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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1881

Last change on this file since 1881 was 1881, checked in by hoffmann, 8 years ago
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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	! -----------------
[1881]	21	!
[1347]	22	!
[1321]	23	! Former revisions:
	24	! -----------------
	25	! $Id: lpm_collision_kernels.f90 1881 2016-04-20 09:37:35Z hoffmann $
	26	!
[1881]	27	! 1880 2016-04-20 09:36:50Z hoffmann
	28	! Bugfix: The index of the larger particle has to be chosen for interpolation.
	29	!
[1874]	30	! 1873 2016-04-18 14:50:06Z maronga
	31	! Module renamed (removed _mod)
	32	!
[1859]	33	! 1858 2016-04-13 13:12:11Z hoffmann
	34	! Interpolation of collision kernels adjusted to more reasonable values.
	35	! Reformatting of the code.
	36	!
[1851]	37	! 1850 2016-04-08 13:29:27Z maronga
	38	! Module renamed
	39	!
[1823]	40	! 1822 2016-04-07 07:49:42Z hoffmann
	41	! PALM kernel has been deleted.
	42	! Bugfix in the calculation of the turbulent enhancement factor of the
	43	! collection efficiency.
	44	!
	45	! Unused variables removed.
	46	!
[1777]	47	! 1776 2016-03-02 17:54:58Z hoffmann
	48	! Bugfix: Collection efficiencies must be calculated for the larger droplet.
	49	!
[1683]	50	! 1682 2015-10-07 23:56:08Z knoop
	51	! Code annotations made doxygen readable
	52	!
[1520]	53	! 1519 2015-01-08 10:20:42Z hoffmann
	54	! Bugfix: Using the new particle structure, particles are not sorted by size.
	55	! Hence, computation of collision efficiencies must ensure that the ratio of
	56	! two colliding droplets is < 1.
	57	!
[1360]	58	! 1359 2014-04-11 17:15:14Z hoffmann
	59	! New particle structure integrated.
	60	! Kind definition added to all floating point numbers.
	61	!
[1347]	62	! 1346 2014-03-27 13:18:20Z heinze
	63	! Bugfix: REAL constants provided with KIND-attribute especially in call of
	64	! intrinsic function like MAX, MIN, SIGN
	65	!
[1323]	66	! 1322 2014-03-20 16:38:49Z raasch
	67	! REAL constants defined as wp_kind
	68	!
[1321]	69	! 1320 2014-03-20 08:40:49Z
[1320]	70	! ONLY-attribute added to USE-statements,
	71	! kind-parameters added to all INTEGER and REAL declaration statements,
	72	! kinds are defined in new module kinds,
	73	! revision history before 2012 removed,
	74	! comment fields (!:) to be used for variable explanations added to
	75	! all variable declaration statements
[1008]	76	!
[1093]	77	! 1092 2013-02-02 11:24:22Z raasch
	78	! unused variables removed
	79	!
[1072]	80	! 1071 2012-11-29 16:54:55Z franke
	81	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
	82	!
[1037]	83	! 1036 2012-10-22 13:43:42Z raasch
	84	! code put under GPL (PALM 3.9)
	85	!
[1008]	86	! 1007 2012-09-19 14:30:36Z franke
[1007]	87	! converted all units to SI units and replaced some parameters by corresponding
	88	! PALM parameters
	89	! Bugfix: factor in calculation of enhancement factor for collision efficencies
	90	! changed from 10. to 1.0
[829]	91	!
[850]	92	! 849 2012-03-15 10:35:09Z raasch
	93	! routine collision_efficiency_rogers added (moved from former advec_particles
	94	! to here)
	95	!
[836]	96	! 835 2012-02-22 11:21:19Z raasch $
	97	! Bugfix: array diss can be used only in case of Wang kernel
	98	!
[829]	99	! 828 2012-02-21 12:00:36Z raasch
[828]	100	! code has been completely reformatted, routine colker renamed
	101	! recalculate_kernel,
	102	! routine init_kernels added, radius is now communicated to the collision
	103	! routines by array radclass
[790]	104	!
[828]	105	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
	106	!
[826]	107	! 825 2012-02-19 03:03:44Z raasch
	108	! routine renamed from wang_kernel to lpm_collision_kernels,
	109	! turbulence_effects on collision replaced by wang_kernel
	110	!
[791]	111	! 790 2011-11-29 03:11:20Z raasch
	112	! initial revision
[790]	113	!
	114	! Description:
	115	! ------------
[1682]	116	!> This module calculates collision efficiencies either due to pure gravitational
	117	!> effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
[1822]	118	!> including the effects of turbulence (Wang kernel, see Wang and
	119	!> Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8, and Ayala et al., 2008:
	120	!> New J. Phys., 10, 075016). The original code has been
[1682]	121	!> provided by L.-P. Wang but is substantially reformatted and speed optimized
	122	!> here.
[790]	123	!------------------------------------------------------------------------------!
[1682]	124	MODULE lpm_collision_kernels_mod
	125
[790]	126
[1320]	127	USE constants, &
	128	ONLY: pi
	129
	130	USE kinds
	131
	132	USE particle_attributes, &
[1822]	133	ONLY: collision_kernel, dissipation_classes, particles, &
	134	radius_classes
[1320]	135
[828]	136	USE pegrid
[790]	137
[828]	138
[790]	139	IMPLICIT NONE
	140
	141	PRIVATE
	142
[1822]	143	PUBLIC ckernel, init_kernels, rclass_lbound, rclass_ubound, &
	144	recalculate_kernel
[790]	145
[1682]	146	REAL(wp) :: epsilon !<
	147	REAL(wp) :: rclass_lbound !<
	148	REAL(wp) :: rclass_ubound !<
	149	REAL(wp) :: urms !<
[790]	150
[1822]	151	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !< dissipation rate class
	152	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !< radius class
	153	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !<
[1320]	154
[1822]	155	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !<
	156	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !<
	157	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !<
	158	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !<
	159	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !<
[1320]	160
[1822]	161	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !<
[792]	162
[828]	163	SAVE
[792]	164
[790]	165	!
	166	!-- Public interfaces
[828]	167	INTERFACE init_kernels
	168	MODULE PROCEDURE init_kernels
	169	END INTERFACE init_kernels
[790]	170
[828]	171	INTERFACE recalculate_kernel
	172	MODULE PROCEDURE recalculate_kernel
	173	END INTERFACE recalculate_kernel
[790]	174
	175
[828]	176	CONTAINS
[790]	177
[792]	178
[828]	179	!------------------------------------------------------------------------------!
[1682]	180	! Description:
	181	! ------------
	182	!> Initialization of the collision efficiency matrix with fixed radius and
	183	!> dissipation classes, calculated at simulation start only.
[828]	184	!------------------------------------------------------------------------------!
[1682]	185
	186	SUBROUTINE init_kernels
[792]	187
[828]	188	IMPLICIT NONE
[792]	189
[1682]	190	INTEGER(iwp) :: i !<
	191	INTEGER(iwp) :: j !<
	192	INTEGER(iwp) :: k !<
[790]	193
[828]	194
	195	!
	196	!-- Calculate collision efficiencies for fixed radius- and dissipation
	197	!-- classes
	198	IF ( collision_kernel(6:9) == 'fast' ) THEN
	199
[1822]	200	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
	201	0:dissipation_classes), epsclass(1:dissipation_classes), &
[828]	202	radclass(1:radius_classes) )
	203
	204	!
	205	!-- Calculate the radius class bounds with logarithmic distances
[1858]	206	!-- in the interval [1.0E-6, 1000.0E-6] m
[1322]	207	rclass_lbound = LOG( 1.0E-6_wp )
[1858]	208	rclass_ubound = LOG( 1000.0E-6_wp )
[1822]	209	radclass(1) = EXP( rclass_lbound )
[828]	210	DO i = 2, radius_classes
	211	radclass(i) = EXP( rclass_lbound + &
[1359]	212	( rclass_ubound - rclass_lbound ) * &
	213	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
[828]	214	ENDDO
	215
	216	!
[1858]	217	!-- Set the class bounds for dissipation in interval [0.0, 600.0] cm2/s3
[828]	218	DO i = 1, dissipation_classes
[1858]	219	epsclass(i) = 0.06_wp * REAL( i, KIND=wp ) / dissipation_classes
[828]	220	ENDDO
	221	!
	222	!-- Calculate collision efficiencies of the Wang/ayala kernel
	223	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
	224	ecf(1:radius_classes,1:radius_classes), &
	225	gck(1:radius_classes,1:radius_classes), &
	226	winf(1:radius_classes) )
	227
	228	DO k = 1, dissipation_classes
	229
	230	epsilon = epsclass(k)
[1359]	231	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
[828]	232
	233	CALL turbsd
	234	CALL turb_enhance_eff
	235	CALL effic
	236
	237	DO j = 1, radius_classes
	238	DO i = 1, radius_classes
	239	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
	240	ENDDO
	241	ENDDO
	242
	243	ENDDO
	244
	245	!
	246	!-- Calculate collision efficiencies of the Hall kernel
	247	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
	248	hwratio(1:radius_classes,1:radius_classes) )
	249
	250	CALL fallg
	251	CALL effic
	252
	253	DO j = 1, radius_classes
	254	DO i = 1, radius_classes
	255	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
	256	* ec(i,j) * ABS( winf(j) - winf(i) )
	257	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
	258	ENDDO
	259	ENDDO
	260
	261	!
	262	!-- Test output of efficiencies
	263	IF ( j == -1 ) THEN
	264
	265	PRINT, '** Hall kernel'
[1359]	266	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
[1007]	267	i = 1,radius_classes )
[828]	268	DO j = 1, radius_classes
[1007]	269	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
	270	( hkernel(i,j), i = 1,radius_classes )
[828]	271	ENDDO
	272
	273	DO k = 1, dissipation_classes
	274	DO i = 1, radius_classes
	275	DO j = 1, radius_classes
[1359]	276	IF ( hkernel(i,j) == 0.0_wp ) THEN
	277	hwratio(i,j) = 9999999.9_wp
[828]	278	ELSE
	279	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
	280	ENDIF
	281	ENDDO
	282	ENDDO
	283
	284	PRINT, '** epsilon = ', epsclass(k)
[1359]	285	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
[1007]	286	i = 1,radius_classes )
[828]	287	DO j = 1, radius_classes
[1359]	288	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
[1007]	289	( hwratio(i,j), i = 1,radius_classes )
[828]	290	ENDDO
	291	ENDDO
	292
	293	ENDIF
	294
	295	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
	296
	297	ENDIF
	298
	299	END SUBROUTINE init_kernels
	300
	301
[790]	302	!------------------------------------------------------------------------------!
[1682]	303	! Description:
	304	! ------------
	305	!> Calculation of collision kernels during each timestep and for each grid box
[790]	306	!------------------------------------------------------------------------------!
[828]	307	SUBROUTINE recalculate_kernel( i1, j1, k1 )
[790]	308
[1320]	309	USE arrays_3d, &
	310	ONLY: diss
[790]	311
[1320]	312	USE particle_attributes, &
[1858]	313	ONLY: number_of_particles, prt_count, radius_classes, wang_kernel
[1320]	314
[790]	315	IMPLICIT NONE
	316
[1682]	317	INTEGER(iwp) :: i !<
	318	INTEGER(iwp) :: i1 !<
	319	INTEGER(iwp) :: j !<
	320	INTEGER(iwp) :: j1 !<
	321	INTEGER(iwp) :: k1 !<
[790]	322
	323
[1858]	324	number_of_particles = prt_count(k1,j1,i1)
	325	radius_classes = number_of_particles ! necessary to use the same
	326	! subroutines as for
	327	! precalculated kernels
[792]	328
[1858]	329	ALLOCATE( ec(1:number_of_particles,1:number_of_particles), &
	330	radclass(1:number_of_particles), winf(1:number_of_particles) )
[790]	331
[828]	332	!
[1007]	333	!-- Store particle radii on the radclass array
[1858]	334	radclass(1:number_of_particles) = particles(1:number_of_particles)%radius
[790]	335
[835]	336	IF ( wang_kernel ) THEN
[1007]	337	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
[835]	338	ELSE
[1359]	339	epsilon = 0.0_wp
[835]	340	ENDIF
[1359]	341	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
[790]	342
[1359]	343	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
[828]	344	!
	345	!-- Call routines to calculate efficiencies for the Wang kernel
[1858]	346	ALLOCATE( gck(1:number_of_particles,1:number_of_particles), &
	347	ecf(1:number_of_particles,1:number_of_particles) )
[790]	348
[828]	349	CALL turbsd
	350	CALL turb_enhance_eff
	351	CALL effic
[790]	352
[1858]	353	DO j = 1, number_of_particles
	354	DO i = 1, number_of_particles
	355	ckernel(1+i-1,1+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
[790]	356	ENDDO
[828]	357	ENDDO
[790]	358
[828]	359	DEALLOCATE( gck, ecf )
[790]	360
	361	ELSE
[828]	362	!
	363	!-- Call routines to calculate efficiencies for the Hall kernel
[790]	364	CALL fallg
	365	CALL effic
	366
[1858]	367	DO j = 1, number_of_particles
	368	DO i = 1, number_of_particles
	369	ckernel(i,j,1) = pi * ( radclass(j) + radclass(i) )**2 &
	370	* ec(i,j) * ABS( winf(j) - winf(i) )
[790]	371	ENDDO
	372	ENDDO
	373
	374	ENDIF
	375
[828]	376	DEALLOCATE( ec, radclass, winf )
[790]	377
[828]	378	END SUBROUTINE recalculate_kernel
[790]	379
[828]	380
[790]	381	!------------------------------------------------------------------------------!
[1682]	382	! Description:
	383	! ------------
[1822]	384	!> Calculation of effects of turbulence on the geometric collision kernel
	385	!> (by including the droplets' average radial relative velocities and their
	386	!> radial distribution function) following the analytic model by Aayala et al.
	387	!> (2008, New J. Phys.). For details check the second part 2 of the publication,
	388	!> page 37ff.
	389	!>
	390	!> Input parameters, which need to be replaced by PALM parameters:
	391	!> water density, air density
[790]	392	!------------------------------------------------------------------------------!
[792]	393	SUBROUTINE turbsd
[799]	394
[1320]	395	USE control_parameters, &
	396	ONLY: g, molecular_viscosity
	397
	398	USE particle_attributes, &
	399	ONLY: radius_classes
[790]	400
	401	IMPLICIT NONE
	402
[1682]	403	INTEGER(iwp) :: i !<
	404	INTEGER(iwp) :: j !<
[790]	405
[1682]	406	REAL(wp) :: ao !<
	407	REAL(wp) :: ao_gr !<
	408	REAL(wp) :: bbb !<
	409	REAL(wp) :: be !<
	410	REAL(wp) :: b1 !<
	411	REAL(wp) :: b2 !<
	412	REAL(wp) :: ccc !<
	413	REAL(wp) :: c1 !<
	414	REAL(wp) :: c1_gr !<
	415	REAL(wp) :: c2 !<
	416	REAL(wp) :: d1 !<
	417	REAL(wp) :: d2 !<
	418	REAL(wp) :: eta !<
	419	REAL(wp) :: e1 !<
	420	REAL(wp) :: e2 !<
	421	REAL(wp) :: fao_gr !<
	422	REAL(wp) :: fr !<
	423	REAL(wp) :: grfin !<
	424	REAL(wp) :: lambda !<
	425	REAL(wp) :: lambda_re !<
	426	REAL(wp) :: lf !<
	427	REAL(wp) :: rc !<
	428	REAL(wp) :: rrp !<
	429	REAL(wp) :: sst !<
	430	REAL(wp) :: tauk !<
	431	REAL(wp) :: tl !<
	432	REAL(wp) :: t2 !<
	433	REAL(wp) :: tt !<
	434	REAL(wp) :: t1 !<
	435	REAL(wp) :: vk !<
	436	REAL(wp) :: vrms1xy !<
	437	REAL(wp) :: vrms2xy !<
	438	REAL(wp) :: v1 !<
	439	REAL(wp) :: v1v2xy !<
	440	REAL(wp) :: v1xysq !<
	441	REAL(wp) :: v2 !<
	442	REAL(wp) :: v2xysq !<
	443	REAL(wp) :: wrfin !<
	444	REAL(wp) :: wrgrav2 !<
	445	REAL(wp) :: wrtur2xy !<
	446	REAL(wp) :: xx !<
	447	REAL(wp) :: yy !<
	448	REAL(wp) :: z !<
[790]	449
[1822]	450	REAL(wp), DIMENSION(1:radius_classes) :: st !< Stokes number
	451	REAL(wp), DIMENSION(1:radius_classes) :: tau !< inertial time scale
[790]	452
[1822]	453	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon )
[1322]	454	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
[1822]	455	tl = urms**2 / epsilon
	456	lf = 0.5_wp * urms**3 / epsilon
	457	tauk = SQRT( molecular_viscosity / epsilon )
	458	eta = ( molecular_viscosity3 / epsilon )0.25_wp
[1007]	459	vk = eta / tauk
[790]	460
[1359]	461	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
[1822]	462	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk
[799]	463
[1822]	464	!
	465	!-- Get terminal velocity of droplets
	466	CALL fallg
[790]	467
[828]	468	DO i = 1, radius_classes
[1822]	469	tau(i) = winf(i) / g ! inertial time scale
	470	st(i) = tau(i) / tauk ! Stokes number
[790]	471	ENDDO
	472
[828]	473	!
[1822]	474	!-- Calculate average radial relative velocity at contact (wrfin)
[828]	475	z = tt / tl
[1322]	476	be = SQRT( 2.0_wp ) * lambda / lf
[1359]	477	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
	478	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
[1822]	479	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp
[1359]	480	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
[1822]	481	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp
[1359]	482	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
	483	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
[1822]	484	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp
[1359]	485	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
[1822]	486	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp
[790]	487
[828]	488	DO i = 1, radius_classes
[790]	489
[1822]	490	v1 = winf(i)
	491	t1 = tau(i)
[790]	492
[828]	493	DO j = 1, i
[1007]	494	rrp = radclass(i) + radclass(j)
[1822]	495	v2 = winf(j)
	496	t2 = tau(j)
[790]	497
[1007]	498	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
	499	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
[1822]	500	v1xysq = v1xysq * urms**2 / t1
	501	vrms1xy = SQRT( v1xysq )
[790]	502
[1007]	503	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
	504	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
[1822]	505	v2xysq = v2xysq * urms**2 / t2
	506	vrms2xy = SQRT( v2xysq )
[790]	507
[828]	508	IF ( winf(i) >= winf(j) ) THEN
[799]	509	v1 = winf(i)
[790]	510	t1 = tau(i)
[799]	511	v2 = winf(j)
[790]	512	t2 = tau(j)
	513	ELSE
[799]	514	v1 = winf(j)
[790]	515	t1 = tau(j)
[799]	516	v2 = winf(i)
[790]	517	t2 = tau(i)
	518	ENDIF
	519
[828]	520	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
	521	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
	522	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
	523	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
	524	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
[1822]	525	v1v2xy = v1v2xy * fr * urms**2 / tau(i) / tau(j)
	526	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy
[1359]	527	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
[1322]	528	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
[1822]	529	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) )
[790]	530
[828]	531	!
[1822]	532	!-- Calculate radial distribution function (grfin)
[828]	533	IF ( st(j) > st(i) ) THEN
	534	sst = st(j)
[790]	535	ELSE
[828]	536	sst = st(i)
[790]	537	ENDIF
	538
[1359]	539	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
	540	sst*2 + 5.3406_wp sst
	541	IF ( xx < 0.0_wp ) xx = 0.0_wp
	542	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
[790]	543
[1007]	544	c1_gr = xx / ( g / vk * tauk )**yy
[790]	545
[1322]	546	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
[1359]	547	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
[1822]	548	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta
[790]	549
[1359]	550	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
	551	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
[790]	552
[1822]	553	!
	554	!-- Calculate general collection kernel (without the consideration of
	555	!-- collection efficiencies)
	556	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin
[790]	557	gck(j,i) = gck(i,j)
	558
	559	ENDDO
	560	ENDDO
	561
[828]	562	END SUBROUTINE turbsd
[790]	563
[1320]	564	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
[1822]	565	!
	566	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	567	!-- effects on the collision kernel
[790]	568	IMPLICIT NONE
	569
[1682]	570	REAL(wp) :: a !<
	571	REAL(wp) :: aa1 !<
	572	REAL(wp) :: b !<
	573	REAL(wp) :: tau0 !<
	574	REAL(wp) :: vsett !<
[790]	575
[1359]	576	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
[1822]	577	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2
[790]	578
[1007]	579	END FUNCTION phi_w
[792]	580
[1320]	581	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
[1822]	582	!
	583	!-- Function used in the Ayala et al. (2008) analytical model for turbulent
	584	!-- effects on the collision kernel
[790]	585	IMPLICIT NONE
	586
[1682]	587	REAL(wp) :: a !<
	588	REAL(wp) :: aa1 !<
	589	REAL(wp) :: aa2 !<
	590	REAL(wp) :: aa3 !<
	591	REAL(wp) :: aa4 !<
	592	REAL(wp) :: aa5 !<
	593	REAL(wp) :: aa6 !<
	594	REAL(wp) :: b !<
	595	REAL(wp) :: tau1 !<
	596	REAL(wp) :: tau2 !<
	597	REAL(wp) :: vsett1 !<
	598	REAL(wp) :: vsett2 !<
[790]	599
[1359]	600	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
	601	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
	602	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
	603	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
	604	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
	605	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
	606	vsett1 / vsett2
	607	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
	608	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
	609	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
[1822]	610	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3
[799]	611
[828]	612	END FUNCTION zhi
[790]	613
[828]	614
[790]	615	!------------------------------------------------------------------------------!
[1682]	616	! Description:
	617	! ------------
[1822]	618	!> Parameterization of terminal velocity following Rogers et al. (1993, J. Appl.
	619	!> Meteorol.)
[790]	620	!------------------------------------------------------------------------------!
[828]	621	SUBROUTINE fallg
[790]	622
[1320]	623	USE particle_attributes, &
	624	ONLY: radius_classes
[790]	625
[828]	626	IMPLICIT NONE
[790]	627
[1822]	628	INTEGER(iwp) :: j !<
[790]	629
[1822]	630	REAL(wp), PARAMETER :: k_cap_rog = 4.0_wp !< parameter
	631	REAL(wp), PARAMETER :: k_low_rog = 12.0_wp !< parameter
	632	REAL(wp), PARAMETER :: a_rog = 9.65_wp !< parameter
	633	REAL(wp), PARAMETER :: b_rog = 10.43_wp !< parameter
	634	REAL(wp), PARAMETER :: c_rog = 0.6_wp !< parameter
	635	REAL(wp), PARAMETER :: d0_rog = 0.745_wp !< seperation diameter
[790]	636
[1822]	637	REAL(wp) :: diameter !< droplet diameter in mm
[790]	638
[799]	639
[828]	640	DO j = 1, radius_classes
[790]	641
[1822]	642	diameter = radclass(j) * 2000.0_wp
[799]	643
[1822]	644	IF ( diameter <= d0_rog ) THEN
	645	winf(j) = k_cap_rog * diameter * ( 1.0_wp - &
	646	EXP( -k_low_rog * diameter ) )
	647	ELSE
	648	winf(j) = a_rog - b_rog * EXP( -c_rog * diameter )
[828]	649	ENDIF
[790]	650
[828]	651	ENDDO
[790]	652
[828]	653	END SUBROUTINE fallg
[790]	654
[828]	655
[790]	656	!------------------------------------------------------------------------------!
[1682]	657	! Description:
	658	! ------------
[1822]	659	!> Interpolation of collision efficiencies (Hall, 1980, J. Atmos. Sci.)
[790]	660	!------------------------------------------------------------------------------!
[828]	661	SUBROUTINE effic
[1320]	662
	663	USE particle_attributes, &
	664	ONLY: radius_classes
[790]	665
[828]	666	IMPLICIT NONE
[790]	667
[1682]	668	INTEGER(iwp) :: i !<
	669	INTEGER(iwp) :: iq !<
	670	INTEGER(iwp) :: ir !<
	671	INTEGER(iwp) :: j !<
	672	INTEGER(iwp) :: k !<
[790]	673
[1682]	674	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[790]	675
[1682]	676	LOGICAL, SAVE :: first = .TRUE. !<
[790]	677
[1682]	678	REAL(wp) :: ek !<
	679	REAL(wp) :: particle_radius !<
	680	REAL(wp) :: pp !<
	681	REAL(wp) :: qq !<
	682	REAL(wp) :: rq !<
[790]	683
[1682]	684	REAL(wp), DIMENSION(1:21), SAVE :: rat !<
[1320]	685
[1682]	686	REAL(wp), DIMENSION(1:15), SAVE :: r0 !<
[1320]	687
[1682]	688	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !<
[790]	689
[792]	690	!
[828]	691	!-- Initial assignment of constants
	692	IF ( first ) THEN
[790]	693
[792]	694	first = .FALSE.
[1822]	695	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
	696	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
[1359]	697	150.0_wp, 200.0_wp, 300.0_wp /)
[790]	698
[1822]	699	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
	700	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
	701	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
[1359]	702	0.90_wp, 0.95_wp, 1.00_wp /)
	703
[1822]	704	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
	705	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
[1359]	706	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
[1822]	707	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
	708	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
[1359]	709	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
[1822]	710	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
	711	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
[1359]	712	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
[1822]	713	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
	714	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
[1359]	715	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
[1822]	716	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
	717	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
[1359]	718	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
[1822]	719	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
	720	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
[1359]	721	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	722	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
	723	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
[1359]	724	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	725	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
	726	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
[1359]	727	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	728	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
	729	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
[1359]	730	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	731	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
	732	0.250_wp, 0.500_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(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
	735	0.240_wp, 0.550_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(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
	738	0.290_wp, 0.580_wp, 0.800_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(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
	741	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
[1359]	742	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	743	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
	744	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
[1359]	745	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	746	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
	747	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
[1359]	748	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	749	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
	750	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
[1359]	751	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	752	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
	753	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
[1359]	754	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
[1822]	755	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
	756	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
[1359]	757	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
[1822]	758	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
	759	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
[1359]	760	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
[1822]	761	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
	762	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
[1359]	763	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
[1822]	764	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
	765	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
[1359]	766	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
[828]	767	ENDIF
[790]	768
[792]	769	!
[828]	770	!-- Calculate the radius class index of particles with respect to array r
[1822]	771	!-- Radius has to be in microns
[828]	772	ALLOCATE( ira(1:radius_classes) )
	773	DO j = 1, radius_classes
[1322]	774	particle_radius = radclass(j) * 1.0E6_wp
[828]	775	DO k = 1, 15
	776	IF ( particle_radius < r0(k) ) THEN
	777	ira(j) = k
	778	EXIT
	779	ENDIF
	780	ENDDO
	781	IF ( particle_radius >= r0(15) ) ira(j) = 16
	782	ENDDO
[790]	783
[792]	784	!
[828]	785	!-- Two-dimensional linear interpolation of the collision efficiency.
[1822]	786	!-- Radius has to be in microns
[828]	787	DO j = 1, radius_classes
	788	DO i = 1, j
[792]	789
[1880]	790	ir = MAX( ira(i), ira(j) )
[1519]	791	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[828]	792	iq = INT( rq * 20 ) + 1
	793	iq = MAX( iq , 2)
[792]	794
[828]	795	IF ( ir < 16 ) THEN
	796	IF ( ir >= 2 ) THEN
[1822]	797	pp = ( ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp ) - &
	798	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[1359]	799	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
	800	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
	801	* ecoll(ir-1,iq-1) &
	802	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
	803	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
[828]	804	+ pp * qq * ecoll(ir,iq)
	805	ELSE
	806	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	807	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
[828]	808	ENDIF
	809	ELSE
	810	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	811	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
[1346]	812	ec(j,i) = MIN( ek, 1.0_wp )
[1071]	813	ENDIF
[792]	814
[1359]	815	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
[1071]	816
[828]	817	ec(i,j) = ec(j,i)
[792]	818
[828]	819	ENDDO
	820	ENDDO
[792]	821
[828]	822	DEALLOCATE( ira )
[792]	823
[828]	824	END SUBROUTINE effic
[792]	825
	826
[790]	827	!------------------------------------------------------------------------------!
[1682]	828	! Description:
	829	! ------------
[1822]	830	!> Interpolation of turbulent enhancement factor for collision efficencies
	831	!> following Wang and Grabowski (2009, Atmos. Sci. Let.)
[790]	832	!------------------------------------------------------------------------------!
[828]	833	SUBROUTINE turb_enhance_eff
[790]	834
[1320]	835	USE particle_attributes, &
	836	ONLY: radius_classes
[790]	837
[828]	838	IMPLICIT NONE
[790]	839
[1682]	840	INTEGER(iwp) :: i !<
	841	INTEGER(iwp) :: iq !<
	842	INTEGER(iwp) :: ir !<
	843	INTEGER(iwp) :: j !<
	844	INTEGER(iwp) :: k !<
	845	INTEGER(iwp) :: kk !<
[790]	846
[1682]	847	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !<
[1320]	848
[1682]	849	LOGICAL, SAVE :: first = .TRUE. !<
[790]	850
[1682]	851	REAL(wp) :: particle_radius !<
	852	REAL(wp) :: pp !<
	853	REAL(wp) :: qq !<
	854	REAL(wp) :: rq !<
	855	REAL(wp) :: y1 !<
	856	REAL(wp) :: y2 !<
	857	REAL(wp) :: y3 !<
[790]	858
[1682]	859	REAL(wp), DIMENSION(1:11), SAVE :: rat !<
	860	REAL(wp), DIMENSION(1:7), SAVE :: r0 !<
[1320]	861
[1682]	862	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !<
	863	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !<
[799]	864
	865	!
[828]	866	!-- Initial assignment of constants
	867	IF ( first ) THEN
[799]	868
[828]	869	first = .FALSE.
[799]	870
[1359]	871	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
	872	100.0_wp /)
	873
	874	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
	875	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
[828]	876	!
[1822]	877	!-- Tabulated turbulent enhancement factor at 100 cm2/s3
[1359]	878	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
	879	1.207_wp, 1.207_wp, 1.0_wp /)
	880	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
	881	1.069_wp, 1.069_wp, 1.0_wp /)
	882	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
	883	1.000_wp, 1.000_wp, 1.0_wp /)
	884	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
	885	1.025_wp, 1.025_wp, 1.0_wp /)
	886	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
	887	1.056_wp, 1.056_wp, 1.0_wp /)
	888	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
	889	1.028_wp, 1.028_wp, 1.0_wp /)
	890	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
	891	1.046_wp, 1.046_wp, 1.0_wp /)
	892	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
	893	1.029_wp, 1.029_wp, 1.0_wp /)
	894	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
	895	1.021_wp, 1.021_wp, 1.0_wp /)
	896	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
	897	1.088_wp, 1.088_wp, 1.0_wp /)
[1822]	898	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
[1359]	899	2.60_wp, 2.60_wp, 1.0_wp /)
[828]	900	!
[1822]	901	!-- Tabulated turbulent enhancement factor at 400 cm2/s3
[1359]	902	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
	903	1.445_wp, 1.445_wp, 1.0_wp /)
	904	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
	905	1.201_wp, 1.201_wp, 1.0_wp /)
	906	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
	907	1.150_wp, 1.150_wp, 1.0_wp /)
	908	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
	909	1.126_wp, 1.126_wp, 1.0_wp /)
	910	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
	911	1.092_wp, 1.092_wp, 1.0_wp /)
	912	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
	913	1.051_wp, 1.051_wp, 1.0_wp /)
	914	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
	915	1.086_wp, 1.086_wp, 1.0_wp /)
	916	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
	917	1.063_wp, 1.063_wp, 1.0_wp /)
	918	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
	919	1.100_wp, 1.100_wp, 1.0_wp /)
	920	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
	921	1.120_wp, 1.120_wp, 1.0_wp /)
	922	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
	923	26.0_wp, 26.0_wp, 1.0_wp /)
[799]	924
[828]	925	ENDIF
[790]	926
[828]	927	!
	928	!-- Calculate the radius class index of particles with respect to array r0
[1822]	929	!-- The droplet radius has to be given in microns.
[828]	930	ALLOCATE( ira(1:radius_classes) )
[790]	931
[828]	932	DO j = 1, radius_classes
[1322]	933	particle_radius = radclass(j) * 1.0E6_wp
[828]	934	DO k = 1, 7
	935	IF ( particle_radius < r0(k) ) THEN
	936	ira(j) = k
	937	EXIT
	938	ENDIF
	939	ENDDO
	940	IF ( particle_radius >= r0(7) ) ira(j) = 8
	941	ENDDO
[799]	942
	943	!
[1822]	944	!-- Two-dimensional linear interpolation of the turbulent enhancement factor.
	945	!-- The droplet radius has to be given in microns.
[828]	946	DO j = 1, radius_classes
	947	DO i = 1, j
[799]	948
[1880]	949	ir = MAX( ira(i), ira(j) )
[1519]	950	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
[799]	951
[828]	952	DO kk = 2, 11
	953	IF ( rq <= rat(kk) ) THEN
	954	iq = kk
	955	EXIT
	956	ENDIF
	957	ENDDO
[790]	958
[1822]	959	y1 = 1.0_wp ! turbulent enhancement factor at 0 m2/s3
[1007]	960
[828]	961	IF ( ir < 8 ) THEN
	962	IF ( ir >= 2 ) THEN
[1822]	963	pp = ( MAX( radclass(j), radclass(i) ) * 1.0E6_wp - &
	964	r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
[828]	965	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	966	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
	967	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
	968	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
	969	pp * qq * ecoll_100(ir,iq)
	970	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
	971	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
	972	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
	973	pp * qq * ecoll_400(ir,iq)
[828]	974	ELSE
	975	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	976	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
	977	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
[828]	978	ENDIF
	979	ELSE
	980	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
[1359]	981	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
	982	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
[828]	983	ENDIF
	984	!
[1822]	985	!-- Linear interpolation of turbulent enhancement factor
[1359]	986	IF ( epsilon <= 0.01_wp ) THEN
	987	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
	988	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
	989	ELSEIF ( epsilon <= 0.06_wp ) THEN
	990	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	991	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	992	ELSE
[1359]	993	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
	994	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
[828]	995	ENDIF
[790]	996
[1359]	997	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
[790]	998
[828]	999	ecf(i,j) = ecf(j,i)
[790]	1000
[828]	1001	ENDDO
	1002	ENDDO
[790]	1003
[828]	1004	END SUBROUTINE turb_enhance_eff
[790]	1005
[825]	1006	END MODULE lpm_collision_kernels_mod

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