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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1426

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1	MODULE lpm_collision_kernels_mod
2
3	!--------------------------------------------------------------------------------!
4	! This file is part of PALM.
5	!
6	! PALM is free software: you can redistribute it and/or modify it under the terms
7	! of the GNU General Public License as published by the Free Software Foundation,
8	! either version 3 of the License, or (at your option) any later version.
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	!
17	! Copyright 1997-2014 Leibniz Universitaet Hannover
18	!--------------------------------------------------------------------------------!
19	!
20	! Current revisions:
21	! -----------------
22	!
23	!
24	! Former revisions:
25	! -----------------
26	! $Id: lpm_collision_kernels.f90 1360 2014-04-11 17:20:32Z knoop $
27	!
28	! 1359 2014-04-11 17:15:14Z hoffmann
29	! New particle structure integrated.
30	! Kind definition added to all floating point numbers.
31	!
32	! 1346 2014-03-27 13:18:20Z heinze
33	! Bugfix: REAL constants provided with KIND-attribute especially in call of
34	! intrinsic function like MAX, MIN, SIGN
35	!
36	! 1322 2014-03-20 16:38:49Z raasch
37	! REAL constants defined as wp_kind
38	!
39	! 1320 2014-03-20 08:40:49Z
40	! ONLY-attribute added to USE-statements,
41	! kind-parameters added to all INTEGER and REAL declaration statements,
42	! kinds are defined in new module kinds,
43	! revision history before 2012 removed,
44	! comment fields (!:) to be used for variable explanations added to
45	! all variable declaration statements
46	!
47	! 1092 2013-02-02 11:24:22Z raasch
48	! unused variables removed
49	!
50	! 1071 2012-11-29 16:54:55Z franke
51	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
52	!
53	! 1036 2012-10-22 13:43:42Z raasch
54	! code put under GPL (PALM 3.9)
55	!
56	! 1007 2012-09-19 14:30:36Z franke
57	! converted all units to SI units and replaced some parameters by corresponding
58	! PALM parameters
59	! Bugfix: factor in calculation of enhancement factor for collision efficencies
60	! changed from 10. to 1.0
61	!
62	! 849 2012-03-15 10:35:09Z raasch
63	! routine collision_efficiency_rogers added (moved from former advec_particles
64	! to here)
65	!
66	! 835 2012-02-22 11:21:19Z raasch $
67	! Bugfix: array diss can be used only in case of Wang kernel
68	!
69	! 828 2012-02-21 12:00:36Z raasch
70	! code has been completely reformatted, routine colker renamed
71	! recalculate_kernel,
72	! routine init_kernels added, radius is now communicated to the collision
73	! routines by array radclass
74	!
75	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
76	!
77	! 825 2012-02-19 03:03:44Z raasch
78	! routine renamed from wang_kernel to lpm_collision_kernels,
79	! turbulence_effects on collision replaced by wang_kernel
80	!
81	! 790 2011-11-29 03:11:20Z raasch
82	! initial revision
83	!
84	! Description:
85	! ------------
86	! This module calculates collision efficiencies either due to pure gravitational
87	! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
88	! including the effects of (SGS) turbulence (Wang kernel, see Wang and
89	! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
90	! provided by L.-P. Wang but is substantially reformatted and speed optimized
91	! here.
92	!
93	! ATTENTION:
94	! Physical quantities (like g, densities, etc.) used in this module still
95	! have to be adjusted to those values used in the main PALM code.
96	! Also, quantities in CGS-units should be converted to SI-units eventually.
97	!------------------------------------------------------------------------------!
98
99	USE constants, &
100	ONLY: pi
101
102	USE kinds
103
104	USE particle_attributes, &
105	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
106
107	USE pegrid
108
109
110	IMPLICIT NONE
111
112	PRIVATE
113
114	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
115	rclass_lbound, rclass_ubound, recalculate_kernel
116
117	REAL(wp) :: epsilon !:
118	REAL(wp) :: eps2 !:
119	REAL(wp) :: rclass_lbound !:
120	REAL(wp) :: rclass_ubound !:
121	REAL(wp) :: urms !:
122	REAL(wp) :: urms2 !:
123
124	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !:
125	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !:
126	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !:
127
128	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !:
129	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !:
130	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !:
131	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !:
132	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !:
133
134	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !:
135
136	SAVE
137
138	!
139	!-- Public interfaces
140	INTERFACE collision_efficiency_rogers
141	MODULE PROCEDURE collision_efficiency_rogers
142	END INTERFACE collision_efficiency_rogers
143
144	INTERFACE init_kernels
145	MODULE PROCEDURE init_kernels
146	END INTERFACE init_kernels
147
148	INTERFACE recalculate_kernel
149	MODULE PROCEDURE recalculate_kernel
150	END INTERFACE recalculate_kernel
151
152
153	CONTAINS
154
155
156	SUBROUTINE init_kernels
157	!------------------------------------------------------------------------------!
158	! Initialization of the collision efficiency matrix with fixed radius and
159	! dissipation classes, calculated at simulation start only.
160	!------------------------------------------------------------------------------!
161
162	IMPLICIT NONE
163
164	INTEGER(iwp) :: i !:
165	INTEGER(iwp) :: j !:
166	INTEGER(iwp) :: k !:
167
168
169	!
170	!-- Calculate collision efficiencies for fixed radius- and dissipation
171	!-- classes
172	IF ( collision_kernel(6:9) == 'fast' ) THEN
173
174	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
175	0:dissipation_classes), epsclass(1:dissipation_classes), &
176	radclass(1:radius_classes) )
177
178	!
179	!-- Calculate the radius class bounds with logarithmic distances
180	!-- in the interval [1.0E-6, 2.0E-4] m
181	rclass_lbound = LOG( 1.0E-6_wp )
182	rclass_ubound = LOG( 2.0E-4_wp )
183	radclass(1) = 1.0E-6_wp
184	DO i = 2, radius_classes
185	radclass(i) = EXP( rclass_lbound + &
186	( rclass_ubound - rclass_lbound ) * &
187	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
188	ENDDO
189
190	!
191	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
192	DO i = 1, dissipation_classes
193	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
194	ENDDO
195	!
196	!-- Calculate collision efficiencies of the Wang/ayala kernel
197	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
198	ecf(1:radius_classes,1:radius_classes), &
199	gck(1:radius_classes,1:radius_classes), &
200	winf(1:radius_classes) )
201
202	DO k = 1, dissipation_classes
203
204	epsilon = epsclass(k)
205	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
206
207	CALL turbsd
208	CALL turb_enhance_eff
209	CALL effic
210
211	DO j = 1, radius_classes
212	DO i = 1, radius_classes
213	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
214	ENDDO
215	ENDDO
216
217	ENDDO
218
219	!
220	!-- Calculate collision efficiencies of the Hall kernel
221	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
222	hwratio(1:radius_classes,1:radius_classes) )
223
224	CALL fallg
225	CALL effic
226
227	DO j = 1, radius_classes
228	DO i = 1, radius_classes
229	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
230	* ec(i,j) * ABS( winf(j) - winf(i) )
231	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
232	ENDDO
233	ENDDO
234
235	!
236	!-- Test output of efficiencies
237	IF ( j == -1 ) THEN
238
239	PRINT, '** Hall kernel'
240	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
241	i = 1,radius_classes )
242	DO j = 1, radius_classes
243	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
244	( hkernel(i,j), i = 1,radius_classes )
245	ENDDO
246
247	DO k = 1, dissipation_classes
248	DO i = 1, radius_classes
249	DO j = 1, radius_classes
250	IF ( hkernel(i,j) == 0.0_wp ) THEN
251	hwratio(i,j) = 9999999.9_wp
252	ELSE
253	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
254	ENDIF
255	ENDDO
256	ENDDO
257
258	PRINT, '** epsilon = ', epsclass(k)
259	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
260	i = 1,radius_classes )
261	DO j = 1, radius_classes
262	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
263	( hwratio(i,j), i = 1,radius_classes )
264	ENDDO
265	ENDDO
266
267	ENDIF
268
269	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
270
271	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
272	THEN
273	!
274	!-- Initial settings for Hall- and Wang-Kernel
275	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
276	ENDIF
277
278	END SUBROUTINE init_kernels
279
280
281	!------------------------------------------------------------------------------!
282	! Calculation of collision kernels during each timestep and for each grid box
283	!------------------------------------------------------------------------------!
284	SUBROUTINE recalculate_kernel( i1, j1, k1 )
285
286	USE arrays_3d, &
287	ONLY: diss
288
289	USE particle_attributes, &
290	ONLY: prt_count, radius_classes, wang_kernel
291
292	IMPLICIT NONE
293
294	INTEGER(iwp) :: i !:
295	INTEGER(iwp) :: i1 !:
296	INTEGER(iwp) :: j !:
297	INTEGER(iwp) :: j1 !:
298	INTEGER(iwp) :: k1 !:
299	INTEGER(iwp) :: pend !:
300	INTEGER(iwp) :: pstart !:
301
302
303	pstart = 1
304	pend = prt_count(k1,j1,i1)
305	radius_classes = prt_count(k1,j1,i1)
306
307	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
308	radclass(1:radius_classes), winf(1:radius_classes) )
309
310	!
311	!-- Store particle radii on the radclass array
312	radclass(1:radius_classes) = particles(pstart:pend)%radius
313
314	IF ( wang_kernel ) THEN
315	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
316	ELSE
317	epsilon = 0.0_wp
318	ENDIF
319	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
320
321	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
322	!
323	!-- Call routines to calculate efficiencies for the Wang kernel
324	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
325	ecf(1:radius_classes,1:radius_classes) )
326
327	CALL turbsd
328	CALL turb_enhance_eff
329	CALL effic
330
331	DO j = 1, radius_classes
332	DO i = 1, radius_classes
333	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
334	ENDDO
335	ENDDO
336
337	DEALLOCATE( gck, ecf )
338
339	ELSE
340	!
341	!-- Call routines to calculate efficiencies for the Hall kernel
342	CALL fallg
343	CALL effic
344
345	DO j = 1, radius_classes
346	DO i = 1, radius_classes
347	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
348	( radclass(j) + radclass(i) )**2 &
349	* ec(i,j) * ABS( winf(j) - winf(i) )
350	ENDDO
351	ENDDO
352
353	ENDIF
354
355	DEALLOCATE( ec, radclass, winf )
356
357	END SUBROUTINE recalculate_kernel
358
359
360	!------------------------------------------------------------------------------!
361	! Calculation of gck
362	! This is from Aayala 2008b, page 37ff.
363	! Necessary input parameters: water density, radii of droplets, air density,
364	! air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
365	! gravitational acceleration --> to be replaced by PALM parameters
366	!------------------------------------------------------------------------------!
367	SUBROUTINE turbsd
368
369	USE control_parameters, &
370	ONLY: g, molecular_viscosity
371
372	USE particle_attributes, &
373	ONLY: radius_classes
374
375	IMPLICIT NONE
376
377	LOGICAL, SAVE :: first = .TRUE. !:
378
379	INTEGER(iwp) :: i !:
380	INTEGER(iwp) :: j !:
381
382	REAL(wp) :: ao !:
383	REAL(wp) :: ao_gr !:
384	REAL(wp) :: bbb !:
385	REAL(wp) :: be !:
386	REAL(wp) :: b1 !:
387	REAL(wp) :: b2 !:
388	REAL(wp) :: ccc !:
389	REAL(wp) :: c1 !:
390	REAL(wp) :: c1_gr !:
391	REAL(wp) :: c2 !:
392	REAL(wp) :: d1 !:
393	REAL(wp) :: d2 !:
394	REAL(wp) :: eta !:
395	REAL(wp) :: e1 !:
396	REAL(wp) :: e2 !:
397	REAL(wp) :: fao_gr !:
398	REAL(wp) :: fr !:
399	REAL(wp) :: grfin !:
400	REAL(wp) :: lambda !:
401	REAL(wp) :: lambda_re !:
402	REAL(wp) :: lf !:
403	REAL(wp) :: rc !:
404	REAL(wp) :: rrp !:
405	REAL(wp) :: sst !:
406	REAL(wp) :: tauk !:
407	REAL(wp) :: tl !:
408	REAL(wp) :: t2 !:
409	REAL(wp) :: tt !:
410	REAL(wp) :: t1 !:
411	REAL(wp) :: vk !:
412	REAL(wp) :: vrms1xy !:
413	REAL(wp) :: vrms2xy !:
414	REAL(wp) :: v1 !:
415	REAL(wp) :: v1v2xy !:
416	REAL(wp) :: v1xysq !:
417	REAL(wp) :: v2 !:
418	REAL(wp) :: v2xysq !:
419	REAL(wp) :: wrfin !:
420	REAL(wp) :: wrgrav2 !:
421	REAL(wp) :: wrtur2xy !:
422	REAL(wp) :: xx !:
423	REAL(wp) :: yy !:
424	REAL(wp) :: z !:
425
426	REAL(wp), DIMENSION(1:radius_classes) :: st !:
427	REAL(wp), DIMENSION(1:radius_classes) :: tau !:
428
429	!
430	!-- Initial assignment of constants
431	IF ( first ) THEN
432
433	first = .FALSE.
434
435	ENDIF
436
437	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
438	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
439	tl = urms**2 / epsilon ! in s
440	lf = 0.5_wp * urms**3 / epsilon ! in m
441	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
442	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
443	vk = eta / tauk
444
445	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
446	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
447
448	CALL fallg ! gives winf in m/s
449
450	DO i = 1, radius_classes
451	tau(i) = winf(i) / g ! in s
452	st(i) = tau(i) / tauk
453	ENDDO
454
455	!
456	!-- Calculate wr (from Aayala 2008b, page 38f)
457	z = tt / tl
458	be = SQRT( 2.0_wp ) * lambda / lf
459	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
460	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
461	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
462	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
463	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
464	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
465	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
466	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
467	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
468	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
469
470	DO i = 1, radius_classes
471
472	v1 = winf(i) ! in m/s
473	t1 = tau(i) ! in s
474
475	DO j = 1, i
476	rrp = radclass(i) + radclass(j)
477	v2 = winf(j) ! in m/s
478	t2 = tau(j) ! in s
479
480	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
481	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
482	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
483	vrms1xy = SQRT( v1xysq ) ! in m/s
484
485	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
486	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
487	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
488	vrms2xy = SQRT( v2xysq ) ! in m/s
489
490	IF ( winf(i) >= winf(j) ) THEN
491	v1 = winf(i)
492	t1 = tau(i)
493	v2 = winf(j)
494	t2 = tau(j)
495	ELSE
496	v1 = winf(j)
497	t1 = tau(j)
498	v2 = winf(i)
499	t2 = tau(i)
500	ENDIF
501
502	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
503	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
504	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
505	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
506	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
507	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
508	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
509	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
510	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
511	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
512
513	!
514	!-- Calculate gr
515	IF ( st(j) > st(i) ) THEN
516	sst = st(j)
517	ELSE
518	sst = st(i)
519	ENDIF
520
521	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
522	sst*2 + 5.3406_wp sst
523	IF ( xx < 0.0_wp ) xx = 0.0_wp
524	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
525
526	c1_gr = xx / ( g / vk * tauk )**yy
527
528	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
529	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
530	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
531
532	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
533	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
534
535	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
536	gck(j,i) = gck(i,j)
537
538	ENDDO
539	ENDDO
540
541	END SUBROUTINE turbsd
542
543
544	!------------------------------------------------------------------------------!
545	! phi_w as a function
546	!------------------------------------------------------------------------------!
547	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
548
549	IMPLICIT NONE
550
551	REAL(wp) :: a !:
552	REAL(wp) :: aa1 !:
553	REAL(wp) :: b !:
554	REAL(wp) :: tau0 !:
555	REAL(wp) :: vsett !:
556
557	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
558	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
559
560	END FUNCTION phi_w
561
562
563	!------------------------------------------------------------------------------!
564	! zhi as a function
565	!------------------------------------------------------------------------------!
566	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
567
568	IMPLICIT NONE
569
570	REAL(wp) :: a !:
571	REAL(wp) :: aa1 !:
572	REAL(wp) :: aa2 !:
573	REAL(wp) :: aa3 !:
574	REAL(wp) :: aa4 !:
575	REAL(wp) :: aa5 !:
576	REAL(wp) :: aa6 !:
577	REAL(wp) :: b !:
578	REAL(wp) :: tau1 !:
579	REAL(wp) :: tau2 !:
580	REAL(wp) :: vsett1 !:
581	REAL(wp) :: vsett2 !:
582
583	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
584	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
585	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
586	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
587	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
588	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
589	vsett1 / vsett2
590	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
591	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
592	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
593	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
594
595	END FUNCTION zhi
596
597
598	!------------------------------------------------------------------------------!
599	! Calculation of terminal velocity winf following Equations 10-138 to 10-145
600	! from (Pruppacher and Klett, 1997)
601	!------------------------------------------------------------------------------!
602	SUBROUTINE fallg
603
604	USE cloud_parameters, &
605	ONLY: rho_l
606
607	USE control_parameters, &
608	ONLY: g
609
610	USE particle_attributes, &
611	ONLY: radius_classes
612
613
614	IMPLICIT NONE
615
616	INTEGER(iwp) :: i !:
617	INTEGER(iwp) :: j !:
618
619	LOGICAL, SAVE :: first = .TRUE. !:
620
621	REAL(wp), SAVE :: cunh !:
622	REAL(wp), SAVE :: eta !:
623	REAL(wp), SAVE :: phy !:
624	REAL(wp), SAVE :: py !:
625	REAL(wp), SAVE :: rho_a !:
626	REAL(wp), SAVE :: sigma !:
627	REAL(wp), SAVE :: stb !:
628	REAL(wp), SAVE :: stok !:
629	REAL(wp), SAVE :: xlamb !:
630
631	REAL(wp) :: bond !:
632	REAL(wp) :: x !:
633	REAL(wp) :: xrey !:
634	REAL(wp) :: y !:
635
636	REAL(wp), DIMENSION(1:7), SAVE :: b !:
637	REAL(wp), DIMENSION(1:6), SAVE :: c !:
638
639	!
640	!-- Initial assignment of constants
641	IF ( first ) THEN
642
643	first = .FALSE.
644	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
645	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
646	-0.327815E-5_wp /)
647	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
648	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
649
650	!
651	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
652	eta = 1.818E-5_wp ! in kg/(m s)
653	xlamb = 6.6E-8_wp ! in m
654	rho_a = 1.204_wp ! in kg/m**3
655	cunh = 1.26_wp * xlamb ! in m
656	sigma = 0.07363_wp ! in kg/s**2
657	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
658	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
659	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
660	py = phy**( 1.0_wp / 6.0_wp )
661
662	ENDIF
663
664	DO j = 1, radius_classes
665
666	IF ( radclass(j) <= 1.0E-5_wp ) THEN
667
668	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
669
670	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
671
672	x = LOG( stb * radclass(j)**3 )
673	y = 0.0_wp
674
675	DO i = 1, 7
676	y = y + b(i) * x**(i-1)
677	ENDDO
678	!
679	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
680	!-- for correct version see (Beard, 1976)
681	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
682
683	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
684
685	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
686
687	IF ( radclass(j) > 0.0035_wp ) THEN
688	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
689	ELSE
690	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
691	ENDIF
692
693	x = LOG( 16.0_wp * bond * py / 3.0_wp )
694	y = 0.0_wp
695
696	DO i = 1, 6
697	y = y + c(i) * x**(i-1)
698	ENDDO
699
700	xrey = py * EXP( y )
701
702	IF ( radclass(j) > 0.0035_wp ) THEN
703	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
704	ELSE
705	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
706	ENDIF
707
708	ENDIF
709
710	ENDDO
711
712	END SUBROUTINE fallg
713
714
715	!------------------------------------------------------------------------------!
716	! Calculation of collision efficiencies for the Hall kernel
717	!------------------------------------------------------------------------------!
718	SUBROUTINE effic
719
720	USE particle_attributes, &
721	ONLY: radius_classes
722
723	IMPLICIT NONE
724
725	INTEGER(iwp) :: i !:
726	INTEGER(iwp) :: iq !:
727	INTEGER(iwp) :: ir !:
728	INTEGER(iwp) :: j !:
729	INTEGER(iwp) :: k !:
730
731	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
732
733	LOGICAL, SAVE :: first = .TRUE. !:
734
735	REAL(wp) :: ek !:
736	REAL(wp) :: particle_radius !:
737	REAL(wp) :: pp !:
738	REAL(wp) :: qq !:
739	REAL(wp) :: rq !:
740
741	REAL(wp), DIMENSION(1:21), SAVE :: rat !:
742
743	REAL(wp), DIMENSION(1:15), SAVE :: r0 !:
744
745	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !:
746
747	!
748	!-- Initial assignment of constants
749	IF ( first ) THEN
750
751	first = .FALSE.
752	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
753	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
754	150.0_wp, 200.0_wp, 300.0_wp /)
755
756	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
757	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
758	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
759	0.90_wp, 0.95_wp, 1.00_wp /)
760
761	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
762	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
763	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
764	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
765	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
766	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
767	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
768	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
769	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
770	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
771	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
772	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
773	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
774	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
775	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
776	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
777	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
778	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
779	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
780	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
781	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
782	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
783	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
784	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
785	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
786	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
787	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
788	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
789	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
790	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
791	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
792	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
793	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
794	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
795	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
796	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
797	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
798	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
799	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
800	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
801	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
802	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
803	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
804	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
805	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
806	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
807	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
808	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
809	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
810	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
811	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
812	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
813	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
814	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
815	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
816	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
817	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
818	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
819	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
820	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
821	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
822	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
823	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
824	ENDIF
825
826	!
827	!-- Calculate the radius class index of particles with respect to array r
828	!-- Radius has to be in Âµm
829	ALLOCATE( ira(1:radius_classes) )
830	DO j = 1, radius_classes
831	particle_radius = radclass(j) * 1.0E6_wp
832	DO k = 1, 15
833	IF ( particle_radius < r0(k) ) THEN
834	ira(j) = k
835	EXIT
836	ENDIF
837	ENDDO
838	IF ( particle_radius >= r0(15) ) ira(j) = 16
839	ENDDO
840
841	!
842	!-- Two-dimensional linear interpolation of the collision efficiency.
843	!-- Radius has to be in Âµm
844	DO j = 1, radius_classes
845	DO i = 1, j
846
847	ir = ira(j)
848	rq = radclass(i) / radclass(j)
849	iq = INT( rq * 20 ) + 1
850	iq = MAX( iq , 2)
851
852	IF ( ir < 16 ) THEN
853	IF ( ir >= 2 ) THEN
854	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
855	( r0(ir) - r0(ir-1) )
856	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
857	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
858	* ecoll(ir-1,iq-1) &
859	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
860	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
861	+ pp * qq * ecoll(ir,iq)
862	ELSE
863	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
864	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
865	ENDIF
866	ELSE
867	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
868	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
869	ec(j,i) = MIN( ek, 1.0_wp )
870	ENDIF
871
872	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
873
874	ec(i,j) = ec(j,i)
875
876	ENDDO
877	ENDDO
878
879	DEALLOCATE( ira )
880
881	END SUBROUTINE effic
882
883
884	!------------------------------------------------------------------------------!
885	! Calculation of enhancement factor for collision efficencies due to turbulence
886	!------------------------------------------------------------------------------!
887	SUBROUTINE turb_enhance_eff
888
889	USE particle_attributes, &
890	ONLY: radius_classes
891
892	IMPLICIT NONE
893
894	INTEGER(iwp) :: i !:
895	INTEGER(iwp) :: iq !:
896	INTEGER(iwp) :: ir !:
897	INTEGER(iwp) :: j !:
898	INTEGER(iwp) :: k !:
899	INTEGER(iwp) :: kk !:
900
901	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
902
903	LOGICAL, SAVE :: first = .TRUE. !:
904
905	REAL(wp) :: particle_radius !:
906	REAL(wp) :: pp !:
907	REAL(wp) :: qq !:
908	REAL(wp) :: rq !:
909	REAL(wp) :: y1 !:
910	REAL(wp) :: y2 !:
911	REAL(wp) :: y3 !:
912
913	REAL(wp), DIMENSION(1:11), SAVE :: rat !:
914
915	REAL(wp), DIMENSION(1:7), SAVE :: r0 !:
916
917	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !:
918	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !:
919
920	!
921	!-- Initial assignment of constants
922	IF ( first ) THEN
923
924	first = .FALSE.
925
926	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
927	100.0_wp /)
928
929	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
930	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
931	!
932	!-- for 100 cm2/s3
933	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
934	1.207_wp, 1.207_wp, 1.0_wp /)
935	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
936	1.069_wp, 1.069_wp, 1.0_wp /)
937	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
938	1.000_wp, 1.000_wp, 1.0_wp /)
939	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
940	1.025_wp, 1.025_wp, 1.0_wp /)
941	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
942	1.056_wp, 1.056_wp, 1.0_wp /)
943	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
944	1.028_wp, 1.028_wp, 1.0_wp /)
945	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
946	1.046_wp, 1.046_wp, 1.0_wp /)
947	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
948	1.029_wp, 1.029_wp, 1.0_wp /)
949	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
950	1.021_wp, 1.021_wp, 1.0_wp /)
951	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
952	1.088_wp, 1.088_wp, 1.0_wp /)
953	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
954	2.60_wp, 2.60_wp, 1.0_wp /)
955	!
956	!-- for 400 cm2/s3
957	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
958	1.445_wp, 1.445_wp, 1.0_wp /)
959	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
960	1.201_wp, 1.201_wp, 1.0_wp /)
961	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
962	1.150_wp, 1.150_wp, 1.0_wp /)
963	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
964	1.126_wp, 1.126_wp, 1.0_wp /)
965	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
966	1.092_wp, 1.092_wp, 1.0_wp /)
967	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
968	1.051_wp, 1.051_wp, 1.0_wp /)
969	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
970	1.086_wp, 1.086_wp, 1.0_wp /)
971	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
972	1.063_wp, 1.063_wp, 1.0_wp /)
973	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
974	1.100_wp, 1.100_wp, 1.0_wp /)
975	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
976	1.120_wp, 1.120_wp, 1.0_wp /)
977	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
978	26.0_wp, 26.0_wp, 1.0_wp /)
979
980	ENDIF
981
982	!
983	!-- Calculate the radius class index of particles with respect to array r0
984	!-- Radius has to be in Âµm
985	ALLOCATE( ira(1:radius_classes) )
986
987	DO j = 1, radius_classes
988	particle_radius = radclass(j) * 1.0E6_wp
989	DO k = 1, 7
990	IF ( particle_radius < r0(k) ) THEN
991	ira(j) = k
992	EXIT
993	ENDIF
994	ENDDO
995	IF ( particle_radius >= r0(7) ) ira(j) = 8
996	ENDDO
997
998	!
999	!-- Two-dimensional linear interpolation of the collision efficiencies
1000	!-- Radius has to be in Âµm
1001	DO j = 1, radius_classes
1002	DO i = 1, j
1003
1004	ir = ira(j)
1005	rq = radclass(i) / radclass(j)
1006
1007	DO kk = 2, 11
1008	IF ( rq <= rat(kk) ) THEN
1009	iq = kk
1010	EXIT
1011	ENDIF
1012	ENDDO
1013
1014	y1 = 0.0001_wp ! for 0 m2/s3
1015
1016	IF ( ir < 8 ) THEN
1017	IF ( ir >= 2 ) THEN
1018	pp = ( radclass(j)*1.0E6_wp - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
1019	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1020	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
1021	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
1022	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
1023	pp * qq * ecoll_100(ir,iq)
1024	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
1025	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
1026	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
1027	pp * qq * ecoll_400(ir,iq)
1028	ELSE
1029	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1030	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
1031	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
1032	ENDIF
1033	ELSE
1034	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1035	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
1036	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
1037	ENDIF
1038	!
1039	!-- Linear interpolation of dissipation rate in m2/s3
1040	IF ( epsilon <= 0.01_wp ) THEN
1041	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
1042	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
1043	ELSEIF ( epsilon <= 0.06_wp ) THEN
1044	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1045	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1046	ELSE
1047	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1048	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1049	ENDIF
1050
1051	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
1052
1053	ecf(i,j) = ecf(j,i)
1054
1055	ENDDO
1056	ENDDO
1057
1058	END SUBROUTINE turb_enhance_eff
1059
1060
1061
1062	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
1063	!------------------------------------------------------------------------------!
1064	! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
1065	! Values are calculated from table by bilinear interpolation.
1066	!------------------------------------------------------------------------------!
1067
1068	IMPLICIT NONE
1069
1070	INTEGER(iwp) :: i !:
1071	INTEGER(iwp) :: j !:
1072	INTEGER(iwp) :: k !:
1073
1074	LOGICAL, SAVE :: first = .TRUE. !:
1075
1076	REAL(wp) :: aa !:
1077	REAL(wp) :: bb !:
1078	REAL(wp) :: cc !:
1079	REAL(wp) :: dd !:
1080	REAL(wp) :: dx !:
1081	REAL(wp) :: dy !:
1082	REAL(wp) :: e !:
1083	REAL(wp) :: gg !:
1084	REAL(wp) :: mean_r !:
1085	REAL(wp) :: mean_rm !:
1086	REAL(wp) :: r !:
1087	REAL(wp) :: rm !:
1088	REAL(wp) :: x !:
1089	REAL(wp) :: y !:
1090
1091	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !:
1092
1093	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !:
1094
1095	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !:
1096
1097	mean_rm = mean_r * 1.0E06_wp
1098	rm = r * 1.0E06_wp
1099
1100	IF ( first ) THEN
1101
1102	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
1103	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
1104	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
1105	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
1106	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
1107	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
1108
1109	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
1110	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
1111	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
1112	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
1113	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
1114	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
1115	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
1116	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
1117	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
1118	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
1119	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
1120	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
1121	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
1122	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
1123	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
1124	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
1125	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
1126	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
1127	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
1128	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
1129	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
1130	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1131	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
1132	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1133	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
1134	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1135	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
1136	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
1137	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
1138	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
1139	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
1140	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
1141	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
1142	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
1143	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
1144	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
1145	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
1146	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
1147
1148	ENDIF
1149
1150	DO k = 1, 8
1151	IF ( collected_r(k) <= mean_rm ) i = k
1152	ENDDO
1153
1154	DO k = 1, 18
1155	IF ( collector_r(k) <= rm ) j = k
1156	ENDDO
1157
1158	IF ( rm < 10.0_wp ) THEN
1159	e = 0.0_wp
1160	ELSEIF ( mean_rm < 2.0_wp ) THEN
1161	e = 0.001_wp
1162	ELSEIF ( mean_rm >= 25.0_wp ) THEN
1163	IF( j <= 2 ) e = 0.0_wp
1164	IF( j == 3 ) e = 0.47_wp
1165	IF( j == 4 ) e = 0.8_wp
1166	IF( j == 5 ) e = 0.9_wp
1167	IF( j >=6 ) e = 1.0_wp
1168	ELSEIF ( rm >= 3000.0_wp ) THEN
1169	IF( i == 1 ) e = 0.02_wp
1170	IF( i == 2 ) e = 0.16_wp
1171	IF( i == 3 ) e = 0.33_wp
1172	IF( i == 4 ) e = 0.55_wp
1173	IF( i == 5 ) e = 0.71_wp
1174	IF( i == 6 ) e = 0.81_wp
1175	IF( i == 7 ) e = 0.90_wp
1176	IF( i >= 8 ) e = 0.94_wp
1177	ELSE
1178	x = mean_rm - collected_r(i)
1179	y = rm - collector_r(j)
1180	dx = collected_r(i+1) - collected_r(i)
1181	dy = collector_r(j+1) - collector_r(j)
1182	aa = x2 + y2
1183	bb = ( dx - x )2 + y2
1184	cc = x2 + ( dy - y )2
1185	dd = ( dx - x )2 + ( dy - y )2
1186	gg = aa + bb + cc + dd
1187
1188	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
1189	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
1190	ENDIF
1191
1192	END SUBROUTINE collision_efficiency_rogers
1193
1194	END MODULE lpm_collision_kernels_mod

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