module_mosaic_coag.F

References to this file elsewhere.
1 !**********************************************************************************  
2 ! This computer software was prepared by Battelle Memorial Institute, hereinafter
3 ! the Contractor, under Contract No. DE-AC05-76RL0 1830 with the Department of 
4 ! Energy (DOE). NEITHER THE GOVERNMENT NOR THE CONTRACTOR MAKES ANY WARRANTY,
5 ! EXPRESS OR IMPLIED, OR ASSUMES ANY LIABILITY FOR THE USE OF THIS SOFTWARE.
6 !
7 ! MOSAIC module: see module_mosaic_driver.F for information and terms of use
8 !**********************************************************************************  
9 	module module_mosaic_coag
10 
11 
12 
13 	use module_peg_util
14 
15 
16 
17 	implicit none
18 
19 
20 
21 	contains
22 
23 
24 
25 !-----------------------------------------------------------------------
26 	subroutine mosaic_coag_1clm( istat_coag,   &
27 		it, jt, kclm_calcbgn, kclm_calcend,   &
28 		idiagbb_in,   &
29 		dtchem, dtcoag_in,   &
30 		id, ktau, ktauc, its, ite, jts, jte, kts, kte )
31 !
32 !   calculates aerosol particle coagulation for grid points in
33 !	the i=it, j=jt vertical column 
34 !	over timestep dtcoag_in
35 !
36 !   uses a version of subr. coagsolv (see additional disclaimer below)
37 !	that was obtained from mark jacobson in june 2003,
38 !	and then modified to work with mosaic aerosol routines
39 !
40 	use module_data_mosaic_asect
41 	use module_data_mosaic_other
42 	use module_state_description, only:  param_first_scalar
43 
44 !   subr arguments
45 	integer, intent(inout) :: istat_coag    ! =0 if no problems
46 	integer, intent(in) ::   &
47 		it, jt, kclm_calcbgn, kclm_calcend,   &
48 		idiagbb_in,   &
49 		id, ktau, ktauc, its, ite, jts, jte, kts, kte
50 	real, intent(in) :: dtchem, dtcoag_in
51 
52 !   NOTE - much information is passed via arrays in 
53 !		module_data_mosaic_asect and module_data_mosaic_other
54 !
55 !   rsub (inout) - aerosol mixing ratios
56 !   aqmassdry_sub, aqvoldry_sub (inout) - 
57 !		aerosol dry-mass and dry-volume mixing ratios
58 !   adrydens_sub (inout) - aerosol dry density
59 !   rsub(ktemp,:,:), ptotclm, cairclm (in) - 
60 !		air temperature, pressure, and molar density
61 
62 
63 !   local variables
64 	integer, parameter :: coag_method = 1
65 	integer, parameter :: ncomp_coag_maxd = maxd_acomp + 3
66 
67 	integer :: k, l, ll, lla, llb, llx, m
68 	integer :: isize, itype, iphase
69 	integer :: iconform_numb
70 	integer :: idiagbb, idiag_coag_onoff, iok
71 	integer :: lunout_coag
72 	integer :: ncomp_coag, nsize, nsubstep_coag, ntau_coag
73 	integer,save :: ncountaa(10), ncountbb(0:ncomp_coag_maxd)
74 	integer :: p1st
75 
76 	real, parameter :: densdefault = 2.0
77 	real, parameter :: factsafe = 1.00001
78 	real, parameter :: onethird = 1.0/3.0
79 	real, parameter :: piover6 = pi/6.0
80 	real, parameter :: smallmassbb = 1.0e-30
81 
82 	real :: cair_box
83 	real :: dtcoag
84 	real :: duma, dumb, dumc
85 	real :: patm_box
86 	real :: temp_box
87 	real :: xxdens, xxmass, xxnumb, xxvolu
88 	real :: xxmasswet, xxvoluwet
89 
90 	real :: dpdry(maxd_asize), dpwet(maxd_asize), denswet(maxd_asize)
91 	real :: num_distrib(maxd_asize)
92 	real :: sumnew(ncomp_coag_maxd), sumold(ncomp_coag_maxd)
93 	real :: vol_distrib(maxd_asize,ncomp_coag_maxd)
94 	real :: xxvolubb(maxd_asize)
95 
96 	character(len=120) :: msg
97 
98 
99 
100 	istat_coag = 0
101 
102 	lunout_coag = 6
103 	if (lunout .gt. 0) lunout_coag = lunout
104 
105 
106 !   when dtcoag_in > dtchem, do not perform coagulation calcs 
107 !   on every chemistry time step
108 	ntau_coag = nint( dtcoag_in/dtchem )
109 	ntau_coag = max( 1, ntau_coag )
110 	if (mod(ktau,ntau_coag) .ne. 0) return
111 	dtcoag = dtchem*ntau_coag
112 
113 
114 !   set variables that do not change
115     p1st = PARAM_FIRST_SCALAR
116 	idiagbb = idiagbb_in
117 
118 !   NOTE - code currently just does 1 type
119 	itype = 1
120 	iphase = ai_phase
121 	nsize = nsize_aer(itype)
122 	ncomp_coag = ncomp_plustracer_aer(itype) + 3
123 
124 
125 !   loop over subareas (currently only 1) and vertical levels
126 	do 2900 m = 1, nsubareas
127 
128 	do 2800 k = kclm_calcbgn, kclm_calcend
129 
130 
131 !   temporary diagnostics
132 	if ((it .eq. its) .and.   &
133 	    (jt .eq. jts) .and. (k .eq. kclm_calcbgn)) then
134 	    ncountaa(:) = 0
135 	    ncountbb(:) = 0
136 	end if
137 
138 
139 	ncountaa(1) = ncountaa(1) + 1
140 	if (afracsubarea(k,m) .lt. 1.e-4) goto 2700
141 
142 	cair_box = cairclm(k)
143 	temp_box = rsub(ktemp,k,m)
144 	patm_box = ptotclm(k)/1.01325e6
145 
146 	nsubstep_coag = 1
147 	idiag_coag_onoff = -1
148 
149 !   do initial calculation of dry mass, volume, and density,
150 !   and initial number conforming (as needed)
151 	vol_distrib(:,:) = 0.0
152 	sumold(:) = 0.0
153 	do isize = 1, nsize
154 	    l = numptr_aer(isize,itype,iphase)
155 	    xxnumb = rsub(l,k,m)
156 	    xxmass = aqmassdry_sub(isize,itype,k,m)
157 	    xxvolu = aqvoldry_sub( isize,itype,k,m)
158 	    xxdens = adrydens_sub( isize,itype,k,m)
159 	    iconform_numb = 1
160 
161 	    duma = max( abs(xxmass), abs(xxvolu*xxdens), 0.1*smallmassbb )
162 	    dumb = abs(xxmass - xxvolu*xxdens)/duma
163 	    if ( (xxdens .lt. 0.1) .or. (xxdens .gt. 20.0)   &
164                                    .or. (dumb .gt. 1.0e-4) ) then
165 !   (exception) case of drydensity not valid, or mass /= volu*dens
166 !   so compute dry mass and volume from rsub
167 		ncountaa(2) = ncountaa(2) + 1
168 		if (idiagbb .ge. 200)   &
169 		    write(*,'(a,i10,4i4,1p,4e10.2)') 'coagaa-2a',   &
170 		    ktau, it, jt, k, isize, xxmass, xxvolu, xxdens
171 		xxmass = 0.0
172 		xxvolu  = 0.0
173 		do ll = 1, ncomp_aer(itype)
174 		    l = massptr_aer(ll,isize,itype,iphase)
175 		    if (l .ge. p1st) then
176 			duma = max( 0.0, rsub(l,k,m) )*mw_aer(ll,itype)
177 			xxmass = xxmass + duma
178 			xxvolu = xxvolu + duma/dens_aer(ll,itype)
179 		    end if
180 		end do
181 		if (xxmass .gt. 0.99*smallmassbb) then
182 		    xxdens = xxmass/xxvolu
183 		    xxvolu = xxmass/xxdens
184 		    if (idiagbb .ge. 200)   &
185 			write(*,'(a,i10,4i4,1p,4e10.2)') 'coagaa-2b',   &
186 			ktau, it, jt, k, isize, xxmass, xxvolu, xxdens
187 		end if
188 	    end if
189 
190 	    if (xxmass .le. 1.01*smallmassbb) then
191 !   when drymass extremely small, use default density and bin center size,
192 !   and zero out water
193 		ncountaa(3) = ncountaa(3) + 1
194 		xxdens = densdefault
195 		xxvolu = xxmass/xxdens
196 		xxnumb = xxmass/(volumcen_sect(isize,itype)*xxdens)
197 		l = hyswptr_aer(isize,itype)
198 		if (l .ge. p1st) rsub(l,k,m) = 0.0
199 		l = waterptr_aer(isize,itype)
200 		if (l .ge. p1st) rsub(l,k,m) = 0.0
201 		iconform_numb = 0
202 		if (idiagbb .ge. 200)   &
203 		    write(*,'(a,i10,4i4,1p,4e10.2)') 'coagaa-2c',   &
204 		    ktau, it, jt, k, isize, xxmass, xxvolu, xxdens
205 	    else
206 		xxvolu = xxmass/xxdens
207 	    end if
208 
209 !   check for mean dry-size 'safely' within bounds, and conform number if not
210 	    if (iconform_numb .gt. 0) then
211 		if (xxnumb .gt.   &
212 			xxvolu/(factsafe*volumlo_sect(isize,itype))) then
213 		    ncountaa(4) = ncountaa(4) + 1
214 		    duma = xxnumb
215 		    xxnumb = xxvolu/(factsafe*volumlo_sect(isize,itype))
216 		    if (idiagbb .ge. 200)   &
217 			write(*,'(a,i10,4i4,1p,3e12.4)') 'coagcc-4 ',   &
218 			ktau, it, jt, k, isize, xxvolu, duma, xxnumb
219 		else if (xxnumb .lt.   &
220 			xxvolu*factsafe/volumhi_sect(isize,itype)) then
221 		    ncountaa(5) = ncountaa(5) + 1
222 		    duma = xxnumb
223 		    xxnumb = xxvolu*factsafe/volumhi_sect(isize,itype)
224 		    if (idiagbb .ge. 200)   &
225 			write(*,'(a,i10,4i4,1p,3e12.4)') 'coagcc-5 ',   &
226 			ktau, it, jt, k, isize, xxvolu, duma, xxnumb
227 		end if
228 	    end if
229 
230 !   load numb, mass, volu, dens back into mosaic_asect arrays
231 	    l = numptr_aer(isize,itype,iphase)
232 	    rsub(l,k,m) = xxnumb
233 	    adrydens_sub( isize,itype,k,m) = xxdens
234 	    aqmassdry_sub(isize,itype,k,m) = xxmass
235 	    aqvoldry_sub( isize,itype,k,m) = xxvolu
236 
237 !
238 !   load coagsolv arrays with number, mass, and volume mixing ratios
239 !
240 !   *** NOTE ***
241 !     num_distrib must be (#/cm3)
242 !     vol_distrib units do not matter - they can be either masses or volumes,
243 !        and either mixing ratios or concentrations
244 !	 (e.g., g/cm3-air, ug/kg-air, cm3/cm3-air, cm3/kg-air, ...)
245 !
246 	    num_distrib(isize) = xxnumb*cair_box
247 
248 	    do ll = 1, ncomp_plustracer_aer(itype)
249 		l = massptr_aer(ll,isize,itype,iphase)
250 		duma = 0.0
251 		if (l .ge. p1st) duma = max( 0.0, rsub(l,k,m) )
252 		vol_distrib(isize,ll)   = duma
253 		sumold(ll) = sumold(ll) + duma
254 	    end do
255 
256 	    do llx = 1, 3
257 		ll = (ncomp_coag-3) + llx
258 		duma = 0.0
259 		if (llx .eq. 1) then
260 		    l = hyswptr_aer(isize,itype)
261 		    if (l .ge. p1st) duma = max( 0.0, rsub(l,k,m) )
262 		else if (llx .eq. 2) then
263 		    l = waterptr_aer(isize,itype)
264 		    if (l .ge. p1st) duma = max( 0.0, rsub(l,k,m) )
265 		else
266 		    duma = max( 0.0, aqvoldry_sub( isize,itype,k,m) )
267 		end if
268 		vol_distrib(isize,ll)   = duma
269 		sumold(ll) = sumold(ll) + duma
270 	    end do
271 
272 !   calculate dry and wet diameters and wet density
273 	    if (xxmass .le. 1.01*smallmassbb) then
274 		dpdry(isize) = dcen_sect(isize,itype)
275 		dpwet(isize) = dpdry(isize)
276 		denswet(isize) = xxdens
277 	    else
278 		dpdry(isize) = (xxvolu/(xxnumb*piover6))**onethird
279 		dpdry(isize) = max( dpdry(isize), dlo_sect(isize,itype) )
280 		l = waterptr_aer(isize,itype)
281 		if (l .ge. p1st) then
282 		    duma = max( 0.0, rsub(l,k,m) )*mw_water_aer
283 		    xxmasswet = xxmass + duma
284 		    xxvoluwet = xxvolu + duma/dens_water_aer
285 		    dpwet(isize) = (xxvoluwet/(xxnumb*piover6))**onethird
286 		    dpwet(isize) = min( dpwet(isize), 30.0*dhi_sect(isize,itype) )
287 		    denswet(isize) = (xxmasswet/xxvoluwet)
288 		else
289 		    dpwet(isize) = dpdry(isize)
290 		    denswet(isize) = xxdens
291 		end if
292 	    end if
293 	end do
294 
295 
296 !
297 !   make call to coagulation routine
298 !
299 	call coagsolv(   &
300 	    nsize, maxd_asize, ncomp_coag, ncomp_coag_maxd,   &
301 	    temp_box, patm_box, dtcoag, nsubstep_coag,   &
302 	    lunout_coag, idiag_coag_onoff, iok,   &
303 	    dpdry, dpwet, denswet, num_distrib, vol_distrib )
304 
305 	if (iok .lt. 0) then
306 	    msg = '*** subr mosaic_coag_1clm -- fatal error in coagsolv'
307 	    call peg_message( lunout, msg )
308 	    call peg_error_fatal( lunout, msg )
309 	else if (iok .gt. 0) then
310 	    ncountaa(6) = ncountaa(6) + 1
311 	    goto 2700
312 	end if
313 
314 
315 !
316 !   unload coagsolv arrays
317 !
318 	sumnew(:) = 0.0
319 	do isize = 1, nsize
320 	    do ll = 1, ncomp_coag
321 		sumnew(ll) = sumnew(ll) + max( 0.0, vol_distrib(isize,ll) )
322 	    end do
323 
324 	    l = numptr_aer(isize,itype,iphase)
325 	    rsub(l,k,m) = max( 0.0, num_distrib(isize)/cair_box )
326 
327 !   unload mass mixing ratios into rsub; also calculate dry mass and volume
328 	    xxmass = 0.0
329 	    xxvolu = 0.0
330 	    do ll = 1, ncomp_aer(itype)
331 		l = massptr_aer(ll,isize,itype,iphase)
332 		if (l .ge. p1st) then
333 		    duma = max( 0.0, vol_distrib(isize,ll) )
334 		    rsub(l,k,m) = duma
335 		    duma = duma*mw_aer(ll,itype)
336 		    xxmass = xxmass + duma
337 		    xxvolu = xxvolu + duma/dens_aer(ll,itype)
338 		end if
339 	    end do
340 	    aqmassdry_sub(isize,itype,k,m) = xxmass
341 	    xxvolubb(isize) = xxvolu
342 
343 	    ll = (ncomp_coag-3) + 1
344 	    l = hyswptr_aer(isize,itype)
345 	    if (l .ge. p1st) rsub(l,k,m) = max( 0.0, vol_distrib(isize,ll) )
346 
347 	    ll = (ncomp_coag-3) + 2
348 	    l = waterptr_aer(isize,itype)
349 	    if (l .ge. p1st) rsub(l,k,m) = max( 0.0, vol_distrib(isize,ll) )
350 
351 	    ll = (ncomp_coag-3) + 3
352 	    aqvoldry_sub( isize,itype,k,m) = max( 0.0, vol_distrib(isize,ll) )
353 	end do
354 
355 
356 !   check for mass and volume conservation
357 	do ll = 1, ncomp_coag
358 	    duma = max( sumold(ll), sumnew(ll), 1.0e-35 )
359 	    if (abs(sumold(ll)-sumnew(ll)) .gt. 1.0e-6*duma) then
360 		ncountbb(ll) = ncountbb(ll) + 1
361 		ncountbb(0) = ncountbb(0) + 1
362 	    end if
363 	end do
364 
365 
366 !
367 !   calculate new dry density,
368 !   and check for new mean dry-size within bounds
369 !
370 	do isize = 1, nsize
371 
372 	    xxmass = aqmassdry_sub(isize,itype,k,m)
373 	    xxvolu = aqvoldry_sub( isize,itype,k,m)
374 	    l = numptr_aer(isize,itype,iphase)
375 	    xxnumb = rsub(l,k,m)
376 	    iconform_numb = 1
377 
378 !   do a cautious calculation of density, using volume from coagsolv
379 	    if (xxmass .le. smallmassbb) then
380 		ncountaa(8) = ncountaa(8) + 1
381 		xxdens = densdefault
382 		xxvolu = xxmass/xxdens
383 		xxnumb = xxmass/(volumcen_sect(isize,itype)*xxdens)
384 		l = hyswptr_aer(isize,itype)
385 		if (l .ge. p1st) rsub(l,k,m) = 0.0
386 		l = waterptr_aer(isize,itype)
387 		if (l .ge. p1st) rsub(l,k,m) = 0.0
388 		iconform_numb = 0
389 		if (idiagbb .ge. 200)   &
390 		    write(*,'(a,i10,4i4,1p,4e10.2)') 'coagaa-7a',   &
391 		    ktau, it, jt, k, isize, xxmass, xxvolu, xxdens
392 	    else if (xxmass .gt. 1000.0*xxvolu) then
393 !   in this case, density is too large.  setting density=1000 forces
394 !   next IF block while avoiding potential divide by zero or overflow
395 		xxdens = 1000.0
396 	    else 
397 		xxdens = xxmass/xxvolu
398 	    end if
399 
400 	    if ((xxdens .lt. 0.1) .or. (xxdens .gt. 20.0)) then
401 !   (exception) case -- new dry density is unrealistic,
402 !   so use dry volume from rsub instead of that from coagsolv
403 		ncountaa(7) = ncountaa(7) + 1
404 		if (idiagbb .ge. 200)   &
405 		    write(*,'(a,i10,4i4,1p,4e10.2)') 'coagaa-7b',   &
406 		    ktau, it, jt, k, isize, xxmass, xxvolu, xxdens
407 		xxvolu = xxvolubb(isize)
408 		xxdens = xxmass/xxvolu
409 		if (idiagbb .ge. 200)   &
410 		    write(*,'(a,26x,1p,4e10.2)') 'coagaa-7c',   &
411 		    xxmass, xxvolu, xxdens
412 	    end if
413 
414 !   check for mean size ok, and conform number if not
415 	    if (iconform_numb .gt. 0) then
416 		if (xxnumb .gt. xxvolu/volumlo_sect(isize,itype)) then
417 		    ncountaa(9) = ncountaa(9) + 1
418 		    duma = xxnumb
419 		    xxnumb = xxvolu/volumlo_sect(isize,itype)
420 		    if (idiagbb .ge. 200)   &
421 			write(*,'(a,i10,4i4,1p,3e12.4)') 'coagcc-9 ',   &
422 			ktau, it, jt, k, isize, xxvolu, duma, xxnumb
423 		else if (xxnumb .lt. xxvolu/volumhi_sect(isize,itype)) then
424 		    ncountaa(10) = ncountaa(10) + 1
425 		    duma = xxnumb
426 		    xxnumb = xxvolu/volumhi_sect(isize,itype)
427 		    if (idiagbb .ge. 200)   &
428 			write(*,'(a,i10,4i4,1p,3e12.4)') 'coagcc-10',   &
429 			ktau, it, jt, k, isize, xxvolu, duma, xxnumb
430 		end if
431 	    end if
432 
433 !   load number, mass, volume, dry-density back into arrays
434 	    l = numptr_aer(isize,itype,iphase)
435 	    rsub(l,k,m) = xxnumb
436 	    adrydens_sub( isize,itype,k,m) = xxdens
437 	    aqmassdry_sub(isize,itype,k,m) = xxmass
438 	    aqvoldry_sub( isize,itype,k,m) = xxvolu
439 
440 	end do
441 
442 
443 2700	continue
444 
445 !   temporary diagnostics
446 	if ((idiagbb .ge. 100) .and.   &
447 	    (it .eq. ite) .and.    &
448 	    (jt .eq. jte) .and. (k .eq. kclm_calcend)) then
449 	    write(msg,93030) 'coagbb ncntaa ', ncountaa(1:10)
450 	    call peg_message( lunerr, msg )
451 	    if (ncountbb(0) .gt. 0) then
452 		do llx = 1, (ncomp_coag+9)/10
453 		    llb = llx*10
454 		    lla = llb - 9
455 		    llb = min( llb, ncomp_coag)
456 		    write(msg,93032) 'coagbb ncntbb',   &
457 			mod(llx,10), ncountbb(lla:llb)
458 		    call peg_message( lunerr, msg )
459 		end do
460 	    end if
461 	end if
462 93020	format( a, 1p, 10e10.2 )
463 93030	format( a, 1p, 10i10 )
464 93032	format( a, 1p, i1, 10i10 )
465 
466 
467 2800	continue	! k levels
468 
469 2900	continue	! subareas
470 
471 
472 	return
473 	end subroutine mosaic_coag_1clm
474 
475 
476 !----------------------------------------------------------------------
477       subroutine coagsolv(   &
478         nbin, nbin_maxd, ncomp, ncomp_maxd,   &
479         tkelvin_inp, patm_inp, deltat_inp, nsubstep,   &
480         lunout, idiag_onoff, iok,   &
481         dpdry_inp, dpwet_inp, denswet_inp,   &
482         num_distrib_inp, vol_distrib_inp )
483 
484       implicit none
485 
486 !
487 ! *********************************************************************
488 ! ***************** written by mark jacobson (1993) *******************
489 ! ***           © copyright, 1993 by mark z. jacobson             ***
490 ! ***              this version modified december, 2001             ***
491 ! ***                       (650) 723-6836                          ***
492 ! *********************************************************************
493 !
494 !   cccccc   ooooo      a      gggggg   ssssss  ooooo   l     v      v
495 !  c        o     o    a a    g        s       o     o  l      v    v
496 !  c        o     o   a   a   g   ggg   sssss  o     o  l       v  v
497 !  c        o     o  aaaaaaa  g     g        s o     o  l        v v
498 !   cccccc   ooooo  a       a  gggggg  ssssss   ooooo   lllllll   v
499 !
500 ! *********************************************************************
501 ! the use of this module implies that the user agrees not to sell the
502 ! module or any portion of it, not to remove the copyright notice from it,
503 ! and not to change the name of the module, "coagsolv". users may
504 ! modify the module as needed or incorporate it into a larger model.
505 ! any special requests with regard to this module may be directed to
506 ! jacobson@stanford.edu.
507 ! *********************************************************************
508 !
509 ! *********************************************************************
510 ! * this is a box-model version of "coagsolv," a semi-implicit        *
511 ! * aerosol coagulation solver. the solver is exactly volume          *
512 ! * conserving, unconditionally stable (regardless of time step),     *
513 ! * and noniterative.                                                 *
514 ! *                                                                   *
515 ! * this program calculates brownian coagulation kernels and solves   *
516 ! * self-coagulation among any number of size bins, one               *
517 ! * particle type and any number of volume fractions.                 *
518 ! *                                                                   *
519 ! * the program is set up as a box-model.                             *
520 ! *                                                                   *
521 ! * the volume ratio of adjacent size bins can be any number > 1      *
522 ! *                                                                   *
523 ! * the scheme can be used to solve coagulation with any size bin     *
524 ! * structure.                                                        *
525 ! *                                                                   *
526 ! * the initial size distribution here is monomer or lognormal        *
527 ! * (ifsmoluc = 1 or 0) with a fixed size bin structure               *
528 ! *                                                                   *
529 ! *********************************************************************
530 ! *                         references                                *
531 ! *********************************************************************
532 ! * semi-implicit scheme using movable or variable bins and with      *
533 ! * any volume ratio  (vrat) > 1                                      *
534 ! *                                                                   *
535 ! * jacobson m. z., turco r. p., jensen, e. j. and toon o. b. (1994)  *
536 ! *  modeling coagulation among particles of different compostion     *
537 ! *  and size. atmos. environ. 28a, 1327 - 1338.                      *
538 ! *                                                                   *
539 ! * jacobson m. z. (1999) fundamentals of atmospheric modeling.       *
540 ! *  cambridge university press, new york, 656 pp.                    *
541 ! *                                                                   *
542 ! *********************************************************************
543 ! * semi-implicit scheme using fixed bins with volume ratio >,= 2     *
544 ! *                                                                   *
545 ! * toon o. b., turco r. p., westphal d., malone r. and liu m. s.     *
546 ! *  (1988) a multidimensional model for aerosols: description of     *
547 ! *  computational analogs. j. atmos. sci. 45, 2123 - 2143            *
548 ! *                                                                   *
549 ! *********************************************************************
550 ! * orig semi-implicit scheme using fixed bins with volume ratio = 2  *
551 ! *                                                                   *
552 ! * turco r. p., hamill p., toon o. b., whitten r. c. and kiang c. s. *
553 ! *  (1979) the nasa-ames research center stratospheric aerosol       *
554 ! *  model: i physical processes and computational analogs. nasa      *
555 ! *  tech. publ. (tp) 1362, iii-94.                                   *
556 ! *********************************************************************
557 !
558 !   modified by y. zhang for incorporation into pnnl's mirage
559 !   june-july, 2003
560 !
561 ! *********************************************************************
562 !
563 !   modified by r.c. easter for incorporation into pnnl's wrf-chem
564 !   feb 2005 (a)
565 !	added "_inp" to all subr arguments
566 !	added iradmaxd_inp & lunout
567 !	define iradmaxd, iaertymaxd, iaeromaxd locally
568 !	no include statements
569 !	changed real*16 to real*8
570 !   feb 2005 (b)
571 !	in coagsolv, distrib_inp is 2-d array that holds both number and
572 !	    volume concentrations; distrib is initialized from it;
573 !	    the "fracnaer" stuff is gone
574 !   feb 2005 ©
575 !	change distrib & cc2 to be 2-d arrays (which simplifies indexing!);
576 !	iaeromaxd and iaero are gone;
577 !	deleted many commented-out lines in coagsolv
578 !   feb 2005 (d)
579 !       changed cc2(i,1) to be number instead of all-species volume;
580 !	    prod term for number distrib now follows jgr-2002 article
581 !	    [multiply by volume(j), divide by volume(k)]
582 !   apr 2006 (a)
583 !	considerable cleanup (mostly cosmetic)
584 !	pass in the bin sizes directly, rather than vrat & dmin_um
585 !       pass in dry and wet sizes separately
586 !       pass in/out number and volume distributions in separate arrays
587 !
588 ! *********************************************************************
589 
590 
591 !   IN arguments
592       integer nbin            ! actual number of size bins
593       integer nbin_maxd       ! size-bin dimension for input (argument) arrays
594       integer ncomp           ! actual number of aerosol volume components
595       integer ncomp_maxd      ! volume-component dimension for input (argument) arrays
596       integer lunout          ! logical unit for warning & diagnostic output
597       integer idiag_onoff     ! if positive, write some mass-conservation diagnostics
598       integer nsubstep        ! number of time sub-steps for the integration
599 
600       real tkelvin_inp             ! air temperature (K)
601       real patm_inp                ! air pressure (atm)
602       real deltat_inp              ! integration time (s)
603       real dpdry_inp(nbin_maxd)    ! bin dry diameter (cm)
604       real dpwet_inp(nbin_maxd)    ! bin wet (ambient) diameter (cm)
605       real denswet_inp(nbin_maxd)  ! bin wet (ambient) density (g/cm3)
606 
607 !   IN-OUT arguments
608       real num_distrib_inp(nbin_maxd)
609 !          num_distrib_inp(i)   = number concentration for bin i (#/cm3)
610       real vol_distrib_inp(nbin_maxd,ncomp_maxd)
611 !          vol_distrib_inp(i,j) = volume concentration for bin i,
612 !                                                component j (cm3/cm3)
613 
614 !   OUT arguments
615       integer iok             ! status flag (0=success, anything else=failure)
616 
617 !
618 ! NOTE -- The sectional representation is based on dry particle size.
619 ! Dry sizes are used to calculate the receiving bin indices and product fractions
620 !   for each (bin-i1, bin-i2) coagulation combination.
621 ! Wet sizes and densities are used to calculate the coagulation rate coefficients.
622 !
623 ! NOTE -- Units for num_distrib and vol_distrib
624 !    num_distrib units MUST BE (#/cm3)
625 !    vol_distrib units do not really matter.  They can be either masses 
626 !        or volumes, and either mixing ratios or concentrations,
627 !        (e.g., g/cm3-air, ug/kg-air, cm3/m3-air, cm3/kg-air, ...).
628 !        Use whatever is convenient.
629 !
630 
631 !
632 !   local variables
633 !
634       integer iradmaxd_wrk, iaertymaxd_wrk
635       parameter (iradmaxd_wrk=16)
636       parameter (iaertymaxd_wrk=32)
637 
638       integer irad
639       integer iaerty
640 ! irad == nbin = actual number of size bins
641 ! iradmaxd_wrk = size-bin dimension for local (working) arrays
642 !
643 ! (iaerty-1) == ncomp = actual number of aerosol volume components
644 ! iaertymaxd_wrk = volume-component dimension for local (working) arrays
645 !
646 ! iaerty = 1 --> calc number concentration only
647 !        > 1 --> calc number concentration + (iaerty-1) volume concentrations
648 
649       integer i, isubstep, j, jaer, jb, k, kout
650 
651       integer jbinik(iradmaxd_wrk,iradmaxd_wrk,iradmaxd_wrk)
652       integer jbins(iradmaxd_wrk,iradmaxd_wrk)
653 
654       real*8 aknud, aloss, amu, avg,   &
655              boltg, bpm,   &
656              cbr, consmu, cpi,   &
657              deltat, deltp1, deltr,   &
658              divis, dti1, dti2,   &
659              finkhi, finklow, fourpi, fourrsq,   &
660              ggr, gmfp,   &
661              onepi,   &
662              patm, pmfp, prod,   &
663              radi, radiust, radj, ratior,   &
664              rgas2, rho3, rsuma, rsumsq,   &
665              sumdc, sumnaft, sumnbef,   &
666              term1, term2, third, tk, tkelvin, tworad,   &
667              viscosk, vk1, voltota, vthermg,   &
668              wtair
669 
670       real*8 cc2(iradmaxd_wrk,iaertymaxd_wrk),   &
671              conc(iradmaxd_wrk),   &
672              denav(iradmaxd_wrk) ,   &
673              difcof(iradmaxd_wrk),   &
674              distrib(iradmaxd_wrk,iaertymaxd_wrk),   &
675              fink(iradmaxd_wrk,iradmaxd_wrk,iradmaxd_wrk),   &
676              floss(iradmaxd_wrk,iradmaxd_wrk),   &
677              radius(iradmaxd_wrk),   &
678              radwet(iradmaxd_wrk),   &
679              rrate(iradmaxd_wrk,iradmaxd_wrk),   &
680              sumdp(iradmaxd_wrk),   &
681              sumvt(iradmaxd_wrk),   &
682              tvolfin(iaertymaxd_wrk),   &
683              tvolinit(iaertymaxd_wrk),   &
684              volume(iradmaxd_wrk),   &
685              volwet(iradmaxd_wrk),   &
686              vthermp(iradmaxd_wrk)
687 
688 
689 ! *********************************************************************
690 !                    set some parameters
691 ! *********************************************************************
692       irad   = nbin
693       iaerty = ncomp + 1
694 
695       kout = lunout
696 
697       if (irad .gt. iradmaxd_wrk) then
698         write(lunout,*) '*** coagsolv: irad > iradmaxd_wrk: ',   &
699           irad, iradmaxd_wrk
700         iok = -1
701         return
702       endif
703       if (iaerty .gt. iaertymaxd_wrk) then
704         write(lunout,*) '*** coagsolv: iaerty > iaertymaxd_wrk: ',   &
705           iaerty, iaertymaxd_wrk
706         iok = -2
707         return
708       endif
709 !
710 ! tkelvin = temperature (k)
711 ! denav   = particle density (g cm-3)
712 ! patm    = air pressure (atm)
713 !
714       tkelvin   = tkelvin_inp
715       patm      = patm_inp
716       do i    = 1, irad
717         denav(i)   = denswet_inp(i)
718       end do
719 
720 !
721 ! deltat_inp = total integration time (s)
722 ! deltat     = individual time step (s)
723 ! nsubstep   = number of time steps
724 !
725       deltat = deltat_inp/nsubstep
726 
727 !
728 ! boltg   = boltzmann's 1.38054e-16        (erg k-1 = g cm**2 sec-1 k-1)
729 ! wtair   = molecular weight of air (g mol-1)
730 ! avg     = avogadro's number (molec. mol-1)
731 ! rgas2   = gas constant (l-atm mol-1 k-1)
732 ! amu     = dynamic viscosity of air (g cm-1 sec-1)
733 !           est value at 20 c = 1.815e-04
734 ! rho3    = air density (g cm-3)
735 ! viscosk = kinematic viscosity = amu / denair = (cm**2 sec-1)
736 ! vthermg = mean thermal velocity of air molecules (cm sec-1)
737 ! gmfp    = mean free path of an air molecule  = 2 x viscosk /
738 !           thermal velocity of air molecules (gmfp units of cm)
739 !
740       tk        = tkelvin
741       third     = 1. / 3.
742       onepi     = 3.14159265358979
743       fourpi    = 4. * onepi
744       boltg     = 1.38054e-16
745       wtair     = 28.966
746       avg       = 6.02252e+23
747       rgas2     = 0.08206
748       consmu    = 1.8325e-04 * (296.16 + 120.0)
749       amu       = (consmu / (tk + 120.)) * (tk / 296.16)**1.5
750       rho3      = patm * wtair * 0.001 / (rgas2 * tk)
751       viscosk   = amu / rho3
752       vthermg   = sqrt(8. * boltg * tk * avg / (onepi * wtair))
753       gmfp      = 2.0 * viscosk / vthermg
754 
755 !
756 ! *********************************************************************
757 ! *                     set volume ratio size bin grid                *
758 ! *********************************************************************
759 !
760       cpi          = fourpi / 3.
761 
762       do 30 j      = 1, irad
763        radius( j)  = dpdry_inp(j) * 0.5
764        volume( j)  = cpi * radius(j) * radius(j) * radius(j)
765        radwet( j)  = dpwet_inp(j) * 0.5
766        volwet( j)  = cpi * radwet(j) * radwet(j) * radwet(j)
767  30   continue
768 
769 !
770 ! *********************************************************************
771 ! *              determine bins where coagulated terms go             *
772 ! *********************************************************************
773 ! finklow        = volume fraction of i+j going to lower  (k  ) bin
774 ! finkhi         = volume fraction of i+j going to higher (k+1) bin
775 ! fink(i,j,k)    = volume fraction of i+j going to bin k
776 ! floss          = simplified fink term used in loss rates
777 !                  no self-coagulation loss out of largest bin
778 ! jbins(i,k)     = number of production terms into bin k from bin i
779 ! jbinik(i,k,jb) = identifies each bin j that coagulates with bin i
780 !                  to produce bin k
781 !
782       do 35 i             = 1, irad
783         do 34 j            = 1, irad
784           jbins(i,j)        = 0
785           floss(i,j)        = 0.
786           do 33 k           = 1, irad
787             jbinik(i,j,k)    = 0
788             fink(  i,j,k)    = 0.
789  33       continue
790  34     continue
791  35   continue
792 
793       do 40 i             = 1, irad
794         do 39 j            = 1, irad
795           voltota           = volume(i) + volume(j)
796           if (voltota.ge.volume(irad)) then
797 
798             if (i.eq.irad) then
799               floss(i,j)      = 0.0
800             else
801               floss(i,j)      = 1.0
802             endif
803 
804             if (j.lt.irad) then
805               jbins(i,irad)     = jbins(i,irad) + 1
806               jb                = jbins(i,irad)
807               jbinik(i,irad,jb) = j
808               fink(  i,jb,irad) = 1.0
809             endif
810 
811           else
812             do 45 k          = 1, irad - 1
813               vk1             = volume(k+1)
814               if (voltota.ge.volume(k).and.voltota.lt.vk1) then
815                 finklow        = ((vk1 - voltota)/(vk1 - volume(k)))   &
816                                * volume(k) / voltota
817                 finkhi         = 1. - finklow
818 
819                 if (i.lt.k) then
820                   floss(i,j)      = 1.
821                 elseif (i.eq.k) then
822                   floss(i,j)      = finkhi
823                 endif
824 
825                 if (j.lt.k) then
826                   jbins(i,k)      = jbins(i,k) + 1
827                   jb              = jbins(i,k)
828                   jbinik(i,k,jb)  = j
829                   fink(  i,jb,k)  = finklow
830                 endif
831 
832                 jbins(i,k+1)     = jbins(i,k+1) + 1
833                 jb               = jbins(i,k+1)
834                 jbinik(i,k+1,jb) = j
835                 fink(  i,jb,k+1) = finkhi
836 
837               endif
838  45         continue
839           endif
840 
841           do 38 k             = 1, irad
842             if (jbins(i,k).gt.irad) then
843               write(21,*)'coagsolv: jbins > irad: ',jbins(i,k),i,k
844               iok = -3
845               return
846             endif
847  38       continue
848 
849  39     continue
850  40   continue
851 
852 !
853 ! ***********************************************************************
854 !                      initialize size distribution
855 !
856 ! copy initial number concentration (#/cm3-air) and volume concentrations
857 !   (cm3/cm3-air) from num/vol_distrib_inp (real*4) to distrib (real*8)
858 ! ***********************************************************************
859        do i = 1, irad
860          distrib(i,1) = num_distrib_inp(i)
861        end do
862 
863        do jaer = 2, iaerty
864          do i = 1, irad
865            distrib(i,jaer) = vol_distrib_inp(i,jaer-1)
866          end do
867        end do
868 
869 
870 !
871 ! *********************************************************************
872 !              coagulation kernel from fuchs equations
873 ! *********************************************************************
874 ! difcof  = brownian particle diffus coef  (cm**2 sec-1)
875 !         = boltg * t * bpm / (6 * pi * mu * r(i))
876 !         = 5.25e-04 (diam = 0.01um); 6.23e-7 (diam = 0.5 um) seinfeld p.325.
877 ! vthermp = avg thermal vel of particle    (cm sec-1)
878 !         = (8 * boltg * t / (pi * masmolec)**0.5
879 ! pmfp    = mean free path of particle     (cm)
880 !         = 8 * di / (pi * vthermp)
881 ! bpm     = correction for particle shape and for effects of low mean
882 !           free path of air. (toon et al., 1989, physical processes in
883 !           polar stratospheric ice clouds, jgr 94, 11,359. f1 and f2 are
884 !           included in the expression below (shape effects correction)
885 !         = 1 + kn[a + bexp(-c/kn)]
886 ! deltp1  = if particles with mean free path pmfp leave the surface of
887 !           an absorbing sphere in all directions, each being probably
888 !           equal, then deltp1 is the mean distance from the surface of the
889 !           sphere reached by particles after covering a distance pmfp. (cm).
890 ! cbr     = coag kernel (cm3 partic-1 s-1) due to brownian motion (fuchs, 1964)
891 ! rrate   = coag kernal (cm3 partic-1 s-1) * time step (s)
892 !
893 ! *** use the wet (ambient) radius and volume here ***
894        do 145 i    = 1, irad
895          radiust    = radwet(i)
896          tworad     = radiust  + radiust
897          fourrsq    = 4.       * radiust * radiust
898          aknud      = gmfp / radiust
899          bpm        = 1. + aknud * (1.257 + 0.42*exp(-1.1/aknud))
900          difcof(i)  = boltg * tk * bpm  / (6. * onepi * radiust * amu)
901 
902 ! use bin-varied aerosol density from mirage
903 !        vthermp(i) = sqrt(8. * boltg * tk / (onepi*denav * volume(i)))
904          vthermp(i) = sqrt(8. * boltg * tk / (onepi*denav(i) *   &
905                       volwet(i)))
906          sumvt(i)   = vthermp(i)  * vthermp(i)
907          pmfp       = 8. * difcof(i) / (onepi * vthermp(i))
908          dti1       = tworad   + pmfp
909          dti2       = (fourrsq + pmfp * pmfp)**1.5
910          divis      = 0.166667 / (radiust * pmfp)
911          deltp1     = divis    * (dti1 * dti1 * dti1 - dti2) - tworad
912          sumdp(i)   = deltp1   * deltp1
913  145   continue
914 
915 !yy    write(kout,9165)
916        do 155 i     = 1, irad
917          do 154 j    = 1, irad
918            radi       = radwet(i)
919            radj       = radwet(j)
920            rsuma      = radi  + radj
921            rsumsq     = rsuma * rsuma
922            ratior     = radi  / radj
923            sumdc      =     difcof(i) + difcof(j)
924            ggr        = sqrt(sumvt(i) + sumvt(j))
925            deltr      = sqrt(sumdp(i) + sumdp(j))
926            term1      = rsuma /         (rsuma + deltr)
927            term2      = 4.    * sumdc / (rsuma * ggr)
928            cbr        = fourpi * rsuma * sumdc / (term1 + term2)
929            rrate(i,j) = cbr * deltat
930 !yy        write(kout,9190) (2.0e4*radius(i)), (2.0e4*radius(j)), cbr
931  154     continue
932  155   continue
933 
934 9165  format(16x,'coagulation coefficients (cm**3 #-1 sec-1)'/   &
935                  'diam1_um diam2_um brownian ')
936 9190  format(1pe15.7,7(1x,1pe15.7))
937 
938 
939 !
940 ! *********************************************************************
941 ! ****************** solve coagulation equations **********************
942 ! *********************************************************************
943 !
944 ! *********************************************************************
945 !                       inialize new arrays
946 ! *********************************************************************
947 ! distrib  = initial conc (# cm-3 for num conc.; cm3 cm-3 for volume fractions)
948 ! cc2      = initial, final volume conc (cm3 cm-3) for all particle types.
949 ! conc     = initial, final number conc (# cm-3) for number distribution
950 ! volume   = volume (cm3 #-1) of particles in bin
951 !
952 !
953 
954       do i = 1, irad
955 !       cc2( i,1) = distrib(i,1) * volume(i)
956         cc2( i,1) = distrib(i,1)
957         conc(i)   = distrib(i,1)
958       end do
959 
960       do jaer = 2, iaerty
961         do i  = 1, irad
962           cc2(i,jaer) = distrib(i,jaer)
963         end do
964       end do
965 
966 ! *********************************************************************
967 !             solve coagulation over several time steps
968 ! *********************************************************************
969 !
970       do 700 isubstep  = 1, nsubstep
971 !
972         do 485 jaer  = 1, iaerty
973           do 484 k    = 1, irad
974 !
975 ! production terms
976 !
977             prod        = 0.
978             if (k.gt.1) then
979               if (jaer .eq. 1) then
980                 do 465 i = 1, k
981                   do 464 jb = 1, jbins(i,k)
982                     j       = jbinik(i,k,jb)
983                     prod    = prod + fink(i,jb,k)*rrate(i,j)*   &
984                               cc2(j,jaer)*volume(j)*conc(i)
985  464              continue
986  465            continue
987                 prod     = prod/volume(k)
988               else
989                 do 469 i = 1, k
990                   do 468 jb = 1, jbins(i,k)
991                     j       = jbinik(i,k,jb)
992                     prod    = prod +   &
993                              fink(i,jb,k)*rrate(i,j)*cc2(j,jaer)*conc(i)
994  468              continue
995  469            continue
996               endif
997             endif
998 !
999 ! loss terms
1000 !
1001             aloss       = 0.
1002             if (k.lt.irad) then
1003               do 475 j = 1, irad
1004                 aloss  = aloss + floss(k,j) * rrate(k,j) * conc(j)
1005  475          continue
1006             endif
1007 !
1008 ! final concentrations
1009 !
1010             cc2(k,jaer) = (cc2(k,jaer) + prod) / (1. + aloss)
1011  484      continue
1012  485    continue
1013 !
1014 ! put updated number concentration into conc array
1015         do i = 1, irad
1016           conc(i) = cc2(i,1)
1017         end do
1018 
1019  700  continue
1020 
1021 
1022 !
1023 ! *********************************************************
1024 ! **    put the advanced concentration back on the grid  **
1025 !       (copy them from the real*8 working array to the
1026 !        real*4 caller arrays)
1027 ! *********************************************************
1028 !
1029        do i = 1, irad
1030          num_distrib_inp(i) = cc2(i,1)
1031        end do
1032        do jaer = 2, iaerty
1033          do i = 1, irad
1034            vol_distrib_inp(i,jaer-1) = cc2(i,jaer)
1035          end do
1036        end do
1037 
1038 !
1039 ! if no diagnostics, then return
1040 !
1041       iok = 0
1042       if (idiag_onoff .le. 0) return
1043 
1044 !
1045 ! *********************************************************************
1046 ! *************         check whether mass is conserved     ***********
1047 ! *********************************************************************
1048 ! tvolinit = initial volume conc (cm3 cm-3), summed over all bins
1049 ! tvolfin  = final   volume conc (cm3 cm-3), summed over all bins
1050 ! sumnbef = summed number conc (# cm-3) before coagulation
1051 ! sumnaft = summed number conc (# cm-3) after coagulation
1052 !
1053       do jaer = 1, iaerty
1054         tvolinit(jaer) = 0.
1055         tvolfin( jaer) = 0.
1056       end do
1057 
1058       sumnbef        = 0.
1059       sumnaft        = 0.
1060 !
1061 ! distrib(jaer=1, i=1:nrad) = initial total number conc in # cm-3
1062 ! cc2    (jaer=1, i=1:nrad) = final   total number conc in # cm-3
1063 !
1064       do i = 1, irad
1065         tvolinit(1)   = tvolinit(1) + distrib(i,1) * volume(i)
1066         tvolfin( 1)   = tvolfin( 1) + cc2(    i,1) * volume(i)
1067         sumnbef       = sumnbef     + distrib(i,1)
1068         sumnaft       = sumnaft     + cc2(    i,1)
1069       end do
1070 
1071 !
1072 ! distrib(jaer=2:iaerty, i=1:nrad) = initial component volume conc in cm3 cm-3
1073 ! cc2    (jaer=2:iaerty, i=1:nrad) = initial component volume conc in cm3 cm-3
1074 !
1075       do jaer = 2, iaerty
1076       do i    = 1, irad
1077         tvolinit(jaer) = tvolinit(jaer) + distrib(i,jaer)
1078         tvolfin( jaer) = tvolfin( jaer) + cc2(    i,jaer)
1079       end do
1080       end do
1081 
1082       write(kout,*)
1083       write(kout,9434) sumnbef, sumnaft,   &
1084                       tvolinit(1)*1.0e+12,tvolfin(1)*1.0e+12
1085 
1086       write(kout,9435) sumnaft-sumnbef
1087       write(kout,9439) tvolinit(1) / tvolfin(1)
1088 
1089       do jaer = 2, iaerty
1090         if (abs(tvolfin(jaer)) .gt. 0.0) then
1091            write(kout,9440) jaer-1, tvolinit(jaer) / tvolfin(jaer)
1092         else
1093            write(kout,9441) jaer-1, tvolinit(jaer),  tvolfin(jaer)
1094         end if
1095       end do
1096 
1097 9434  format('# bef, aft; vol bef, aft =',/4(1pe16.10,1x)/)
1098 9435  format('total partic change in  # cm-3 = ',1pe17.10)
1099 9439  format('total partic vol bef / vol aft = ',1pe17.10,   &
1100              ': if 1.0 -> exact vol conserv')
1101 9440  format('vol comp',i4,' vol bef / vol aft = ',1pe17.10,   &
1102              ': if 1.0 -> exact vol conserv')
1103 9441  format('vol comp',i4,' vol bef,  vol aft = ',2(1pe17.10))
1104 
1105 
1106 !
1107 ! ************************** print results ****************************
1108 ! distrib = initial conc in # cm-3 for total particle (jaer=1, i=1,nrad)
1109 ! conc    = final   conc in # cm-3 for total particle (jaer=1, i=1,nrad)
1110 !
1111 
1112 
1113 !
1114 ! *********************************************************************
1115 !                      end of program coagsolv.f
1116 ! *********************************************************************
1117 !
1118       return
1119       end subroutine coagsolv
1120 
1121 
1122 
1123 
1124 
1125 !-----------------------------------------------------------------------
1126 
1127 
1128 
1129 	end module module_mosaic_coag