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source: palm/trunk/SOURCE/lpm_collision_kernels.f90 @ 1573

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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 1520 2015-01-08 10:27:21Z suehring $
27	!
28	! 1519 2015-01-08 10:20:42Z hoffmann
29	! Bugfix: Using the new particle structure, particles are not sorted by size.
30	! Hence, computation of collision efficiencies must ensure that the ratio of
31	! two colliding droplets is < 1.
32	!
33	! 1359 2014-04-11 17:15:14Z hoffmann
34	! New particle structure integrated.
35	! Kind definition added to all floating point numbers.
36	!
37	! 1346 2014-03-27 13:18:20Z heinze
38	! Bugfix: REAL constants provided with KIND-attribute especially in call of
39	! intrinsic function like MAX, MIN, SIGN
40	!
41	! 1322 2014-03-20 16:38:49Z raasch
42	! REAL constants defined as wp_kind
43	!
44	! 1320 2014-03-20 08:40:49Z
45	! ONLY-attribute added to USE-statements,
46	! kind-parameters added to all INTEGER and REAL declaration statements,
47	! kinds are defined in new module kinds,
48	! revision history before 2012 removed,
49	! comment fields (!:) to be used for variable explanations added to
50	! all variable declaration statements
51	!
52	! 1092 2013-02-02 11:24:22Z raasch
53	! unused variables removed
54	!
55	! 1071 2012-11-29 16:54:55Z franke
56	! Bugfix: collision efficiencies for Hall kernel should not be < 1.0E-20
57	!
58	! 1036 2012-10-22 13:43:42Z raasch
59	! code put under GPL (PALM 3.9)
60	!
61	! 1007 2012-09-19 14:30:36Z franke
62	! converted all units to SI units and replaced some parameters by corresponding
63	! PALM parameters
64	! Bugfix: factor in calculation of enhancement factor for collision efficencies
65	! changed from 10. to 1.0
66	!
67	! 849 2012-03-15 10:35:09Z raasch
68	! routine collision_efficiency_rogers added (moved from former advec_particles
69	! to here)
70	!
71	! 835 2012-02-22 11:21:19Z raasch $
72	! Bugfix: array diss can be used only in case of Wang kernel
73	!
74	! 828 2012-02-21 12:00:36Z raasch
75	! code has been completely reformatted, routine colker renamed
76	! recalculate_kernel,
77	! routine init_kernels added, radius is now communicated to the collision
78	! routines by array radclass
79	!
80	! Bugfix: transformation factor for dissipation changed from 1E5 to 1E4
81	!
82	! 825 2012-02-19 03:03:44Z raasch
83	! routine renamed from wang_kernel to lpm_collision_kernels,
84	! turbulence_effects on collision replaced by wang_kernel
85	!
86	! 790 2011-11-29 03:11:20Z raasch
87	! initial revision
88	!
89	! Description:
90	! ------------
91	! This module calculates collision efficiencies either due to pure gravitational
92	! effects (Hall kernel, see Hall, 1980: J. Atmos. Sci., 2486-2507) or
93	! including the effects of (SGS) turbulence (Wang kernel, see Wang and
94	! Grabowski, 2009: Atmos. Sci. Lett., 10, 1-8). The original code has been
95	! provided by L.-P. Wang but is substantially reformatted and speed optimized
96	! here.
97	!
98	! ATTENTION:
99	! Physical quantities (like g, densities, etc.) used in this module still
100	! have to be adjusted to those values used in the main PALM code.
101	! Also, quantities in CGS-units should be converted to SI-units eventually.
102	!------------------------------------------------------------------------------!
103
104	USE constants, &
105	ONLY: pi
106
107	USE kinds
108
109	USE particle_attributes, &
110	ONLY: collision_kernel, dissipation_classes, particles, radius_classes
111
112	USE pegrid
113
114
115	IMPLICIT NONE
116
117	PRIVATE
118
119	PUBLIC ckernel, collision_efficiency_rogers, init_kernels, &
120	rclass_lbound, rclass_ubound, recalculate_kernel
121
122	REAL(wp) :: epsilon !:
123	REAL(wp) :: eps2 !:
124	REAL(wp) :: rclass_lbound !:
125	REAL(wp) :: rclass_ubound !:
126	REAL(wp) :: urms !:
127	REAL(wp) :: urms2 !:
128
129	REAL(wp), DIMENSION(:), ALLOCATABLE :: epsclass !:
130	REAL(wp), DIMENSION(:), ALLOCATABLE :: radclass !:
131	REAL(wp), DIMENSION(:), ALLOCATABLE :: winf !:
132
133	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ec !:
134	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: ecf !:
135	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: gck !:
136	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hkernel !:
137	REAL(wp), DIMENSION(:,:), ALLOCATABLE :: hwratio !:
138
139	REAL(wp), DIMENSION(:,:,:), ALLOCATABLE :: ckernel !:
140
141	SAVE
142
143	!
144	!-- Public interfaces
145	INTERFACE collision_efficiency_rogers
146	MODULE PROCEDURE collision_efficiency_rogers
147	END INTERFACE collision_efficiency_rogers
148
149	INTERFACE init_kernels
150	MODULE PROCEDURE init_kernels
151	END INTERFACE init_kernels
152
153	INTERFACE recalculate_kernel
154	MODULE PROCEDURE recalculate_kernel
155	END INTERFACE recalculate_kernel
156
157
158	CONTAINS
159
160
161	SUBROUTINE init_kernels
162	!------------------------------------------------------------------------------!
163	! Initialization of the collision efficiency matrix with fixed radius and
164	! dissipation classes, calculated at simulation start only.
165	!------------------------------------------------------------------------------!
166
167	IMPLICIT NONE
168
169	INTEGER(iwp) :: i !:
170	INTEGER(iwp) :: j !:
171	INTEGER(iwp) :: k !:
172
173
174	!
175	!-- Calculate collision efficiencies for fixed radius- and dissipation
176	!-- classes
177	IF ( collision_kernel(6:9) == 'fast' ) THEN
178
179	ALLOCATE( ckernel(1:radius_classes,1:radius_classes, &
180	0:dissipation_classes), epsclass(1:dissipation_classes), &
181	radclass(1:radius_classes) )
182
183	!
184	!-- Calculate the radius class bounds with logarithmic distances
185	!-- in the interval [1.0E-6, 2.0E-4] m
186	rclass_lbound = LOG( 1.0E-6_wp )
187	rclass_ubound = LOG( 2.0E-4_wp )
188	radclass(1) = 1.0E-6_wp
189	DO i = 2, radius_classes
190	radclass(i) = EXP( rclass_lbound + &
191	( rclass_ubound - rclass_lbound ) * &
192	( i - 1.0_wp ) / ( radius_classes - 1.0_wp ) )
193	ENDDO
194
195	!
196	!-- Set the class bounds for dissipation in interval [0.0, 0.1] m2/s3
197	DO i = 1, dissipation_classes
198	epsclass(i) = 0.1_wp * REAL( i, KIND=wp ) / dissipation_classes
199	ENDDO
200	!
201	!-- Calculate collision efficiencies of the Wang/ayala kernel
202	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
203	ecf(1:radius_classes,1:radius_classes), &
204	gck(1:radius_classes,1:radius_classes), &
205	winf(1:radius_classes) )
206
207	DO k = 1, dissipation_classes
208
209	epsilon = epsclass(k)
210	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 1.0_wp / 3.0_wp )
211
212	CALL turbsd
213	CALL turb_enhance_eff
214	CALL effic
215
216	DO j = 1, radius_classes
217	DO i = 1, radius_classes
218	ckernel(i,j,k) = ec(i,j) * gck(i,j) * ecf(i,j)
219	ENDDO
220	ENDDO
221
222	ENDDO
223
224	!
225	!-- Calculate collision efficiencies of the Hall kernel
226	ALLOCATE( hkernel(1:radius_classes,1:radius_classes), &
227	hwratio(1:radius_classes,1:radius_classes) )
228
229	CALL fallg
230	CALL effic
231
232	DO j = 1, radius_classes
233	DO i = 1, radius_classes
234	hkernel(i,j) = pi * ( radclass(j) + radclass(i) )**2 &
235	* ec(i,j) * ABS( winf(j) - winf(i) )
236	ckernel(i,j,0) = hkernel(i,j) ! hall kernel stored on index 0
237	ENDDO
238	ENDDO
239
240	!
241	!-- Test output of efficiencies
242	IF ( j == -1 ) THEN
243
244	PRINT, '** Hall kernel'
245	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i)1.0E6_wp, &
246	i = 1,radius_classes )
247	DO j = 1, radius_classes
248	WRITE ( *,'(F4.0,1X,20(F8.4,1X))' ) radclass(j), &
249	( hkernel(i,j), i = 1,radius_classes )
250	ENDDO
251
252	DO k = 1, dissipation_classes
253	DO i = 1, radius_classes
254	DO j = 1, radius_classes
255	IF ( hkernel(i,j) == 0.0_wp ) THEN
256	hwratio(i,j) = 9999999.9_wp
257	ELSE
258	hwratio(i,j) = ckernel(i,j,k) / hkernel(i,j)
259	ENDIF
260	ENDDO
261	ENDDO
262
263	PRINT, '** epsilon = ', epsclass(k)
264	WRITE ( ,'(5X,20(F4.0,1X))' ) ( radclass(i) 1.0E6_wp, &
265	i = 1,radius_classes )
266	DO j = 1, radius_classes
267	WRITE ( ,'(F4.0,1X,20(F8.4,1X))' ) radclass(j) 1.0E6_wp, &
268	( hwratio(i,j), i = 1,radius_classes )
269	ENDDO
270	ENDDO
271
272	ENDIF
273
274	DEALLOCATE( ec, ecf, epsclass, gck, hkernel, winf )
275
276	ELSEIF( collision_kernel == 'hall' .OR. collision_kernel == 'wang' ) &
277	THEN
278	!
279	!-- Initial settings for Hall- and Wang-Kernel
280	!-- To be done: move here parts from turbsd, fallg, ecoll, etc.
281	ENDIF
282
283	END SUBROUTINE init_kernels
284
285
286	!------------------------------------------------------------------------------!
287	! Calculation of collision kernels during each timestep and for each grid box
288	!------------------------------------------------------------------------------!
289	SUBROUTINE recalculate_kernel( i1, j1, k1 )
290
291	USE arrays_3d, &
292	ONLY: diss
293
294	USE particle_attributes, &
295	ONLY: prt_count, radius_classes, wang_kernel
296
297	IMPLICIT NONE
298
299	INTEGER(iwp) :: i !:
300	INTEGER(iwp) :: i1 !:
301	INTEGER(iwp) :: j !:
302	INTEGER(iwp) :: j1 !:
303	INTEGER(iwp) :: k1 !:
304	INTEGER(iwp) :: pend !:
305	INTEGER(iwp) :: pstart !:
306
307
308	pstart = 1
309	pend = prt_count(k1,j1,i1)
310	radius_classes = prt_count(k1,j1,i1)
311
312	ALLOCATE( ec(1:radius_classes,1:radius_classes), &
313	radclass(1:radius_classes), winf(1:radius_classes) )
314
315	!
316	!-- Store particle radii on the radclass array
317	radclass(1:radius_classes) = particles(pstart:pend)%radius
318
319	IF ( wang_kernel ) THEN
320	epsilon = diss(k1,j1,i1) ! dissipation rate in m2/s3
321	ELSE
322	epsilon = 0.0_wp
323	ENDIF
324	urms = 2.02_wp * ( epsilon / 0.04_wp )**( 0.33333333333_wp )
325
326	IF ( wang_kernel .AND. epsilon > 1.0E-7_wp ) THEN
327	!
328	!-- Call routines to calculate efficiencies for the Wang kernel
329	ALLOCATE( gck(1:radius_classes,1:radius_classes), &
330	ecf(1:radius_classes,1:radius_classes) )
331
332	CALL turbsd
333	CALL turb_enhance_eff
334	CALL effic
335
336	DO j = 1, radius_classes
337	DO i = 1, radius_classes
338	ckernel(pstart+i-1,pstart+j-1,1) = ec(i,j) * gck(i,j) * ecf(i,j)
339	ENDDO
340	ENDDO
341
342	DEALLOCATE( gck, ecf )
343
344	ELSE
345	!
346	!-- Call routines to calculate efficiencies for the Hall kernel
347	CALL fallg
348	CALL effic
349
350	DO j = 1, radius_classes
351	DO i = 1, radius_classes
352	ckernel(pstart+i-1,pstart+j-1,1) = pi * &
353	( radclass(j) + radclass(i) )**2 &
354	* ec(i,j) * ABS( winf(j) - winf(i) )
355	ENDDO
356	ENDDO
357
358	ENDIF
359
360	DEALLOCATE( ec, radclass, winf )
361
362	END SUBROUTINE recalculate_kernel
363
364
365	!------------------------------------------------------------------------------!
366	! Calculation of gck
367	! This is from Aayala 2008b, page 37ff.
368	! Necessary input parameters: water density, radii of droplets, air density,
369	! air viscosity, turbulent dissipation rate, taylor microscale reynolds number,
370	! gravitational acceleration --> to be replaced by PALM parameters
371	!------------------------------------------------------------------------------!
372	SUBROUTINE turbsd
373
374	USE control_parameters, &
375	ONLY: g, molecular_viscosity
376
377	USE particle_attributes, &
378	ONLY: radius_classes
379
380	IMPLICIT NONE
381
382	LOGICAL, SAVE :: first = .TRUE. !:
383
384	INTEGER(iwp) :: i !:
385	INTEGER(iwp) :: j !:
386
387	REAL(wp) :: ao !:
388	REAL(wp) :: ao_gr !:
389	REAL(wp) :: bbb !:
390	REAL(wp) :: be !:
391	REAL(wp) :: b1 !:
392	REAL(wp) :: b2 !:
393	REAL(wp) :: ccc !:
394	REAL(wp) :: c1 !:
395	REAL(wp) :: c1_gr !:
396	REAL(wp) :: c2 !:
397	REAL(wp) :: d1 !:
398	REAL(wp) :: d2 !:
399	REAL(wp) :: eta !:
400	REAL(wp) :: e1 !:
401	REAL(wp) :: e2 !:
402	REAL(wp) :: fao_gr !:
403	REAL(wp) :: fr !:
404	REAL(wp) :: grfin !:
405	REAL(wp) :: lambda !:
406	REAL(wp) :: lambda_re !:
407	REAL(wp) :: lf !:
408	REAL(wp) :: rc !:
409	REAL(wp) :: rrp !:
410	REAL(wp) :: sst !:
411	REAL(wp) :: tauk !:
412	REAL(wp) :: tl !:
413	REAL(wp) :: t2 !:
414	REAL(wp) :: tt !:
415	REAL(wp) :: t1 !:
416	REAL(wp) :: vk !:
417	REAL(wp) :: vrms1xy !:
418	REAL(wp) :: vrms2xy !:
419	REAL(wp) :: v1 !:
420	REAL(wp) :: v1v2xy !:
421	REAL(wp) :: v1xysq !:
422	REAL(wp) :: v2 !:
423	REAL(wp) :: v2xysq !:
424	REAL(wp) :: wrfin !:
425	REAL(wp) :: wrgrav2 !:
426	REAL(wp) :: wrtur2xy !:
427	REAL(wp) :: xx !:
428	REAL(wp) :: yy !:
429	REAL(wp) :: z !:
430
431	REAL(wp), DIMENSION(1:radius_classes) :: st !:
432	REAL(wp), DIMENSION(1:radius_classes) :: tau !:
433
434	!
435	!-- Initial assignment of constants
436	IF ( first ) THEN
437
438	first = .FALSE.
439
440	ENDIF
441
442	lambda = urms * SQRT( 15.0_wp * molecular_viscosity / epsilon ) ! in m
443	lambda_re = urms*2 SQRT( 15.0_wp / epsilon / molecular_viscosity )
444	tl = urms**2 / epsilon ! in s
445	lf = 0.5_wp * urms**3 / epsilon ! in m
446	tauk = SQRT( molecular_viscosity / epsilon ) ! in s
447	eta = ( molecular_viscosity3 / epsilon )0.25_wp ! in m
448	vk = eta / tauk
449
450	ao = ( 11.0_wp + 7.0_wp * lambda_re ) / ( 205.0_wp + lambda_re )
451	tt = SQRT( 2.0_wp * lambda_re / ( SQRT( 15.0_wp ) * ao ) ) * tauk ! in s
452
453	CALL fallg ! gives winf in m/s
454
455	DO i = 1, radius_classes
456	tau(i) = winf(i) / g ! in s
457	st(i) = tau(i) / tauk
458	ENDDO
459
460	!
461	!-- Calculate wr (from Aayala 2008b, page 38f)
462	z = tt / tl
463	be = SQRT( 2.0_wp ) * lambda / lf
464	bbb = SQRT( 1.0_wp - 2.0_wp * be**2 )
465	d1 = ( 1.0_wp + bbb ) / ( 2.0_wp * bbb )
466	e1 = lf * ( 1.0_wp + bbb ) * 0.5_wp ! in m
467	d2 = ( 1.0_wp - bbb ) * 0.5_wp / bbb
468	e2 = lf * ( 1.0_wp - bbb ) * 0.5_wp ! in m
469	ccc = SQRT( 1.0_wp - 2.0_wp * z**2 )
470	b1 = ( 1.0_wp + ccc ) * 0.5_wp / ccc
471	c1 = tl * ( 1.0_wp + ccc ) * 0.5_wp ! in s
472	b2 = ( 1.0_wp - ccc ) * 0.5_wp / ccc
473	c2 = tl * ( 1.0_wp - ccc ) * 0.5_wp ! in s
474
475	DO i = 1, radius_classes
476
477	v1 = winf(i) ! in m/s
478	t1 = tau(i) ! in s
479
480	DO j = 1, i
481	rrp = radclass(i) + radclass(j)
482	v2 = winf(j) ! in m/s
483	t2 = tau(j) ! in s
484
485	v1xysq = b1 * d1 * phi_w(c1,e1,v1,t1) - b1 * d2 * phi_w(c1,e2,v1,t1) &
486	- b2 * d1 * phi_w(c2,e1,v1,t1) + b2 * d2 * phi_w(c2,e2,v1,t1)
487	v1xysq = v1xysq * urms2 / t1 ! in m2/s**2
488	vrms1xy = SQRT( v1xysq ) ! in m/s
489
490	v2xysq = b1 * d1 * phi_w(c1,e1,v2,t2) - b1 * d2 * phi_w(c1,e2,v2,t2) &
491	- b2 * d1 * phi_w(c2,e1,v2,t2) + b2 * d2 * phi_w(c2,e2,v2,t2)
492	v2xysq = v2xysq * urms2 / t2 ! in m2/s**2
493	vrms2xy = SQRT( v2xysq ) ! in m/s
494
495	IF ( winf(i) >= winf(j) ) THEN
496	v1 = winf(i)
497	t1 = tau(i)
498	v2 = winf(j)
499	t2 = tau(j)
500	ELSE
501	v1 = winf(j)
502	t1 = tau(j)
503	v2 = winf(i)
504	t2 = tau(i)
505	ENDIF
506
507	v1v2xy = b1 * d1 * zhi(c1,e1,v1,t1,v2,t2) - &
508	b1 * d2 * zhi(c1,e2,v1,t1,v2,t2) - &
509	b2 * d1 * zhi(c2,e1,v1,t1,v2,t2) + &
510	b2 * d2* zhi(c2,e2,v1,t1,v2,t2)
511	fr = d1 * EXP( -rrp / e1 ) - d2 * EXP( -rrp / e2 )
512	v1v2xy = v1v2xy * fr * urms2 / tau(i) / tau(j) ! in m2/s**2
513	wrtur2xy = vrms1xy2 + vrms2xy2 - 2.0_wp * v1v2xy ! in m2/s2
514	IF ( wrtur2xy < 0.0_wp ) wrtur2xy = 0.0_wp
515	wrgrav2 = pi / 8.0_wp * ( winf(j) - winf(i) )**2
516	wrfin = SQRT( ( 2.0_wp / pi ) * ( wrtur2xy + wrgrav2) ) ! in m/s
517
518	!
519	!-- Calculate gr
520	IF ( st(j) > st(i) ) THEN
521	sst = st(j)
522	ELSE
523	sst = st(i)
524	ENDIF
525
526	xx = -0.1988_wp * sst*4 + 1.5275_wp sst*3 - 4.2942_wp &
527	sst*2 + 5.3406_wp sst
528	IF ( xx < 0.0_wp ) xx = 0.0_wp
529	yy = 0.1886_wp * EXP( 20.306_wp / lambda_re )
530
531	c1_gr = xx / ( g / vk * tauk )**yy
532
533	ao_gr = ao + ( pi / 8.0_wp) * ( g / vk * tauk )**2
534	fao_gr = 20.115_wp * SQRT( ao_gr / lambda_re )
535	rc = SQRT( fao_gr * ABS( st(j) - st(i) ) ) * eta ! in cm
536
537	grfin = ( ( eta2 + rc2 ) / ( rrp2 + rc2) )*( c1_gr0.5_wp )
538	IF ( grfin < 1.0_wp ) grfin = 1.0_wp
539
540	gck(i,j) = 2.0_wp * pi * rrp*2 wrfin * grfin ! in cm**3/s
541	gck(j,i) = gck(i,j)
542
543	ENDDO
544	ENDDO
545
546	END SUBROUTINE turbsd
547
548
549	!------------------------------------------------------------------------------!
550	! phi_w as a function
551	!------------------------------------------------------------------------------!
552	REAL(wp) FUNCTION phi_w( a, b, vsett, tau0 )
553
554	IMPLICIT NONE
555
556	REAL(wp) :: a !:
557	REAL(wp) :: aa1 !:
558	REAL(wp) :: b !:
559	REAL(wp) :: tau0 !:
560	REAL(wp) :: vsett !:
561
562	aa1 = 1.0_wp / tau0 + 1.0_wp / a + vsett / b
563	phi_w = 1.0_wp / aa1 - 0.5_wp * vsett / b / aa1**2 ! in s
564
565	END FUNCTION phi_w
566
567
568	!------------------------------------------------------------------------------!
569	! zhi as a function
570	!------------------------------------------------------------------------------!
571	REAL(wp) FUNCTION zhi( a, b, vsett1, tau1, vsett2, tau2 )
572
573	IMPLICIT NONE
574
575	REAL(wp) :: a !:
576	REAL(wp) :: aa1 !:
577	REAL(wp) :: aa2 !:
578	REAL(wp) :: aa3 !:
579	REAL(wp) :: aa4 !:
580	REAL(wp) :: aa5 !:
581	REAL(wp) :: aa6 !:
582	REAL(wp) :: b !:
583	REAL(wp) :: tau1 !:
584	REAL(wp) :: tau2 !:
585	REAL(wp) :: vsett1 !:
586	REAL(wp) :: vsett2 !:
587
588	aa1 = vsett2 / b - 1.0_wp / tau2 - 1.0_wp / a
589	aa2 = vsett1 / b + 1.0_wp / tau1 + 1.0_wp / a
590	aa3 = ( vsett1 - vsett2 ) / b + 1.0_wp / tau1 + 1.0_wp / tau2
591	aa4 = ( vsett2 / b )2 - ( 1.0_wp / tau2 + 1.0_wp / a )2
592	aa5 = vsett2 / b + 1.0_wp / tau2 + 1.0_wp / a
593	aa6 = 1.0_wp / tau1 - 1.0_wp / a + ( 1.0_wp / tau2 + 1.0_wp / a) * &
594	vsett1 / vsett2
595	zhi = (1.0_wp / aa1 - 1.0_wp / aa2 ) * ( vsett1 - vsett2 ) * 0.5_wp / &
596	b / aa32 + ( 4.0_wp / aa4 - 1.0_wp / aa52 - 1.0_wp / aa1**2 ) &
597	* vsett2 * 0.5_wp / b /aa6 + ( 2.0_wp * ( b / aa2 - b / aa1 ) - &
598	vsett1 / aa22 + vsett2 / aa12 ) * 0.5_wp / b / aa3 ! in s**2
599
600	END FUNCTION zhi
601
602
603	!------------------------------------------------------------------------------!
604	! Calculation of terminal velocity winf following Equations 10-138 to 10-145
605	! from (Pruppacher and Klett, 1997)
606	!------------------------------------------------------------------------------!
607	SUBROUTINE fallg
608
609	USE cloud_parameters, &
610	ONLY: rho_l
611
612	USE control_parameters, &
613	ONLY: g
614
615	USE particle_attributes, &
616	ONLY: radius_classes
617
618
619	IMPLICIT NONE
620
621	INTEGER(iwp) :: i !:
622	INTEGER(iwp) :: j !:
623
624	LOGICAL, SAVE :: first = .TRUE. !:
625
626	REAL(wp), SAVE :: cunh !:
627	REAL(wp), SAVE :: eta !:
628	REAL(wp), SAVE :: phy !:
629	REAL(wp), SAVE :: py !:
630	REAL(wp), SAVE :: rho_a !:
631	REAL(wp), SAVE :: sigma !:
632	REAL(wp), SAVE :: stb !:
633	REAL(wp), SAVE :: stok !:
634	REAL(wp), SAVE :: xlamb !:
635
636	REAL(wp) :: bond !:
637	REAL(wp) :: x !:
638	REAL(wp) :: xrey !:
639	REAL(wp) :: y !:
640
641	REAL(wp), DIMENSION(1:7), SAVE :: b !:
642	REAL(wp), DIMENSION(1:6), SAVE :: c !:
643
644	!
645	!-- Initial assignment of constants
646	IF ( first ) THEN
647
648	first = .FALSE.
649	b = (/ -0.318657E1_wp, 0.992696E0_wp, -0.153193E-2_wp, &
650	-0.987059E-3_wp, -0.578878E-3_wp, 0.855176E-4_wp, &
651	-0.327815E-5_wp /)
652	c = (/ -0.500015E1_wp, 0.523778E1_wp, -0.204914E1_wp, &
653	0.475294E0_wp, -0.542819E-1_wp, 0.238449E-2_wp /)
654
655	!
656	!-- Parameter values for p = 1013,25 hPa and T = 293,15 K
657	eta = 1.818E-5_wp ! in kg/(m s)
658	xlamb = 6.6E-8_wp ! in m
659	rho_a = 1.204_wp ! in kg/m**3
660	cunh = 1.26_wp * xlamb ! in m
661	sigma = 0.07363_wp ! in kg/s**2
662	stok = 2.0_wp * g * ( rho_l - rho_a ) / ( 9.0_wp * eta ) ! in 1/(m s)
663	stb = 32.0_wp * rho_a * ( rho_l - rho_a) * g / (3.0_wp * eta * eta)
664	phy = sigma*3 rho_a2 / ( eta4 * g * ( rho_l - rho_a ) )
665	py = phy**( 1.0_wp / 6.0_wp )
666
667	ENDIF
668
669	DO j = 1, radius_classes
670
671	IF ( radclass(j) <= 1.0E-5_wp ) THEN
672
673	winf(j) = stok * ( radclass(j)*2 + cunh radclass(j) )
674
675	ELSEIF ( radclass(j) > 1.0E-5_wp .AND. radclass(j) <= 5.35E-4_wp ) THEN
676
677	x = LOG( stb * radclass(j)**3 )
678	y = 0.0_wp
679
680	DO i = 1, 7
681	y = y + b(i) * x**(i-1)
682	ENDDO
683	!
684	!-- Note: this Eq. is wrong in (Pruppacher and Klett, 1997, p. 418)
685	!-- for correct version see (Beard, 1976)
686	xrey = ( 1.0_wp + cunh / radclass(j) ) * EXP( y )
687
688	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
689
690	ELSEIF ( radclass(j) > 5.35E-4_wp ) THEN
691
692	IF ( radclass(j) > 0.0035_wp ) THEN
693	bond = g * ( rho_l - rho_a ) * 0.0035_wp**2 / sigma
694	ELSE
695	bond = g * ( rho_l - rho_a ) * radclass(j)**2 / sigma
696	ENDIF
697
698	x = LOG( 16.0_wp * bond * py / 3.0_wp )
699	y = 0.0_wp
700
701	DO i = 1, 6
702	y = y + c(i) * x**(i-1)
703	ENDDO
704
705	xrey = py * EXP( y )
706
707	IF ( radclass(j) > 0.0035_wp ) THEN
708	winf(j) = xrey * eta / ( 2.0_wp * rho_a * 0.0035_wp )
709	ELSE
710	winf(j) = xrey * eta / ( 2.0_wp * rho_a * radclass(j) )
711	ENDIF
712
713	ENDIF
714
715	ENDDO
716
717	END SUBROUTINE fallg
718
719
720	!------------------------------------------------------------------------------!
721	! Calculation of collision efficiencies for the Hall kernel
722	!------------------------------------------------------------------------------!
723	SUBROUTINE effic
724
725	USE particle_attributes, &
726	ONLY: radius_classes
727
728	IMPLICIT NONE
729
730	INTEGER(iwp) :: i !:
731	INTEGER(iwp) :: iq !:
732	INTEGER(iwp) :: ir !:
733	INTEGER(iwp) :: j !:
734	INTEGER(iwp) :: k !:
735
736	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
737
738	LOGICAL, SAVE :: first = .TRUE. !:
739
740	REAL(wp) :: ek !:
741	REAL(wp) :: particle_radius !:
742	REAL(wp) :: pp !:
743	REAL(wp) :: qq !:
744	REAL(wp) :: rq !:
745
746	REAL(wp), DIMENSION(1:21), SAVE :: rat !:
747
748	REAL(wp), DIMENSION(1:15), SAVE :: r0 !:
749
750	REAL(wp), DIMENSION(1:15,1:21), SAVE :: ecoll !:
751
752	!
753	!-- Initial assignment of constants
754	IF ( first ) THEN
755
756	first = .FALSE.
757	r0 = (/ 6.0_wp, 8.0_wp, 10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp, &
758	30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, 70.0_wp, 100.0_wp, &
759	150.0_wp, 200.0_wp, 300.0_wp /)
760
761	rat = (/ 0.00_wp, 0.05_wp, 0.10_wp, 0.15_wp, 0.20_wp, 0.25_wp, &
762	0.30_wp, 0.35_wp, 0.40_wp, 0.45_wp, 0.50_wp, 0.55_wp, &
763	0.60_wp, 0.65_wp, 0.70_wp, 0.75_wp, 0.80_wp, 0.85_wp, &
764	0.90_wp, 0.95_wp, 1.00_wp /)
765
766	ecoll(:,1) = (/ 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
767	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, &
768	0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp, 0.001_wp /)
769	ecoll(:,2) = (/ 0.003_wp, 0.003_wp, 0.003_wp, 0.004_wp, 0.005_wp, &
770	0.005_wp, 0.005_wp, 0.010_wp, 0.100_wp, 0.050_wp, &
771	0.200_wp, 0.500_wp, 0.770_wp, 0.870_wp, 0.970_wp /)
772	ecoll(:,3) = (/ 0.007_wp, 0.007_wp, 0.007_wp, 0.008_wp, 0.009_wp, &
773	0.010_wp, 0.010_wp, 0.070_wp, 0.400_wp, 0.430_wp, &
774	0.580_wp, 0.790_wp, 0.930_wp, 0.960_wp, 1.000_wp /)
775	ecoll(:,4) = (/ 0.009_wp, 0.009_wp, 0.009_wp, 0.012_wp, 0.015_wp, &
776	0.010_wp, 0.020_wp, 0.280_wp, 0.600_wp, 0.640_wp, &
777	0.750_wp, 0.910_wp, 0.970_wp, 0.980_wp, 1.000_wp /)
778	ecoll(:,5) = (/ 0.014_wp, 0.014_wp, 0.014_wp, 0.015_wp, 0.016_wp, &
779	0.030_wp, 0.060_wp, 0.500_wp, 0.700_wp, 0.770_wp, &
780	0.840_wp, 0.950_wp, 0.970_wp, 1.000_wp, 1.000_wp /)
781	ecoll(:,6) = (/ 0.017_wp, 0.017_wp, 0.017_wp, 0.020_wp, 0.022_wp, &
782	0.060_wp, 0.100_wp, 0.620_wp, 0.780_wp, 0.840_wp, &
783	0.880_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
784	ecoll(:,7) = (/ 0.030_wp, 0.030_wp, 0.024_wp, 0.022_wp, 0.032_wp, &
785	0.062_wp, 0.200_wp, 0.680_wp, 0.830_wp, 0.870_wp, &
786	0.900_wp, 0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
787	ecoll(:,8) = (/ 0.025_wp, 0.025_wp, 0.025_wp, 0.036_wp, 0.043_wp, &
788	0.130_wp, 0.270_wp, 0.740_wp, 0.860_wp, 0.890_wp, &
789	0.920_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
790	ecoll(:,9) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.040_wp, 0.052_wp, &
791	0.200_wp, 0.400_wp, 0.780_wp, 0.880_wp, 0.900_wp, &
792	0.940_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
793	ecoll(:,10) = (/ 0.030_wp, 0.030_wp, 0.030_wp, 0.047_wp, 0.064_wp, &
794	0.250_wp, 0.500_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
795	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
796	ecoll(:,11) = (/ 0.040_wp, 0.040_wp, 0.033_wp, 0.037_wp, 0.068_wp, &
797	0.240_wp, 0.550_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
798	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
799	ecoll(:,12) = (/ 0.035_wp, 0.035_wp, 0.035_wp, 0.055_wp, 0.079_wp, &
800	0.290_wp, 0.580_wp, 0.800_wp, 0.900_wp, 0.910_wp, &
801	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
802	ecoll(:,13) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.062_wp, 0.082_wp, &
803	0.290_wp, 0.590_wp, 0.780_wp, 0.900_wp, 0.910_wp, &
804	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
805	ecoll(:,14) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.060_wp, 0.080_wp, &
806	0.290_wp, 0.580_wp, 0.770_wp, 0.890_wp, 0.910_wp, &
807	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
808	ecoll(:,15) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.041_wp, 0.075_wp, &
809	0.250_wp, 0.540_wp, 0.760_wp, 0.880_wp, 0.920_wp, &
810	0.950_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
811	ecoll(:,16) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.052_wp, 0.067_wp, &
812	0.250_wp, 0.510_wp, 0.770_wp, 0.880_wp, 0.930_wp, &
813	0.970_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
814	ecoll(:,17) = (/ 0.037_wp, 0.037_wp, 0.037_wp, 0.047_wp, 0.057_wp, &
815	0.250_wp, 0.490_wp, 0.770_wp, 0.890_wp, 0.950_wp, &
816	1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp, 1.000_wp /)
817	ecoll(:,18) = (/ 0.036_wp, 0.036_wp, 0.036_wp, 0.042_wp, 0.048_wp, &
818	0.230_wp, 0.470_wp, 0.780_wp, 0.920_wp, 1.000_wp, &
819	1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp, 1.020_wp /)
820	ecoll(:,19) = (/ 0.040_wp, 0.040_wp, 0.035_wp, 0.033_wp, 0.040_wp, &
821	0.112_wp, 0.450_wp, 0.790_wp, 1.010_wp, 1.030_wp, &
822	1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp, 1.040_wp /)
823	ecoll(:,20) = (/ 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, 0.033_wp, &
824	0.119_wp, 0.470_wp, 0.950_wp, 1.300_wp, 1.700_wp, &
825	2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp, 2.300_wp /)
826	ecoll(:,21) = (/ 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, 0.027_wp, &
827	0.125_wp, 0.520_wp, 1.400_wp, 2.300_wp, 3.000_wp, &
828	4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp, 4.000_wp /)
829	ENDIF
830
831	!
832	!-- Calculate the radius class index of particles with respect to array r
833	!-- Radius has to be in Âµm
834	ALLOCATE( ira(1:radius_classes) )
835	DO j = 1, radius_classes
836	particle_radius = radclass(j) * 1.0E6_wp
837	DO k = 1, 15
838	IF ( particle_radius < r0(k) ) THEN
839	ira(j) = k
840	EXIT
841	ENDIF
842	ENDDO
843	IF ( particle_radius >= r0(15) ) ira(j) = 16
844	ENDDO
845
846	!
847	!-- Two-dimensional linear interpolation of the collision efficiency.
848	!-- Radius has to be in Âµm
849	DO j = 1, radius_classes
850	DO i = 1, j
851
852	ir = ira(j)
853	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
854	iq = INT( rq * 20 ) + 1
855	iq = MAX( iq , 2)
856
857	IF ( ir < 16 ) THEN
858	IF ( ir >= 2 ) THEN
859	pp = ( ( radclass(j) * 1.0E06_wp ) - r0(ir-1) ) / &
860	( r0(ir) - r0(ir-1) )
861	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
862	ec(j,i) = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) &
863	* ecoll(ir-1,iq-1) &
864	+ pp * ( 1.0_wp - qq ) * ecoll(ir,iq-1) &
865	+ qq * ( 1.0_wp - pp ) * ecoll(ir-1,iq) &
866	+ pp * qq * ecoll(ir,iq)
867	ELSE
868	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
869	ec(j,i) = ( 1.0_wp - qq ) * ecoll(1,iq-1) + qq * ecoll(1,iq)
870	ENDIF
871	ELSE
872	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
873	ek = ( 1.0_wp - qq ) * ecoll(15,iq-1) + qq * ecoll(15,iq)
874	ec(j,i) = MIN( ek, 1.0_wp )
875	ENDIF
876
877	IF ( ec(j,i) < 1.0E-20_wp ) ec(j,i) = 0.0_wp
878
879	ec(i,j) = ec(j,i)
880
881	ENDDO
882	ENDDO
883
884	DEALLOCATE( ira )
885
886	END SUBROUTINE effic
887
888
889	!------------------------------------------------------------------------------!
890	! Calculation of enhancement factor for collision efficencies due to turbulence
891	!------------------------------------------------------------------------------!
892	SUBROUTINE turb_enhance_eff
893
894	USE particle_attributes, &
895	ONLY: radius_classes
896
897	IMPLICIT NONE
898
899	INTEGER(iwp) :: i !:
900	INTEGER(iwp) :: iq !:
901	INTEGER(iwp) :: ir !:
902	INTEGER(iwp) :: j !:
903	INTEGER(iwp) :: k !:
904	INTEGER(iwp) :: kk !:
905
906	INTEGER(iwp), DIMENSION(:), ALLOCATABLE :: ira !:
907
908	LOGICAL, SAVE :: first = .TRUE. !:
909
910	REAL(wp) :: particle_radius !:
911	REAL(wp) :: pp !:
912	REAL(wp) :: qq !:
913	REAL(wp) :: rq !:
914	REAL(wp) :: y1 !:
915	REAL(wp) :: y2 !:
916	REAL(wp) :: y3 !:
917
918	REAL(wp), DIMENSION(1:11), SAVE :: rat !:
919
920	REAL(wp), DIMENSION(1:7), SAVE :: r0 !:
921
922	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_100 !:
923	REAL(wp), DIMENSION(1:7,1:11), SAVE :: ecoll_400 !:
924
925	!
926	!-- Initial assignment of constants
927	IF ( first ) THEN
928
929	first = .FALSE.
930
931	r0 = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, 60.0_wp, &
932	100.0_wp /)
933
934	rat = (/ 0.0_wp, 0.1_wp, 0.2_wp, 0.3_wp, 0.4_wp, 0.5_wp, 0.6_wp, &
935	0.7_wp, 0.8_wp, 0.9_wp, 1.0_wp /)
936	!
937	!-- for 100 cm2/s3
938	ecoll_100(:,1) = (/ 1.74_wp, 1.74_wp, 1.773_wp, 1.49_wp, &
939	1.207_wp, 1.207_wp, 1.0_wp /)
940	ecoll_100(:,2) = (/ 1.46_wp, 1.46_wp, 1.421_wp, 1.245_wp, &
941	1.069_wp, 1.069_wp, 1.0_wp /)
942	ecoll_100(:,3) = (/ 1.32_wp, 1.32_wp, 1.245_wp, 1.123_wp, &
943	1.000_wp, 1.000_wp, 1.0_wp /)
944	ecoll_100(:,4) = (/ 1.250_wp, 1.250_wp, 1.148_wp, 1.087_wp, &
945	1.025_wp, 1.025_wp, 1.0_wp /)
946	ecoll_100(:,5) = (/ 1.186_wp, 1.186_wp, 1.066_wp, 1.060_wp, &
947	1.056_wp, 1.056_wp, 1.0_wp /)
948	ecoll_100(:,6) = (/ 1.045_wp, 1.045_wp, 1.000_wp, 1.014_wp, &
949	1.028_wp, 1.028_wp, 1.0_wp /)
950	ecoll_100(:,7) = (/ 1.070_wp, 1.070_wp, 1.030_wp, 1.038_wp, &
951	1.046_wp, 1.046_wp, 1.0_wp /)
952	ecoll_100(:,8) = (/ 1.000_wp, 1.000_wp, 1.054_wp, 1.042_wp, &
953	1.029_wp, 1.029_wp, 1.0_wp /)
954	ecoll_100(:,9) = (/ 1.223_wp, 1.223_wp, 1.117_wp, 1.069_wp, &
955	1.021_wp, 1.021_wp, 1.0_wp /)
956	ecoll_100(:,10) = (/ 1.570_wp, 1.570_wp, 1.244_wp, 1.166_wp, &
957	1.088_wp, 1.088_wp, 1.0_wp /)
958	ecoll_100(:,11) = (/ 20.3_wp, 20.3_wp, 14.6_wp, 8.61_wp, &
959	2.60_wp, 2.60_wp, 1.0_wp /)
960	!
961	!-- for 400 cm2/s3
962	ecoll_400(:,1) = (/ 4.976_wp, 4.976_wp, 3.593_wp, 2.519_wp, &
963	1.445_wp, 1.445_wp, 1.0_wp /)
964	ecoll_400(:,2) = (/ 2.984_wp, 2.984_wp, 2.181_wp, 1.691_wp, &
965	1.201_wp, 1.201_wp, 1.0_wp /)
966	ecoll_400(:,3) = (/ 1.988_wp, 1.988_wp, 1.475_wp, 1.313_wp, &
967	1.150_wp, 1.150_wp, 1.0_wp /)
968	ecoll_400(:,4) = (/ 1.490_wp, 1.490_wp, 1.187_wp, 1.156_wp, &
969	1.126_wp, 1.126_wp, 1.0_wp /)
970	ecoll_400(:,5) = (/ 1.249_wp, 1.249_wp, 1.088_wp, 1.090_wp, &
971	1.092_wp, 1.092_wp, 1.0_wp /)
972	ecoll_400(:,6) = (/ 1.139_wp, 1.139_wp, 1.130_wp, 1.091_wp, &
973	1.051_wp, 1.051_wp, 1.0_wp /)
974	ecoll_400(:,7) = (/ 1.220_wp, 1.220_wp, 1.190_wp, 1.138_wp, &
975	1.086_wp, 1.086_wp, 1.0_wp /)
976	ecoll_400(:,8) = (/ 1.325_wp, 1.325_wp, 1.267_wp, 1.165_wp, &
977	1.063_wp, 1.063_wp, 1.0_wp /)
978	ecoll_400(:,9) = (/ 1.716_wp, 1.716_wp, 1.345_wp, 1.223_wp, &
979	1.100_wp, 1.100_wp, 1.0_wp /)
980	ecoll_400(:,10) = (/ 3.788_wp, 3.788_wp, 1.501_wp, 1.311_wp, &
981	1.120_wp, 1.120_wp, 1.0_wp /)
982	ecoll_400(:,11) = (/ 36.52_wp, 36.52_wp, 19.16_wp, 22.80_wp, &
983	26.0_wp, 26.0_wp, 1.0_wp /)
984
985	ENDIF
986
987	!
988	!-- Calculate the radius class index of particles with respect to array r0
989	!-- Radius has to be in Âµm
990	ALLOCATE( ira(1:radius_classes) )
991
992	DO j = 1, radius_classes
993	particle_radius = radclass(j) * 1.0E6_wp
994	DO k = 1, 7
995	IF ( particle_radius < r0(k) ) THEN
996	ira(j) = k
997	EXIT
998	ENDIF
999	ENDDO
1000	IF ( particle_radius >= r0(7) ) ira(j) = 8
1001	ENDDO
1002
1003	!
1004	!-- Two-dimensional linear interpolation of the collision efficiencies
1005	!-- Radius has to be in Âµm
1006	DO j = 1, radius_classes
1007	DO i = 1, j
1008
1009	ir = ira(j)
1010	rq = MIN( radclass(i) / radclass(j), radclass(j) / radclass(i) )
1011
1012	DO kk = 2, 11
1013	IF ( rq <= rat(kk) ) THEN
1014	iq = kk
1015	EXIT
1016	ENDIF
1017	ENDDO
1018
1019	y1 = 0.0001_wp ! for 0 m2/s3
1020
1021	IF ( ir < 8 ) THEN
1022	IF ( ir >= 2 ) THEN
1023	pp = ( radclass(j)*1.0E6_wp - r0(ir-1) ) / ( r0(ir) - r0(ir-1) )
1024	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1025	y2 = ( 1.0_wp - pp ) * ( 1.0_wp - qq ) * ecoll_100(ir-1,iq-1) + &
1026	pp * ( 1.0_wp - qq ) * ecoll_100(ir,iq-1) + &
1027	qq * ( 1.0_wp - pp ) * ecoll_100(ir-1,iq) + &
1028	pp * qq * ecoll_100(ir,iq)
1029	y3 = ( 1.0-pp ) * ( 1.0_wp - qq ) * ecoll_400(ir-1,iq-1) + &
1030	pp * ( 1.0_wp - qq ) * ecoll_400(ir,iq-1) + &
1031	qq * ( 1.0_wp - pp ) * ecoll_400(ir-1,iq) + &
1032	pp * qq * ecoll_400(ir,iq)
1033	ELSE
1034	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1035	y2 = ( 1.0_wp - qq ) * ecoll_100(1,iq-1) + qq * ecoll_100(1,iq)
1036	y3 = ( 1.0_wp - qq ) * ecoll_400(1,iq-1) + qq * ecoll_400(1,iq)
1037	ENDIF
1038	ELSE
1039	qq = ( rq - rat(iq-1) ) / ( rat(iq) - rat(iq-1) )
1040	y2 = ( 1.0_wp - qq ) * ecoll_100(7,iq-1) + qq * ecoll_100(7,iq)
1041	y3 = ( 1.0_wp - qq ) * ecoll_400(7,iq-1) + qq * ecoll_400(7,iq)
1042	ENDIF
1043	!
1044	!-- Linear interpolation of dissipation rate in m2/s3
1045	IF ( epsilon <= 0.01_wp ) THEN
1046	ecf(j,i) = ( epsilon - 0.01_wp ) / ( 0.0_wp - 0.01_wp ) * y1 &
1047	+ ( epsilon - 0.0_wp ) / ( 0.01_wp - 0.0_wp ) * y2
1048	ELSEIF ( epsilon <= 0.06_wp ) THEN
1049	ecf(j,i) = ( epsilon - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1050	+ ( epsilon - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1051	ELSE
1052	ecf(j,i) = ( 0.06_wp - 0.04_wp ) / ( 0.01_wp - 0.04_wp ) * y2 &
1053	+ ( 0.06_wp - 0.01_wp ) / ( 0.04_wp - 0.01_wp ) * y3
1054	ENDIF
1055
1056	IF ( ecf(j,i) < 1.0_wp ) ecf(j,i) = 1.0_wp
1057
1058	ecf(i,j) = ecf(j,i)
1059
1060	ENDDO
1061	ENDDO
1062
1063	END SUBROUTINE turb_enhance_eff
1064
1065
1066
1067	SUBROUTINE collision_efficiency_rogers( mean_r, r, e)
1068	!------------------------------------------------------------------------------!
1069	! Collision efficiencies from table 8.2 in Rogers and Yau (1989, 3rd edition).
1070	! Values are calculated from table by bilinear interpolation.
1071	!------------------------------------------------------------------------------!
1072
1073	IMPLICIT NONE
1074
1075	INTEGER(iwp) :: i !:
1076	INTEGER(iwp) :: j !:
1077	INTEGER(iwp) :: k !:
1078
1079	LOGICAL, SAVE :: first = .TRUE. !:
1080
1081	REAL(wp) :: aa !:
1082	REAL(wp) :: bb !:
1083	REAL(wp) :: cc !:
1084	REAL(wp) :: dd !:
1085	REAL(wp) :: dx !:
1086	REAL(wp) :: dy !:
1087	REAL(wp) :: e !:
1088	REAL(wp) :: gg !:
1089	REAL(wp) :: mean_r !:
1090	REAL(wp) :: mean_rm !:
1091	REAL(wp) :: r !:
1092	REAL(wp) :: rm !:
1093	REAL(wp) :: x !:
1094	REAL(wp) :: y !:
1095
1096	REAL(wp), DIMENSION(1:9), SAVE :: collected_r = 0.0_wp !:
1097
1098	REAL(wp), DIMENSION(1:19), SAVE :: collector_r = 0.0_wp !:
1099
1100	REAL(wp), DIMENSION(1:9,1:19), SAVE :: ef = 0.0_wp !:
1101
1102	mean_rm = mean_r * 1.0E06_wp
1103	rm = r * 1.0E06_wp
1104
1105	IF ( first ) THEN
1106
1107	collected_r = (/ 2.0_wp, 3.0_wp, 4.0_wp, 6.0_wp, 8.0_wp, &
1108	10.0_wp, 15.0_wp, 20.0_wp, 25.0_wp /)
1109	collector_r = (/ 10.0_wp, 20.0_wp, 30.0_wp, 40.0_wp, 50.0_wp, &
1110	60.0_wp, 80.0_wp, 100.0_wp, 150.0_wp, 200.0_wp, &
1111	300.0_wp, 400.0_wp, 500.0_wp, 600.0_wp, 1000.0_wp, &
1112	1400.0_wp, 1800.0_wp, 2400.0_wp, 3000.0_wp /)
1113
1114	ef(:,1) = (/ 0.017_wp, 0.027_wp, 0.037_wp, 0.052_wp, 0.052_wp, &
1115	0.052_wp, 0.052_wp, 0.0_wp, 0.0_wp /)
1116	ef(:,2) = (/ 0.001_wp, 0.016_wp, 0.027_wp, 0.060_wp, 0.12_wp, &
1117	0.17_wp, 0.17_wp, 0.17_wp, 0.0_wp /)
1118	ef(:,3) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.13_wp, 0.28_wp, &
1119	0.37_wp, 0.54_wp, 0.55_wp, 0.47_wp/)
1120	ef(:,4) = (/ 0.001_wp, 0.001_wp, 0.02_wp, 0.23_wp, 0.4_wp, &
1121	0.55_wp, 0.7_wp, 0.75_wp, 0.75_wp/)
1122	ef(:,5) = (/ 0.01_wp, 0.01_wp, 0.03_wp, 0.3_wp, 0.4_wp, &
1123	0.58_wp, 0.73_wp, 0.75_wp, 0.79_wp/)
1124	ef(:,6) = (/ 0.01_wp, 0.01_wp, 0.13_wp, 0.38_wp, 0.57_wp, &
1125	0.68_wp, 0.80_wp, 0.86_wp, 0.91_wp/)
1126	ef(:,7) = (/ 0.01_wp, 0.085_wp, 0.23_wp, 0.52_wp, 0.68_wp, &
1127	0.76_wp, 0.86_wp, 0.92_wp, 0.95_wp/)
1128	ef(:,8) = (/ 0.01_wp, 0.14_wp, 0.32_wp, 0.60_wp, 0.73_wp, &
1129	0.81_wp, 0.90_wp, 0.94_wp, 0.96_wp/)
1130	ef(:,9) = (/ 0.025_wp, 0.25_wp, 0.43_wp, 0.66_wp, 0.78_wp, &
1131	0.83_wp, 0.92_wp, 0.95_wp, 0.96_wp/)
1132	ef(:,10) = (/ 0.039_wp, 0.3_wp, 0.46_wp, 0.69_wp, 0.81_wp, &
1133	0.87_wp, 0.93_wp, 0.95_wp, 0.96_wp/)
1134	ef(:,11) = (/ 0.095_wp, 0.33_wp, 0.51_wp, 0.72_wp, 0.82_wp, &
1135	0.87_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1136	ef(:,12) = (/ 0.098_wp, 0.36_wp, 0.51_wp, 0.73_wp, 0.83_wp, &
1137	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1138	ef(:,13) = (/ 0.1_wp, 0.36_wp, 0.52_wp, 0.74_wp, 0.83_wp, &
1139	0.88_wp, 0.93_wp, 0.96_wp, 0.97_wp/)
1140	ef(:,14) = (/ 0.17_wp, 0.4_wp, 0.54_wp, 0.72_wp, 0.83_wp, &
1141	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
1142	ef(:,15) = (/ 0.15_wp, 0.37_wp, 0.52_wp, 0.74_wp, 0.82_wp, &
1143	0.88_wp, 0.94_wp, 0.98_wp, 1.0_wp /)
1144	ef(:,16) = (/ 0.11_wp, 0.34_wp, 0.49_wp, 0.71_wp, 0.83_wp, &
1145	0.88_wp, 0.94_wp, 0.95_wp, 1.0_wp /)
1146	ef(:,17) = (/ 0.08_wp, 0.29_wp, 0.45_wp, 0.68_wp, 0.8_wp, &
1147	0.86_wp, 0.96_wp, 0.94_wp, 1.0_wp /)
1148	ef(:,18) = (/ 0.04_wp, 0.22_wp, 0.39_wp, 0.62_wp, 0.75_wp, &
1149	0.83_wp, 0.92_wp, 0.96_wp, 1.0_wp /)
1150	ef(:,19) = (/ 0.02_wp, 0.16_wp, 0.33_wp, 0.55_wp, 0.71_wp, &
1151	0.81_wp, 0.90_wp, 0.94_wp, 1.0_wp /)
1152
1153	ENDIF
1154
1155	DO k = 1, 8
1156	IF ( collected_r(k) <= mean_rm ) i = k
1157	ENDDO
1158
1159	DO k = 1, 18
1160	IF ( collector_r(k) <= rm ) j = k
1161	ENDDO
1162
1163	IF ( rm < 10.0_wp ) THEN
1164	e = 0.0_wp
1165	ELSEIF ( mean_rm < 2.0_wp ) THEN
1166	e = 0.001_wp
1167	ELSEIF ( mean_rm >= 25.0_wp ) THEN
1168	IF( j <= 2 ) e = 0.0_wp
1169	IF( j == 3 ) e = 0.47_wp
1170	IF( j == 4 ) e = 0.8_wp
1171	IF( j == 5 ) e = 0.9_wp
1172	IF( j >=6 ) e = 1.0_wp
1173	ELSEIF ( rm >= 3000.0_wp ) THEN
1174	IF( i == 1 ) e = 0.02_wp
1175	IF( i == 2 ) e = 0.16_wp
1176	IF( i == 3 ) e = 0.33_wp
1177	IF( i == 4 ) e = 0.55_wp
1178	IF( i == 5 ) e = 0.71_wp
1179	IF( i == 6 ) e = 0.81_wp
1180	IF( i == 7 ) e = 0.90_wp
1181	IF( i >= 8 ) e = 0.94_wp
1182	ELSE
1183	x = mean_rm - collected_r(i)
1184	y = rm - collector_r(j)
1185	dx = collected_r(i+1) - collected_r(i)
1186	dy = collector_r(j+1) - collector_r(j)
1187	aa = x2 + y2
1188	bb = ( dx - x )2 + y2
1189	cc = x2 + ( dy - y )2
1190	dd = ( dx - x )2 + ( dy - y )2
1191	gg = aa + bb + cc + dd
1192
1193	e = ( (gg-aa)ef(i,j) + (gg-bb)ef(i+1,j) + (gg-cc)*ef(i,j+1) + &
1194	(gg-dd)ef(i+1,j+1) ) / (3.0_wp gg)
1195	ENDIF
1196
1197	END SUBROUTINE collision_efficiency_rogers
1198
1199	END MODULE lpm_collision_kernels_mod

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