like MAX, MIN, SIGN
	62	!
[1323]	63	! 1322 2014-03-20 16:38:49Z raasch
	64	! REAL constants defined as wp_kind
	65	!
[1321]	66	! 1320 2014-03-20 08:40:49Z
[1320]	67	! ONLY-attribute added to USE-statements,
	68	! kind-parameters added to all INTEGER and REAL declaration statements,
	69	! kinds are defined in new module kinds,
	70	! revision history before 2012 removed,
	71	! comment fields (!:) to be used for variable explanations added to
	72	! all variable declaration statements
[1008]	73	!
[1093]	74	! 1092 2013-02-02 11:24:22Z raasch
	75	! unused variables removed
	76	!
[1072]	77	! 1071 2012-11-29 16:54:55Z franke
	78	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	79	!
[1037]	80	! 1036 2012-10-22 13:43:42Z raasch
	81	! code put under GPL (PALM 3.9)
	82	!
[1008]	83	! 1007 2012-09-19 14:30:36Z franke
[1007]	84	! converted all units to SI units and replaced some parameters by corresponding
	85	! PALM parameters
	86	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	87	! changed from 10. to 1.0
[829]	88	!
[850]	89	! 849 2012-03-15 10:35:09Z raasch
	90	! routine collision_efficiency_rogers added (moved from former advec_particles
	91	! to here)
	92	!
[836]	93	! 835 2012-02-22 11:21:19Z raasch $
	94	! Bugfix: array diss can be used only in case of Wang kernel
	95	!
[829]	96	! 828 2012-02-21 12:00:36Z raasch
[828]	97	! code has been completely reformatted, routine colker renamed
	98	! recalculate_kernel,
	99	! routine init_kernels added, radius is now communicated to the collision
	100	! routines by array radclass
[790]	101	!
[828]	102	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	103	!
[826]	104	! 825 2012-02-19 03:03:44Z raasch
	105	! routine renamed from wang_kernel to lpm_collision_kernels,
	106	! turbulence_effects on collision replaced by wang_kernel
	107	!
[791]	108	! 790 2011-11-29 03:11:20Z raasch
	109	! initial revision
[790]	110	!
	111	! Description:
	112	! ------------
[1682]	113	!> This module calculates collision efficiencies either due to pure gravitational
	114	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	115	!> including the effects of turbulence (Wang kernel, see Wang and
	116	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	117	!> New J. Phys., 10, 075016). The original code has been
[1682]	118	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	119	!> here.
[790]	120	!------------------------------------------------------------------------------!
[1682]	121	MODULE lpm_collision_kernels_mod
	122
[790]	123
[1320]	124	USE constants, &
	125	ONLY: pi
	126
	127	USE kinds
	128
	129	USE particle_attributes, &
[1822]	130	ONLY: collision_kernel, dissipation_classes, particles, &
	131	radius_classes
[1320]	132
[828]	133	USE pegrid
[790]	134
[828]	135
[790]	136	IMPLICIT NONE
	137
	138	PRIVATE
	139
[1822]	140	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	141	recalculate_kernel
[790]	142
[1682]	143	REAL(wp) :: epsilon !<
	144	REAL(wp) :: rclass_lbound !<
	145	REAL(wp) :: rclass_ubound !<
	146	REAL(wp) :: urms !<
[790]	147
[1822]	148	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	149	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	150	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	151
[1822]	152	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	153	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	154	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	155	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	156	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	157
[1822]	158	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	159
[828]	160	SAVE
[792]	161
[790]	162	!
	163	!-- Public interfaces
[828]	164	INTERFACE init_kernels
	165	MODULE PROCEDURE init_kernels
	166	END INTERFACE init_kernels
[790]	167
[828]	168	INTERFACE recalculate_kernel
	169	MODULE PROCEDURE recalculate_kernel
	170	END INTERFACE recalculate_kernel
[790]	171
	172
[828]	173	CONTAINS
[790]	174
[792]	175
[828]	176	!------------------------------------------------------------------------------!
[1682]	177	! Description:
	178	! ------------
	179	!> Initialization of the collision efficiency matrix with fixed radius and
	180	!> dissipation classes, calculated at simulation start only.
[828]	181	!------------------------------------------------------------------------------!
[1682]	182
	183	SUBROUTINE init_kernels
[792]	184
[828]	185	IMPLICIT NONE
[792]	186
[1682]	187	INTEGER(iwp) :: i !<
	188	INTEGER(iwp) :: j !<
	189	INTEGER(iwp) :: k !<
[790]	190
[828]	191
	192	!
	193	!-- Calculate collision efficiencies for fixed radius- and dissipation
	194	!-- classes
	195	IF ( collision_kernel(6:9) == 'fast' ) THEN
	196
[1822]	197	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	198	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	199	radclass(1:radius_classes) )
	200
	201	!
	202	!-- Calculate the radius class bounds with logarithmic distances
[1858]	203	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	204	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	205	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	206	radclass(1) = EXP( rclass_lbound )
[828]	207	DO i = 2, radius_classes
	208	radclass(i) = EXP( rclass_lbound + &
[1359]	209	( rclass_ubound - rclass_lbound ) * &
	210	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	211	ENDDO
	212
	213	!
[1858]	214	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	215	DO i = 1, dissipation_classes
[1858]	216	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	217	ENDDO
	218	!
	219	!-- Calculate collision efficiencies of the Wang/ayala kernel
	220	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	221	ecf(1:radius_classes,1:radius_classes), &
	222	gck(1:radius_classes,1:radius_classes), &
	223	winf(1:radius_classes) )
	224
	225	DO k = 1, dissipation_classes
	226
	227	epsilon = epsclass(k)
[1359]	228	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	229
	230	CALL turbsd
	231	CALL turb_enhance_eff
	232	CALL effic
	233
	234	DO j = 1, radius_classes
	235	DO i = 1, radius_classes
	236	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	237	ENDDO
	238	ENDDO
	239
	240	ENDDO
	241
	242	!
	243	!-- Calculate collision efficiencies of the Hall kernel
	244	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	245	hwratio(1:radius_classes,1:radius_classes) )
	246
	247	CALL fallg
	248	CALL effic
	249
	250	DO j = 1, radius_classes
	251	DO i = 1, radius_classes
	252	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	253	* ec(i,j) * ABS( winf(j) - winf(i) )
	254	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	255	ENDDO
	256	ENDDO
	257
	258	!
	259	!-- Test output of efficiencies
	260	IF ( j == -1 ) THEN
	261
	262	PRINT, '** Hall kernel'
[1359]	263	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	264	i = 1,radius_classes )
[828]	265	DO j = 1, radius_classes
[1007]	266	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	267	( hkernel(i,j), i = 1,radius_classes )
[828]	268	ENDDO
	269
	270	DO k = 1, dissipation_classes
	271	DO i = 1, radius_classes
	272	DO j = 1, radius_classes
[1359]	273	IF ( hkernel(i,j) == 0.0_wp ) THEN
	274	hwratio(i,j) = 9999999.9_wp
[828]	275	ELSE
	276	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	277	ENDIF
	278	ENDDO
	279	ENDDO
	280
	281	PRINT, '** epsilon = ', epsclass(k)
[1359]	282	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	283	i = 1,radius_classes )
[828]	284	DO j = 1, radius_classes
[1359]	285	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	286	( hwratio(i,j), i = 1,radius_classes )
[828]	287	ENDDO
	288	ENDDO
	289
	290	ENDIF
	291
	292	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	293
	294	ENDIF
	295
	296	END SUBROUTINE init_kernels
	297
	298
[790]	299	!------------------------------------------------------------------------------!
[1682]	300	! Description:
	301	! ------------
	302	!> Calculation of collision kernels during each timestep and for each grid box
[790]	303	!------------------------------------------------------------------------------!
[828]	304	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	305
[1320]	306	USE arrays_3d, &
	307	ONLY: diss
[790]	308
[1320]	309	USE particle_attributes, &
[1858]	310	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	311
[790]	312	IMPLICIT NONE
	313
[1682]	314	INTEGER(iwp) :: i !<
	315	INTEGER(iwp) :: i1 !<
	316	INTEGER(iwp) :: j !<
	317	INTEGER(iwp) :: j1 !<
	318	INTEGER(iwp) :: k1 !<
[790]	319
	320
[1858]	321	number_of_particles = prt_count(k1,j1,i1)
	322	radius_classes = number_of_particles ! necessary to use the same
	323	! subroutines as for
	324	! precalculated kernels
[792]	325
[1858]	326	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	327	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	328
[828]	329	!
[1007]	330	!-- Store particle radii on the radclass array
[1858]	331	radclass(1:number_of_particles) = particles(1:number_of_particles)%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
[1858]	343	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	344	ecf(1:number_of_particles,1:number_of_particles) )
[790]	345
[828]	346	CALL turbsd
	347	CALL turb_enhance_eff
	348	CALL effic
[790]	349
[1858]	350	DO j = 1, number_of_particles
	351	DO i = 1, number_of_particles
	352	ckernel(1+i-1,1+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
[1858]	364	DO j = 1, number_of_particles
	365	DO i = 1, number_of_particles
	366	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	367	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	368	ENDDO
	369	ENDDO
	370
	371	ENDIF
	372
[828]	373	DEALLOCATE( ec, radclass, winf )
[790]	374
[828]	375	END SUBROUTINE recalculate_kernel
[790]	376
[828]	377
[790]	378	!------------------------------------------------------------------------------!
[1682]	379	! Description:
	380	! ------------
[1822]	381	!> Calculation of effects of turbulence on the geometric collision kernel
	382	!> (by including the droplets' average radial relative velocities and their
	383	!> radial distribution function) following the analytic model by Aayala et al.
	384	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	385	!> page 37ff.
	386	!>
	387	!> Input parameters, which need to be replaced by PALM parameters:
	388	!> water density, air density
[790]	389	!------------------------------------------------------------------------------!
[792]	390	SUBROUTINE turbsd
[799]	391
[1320]	392	USE control_parameters, &
	393	ONLY: g, molecular_viscosity
	394
	395	USE particle_attributes, &
	396	ONLY: radius_classes
[790]	397
	398	IMPLICIT NONE
	399
[1682]	400	INTEGER(iwp) :: i !<
	401	INTEGER(iwp) :: j !<
[790]	402
[1682]	403	REAL(wp) :: ao !<
	404	REAL(wp) :: ao_gr !<
	405	REAL(wp) :: bbb !<
	406	REAL(wp) :: be !<
	407	REAL(wp) :: b1 !<
	408	REAL(wp) :: b2 !<
	409	REAL(wp) :: ccc !<
	410	REAL(wp) :: c1 !<
	411	REAL(wp) :: c1_gr !<
	412	REAL(wp) :: c2 !<
	413	REAL(wp) :: d1 !<
	414	REAL(wp) :: d2 !<
	415	REAL(wp) :: eta !<
	416	REAL(wp) :: e1 !<
	417	REAL(wp) :: e2 !<
	418	REAL(wp) :: fao_gr !<
	419	REAL(wp) :: fr !<
	420	REAL(wp) :: grfin !<
	421	REAL(wp) :: lambda !<
	422	REAL(wp) :: lambda_re !<
	423	REAL(wp) :: lf !<
	424	REAL(wp) :: rc !<
	425	REAL(wp) :: rrp !<
	426	REAL(wp) :: sst !<
	427	REAL(wp) :: tauk !<
	428	REAL(wp) :: tl !<
	429	REAL(wp) :: t2 !<
	430	REAL(wp) :: tt !<
	431	REAL(wp) :: t1 !<
	432	REAL(wp) :: vk !<
	433	REAL(wp) :: vrms1xy !<
	434	REAL(wp) :: vrms2xy !<
	435	REAL(wp) :: v1 !<
	436	REAL(wp) :: v1v2xy !<
	437	REAL(wp) :: v1xysq !<
	438	REAL(wp) :: v2 !<
	439	REAL(wp) :: v2xysq !<
	440	REAL(wp) :: wrfin !<
	441	REAL(wp) :: wrgrav2 !<
	442	REAL(wp) :: wrtur2xy !<
	443	REAL(wp) :: xx !<
	444	REAL(wp) :: yy !<
	445	REAL(wp) :: z !<
[790]	446
[1822]	447	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	448	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	449
[1822]	450	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	451	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	452	tl = urms**2 / epsilon
	453	lf = 0.5_wp * urms**3 / epsilon
	454	tauk = SQRT( molecular_viscosity / epsilon )
	455	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	456	vk = eta / tauk
[790]	457
[1359]	458	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	459	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	460
[1822]	461	!
	462	!-- Get terminal velocity of droplets
	463	CALL fallg
[790]	464
[828]	465	DO i = 1, radius_classes
[1822]	466	tau(i) = winf(i) / g ! inertial time scale
	467	st(i) = tau(i) / tauk ! Stokes number
[790]	468	ENDDO
	469
[828]	470	!
[1822]	471	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	472	z = tt / tl
[1322]	473	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	474	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	475	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	476	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	477	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	478	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	479	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	480	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	481	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	482	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	483	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	484
[828]	485	DO i = 1, radius_classes
[790]	486
[1822]	487	v1 = winf(i)
	488	t1 = tau(i)
[790]	489
[828]	490	DO j = 1, i
[1007]	491	rrp = radclass(i) + radclass(j)
[1822]	492	v2 = winf(j)
	493	t2 = tau(j)
[790]	494
[1007]	495	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	496	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	497	v1xysq = v1xysq * urms**2 / t1
	498	vrms1xy = SQRT( v1xysq )
[790]	499
[1007]	500	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	501	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	502	v2xysq = v2xysq * urms**2 / t2
	503	vrms2xy = SQRT( v2xysq )
[790]	504
[828]	505	IF ( winf(i) >= winf(j) ) THEN
[799]	506	v1 = winf(i)
[790]	507	t1 = tau(i)
[799]	508	v2 = winf(j)
[790]	509	t2 = tau(j)
	510	ELSE
[799]	511	v1 = winf(j)
[790]	512	t1 = tau(j)
[799]	513	v2 = winf(i)
[790]	514	t2 = tau(i)
	515	ENDIF
	516
[828]	517	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	518	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	519	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	520	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	521	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	522	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	523	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	524	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	525	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	526	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	527
[828]	528	!
[1822]	529	!-- Calculate radial distribution function (grfin)
[828]	530	IF ( st(j) > st(i) ) THEN
	531	sst = st(j)
[790]	532	ELSE
[828]	533	sst = st(i)
[790]	534	ENDIF
	535
[1359]	536	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	537	sst*2 + 5.3406_wp sst
	538	IF ( xx < 0.0_wp ) xx = 0.0_wp
	539	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	540
[1007]	541	c1_gr = xx / ( g / vk * tauk )**yy
[790]	542
[1322]	543	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	544	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	545	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	546
[1359]	547	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	548	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	549
[1822]	550	!
	551	!-- Calculate general collection kernel (without the consideration of
	552	!-- collection efficiencies)
	553	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	554	gck(j,i) = gck(i,j)
	555
	556	ENDDO
	557	ENDDO
	558
[828]	559	END SUBROUTINE turbsd
[790]	560
[1320]	561	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	562	!
	563	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	564	!-- effects on the collision kernel
[790]	565	IMPLICIT NONE
	566
[1682]	567	REAL(wp) :: a !<
	568	REAL(wp) :: aa1 !<
	569	REAL(wp) :: b !<
	570	REAL(wp) :: tau0 !<
	571	REAL(wp) :: vsett !<
[790]	572
[1359]	573	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	574	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	575
[1007]	576	END FUNCTION phi_w
[792]	577
[1320]	578	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	579	!
	580	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	581	!-- effects on the collision kernel
[790]	582	IMPLICIT NONE
	583
[1682]	584	REAL(wp) :: a !<
	585	REAL(wp) :: aa1 !<
	586	REAL(wp) :: aa2 !<
	587	REAL(wp) :: aa3 !<
	588	REAL(wp) :: aa4 !<
	589	REAL(wp) :: aa5 !<
	590	REAL(wp) :: aa6 !<
	591	REAL(wp) :: b !<
	592	REAL(wp) :: tau1 !<
	593	REAL(wp) :: tau2 !<
	594	REAL(wp) :: vsett1 !<
	595	REAL(wp) :: vsett2 !<
[790]	596
[1359]	597	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	598	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	599	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	600	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	601	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	602	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	603	vsett1 / vsett2
	604	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	605	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	606	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	607	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	608
[828]	609	END FUNCTION zhi
[790]	610
[828]	611
[790]	612	!------------------------------------------------------------------------------!
[1682]	613	! Description:
	614	! ------------
[1822]	615	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	616	!> Meteorol.)
[790]	617	!------------------------------------------------------------------------------!
[828]	618	SUBROUTINE fallg
[790]	619
[1320]	620	USE particle_attributes, &
	621	ONLY: radius_classes
[790]	622
[828]	623	IMPLICIT NONE
[790]	624
[1822]	625	INTEGER(iwp) :: j !<
[790]	626
[1822]	627	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	628	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	629	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	630	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	631	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	632	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	633
[1822]	634	REAL(wp) :: diameter !< droplet diameter in mm
[790]	635
[799]	636
[828]	637	DO j = 1, radius_classes
[790]	638
[1822]	639	diameter = radclass(j) * 2000.0_wp
[799]	640
[1822]	641	IF ( diameter <= d0_rog ) THEN
	642	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	643	EXP( -k_low_rog * diameter ) )
	644	ELSE
	645	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	646	ENDIF
[790]	647
[828]	648	ENDDO
[790]	649
[828]	650	END SUBROUTINE fallg
[790]	651
[828]	652
[790]	653	!------------------------------------------------------------------------------!
[1682]	654	! Description:
	655	! ------------
[1822]	656	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	657	!------------------------------------------------------------------------------!
[828]	658	SUBROUTINE effic
[1320]	659
	660	USE particle_attributes, &
	661	ONLY: radius_classes
[790]	662
[828]	663	IMPLICIT NONE
[790]	664
[1682]	665	INTEGER(iwp) :: i !<
	666	INTEGER(iwp) :: iq !<
	667	INTEGER(iwp) :: ir !<
	668	INTEGER(iwp) :: j !<
	669	INTEGER(iwp) :: k !<
[790]	670
[1682]	671	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	672
[1682]	673	LOGICAL, SAVE :: first = .TRUE. !<
[790]	674
[1682]	675	REAL(wp) :: ek !<
	676	REAL(wp) :: particle_radius !<
	677	REAL(wp) :: pp !<
	678	REAL(wp) :: qq !<
	679	REAL(wp) :: rq !<
[790]	680
[1682]	681	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	682
[1682]	683	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	684
[1682]	685	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	686
[792]	687	!
[828]	688	!-- Initial assignment of constants
	689	IF ( first ) THEN
[790]	690
[792]	691	first = .FALSE.
[1822]	692	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	693	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	694	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	695
[1822]	696	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	697	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	698	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	699	0.90_wp, 0.95_wp, 1.00_wp /)
	700
[1822]	701	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	702	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	703	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	704	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	705	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	706	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	707	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	708	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	709	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	710	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	711	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	712	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	713	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	714	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	715	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	716	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	717	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	718	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	719	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	720	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	721	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	722	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	723	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	724	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	725	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	726	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	727	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	728	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	729	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	730	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	731	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	732	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	733	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	734	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	735	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
[1359]	736	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	737	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	738	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	739	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	740	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	741	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	742	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	743	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	744	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	745	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	746	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	747	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	748	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	749	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	750	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	751	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	752	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	753	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	754	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	755	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	756	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	757	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	758	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	759	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	760	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	761	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	762	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	763	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	764	ENDIF
[790]	765
[792]	766	!
[828]	767	!-- Calculate the radius class index of particles with respect to array r
[1822]	768	!-- Radius has to be in microns
[828]	769	ALLOCATE( ira(1:radius_classes) )
	770	DO j = 1, radius_classes
[1322]	771	particle_radius = radclass(j) * 1.0E6_wp
[828]	772	DO k = 1, 15
	773	IF ( particle_radius < r0(k) ) THEN
	774	ira(j) = k
	775	EXIT
	776	ENDIF
	777	ENDDO
	778	IF ( particle_radius >= r0(15) ) ira(j) = 16
	779	ENDDO
[790]	780
[792]	781	!
[828]	782	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	783	!-- Radius has to be in microns
[828]	784	DO j = 1, radius_classes
	785	DO i = 1, j
[792]	786
[1880]	787	ir = MAX( ira(i), ira(j) )
[1519]	788	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	789	iq = INT( rq * 20 ) + 1
	790	iq = MAX( iq , 2)
[792]	791
[828]	792	IF ( ir < 16 ) THEN
	793	IF ( ir >= 2 ) THEN
[1822]	794	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	795	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	796	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	797	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	798	* ecoll(ir-1,iq-1) &
	799	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	800	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	801	+ pp * qq * ecoll(ir,iq)
	802	ELSE
	803	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	804	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	805	ENDIF
	806	ELSE
	807	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	808	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	809	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	810	ENDIF
[792]	811
[1359]	812	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	813
[828]	814	ec(i,j) = ec(j,i)
[792]	815
[828]	816	ENDDO
	817	ENDDO
[792]	818
[828]	819	DEALLOCATE( ira )
[792]	820
[828]	821	END SUBROUTINE effic
[792]	822
	823
[790]	824	!------------------------------------------------------------------------------!
[1682]	825	! Description:
	826	! ------------
[1822]	827	!> Interpolation of turbulent enhancement factor for collision efficencies
	828	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	829	!------------------------------------------------------------------------------!
[828]	830	SUBROUTINE turb_enhance_eff
[790]	831
[1320]	832	USE particle_attributes, &
	833	ONLY: radius_classes
[790]	834
[828]	835	IMPLICIT NONE
[790]	836
[1682]	837	INTEGER(iwp) :: i !<
	838	INTEGER(iwp) :: iq !<
	839	INTEGER(iwp) :: ir !<
	840	INTEGER(iwp) :: j !<
	841	INTEGER(iwp) :: k !<
	842	INTEGER(iwp) :: kk !<
[790]	843
[1682]	844	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	845
[1682]	846	LOGICAL, SAVE :: first = .TRUE. !<
[790]	847
[1682]	848	REAL(wp) :: particle_radius !<
	849	REAL(wp) :: pp !<
	850	REAL(wp) :: qq !<
	851	REAL(wp) :: rq !<
	852	REAL(wp) :: y1 !<
	853	REAL(wp) :: y2 !<
	854	REAL(wp) :: y3 !<
[790]	855
[1682]	856	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	857	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	858
[1682]	859	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	860	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	861
	862	!
[828]	863	!-- Initial assignment of constants
	864	IF ( first ) THEN
[799]	865
[828]	866	first = .FALSE.
[799]	867
[1359]	868	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	869	100.0_wp /)
	870
	871	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	872	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	873	!
[1822]	874	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	875	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	876	1.207_wp, 1.207_wp, 1.0_wp /)
	877	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	878	1.069_wp, 1.069_wp, 1.0_wp /)
	879	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	880	1.000_wp, 1.000_wp, 1.0_wp /)
	881	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	882	1.025_wp, 1.025_wp, 1.0_wp /)
	883	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	884	1.056_wp, 1.056_wp, 1.0_wp /)
	885	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	886	1.028_wp, 1.028_wp, 1.0_wp /)
	887	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	888	1.046_wp, 1.046_wp, 1.0_wp /)
	889	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	890	1.029_wp, 1.029_wp, 1.0_wp /)
	891	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	892	1.021_wp, 1.021_wp, 1.0_wp /)
	893	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	894	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	895	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	896	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	897	!
[1822]	898	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	899	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	900	1.445_wp, 1.445_wp, 1.0_wp /)
	901	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	902	1.201_wp, 1.201_wp, 1.0_wp /)
	903	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	904	1.150_wp, 1.150_wp, 1.0_wp /)
	905	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	906	1.126_wp, 1.126_wp, 1.0_wp /)
	907	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	908	1.092_wp, 1.092_wp, 1.0_wp /)
	909	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	910	1.051_wp, 1.051_wp, 1.0_wp /)
	911	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	912	1.086_wp, 1.086_wp, 1.0_wp /)
	913	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	914	1.063_wp, 1.063_wp, 1.0_wp /)
	915	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	916	1.100_wp, 1.100_wp, 1.0_wp /)
	917	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	918	1.120_wp, 1.120_wp, 1.0_wp /)
	919	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	920	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	921
[828]	922	ENDIF
[790]	923
[828]	924	!
	925	!-- Calculate the radius class index of particles with respect to array r0
[1822]	926	!-- The droplet radius has to be given in microns.
[828]	927	ALLOCATE( ira(1:radius_classes) )
[790]	928
[828]	929	DO j = 1, radius_classes
[1322]	930	particle_radius = radclass(j) * 1.0E6_wp
[828]	931	DO k = 1, 7
	932	IF ( particle_radius < r0(k) ) THEN
	933	ira(j) = k
	934	EXIT
	935	ENDIF
	936	ENDDO
	937	IF ( particle_radius >= r0(7) ) ira(j) = 8
	938	ENDDO
[799]	939
	940	!
[1822]	941	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	942	!-- The droplet radius has to be given in microns.
[828]	943	DO j = 1, radius_classes
	944	DO i = 1, j
[799]	945
[1880]	946	ir = MAX( ira(i), ira(j) )
[1519]	947	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	948
[828]	949	DO kk = 2, 11
	950	IF ( rq <= rat(kk) ) THEN
	951	iq = kk
	952	EXIT
	953	ENDIF
	954	ENDDO
[790]	955
[1822]	956	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	957
[828]	958	IF ( ir < 8 ) THEN
	959	IF ( ir >= 2 ) THEN
[1822]	960	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	961	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	962	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	963	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	964	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	965	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	966	pp * qq * ecoll_100(ir,iq)
	967	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	968	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	969	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	970	pp * qq * ecoll_400(ir,iq)
[828]	971	ELSE
	972	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	973	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	974	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	975	ENDIF
	976	ELSE
	977	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	978	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	979	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	980	ENDIF
	981	!
[1822]	982	!-- Linear interpolation of turbulent enhancement factor
[1359]	983	IF ( epsilon <= 0.01_wp ) THEN
	984	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	985	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	986	ELSEIF ( epsilon <= 0.06_wp ) THEN
	987	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	988	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	989	ELSE
[1359]	990	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	991	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	992	ENDIF
[790]	993
[1359]	994	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	995
[828]	996	ecf(i,j) = ecf(j,i)
[790]	997
[828]	998	ENDDO
	999	ENDDO
[790]	1000
[828]	1001	END SUBROUTINE turb_enhance_eff
[790]	1002
[825]	1003	END MODULE lpm_collision_kernels_mod

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