1402.pdf

E F F E

C

T

O

F

S

I Z E D I

ST R I B U T I

O

N I N E

S

T I

M

A T I N

G

b_{, ,} t, bs c at, a n d babs F R

O

M

A T

M

O SP

H

E R I C P O L L U T A N T

M

E A SU R E

M

E N T

S

B y

A l p

M

. Ref ik

De_pa rtme nt of En vir o nme ntal Scie n c e s a nd En_gin e e rin_g

Scho ol of Pub l ic He alth

Univ e r sit_y of No rth Ca r ol in a at C ha_pel H i l l

C ha_pel H i l l, No rth Ca r ol in a 27 5 9 9

A B ST R A C T

Co ef f icie nts of e xtin ctio n, s c at te ring, a nd abs o rptio n a r e c alc ulated u sin g a n a rbritr atry

siz e d istri butio n a nd p h ysic al a nd chemic al a e r o s ol data fr om the Inte r a_ge n c_y

M

o nito rin_g of Pr ote cted Vis u al En vir o nme nts

(

I

M

PR OV E

)

a nd the Ea ste r n F in e Pa rtic ulate V isi b i l it_y Netwo rk

(

EF_{P V}N

)

_data s_ystems. Calc ulated r e s ults a r e c o m pa r ed with the me a s u r ed v alu e s u sin _{g l i}n e a r r e_gr e s sio n a n a_{l y}sis a nd c o r r elatio n c o ef fi cie nt. T he r e s ults fr om both data s ets ind ic ate that fair_{l y} a c c u r ate

(

+ 50 %₎ e stimate s of the c o ef f icie nts a r e _po s sib le whe n the siz e distributio n is in the r a n_ge of me a n d iamete r 0.2

-0

.4 with ge ometr ic sta nda rd de viatio n 1.2

A

C K

N

O

W

L E D

G

M

E N T S

I wa nt to tha nk Pr ofe s s o r Reist, my advis o r, w ho s e v alu ab le guida n c e a nd patie n c e made m y wo rk po s sib le. I owe spe cial tha nks t o (n ot in a ny pa rtic ula r o rde r);

Dr. Fr a n cis B inkow sk i o f the U S E P A fo r h is hel p in obtaining the A R E S

pr o_gr am,

A ir

Q

u al it_y Gr o u_p at the Univ e r sit_y of Cal ifo r nia

-Da vis fo r the I

M

P R OV E data I

used in m_{y w} o rk a nd fo r its fu nd in_g, the Natio n al Pa rk Se r v ic e, US Depa rtme nt of Inte rio r

Ji m Sisle r of Color ado State Univ e r sit_y-F_{o rt} C_ol l i_{n s} f_{o r} th_{e s c at te r}i_n

g data u s ed in

con

j

u n ctio n with the I

M

P R O V E dat a

T om E l le n stad, Ga rdn e r Ev a n s, a nd

W

illiam

W

i ls o n fo r their hel p in obtaining the

EFPV N data u s ed in the stud_y

Pete r H

M

c

M

u r r_y of Univ e r sit_y of

M

in n e s ota fo r h is hel_{p i}n obtainin_{g d}ata

s o u r c e s a nd l ite r atu r e fo r m_y stud y.

And fi n al_{l y}, I wo uld l i ke to tha nk m y r e ade r s D r Da v i d Leith a n dT om El le n stad w ho as

r e ade r s _pr o vi ded v alu a_ble s u_{g g}e stio n s in r efi nin _{g my w}o rk.

Fu nd in _{g f}o r th is _pr o

j

e ct wa s r e c eiv ed fr om T he United State s En vir o nme ntal Pr ote ctio n A ge n c _y,

W

a sh ingto n , D. C.

(

Grant # 5

-3 549 6

T

A

B L E

O

F

C O

N T E N T

S

L IST OF F I G U R E S 3

L I S T O F T A B L E S 4

1.0 I N T R ODU C T I O N: 5

2.0 B A CK G R O U N D: 7

3.0

M

I E A R E S P R O G R A

M

: 1 1

4.0

M

E T H O D O L O G Y A N D D E S C R I P T I O N O F T H E D A T A SE T S U S E D : 18

4.1 Ea s t e r n Fi n e Pa r t i c u l a t e Vi sro i L i T Y N e two r k

(

E F P V N

)

: 1 8

4.2 In t e r a g e n c y

M

o n i t o r i n g o f Pr o t e c t e d V i s u a l En v i r o n me n t s

(

I

M

P R OV E

)

: .. 19

4.3

M

e t h o d o l o g y : 21

5.0 R E S U L T S A N D D I S C U S SI O N: 2 3

5.1 RE SU L TS:. 23

5 1 1 Re s u l t s f o r I

M

P R O V E D a t a: 2 4

5 1.2 Re s u l t s F O R E F PV N Da t a: 26

5.2 DIS C U SSIO N: 29

5.2. 1 T h e Ab s o r p t i o n Co E FH C BEN T: 2 9

5 2.3 EF F E C T O F Si z e D i s t r i b u t i o n o n Es t ima t i n g Ex t i n c t i o n a n d Sc a t t e r i n g

c o e f hc i e n t s : 32

5 2.4 Ot h e r Fa c t o r s t h a t

M

a y Ef f e c t Ac c u r a c y o f t he Es t ima t e s o f t h e

c o e fhc i e n t s: 3 6

5.3 RES U L T S A N D D I S C U S SI O N F O R T H E

M

O D I F I E D I N P U T DAT A

C O NT A I N I N G N O A

M M

O N I U

M

M

A SS: 3 8

5.3. 1 RE S U L T S f o r I

M

P ROV E Da t a

(

WI T H O U T T H E A m mo n i um

M

a s s): 3 9

5.3.2 RE S U L T S f o r E FP V N Da t a

(

W

it h o u t T H E A m mo n i um

M

a s s

)

: 42

5 3.3 Di s c u s s i o n : 46

6.0 C O N C L U SI O N S: 4 9

7.0 R E C O

M

M

E N D A T I O N S F O R A D D I T I O N A L R E S E A R C H : 5 1

R E F E R E N C E S: 5 2

A P P E N D I X 1

L I

S

T

O

F F I

G U

R E S

F i_gu r e 1. Compa r is o n of B_abs v s_, E C

M

(I

M

P R O V E Da ta Set

)

2 9

F i_gur e 2. Compa r is o n of Babs v s. E C

M

(

E F P V N Data Set

)

3 0

Fi_gur e 3. G r ad ien t of B

e xt v s.

M

e a n D ia mete r

(

I

M

P R O V E Data Set) 3 3

F i gur e 4. Gr ad ien t of Bs c at v s.

M

ea n D iamete r

(

I

M

P R O V E Data Set

)

3 3

F i gu r e 5. G r ad ien t of B_{e xt} v s.

M

e an D iamete r

(

E F P V N Data Set

)

3 4

F i gur e 6. Gr ad ien t of B_{s c at} v s.

M

e a n D iamete r

(

E F P V N Data Set

)

34

F i gur e 7. Gr ad ien t of B_ext v s.

M

e an D iamete r

(

I

M

P R O V E Data Set

"

with No

Am mo n ium

M

a s s" ) 4 7

F i gur e 8. Gr ad ient of Bs c atvs.

M

e a n D iamete r

(

I

M

P R O V E Data Set

"

with No

Am monium

M

a s s"

)

47

Fi_gur e 9. Gr ad ient of B _{ext v s}.

M

e an D iamete r

(

E F P V N Data Set

"_{w i}

th No

Am monium

M

a s s"

)

4 8

F i_gu r e 10. G r ad ie n t of B^ c at vs.

M

e an D iamete r

(

E F P V N Data Set

"

with No

L I

S

T

O

F T

A

B L E

S

Tab le 1. I

M

P R O V E Data Re sults 25

Tab le 2. E F P V N Data Re sults 27

Tab le 3. I

M

P R O V E Data Re sults

(

"

w ith No A m monium

M

as s"

)

4 1

T able 4. E F P V N Data Res ults ( "

1.0 I N T R

O

D

U C

T I

O N

:

V isi b i l it_{y i m p}airme nt is o n e of the mo st a_{p p}a r e nt ef fe cts of air _pollutio n . V isibi l it y

r edu ctio n ma_y a ris e du e to n atu r al a n_{d /}o r ma n-m_ad_{e s o u r c e e}m i_ssi_{o n s a n}d m_a

y be

inte n si fi ed b y mete o r olo_{g i}c al effe cts. Extin ctio n of l i g ht (s c at te ring a nd abs o rptio n) b y

fi n e _pa rticle s is the ma

_j

o r c a u s e of visi b il it_y r edu ctio n. Extin ctio n c o effi cie nts of l i g ht in

the atmos_{p h}ere ha v e be e n u s ed to _qu a ntitativ el y desc ri be the vis u al r a n_ge in the

atmo s_{p h}e r e D ir e ct me a s u r eme nts of s c at te rin_g a nd abs o r_ptio n c o ef fi cie nts c o ul d be

made u sin_g n e_{p h}elomete rs and tr a n sm iss omete r s. Howe v e r, it is als o po s si b le to e stimate

the s e c o ef ficie nts u sin_g M ie the o r_y c alc ulatio n s a s a fu n ctio n of a e r o s ol ma s s ba s ed o n

tr a c e _pol luta nts in the atmo s_phe r e.

Fin e _pa rticle s in the s o-_{c a}l l_ed _{a c c u}m_ul_ati_{o n} m_od_e

(

0. 1

- 1

.0 |i m

)

str o n gl y infl u e n c e

visibi l it_y r edu ctio n . T he pa rticle r emo v al me c ha nisms in the atmo sphe r e a r e le a st

ef fi cie nt fo r _pa rticle s in th is siz e r a n_ge. T he r efo r e, atmo sp he ric pa rticle s te nd to

a c c umulate in th is siz e r a n_ge he n c e, the n ame. Pa rticle s in th is siz e r a n ge a r e the mo st

eff icie nt s c at te r e r s _pe r u nit ma s s. T he chem ic al c om po sitio n of pa rticle s a nd the r elativ e

humi d it_y of the ambie nt atmo s_{p h}e r e a r e im po rta nt fa c to r s in visib i l it_y de_gr adatio n.

Kn owled ge of c o n c e ntr atio n of s ulfate s fo r s c at te rin_g a nd c a rbo n fo r abs o r_ption is

T here are a n um be r of stud ie s in the l ite ratu re

(

Hasa n and Dzuba_y, 19 8 3; Ou i mette, 19 8 2;

S lo a n e, 19 83;Slo a n e a nd

W

olff, 1985; Elde ring a nd Ca s s, 19 94;Z ha ng, et al.

, 199 4) that

use

M

ie the o r_{y (}

M

ie, 190 8)c alc ulatio n s to e sti mate e xtin ctio n a nds c at te ring c o ef ficie nts

wh ich the n c a n be c om pa r ed t o me a s u r ed v alu e s. In al l of the s e stud ie s a signi fica nt

amo u nt of ef fo rt wa s _put into obtainin_g the siz e d is tri butio n of the am b ie nt a e r osol

A ltho u_gh s ome im pr o v eme nts in obtainin_g siz e d is tri butio n data ha v e be e n a ch ie v ed, it

sti l l r emain s a c om p lic ated a nd e x _pe n siv e ta sk to c ol le ct siz e d istri butio n data. T he r efo r e,

the s e studie s c o ul d o nl y be c o ndu cted fo r brief pe riods du rin_g the o v e r all lo n _g-_{t e}

rm

stud ie s of am b ie nt atmo s_{p h}e ric c o n d itio n s.

In the _pa st te n _ye a r s a n umbe r of databa s e s ha v e be e n _ge n e r ated that c o ntain the n e c e s s a r_y

data fo r

M

ie the o r_y c alc ulatio n s of e xtin ctio n, with the e x c eptio n of siz e d istributio n .

S in c e it is w el l a c c e_pted that a e r o s ol pa rticle s in the a c c umulatio n mode a r e r e s_po n si b le

fo r the mo s t visi b i l it_{y d}e_gr adatio n, a nd sho rt te rm stud ie s whe r e in v e sti gato r s dete rm in ed

the siz e d is tributio n fo r the s am ple a e r o s ols ha v e show n that siz e distri butio n s w ith in this

r a n _ge a r e usu al l_y fo u nd, it wa s the o riz ed that it mig ht be po s si b le to ide nti fy a n a e r o s ol

siz e distri_butio n wh ich c o uld be u niv e r s al l y u s edto cha r a cte riz e al l a e r o s ols in co_{m p}utin_g

e xtin ctio n, s c at te rin g, a nd abs o rptio n c o ef fi cie nts.

T h is wo rk a n al_y s e s a n um be r of databa s e s to obtain data s uitab le fo r

M

ie the o r_y

c alc ulatio n s. Usin g the c ol le cted data

, e xtin ctio n, s c at te rin g, a nd abs o rptio n c o ef f icie nts

a r e e sti mated a nd the n c om pa r ed to the me a s u r ed v alu e s of the e xtin ctio n, s c at te ring, a nd

2.0 B A

C K G

R

O U N

D :

V isi b i l it_y r edu ctio n is a r e s ult of abs o r_ptio n a nd s c at te rin_g of l i_ght _{b y g}a s mole c ule s a nd

pa rticle s in the atmo s_{p h}e r e . A ltho ug h abs o rptio n of c e rtain wa v ele ngths of visi b le

r ad iatio n c a u s e s atmo s_phe ric c olo r atio n , by fa r l i g ht s c at te rin g is the mo r e impo rta nt

p he n ome n o n r e s_po n si b le fo r i m pairme nt o f visi b i l it_y.

L _{i g h}t s c at te rin _g r efe r s to the defle ctio n of dir e ctio n of tr a v el of l i g ht b_y airbo r n e mate rial.

V isibil it_y r edu ctio n o c c u r s whe n the r e is si gnifi c a nt s c at te rin_g of l i_ght b_y a e r o s ols

betw e e n the ob

j

e ct a nd the obs e r v e r. Atmo sp he ric pa rticle s s c at te r visi b le l i g ht fr om the

s u n a nd othe r _pa rts of the sk y thr o u_{g h} the l in e of si g ht of the obs e r v e r cha n_{g i}n_g the

c o ntr a st betwe e n the ob

_j

ect a nd its ba ck gr o u nd. Th is c ha nge of c o ntr a st is pe r c eiv ed a s

dete rio r atio n of visi b i l it_{y by} the obs e r v e r

W

itho ut c o ntr a st the ob

_j

e ct b le nds into the

ba c k_gr o u nd, be c omin g in visi b le

(

Reist, 19 9 3

)

.

T he ef fe cts of atmo s_{p h}e ric c o n stitu e nts o n visi b i l it_y r edu ctio n c a n _be in v e sti gated b y

mak in _gc e rtain sim p l i f yin_g a s s um ptio n s. C o n side r a bla ck ob

j

e ct (o n e that r ef le cts n o

l i_ght₎bein_g view ed a_gain st a n i de al w h ite ba ck_gr o u nd, a homoge n e o u s atmo sphe r e s u ch

that the s c at te rin_g a nd abso r_ptio n of l i_ght is the s ame a n_{y w}he r e betw e e n the obs e r v e r a nd

the ob

_j

e ct, a u ni form sky bri g htn e s s betwe e n the ob

j

e ct a n d the obs er v e r, a nd a ho riz o ntal

viewin_{g d i}sta n c e sho r t e nou_{g h} that e a rth '

defi n ed a s the r elativ e d i f fe r e n c e betwe e n the li_{g h}t inte n sit_y of the ob

j

e ct a nd the

ba ck gr o u nd w he n view ed at a dista n c e, X fr om the ob

j

e ct. The c o ntr a st is

g iv e n b y

C

₍

x

)

=

/_b

₍

x)- /_o(x )

w he r e /„ (j c) a nd /„ (x ) a r e the inte n sitie s of th

e ba ck_gr o u nd a n d the ob

_j

e ct, r e spe ctiv ely

W

he n the inte n sitie s of the ob

_j

e ct a n d the ba ckgr o u nd a r e e_qu al, the c o ntr a st is z e r o

ind ic atin_g that the ob

j

e ct is in visi b le. In o u r si m p l i f ied model fo r a b la ck ob

j

e ct again st a

wh ite ba ck gr o u nd, whe n X = 0 (at the ob

j

e ct

)

the inte n sity of the ob

j

e ct is /„

(

x )

= _{0 sin c e}

the ob

j

e ct is b la c k a nd abs o rbs al l the visi ble r ad iatio n in ci de nt o n it. T he n C(0)= 1,

ind ic atin _gthat the ob

j

e ct is _pe rfe ctl y visi b le. T he inte n sity of l i g ht wh ich appe a r s to

c ome fr om the ob

_j

e c t /_„(x) w i l l cha n _ge w ith d ista n c e be c a u s e of _{l i g h}t s c at te rin_g o r

abs o r_ptio n b_{y p}a rticle s a nd _ga s e s alo n_g the _path betwe e n the ob

j

e c t a nd obs e r v e r The

fr a ctio n al r edu ction in /

„ c a n be e x pr e ssed a s,

w he r e b

^^^

a nd b^^ ^, a r e the c o ef fi cie nts of abs o rptio n a nd s c at te rin g, r e spe ctiv el y The

b_^i, ^dx r epr e s e nts the d if fe r e ntial inte n sity betwe e n the ba ckgr o u nd a nd the ob

j

e ct lo st by

abs o r_ptio n, wh i le b^ ^ ^ ^dx r epr e s e nts the d i f fe r e ntial inte n sity lost b y s c at te ring of l i ght o ut

of the l in e of si g ht of the obse r v e r. Co ef ficie n ts of abs o r ptio n a nd s c at te ring a r e u s u al l y

inde_pe nde nt o f viewin_{g d i}st an c e, X . Howe v e r, they a r e depe nde nt o n a e r o s ol

c o n c e ntr atio n . To c om p lete the def initio n of /

„ , we n e ed to in clude the ef fe ct of the

c o ul d be r e_pr e s e nted a s, V i„ {x)dx w he r e b

'

is a c o n sta nt.

W

ith the ad ded v a riab le, n et

cha n _ge in ob

_j

e ct inte n sit_{y i}s _{g i}v e n b y

Ba ck_gr o u nd inte n sit_{y i}s inde_pe nde nt of X a nd _{g i}v e n b_y the fol low in_g e x _pr e s sio n;

T h is e_qu atio n show s that V = b , + b Thu s cha nge in co ntr a st is g iv e n b y

d C (x)= - (b , + b )C{x )dx

abs s c at

Inte_gr atin_g th is e_qu atio n _giv e s the Ko s chmei de r e_qu atio n a nd shows a n e x_po n e ntial

de c r e a s e in c o ntr a st w ith d ista n c e, X .

- _{b

. + b )x

C{x )= e « *^ ^ ' ^ "^

T he s c at te rin_g c o eff icie nt, b , a c c o u nts fo r both the s c at te ring du e to atmo sp he ric

ga s e s a nd the s c at te rin_{g d}u e to a e r o s ol pa rticle s. Simi la rl y, abs o rptio n c o effi cie n t, b , ,

a c c o u nts fo r abs o r_ptio n b_y both atmos_{p h}e ric _ga s e s a nd a e ros ols

W

ith the e x c e_ptio n of

a nd extr emel y cle a n atmo s_phe r e, s c at te ring a nd abs o rptio n coef f icie nts a r e domin ated b y

partic ulate s c at te rin_g. The s c at te ring b y atmo sp he ric mole c ule s ha s a m inimal ef fe ct,

howe v e r, it l i m its the ma x i mum vis u al r a nge fo r a b la ck ob

j

e ct viewed o n a w h ite ba ck

gr o u nd to 1 0 0-3₀0 _km _{(H inds} 19 82₎

Ae r o s ols in siz e r a n _ge s c om pa r able to the w a v ele n_gths of visi b le l i_ght ha v e be e n show n

t o be r e s_po n si b le fo r v isi b i l it_{y d}e_gr adatio n . A s the wa v elengths of visi b le l i g ht spa n fr om

shown to be mo st ef fi c ie nt s c at te r e r s _pe r u nit ma s s. Fo r th is siz e r a nge the

M

ie the o ry of

r ad iatio n s c at te rin _g c a n be u s ed to dete rmin e v alu e s of i»

,^ „ , .

Extin ctio n c o ef f icie nt, b , is def in ed a s the s um of the abs o rptio n a nd s c at te ring

c o ef ficie nts. It is po s sib le to r elate vis u al r a nge to e xtin c tio n c o ef f icie nt b y a s s u ming a

v alu e fo r the c o ntr a st in the abo v e e_qu atio n . Fo r the sim p l i f ied c a s e o f v iew ing a bla ck

ob

_j

e ct in a white ba ck_gr o u nd, a n a v e r age obs e r v e r is a c c epted to be able to s e e a n ob

j

e ct

with a c o ntr a st v alu e of 2 _pe r c e nt. Using th is a s s um ptio n, the equ atio n showin g the

e x _po n e ntial de c a_y of c o ntr a st w ith d ista n c e c o ul d be s olv ed y iel d in_g a n e_qu atio n fo r

visu al r a n_ge

3.91 2

X =

b _^

e x t

wher e, X , n ow r epr e s e nts the vis u al r a nge. T hu s the vis u al r a n

ge c a n be e x_pr e s s ed in

terms of a n e xtin ctio n c o ef fi cie nt, b . As e v i de nt fr om the equ atio n , the u nit of b is

e xt ^ e xt

r e c _{i p}r o c al of d ista n c e, s u ch a s m

"'

(Seinfeld, 19 82;

M

id d leto n , 1 952;

W

ag go n e r, et al.

3.0

M

I E

- A R E S P R O

G

R A

M

:

The

M

ie-A R E S p_{r o}

gr am wa s u s ed in calc ulatin_g the c o ef f icie nts of e xtin ctio n , s c at teri ng,

a nd abs o r_ptio n fo r th is stu d y. T he

M

ie

-A R E S_pr o_gr am is a c om bin atio n of the

M

ie c ode

a nd the A R E S

(

AeRo s ol E qui l i brium S_ystem

)

_pr o_gr am The AR E S pr o_gr am is a n u_{p d}ate

to the o ri g in al

M

A R S

(M

odel fo r a n A e r o s ol Re a ctin_{g Sy}stem)_pr o_gr am

(

B inkow sk i,

19 9 5). T hu s, the M ie

-A R E S pr o_gr am is an u_{p d}ate of the o ri g in al Mie-

M

A R S pr o_gr am

de s c ri bed b y

W

i ls o n a nd Reist (19 94

)

.

The A R ES c ode is ba s ed o n the MA R Sc ode a nd the S CAPE c ode

(

Binkowsk i, 19 9 5).

MA _{R S p}r ed icts the _qu a ntit_y a nd the c om po sitio n of s e c o nda r_y atmo s_{p h}e ric a e r o s ols

c o ntainin _g sul fate, nitr ate, a nd am m o nium c om po u nds. C hemic al c om po sitio n of

multi p ha s e a e r os ols c o ntainin_g wate r, (NH 4)2S 0 4, NH4HS O4, (NH4)3H(S 0 4)2, H2S O4,

H N O3, N H4N O3 is pr edicted by a the rmodyn amic appr o a ch (Sa x e n a, et al 19 86). T he

MA R_{S p}r o_gr am is c om putatio n al l y in e x_pe n siv e a s _its tr e atme nt of inte r_fa cial e_quili bria

fo c u s e s o nl y o n ma

j

o r c om_po n e nt s, thu s m ini m izingthe equ atio n s to be s olv ed. T he r e

a r e othe r models with ri go r o u s the rmod_yn am ic r o utin e s but the_y a r e c om putatio n al l y

e x _pe n siv e and the

M

AR S pr o _gr am ha s be e n shown to _pr odu c e c om pa r ab le r e s ults

(

Sa x e n a, et al, 19 8 6; K i m et al 19 9 3

)

. A mo r e detai led de s c ri ptio n of the

M

A R Sa nd

S CA PE _pr o_gr ams a r e _pr o vi ded in a rticle s b_y Sa x e n a, et al

(

19 8 6) a nd K i m, et al (19 9 3

)

.

T he AR ES _pr o_gr am u s e s chem ic al a nd p h_ysic al a e r o s ol data s u ch a s s u l fate s

(

S 0₄

"_^

s et to be u s ed in the M ie c ode fo r c om putin _g Mie v alu e s T he A RE Sc ode c alc ulate s

c om po sitio n of a s ul fate, nitr ate, am mo nium, a nd wate r a e r o s ol ba s ed o n equi li brium

the rmod yn amic s. T he A RE S c ode c o n si de r s tw o r e

g ime s de_pe nd in_g o n the mola r r atio of

am mo nium to s ul fate Fo r the mola r r atio s of le s s tha n two , the c ode s olv e s a c ub ic fo r

the h_ydr o_ge n molal it_y . In this mode, the nitr ate s a r e a s s umed n ot to be pr e s e nt whe n

molal io nic str e n_gths a r e _gr e ate r tha n 5 0 o r nitr ate s a r e c alc ulated i f s u f fi c ie nt ammo nium

a nd l i_quid w ate r is _pr e s e nt. Fo r mola r r atio s of two o r gr e ate r, al l s ulfate is a s s umed to be

ammo nium s ul fate a nd the ammo nium nitr ate is c alc ulated to dete rmin e its _pr e s e n c e

(

Binkow sk i, 19 9 5

)

.

T he

M

ie c ode u s ed in the _pr o_gr am c om pute s the Mie v alu e s. Fo r the

M

ie the o ry

c alc ulatio n s a s et of the o r etic al lo_g-_{n o r}m_al _si_{z e} d i_stri b_uti_{o n s} w

e r e u s ed In the s e

c alc ulatio n s the a e r o s ol wa s a s s umed to be at its fi n al siz e distributio n afte r chem ic al

r e a ctio n s a nd the a c_quisitio n of w ate r. Fo r a lo g

-n o rmal d istri butio n the _ge ometric me a n,

d

g, a nd ge ometric sta nda rd de v iatio n , O_g, a r e c ho s e n a nd 15 d is c r ete siz e inte r v als

c om puted s u ch that abo ut 9 9 pe r c e nt of al_{l p}a rticle s a r e in cluded

(

the tai ls at eithe r e nd of

the d istri butio n a r e n e_gle cted

₎

A s_pr e ad fa cto r, s, is defi n ed by;

s = o

t

8 lowe st

a nd a fa cto r,

/

, is def in ed a s;

15 ^ ^

T he n , the up pe r siz e of e a ch inte r v al is s u c c e s siv el y dete rm in ed a c c o rd ing to;

d = _d, e x _p

f

f

)

u_{p p} e r low e r ^ ^ ^

with the a v e r a_ge siz e defi n ed a s_;

d

d + d,

u_{p p}e r low e r a v_g

For the n e xt inte r v al the u_{p p}e r siz e be c ome s the low e r siz e. The fr a ctio n of pa rticle s, n,

in a siz e inte r v al is _{g i}v e n b y_;

d + d,

u_{p p} e r lo w e r

d * _l

n

\

a

\

* -_y

/

2n

a v_g I _g '

-e x _p - _In

d

y 8 J

2 ^

2 1n ^ a

Usin _g the abo v e e_qu atio n a nd the e_qu atio n fo r d_{a v}

g the fr a ctio n al n umbe r of pa rticle s in a

siz e inte r v al c a n be dete rm in ed alo n_g w ith the a v e r a_ge d iamete r fo r that siz e inte r v al fo r a

g iv e n d_g a nd <₃ g.

E lemental Ca rbo n

M

ass

(

ECM

₎

, Sul fu r

M

a ss

(

S

M )

,

M

e a s u r ed Co ef f icie nt o f Sc at te ring,

a nd M e a s u r ed Co ef f icie nt of Abs o r_ptio n.

T he

M

ie-A R E S p_{r o}g_{r a}m i_{s c o}m b i_{n e}d w ith _{a s e}p_{a r a}t_{e c}ode th_at p_{r e}

pa r e s the r aw in_put

data _{g i}v e n a_bo v e to be u s ed b_y the AR ES _pr o_gr am a n d intr o du c e s the v a riab le s c alc ulated

b_y the AR E S_pr o_gr am to the

M

ie c ode. To ap p l y the abo v e l isted a e r o s ol mo nito ring data

to the

M

ie-A R

E S pr o_gr am, it wa s n e c e s s a ry to make a s et of a s s u m ptio n s a nd

c alc ulatio n s. Using the s e a s s um ptio n s, a n input f i le wa s ge n e r ated fo r the A R E S

pr o_gr a_m. The s e a s s um ptio n s a nd c alc ulatio n s a r e s umma riz ed below :

a

)

Or_ga nic Ca rbo n

M

as s

₍

O C

M

₎ is _giv e n b y_;

O C

M

= _TC

_M

- _EC

_M

In this a s s um ptio n total c a rbo n ma s s wa s c o n side r ed to be made u_p of o r_ga n ic

a nd eleme ntal c a rbo n ma s s e s.

b

₎

Sul fate

M

a s s

(

S O_^

M

₎is _giv e n b_y;

S O_^

M

=

_t

_S

_M

₎

In this c alc ulatio n al l of the s ul fu r

(

3 2 _g/mole

)

ma s s is a s s umed to be

c o ntain ed in s ul fate

(9 6 g / m

ole₎ fo rm. A s the r e is o n e mole of s ul fu r in e a ch

s ulfate mole c ule, the n ba s ed o n their mole c ular w ei g hts, the ma s s of Sul fate

c

₎

A mmonium

M

a s s

(

A

M )

is _giv e n b y_;

A

M

= TA

M

- _{T C}

M

- _{S O}

^

M

In this case total a e r o s ol ma s s is a s s umed to be made of ammo nium, c a rbo n,

a nd s ul fate s. T he r efo r e, we c a n dete rmin e the am mo nium mass by kn owin g

thr e e of the fo u r v a riable s (Reist, 19 9 5).

d

₎

If the r e s ultin _g am mo nium ma s s is le s s tha n z e r o the n ammo nium ma s s is s et

to z e r o.

e

)

I f the sul fu r ma s s is _gr e ate r tha n z e r o the n the

M

ole Ratio

( M

R A TIO )is _{g i}v e n

b_y;

M

RA T IO = A

M

/ 18

y

S O^

M

/ 9 6

T h is ra tio is c alc ulated to dete rmin e the r elativ e amo u nts of ammo nium a nd

sul fate _pr e s e nt in the total a e r o s ol ma s s.

f

₎

I f

M

R A T IO is _gr e ate r tha n 2 the n A

M

is _{g i}v e n b y;

S O

M

A

M

=

₍

2₎

₍

18

₎

—

^

I f the r e a r e mo r e tha n two mole s of am mo nium pe r mole of sul fa te the n

fr om the abo v e fo rmula th is is e stab l ishe_{d b y} mult_{i p l y i}n_g the mole s of s ulfate

b_y the mole c ula r w ei g ht of am mo nium ₍1_{8 g/ m}ole

)

a nd a fa cto r of tw o

g

)

In e rt M a s s (/

M

)is _giv e n b_y;

I

M

= _{T A}

M

- _SO ^

M

- _A

M

In e rt ma s s is a s s umed to be c a rbo n ma s s a nd a n_y othe r fr a ctio n of the a e r o s ol

u n a c cou nted fo r b_y the s ul fate a nd the ammo nium ma s s e s.

h

₎

If I

M

is _gr e ate r tha n z e r o , r e al

{

R I R

)

a n dimagin a ry

{

R I I

)

r efr a ctiv e indic e s

a r e _giv e n b_{y ;}

E C

M

^

R I R ^

(

I

M

- _EC

_M

_\ ^

2

-V I

M

(

EC

M \

R I I =

I

I

M

_J

T he r e al a nd the i ma_gin a r_y r efr a ctiv e ind ic e s a r e ba s ed o n a n e stimated

in o r_ga nic mate rial r efr a ctiv e inde x

(

1 5₎ a nd the c a rbo n r efr a ctiv e inde x

(

2+ i₎

In e sti matin_g the r e al r efr a ctiv e inde x the in o r_ga nic mate rial fr a ctio n of the

in e rt ma s s is multipl ie_{d b y} the in o r_ga nic mate rial r efr a ctiv e inde x a nd the

c a rbo n fr a c tio n of the in e rt ma s s is multi_pl ied b y the r e al pa rt of the c a rbo n

r efr a ctiv e inde x. In e sti matin

g the i m a_{g i}n a r_y r efr a ctiv e inde x the c a rbo n

fr a ctio n of the in e rt ma s s is multip l ied b_y the i ma_{g i}n a r_{y p}a rt of the c a rbo n

And, In e rt De n sity , p . , is giv e n by;

, ^ IM

- _{E CM} - _{O CM\ f}

^ E CM + O CM

P,

= _{2 5} + 2

I

_{

IM J

{

IM

In e rt de n sit_y is ba s ed o n the de n s_it_y of s a nd (2.5 g/c c) a nd the de n sity of

c a rbo n (2 _{g /}c c

)

. T o e sti mate the in e rt de n sity , the in o rga nic fr a ctio n of the

in e rt ma s s is mult_{i p li}ed b_y the de n sit_y of s a nd a ndthe c a rbo n fr a ctio n is

4.0

M

E T

H

O D O L O G Y A N

D

D E S C RI P T IO N OF T

H

E D A T A SE T S

U

SE D

:

A si_gnifi c a nt amo u nt of am bie nt data o n a e r o s ol c o n c e ntr ation s a nd c om po sitio n a nd

visi b i l it_y r elate_{d p}a r amete rs ha s be e n obtain ed b_y a v a riet_y of _pub l ic a nd priv ate studie s

As a r e s ult the r e n ow e xists a bo_{d y} of data in clud in_{g h i}sto ric al data w h ich m_{i g h}t be u s ed

to de v elo_p a c c u r ate _pr ed ictio n s of the r elatio n sh i_{p b}etw e e n _pol lutio n tr e nds a nd visi bi lit_y.

Fo r th is _pr o

j

e c t, w e u s ed s ev e r al databa s e s that c o ntain ed the n eces sa r_y v a riab le s fo r

c om_putatio n. Fo l lowing is a brief de s c ri ptio n of the databa s e s u s ed:

4.1 Ea ste r n F in e Pa r tic u la te V isib i l ity Netwo rk

(

E FP VN

)

:

The E F PV N is a U SEPA s_po n s o r ed ef fo rt to a c_quir e lo n_g te rm, r egio n al ly

-s c aled

visi biht_y a nd f me _pa rticle mo nito rin_{g d}ata in the e a ste r n United St ate s

M

o nito rin_{g d}ata

fo r the E F P VN we r e _gathe r ed at fi v e mo nito rin_g statio n s. T he s e mo nito rin g statio n s we r e

lo c ated at Ho rto n Statio n , V irg inia; Pe r ryvi lle, Ke ntu cky; Lo ok Ro ck, Te n n e s s e e; Itha c a,

New Y o rk_; a nd

Q

u ab in Summit, Ma s s a chu s et ts.

M

o nito ring in str ume ntatio n, s am p l ing

metho dolo_{g y}, a nd a n al ysis te chni qu e s we r e cho s e n to pr o v ide r epr e s e ntativ e

me a s u r eme nt s of visu al r a n_ge a nd f in e _pa rticle s c at te rin_g, abs o rptio n, a nd c om po sitio n

L i g ht s c at te rin_{g m}e a s u r eme nts we r e obtain ed b_y n e_{p h}elometr_y. F in e pa rticle abs o rptio n

c o ef fi cie nts we r e dete rm in ed u sin_{g i}nte_gr atin_{g p l}ate a n al_ysis o n de_po sits c ol le cted o n

Tefl on filte rs. Tefl o n filters we r e gr a vi metric al l y a n al yz ed fo r fine

pa rtic ulate ma s s. X

c om po sitio n. F in e eleme ntal a nd o rga nic c a rbo n c o n c e ntr atio n s o n qu a rtz fibe r fi lte r s

w ere a n al yz ed b y a the rmo

-o_ptic al method. In ad d itio n to the s e data

, ambie nt

tem_pe r atu r e a nd humi d it_{y d}ata we r e _pr o vi ded. Fo r the data ba s e the data integrity a nd

qu al it_{y w} a s ind ic ated b y a v al i datio n s_y stem w h ich f la_{g g}ed e a ch data e ntr_y a c c o rd in_{g l y}.

T he E F P V N data fo r 198 8

-8 9 we r e a v ai lable fr om the E P A . T he data we r e pr o vi ded in

A SCn fo rmat a nd we r e divi ded into thr e e data fi le s : dai l_y, qu a rtz f i lte r, a nd Tef lo n f i lte r

data. In o rde r to obtain a c om plete s et of pa r amete r s fo r o u r c alc ulatio n s we n e eded

v a riable s fr om e a ch data f i le. In ma ny in sta n c e s o n e o r two v a riable s we r e mis sing o r

we r e n ot me a s u r ed fo r a _{g i}v e n da_y T h is r e s ulted in in c om p lete data fo r that _{g i}v e n da_y.

T he r efo r e, we w e r e ab le to obtain o nl y 55c omp lete data points fo r the f iv e mo nito ring

statio n s Th is data s et is _pr o vi ded in A p pe nd ix A .

4.2 In te r agen cy

M

on ito ring o

f

Pr ote cted Vis u al En vir o n me n ts

(

I

M

P R O V E

)

:

T he I

M

PR O V E pr o_gr am is u s ed b_y T he Natio n al Pa rk Se r vic e ₍NPS

)

a nd othe r Fede r al

L a nd

M

a n a_ge r s to _pr ote ct the visibil it_{y i}n C la s s I a r e a s. Visi b i l ity is pr ote c ted by the

Cle a n A ir A ct in Cla s s I a r e a s

, w hich c o v e r mo st of the n atio n al pa rks a nd wi l de r n e s s

a r e a s The I

M

P R O V E pr o_gr am in clude s the cha r a cte riz atio n of ha z e b y p hoto_gr a_{p h y}, the

me a s u r eme nt o f o_ptic al e xtin ctio n with tr a n sm is s omete r s a ndn e_{p h}elomete r s, a nd

me a s u r eme nt of the c om positio n a nd c o n c e ntr atio n o f the fi n e _pa rticle s that _pr odu c e the

s am p le r ha s fou r s am p l in_{g m}odule s : A, B, a nd C c ol le ct f in e pa rticle s

(

< 2.5 |i m)

, a nd D

c ol le ct s P

M

I O

₍

< 10.0 )i m

)

, pa rticle s a nd S O2 ga s. In th is stud y the r ele v a nt data a r e

pr o v i ded b y the A a nd C module s.

M

odule A is the prima ry Teflo n fi lte r pr o vi d ing mo st

of the fi n e _pa rticle data, s u ch a s gr a vimetric total ma s s, s ul fu r ma s s, a nd c o ef fi cie nt of

abs o r_ptio n

(

L a s e r Inte_gr atin_{g P l}ate

M

ethod

)

.

M

odule C

, w ith ta n dem qu a rtz fi lte r s,

me a s u r e s o r_ga nic a nd eleme ntal c a rbo n ₍T he rmal O_ptic al Refl e cta n c e Method₎.

T he I

M

P ROV E data we r e obtain ed u sin_g the inte r n et fi le tr a n sfe r _pr oto c ol (F T P) fr om

two s e_pa r ate s o u r c e s. The chemic al c ompo sitio n a nd physic al a e r o s ol data a r e c om pi led

b_y the Univ e r sit_y of Califo r nia-D_{a v} i_s

. T he s c at te ring me a s u r eme nts b y n ep helometr

y a r e

c ol le cted a nd c om p i ledb y Colo r ado State Univ e r sit_y at Fo rt Col lin s. T he chemic al a nd

p h ysic al a e r o sol data _pr o vi ded b y Univ e r sit_y of Cal i fo r nia-D

a vis a r e 2 4-h

o u r s am p le s

take n tw ic e-w

e ek l y (

W

edn e sda_y a n d Satu rda_y of a _giv e n w e ek₎, wh i le the s c at te ring

c o ef fi cie nt data obtain ed fr om Colo r ado State a r e ho u rl_y s am ple s c ol le cted e v e r_{y d}a_y.

T h is r e_quir ed the a v e r a_{g i}n _g of the ho u rl y s c at te rin_g c o ef fi cie nt v alu e s to obtain a dai l y

a v e r a_ge s c at te rin _gc o ef fi cie nt. A ls o, s c at te ring data w e r e fi lte r ed to obtain o nly the

W

edn e sda_y a nd Satu rda_y v alu e s to match w ith the a v ai lab le chemic al a nd _ph_ysic al data.

A ltho u_{g h}, chem ic al c om position data wer e a v ai lab le fo r ye a r s a s fa r ba ck a s the 19 8 0s,

s c at te rin_{g d}ata b y n e_{p h}elometr_y w e r e a v ai lable fo r o nl y the _pa st _{3 y}e a r s. T her efo r e

, we

we r e fo r c edt o u s e the data fo r the r e c e nt _ye a r s. T he r e we r e als o s ome m is sin

g a nd

ou r a n al ysis. In spite of al l the s e fa c to r s we w e r e ab le to obtain 154 data points fr om the

I

M

PROV E s_y stem.

T he I

M

PR OV E data is c olle cted at n ume r o u s lo c atio n s thr o u_{g h}o ut the U S. How e v e r, fo r

o u r stud_y, 4 lo c atio n s w e r e u s ed to obtain the input data. T he s e lo c atio n s w e r e Gr e at

Smok y

M

o u ntain s Natio n al Pa rk (at L o ok Ro ck), T e n n e s s e e (8 4 data points); M ammoth

Ca v e Natio n al Pa rk

(

at Oz o n e

M

o nito rin_g Site

)

, Ke ntu ck y (18 data points); A c ad ia

N atio n al Pa rk

(

at Pa rk He adqu a rte r s₎, M ain e (35 data points); a nd D ol l y Sods

W

i l de r n e s s

(

at Be a rde n Kn ob

₎

,

W

e st V irg inia

(

17 data points

)

.

4.3

M

ethodolog y:

T he data obtain ed fr om the abo v e s o u r c e s we r e u s ed in the

M

ie-A R E

S pr o_gr am to

e s ti m ate e xtin ctio n c o ef f icie nts. Esti mated c o ef fi cie nts we r e c om pa r ed to the me a s u r ed

c o ef ficients A matrix of sta nda rd de v iatio n a n_{d m}e a n d iamete r w a s u s ed a s the siz e

d istri butio n data in the

M

ie-A R

E_{S p}r o_gr am. T h is matrix wa s de v eloped to c o ntain the

a c c umulatio n mo de a e r o s ols w h ich a r e b lamed fo r ma

j

o rit_y of the atmo s_phe ric visi b i l it_y

r edu ction.

A 3X 6 ma t rix c o ntainin _gs ta nda rd de v iations of 1 2, 1.5, 1.8a nd me a n pa rticle d iamete r s

of 0. 1, 0.2, 0.3, 0.4, 0.5, a n d 0.7 we r e u s ed a s the siz e d istributio n fo r the Mie

-A RE S

T he e xtin ctio n, s c at te ring, a nd abs o rptio n c o ef fi c ie nts c alc ulated u sing the s e siz e

d istri butio n s we r e c om_pa r ed to me a s u r ed v alu e s. T he c ompa ris o n w a s a c c om pl ished b y

pe rfo rm in_g l in e a r r e_gr e s sio n a n al ysis o n the obtain ed data a nd dete rminin_{g w h i}ch siz e

distributio n r e s u lted in c o ef fi cie nts clo s e st to the me a s u r ed v alu e s. T h is methodolog y

allow ed u s to statistic al l y dete rm in e the be st e stimate of the me a s u r ed v alu e s.

Afte r the abo v e de s c ri bed a n al ysis, the r e s u lts of o n e of the siz e dis tributio n s w e r e fu rthe r

stud ied. T he data we r e br oke n dow n into d i f fe r e nt s egme nts s u ch a s r elativ e hum id it y,

lo c atio n , total a e r o s ol ma s s, a nd s ulfu r ma s s, to a n al yz e the ef fe cts of s u ch fa cto r s. Fo r

th is stud_{y I}

M

P RO V E data we r e _pr efe r r ed du e to the l i mited n umbe r of data _points in the

E F P VN data.

In ad d itio n , the effe cts of the pr e s e n c e of am mo nium ma s s in the total a e r o s ol ma s s w a s

stud ied F o r th is stud y the o ri g in al s et of data we r e modi fi ed n ot to c o ntain the

ammo nium m a s s in the a n al ysis. T h is way it wo ul d be po s si b le to c om pa r e the ef fe ct of

am mo nium m a s s in the a e r o s ol a nd its ef fe ct o n the e xtin ctio n, a nd s c at te ring

5.0 R E

S

U L T

S

A N D D I

S

C U

S S

I

O

N :

5.1 R ESU L TS:

T he r e s ults fo r the I

M

P R OVE a nd E F P V N data s ets u s ed in o u r _pr o

j

e ct a r e a n al_yz ed

below . T he c alc ulated e xtin ctio n (b

^^ ,

)

, s c at te ring (&

,^ ^ ,

)

, a nd abs o rptio n (Z)_^^

^ )

c o ef fi c ie nts a r e c om_pa r ed to the me a s u r ed v alu e s u sin_{g l i}n e a r r e_gr e s sio n a n al ysis. Fo r

e a ch siz e d istributio n , a gr adie nt fo r the me a s u r ed v e r s us the c alc ulated v alu e s a nd a

s_qu a r e of s am_{p l}e c o r r elatio n c o efficie nt ₍R

₎

a r e c alc ulated S qu a r e of s am_{p l}e c o r r elatio n

c o ef f icie nt is a _qu a ntitativ e me a s u r e of the im_pr o v eme nt in fi t of the l in e a r r e_gr e s sio n l in e

b_y the u s e of the inde_pe nde nt v a riable (fo r o u r stud y inde_pe nde nt v a riab le is the me a s u r ed

c o ef f icie nt a nd the de_pe nde nt variab le is the c alc u lated co ef f icie nt). T hu s, the R

^

me a s u r e s the str e n_gth of the l in e a r r elatio n sh i p betwe e n the inde_pe nde nt a nd the

de_pe nde nt v a riable in the s e n s e that it _{g i}v e s the _pr o_po rtio n ate r edu ctio n in s um of the

s_qu a r e s of v e rtic al de viatio n s obtain ed u sin_g the le a st

-s_qu a r e s l in e r elativ e to the me a n .

T he R v alu e c a n r a n_ge betwe e n 0 a nd 1 T he la r_ge r the v alu e of R ^

, the gr e ate r the

r edu ctio n in s um of the s_qu a r e s a nd str o n_ge r the l in e a r r elatio n sh i_{p b}etwe e n the

5.1.1 Re s u lts

f

o r I

M

P R O VE Data :

T ab le 1 shows the c alc ulated _gr ad ie nt a nd c o r r elatio n c o ef f icie nt v alu e s fo r e a ch siz e

d istri_butio n u s ed in e sti matin_{g b}

^ ^ , , b^ ^ ^ , , Z?^^^ fo r the I

M

P ROV E data. T he R

^

v alu e s fo r

Z7_„

, r a nge fr om 0.7 9 2 to 0.8 4 0, w h i le the gr ad ie nt v alu e s r a nge fr om 0.8 29 to 5.2 0 3. T he

R^ v alu e s fo r b

^^^, r a nge fr om 0 7 8 6 to 0.8 2 2

, w h i le the gr adie nt v alu e s r a nge fr om 0.76 8

to 6. 14 7. T he R

^

v alu e s fo r Z?

^^^ r a nge fr om 0 4 49 to 0.60 3, w h i le the gr ad ie nt v alu e s

r a n_ge fr om 1 499 to 2.4 5 5.

A c c o rd in _gto the s e r e s ults, the be st ( + 5 0 % de viatio n fr om gr ad ie nt of u nity) es ti mate of

b_^^ is obtain ed w he n the fol lowin_g siz e d istri butio n s a r e u s ed:

Me a n Diamete r Std. De viatio n Gr ad ie nt = M/C R

^

0 4 1.2 0.82 9 0 8 3 4

0.5 1.2 0.8 85 0.8 3 0

0.3 1.2 0.920 0.838

0.3 1.5 0.9 7 9 0.8 34

0.2 1.5 1.0 2 5 0.8 3 8

0.4 1.5 1. 1 33 0.8 3 8

0.2 1.8 1. 146 0.8 32

0.1 1.8 1.2 34 0.8 3 9

0.7 1.2 1.3 3 6 0 8 2 0

0.5 1.5 1.4 2 2 0.8 2 4

0.2 1.2 1.4 4 8 0 8 40

T

a

b

l

e

1

.

I

M

P R O

V E D

a ta

R

e s u

l t

s

Be xt Valu e s fo r I M P R OVE Data Bs c at Valu e s fo r I M P R O VE Data Babs Valu e s fo r _{I M P R O V E D}ata

MD 0 1 0 1 0 1 0 2 0 2 0 2 0 3 0 3 0 3 0 4 0 4 0 4 0 5 0 5 0 5 0 7 0 7 0 7 SD 1 2

Gr ad=_{M / C}

5 2 0 3

2 1 2 7

1 2 3 4

1 4 4 8

1 0 2 5

1 1 4 6

0 9 2 0

0 9 7 9

1 4 9 4

0.8 2 9

1 1 3 3

1 9 6 9

0 8 8 5

1 4 2 2

2 5 1 0

1 3 3 6

2 2 4 0

3 7 6 8

R^

0 7 9 2

0 8 3 7 0 8 3 9

0 8 4 0

0 8 3 8

0 8 3 2

0.8 3 8

0.834

0.8 2 9

0 83 4

0 8 2 8

0.8 2 7

0.8 3 0

0 8 2 4

0.8 2 7

0 8 2 0

0 8 2 4

0 8 2 4

M D 0 1 0 1 0 1 0 2 0 2 0 2 0 3 0 3 0 3 0 4 0 4

0.4

0 5 0 5 0 5 0 7 0 7 0 7 SD 1 2 5 8 2 5 8 2 5 8 2 5 8 2 5 8 2 5 8

Gr ad=_M/C

6 1 4 7

2 1 3 5

1 1 7 3

1.4 0 0

0.9 6 2

1 0 8 8

0 8 5 8

0 9 1 7

1 4 5 2

0 7 6 8

1 0 7 6

1 9 7 3

0 8 2 3

1 3 8 0

2 5 9 5

1.2 9 3

2.3 0 7

4 1 2 5

R^

0 8 2 2

0 8 1 8

0 8 1 3

0 8 1 7

0.8 1 1

0 8 0 3

0 8 1 1

0 8 0 6

0 7 9 9

0 8 0 6

0 7 9 7

0 7 9 4

0 8 0 0

0.7 9 3

0.7 9 4

0 7 8 6

0 7 9 1

0 7 9 0

M D 0 1 0 1 0 1 0 2 0 2 0 2 0 3 0 3 0 3 0 4 0 4 0 4

0.5

0 5 0 5 0 7 0 7 0 7 SD 1 2 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Gr ad=_{M / C}

2 2 9 4

1 9 2 4

1 6 5 0

1 6 8 0 1 5 5 4

1 5 8 1

1 5 1 0

1 5 2 1

1 725

1.4 8 4

1 5 6 8

1 8 8 6

1 4 9 9 1 6 5 1

2.0 5 4

1 5 8 3

1.8 5 3

2.4 5 5

R^

0.4 4 9

0.4 8 6

0 5 0 8

0 4 7 6 0 5 1 8

0.5 6 8

0 5 1 0

0.5 4 9

0 5 8 5

0 5 3 6

0 5 7 5

0.6 0 3

0 5 5 6

0 5 8 6

0 6 0 0

0 5 8 6

0 5 9 4

T he be st e stimate

(

+ 50 % de viatio n fr om _gr ad ie nt of u nit_y) of b

^^^ v alu es c a n be

obtain ed u sin_g the fol low in_g the siz e d istributio n s :

Me a n D iamete r Std. De viatio n Gr ad ie nt = M/ C R

^

0.4 1.2 0 76 8 0 80 6

0.5 1.2 0.8 2 3 0.8 0 0

0.3 1.2 0.858 0.811

0.3 1.5 0 9 17 0 8 0 6

0.2 1.5 0 9 6 2 0 81 1

0.4 1.5 1.0 76 0.7 97

0.2 1.8 1.0 8 8 0.8 0 3

0 1 1 8 1.1 73 0.81 3

0 7 1 2 1.29 3 0.786

0.5 1.5 1.3 80 0

.7 9 3

0.2 1.2 1.40 0 0.8 17

0.3 L8 1 4 5 2 0.79 9

T he be st e stimate (+ 5 0 % de viatio n fr om gr adie nt of u nit_y

₎

of b

^^^ v alu e s c a n be

obtained u sin _g the fol lowin_gthe siz e d istri butio n s :

M

e a n D iamete r Std De viatio n Gr ad ie nt =

M

/C R^

0.4 1.2 1.4 8 4 0.5 36

0 5 1.2 1.49 9 0.5 5 6

5. 1.2 Re s u lts

f

o r E F P VN Data :

Table 2 shows the c alc ulated gr ad ie nt a nd c o r r elatio n c o ef f icie nt v alu e s fo r e a ch siz e

d istri butio n u s ed in es timatin_{g b}

^„ , b^^ ^,, a nd b

^,,^fo r the E FPV N data

. T he R

^

v alu e s fo r

b

^ ^ , r a nge fr om 0.3 5 9to 0.7 6 6, w h i le the gr ad ie nt v alu e s r a nge fr om 0.5 0 3 to 2

.5 7 8. T he

R^ v alu e s fo r b

^ ^ ^ , r a nge fr om 0.33 6 to 0.7 5 1, wh i le the gr ad ie nt v alu e s r a nge fr om 0.5 0 2

to 2.7 7 T he R ^

v alu e s fo r b

^^^ r a nge fr om 0.0 14 to 0.0 2 6

, wh ile the gr ad ie nt v alu e s r a nge

T

a

b l

e

2

.

E F P

V N

D

a

t

a

R

e s u

l

ts

Be xt Valu e s fo r E F P V N Data _Bs c at Valu e s fo r E F P V N Data Ba_bs Valu e s fo r E F P V N Data

M D 0 1

0 1

0 1

0 2

0.2

0.2

0 3 0 3 0 3 0 4 0 4 0 4 0 5 0 5 0 5 0 7 0 7

0 .7

S D 1 2

Gr ad=M / C

2.1 0 9

0.9 9 8

0 6 8 6

0 6 8 4

0 5 7 7

0 7 2 4

0 5 0 9

0 6 0 6

0 9 7 4

0.5 0 3

0 7 5 1

1 3 2 3

0 5 78

0 9 7 0

1 7 1 7

0 9 6 4

1 5 4 4

2 5 7 8

0.3 5 9

0 5 0 6

0,6 4 0

0.5 3 3

0 6 5 4

0 7 1 6

0.6 4 2

0 7 1 2

0 7 3 2

0 7 0 0

0 .7 3 8

0 7 4 3

0 7 3 5

0.7 4 6

0.7 4 5

0.7 6 6

0.7 4 8

0.7 4 2

M D

0 1

0. 1

0 1

0 2

0 2

0 2

0.3

0 3 0 3

0 4

0 4

0 4

0.5

0 5

0.5

0 7

0 7

0 7

S D

1. 2

Gr a cl= M / C

2 1 5 4

1.0 0 5

0 6 8 8

0 6 8 9

0 5 7 8

0 7 2 9

0 5 0 8

0 6 0 8

0 9 9 2

0 5 0 2

0 7 5 9

1 3 6 6

0 5 8 0

0 9 8 9

1 7 9 8

0 9 8 3

1 6 1 1

2 7 7 0

R^

0 33 6

0.5 0 5

0 6 4 1

0 5 3 5

0 .6 5 6

0.7 1 5

0 64 4

0 7 1 2

0 .7 3 0

0 7 0 1

0.73 6

0 7 3 8

0 7 3 4

0 7 4 3

0 7 4 0

0 7 5 1

0 7 4 3

0 7 3 4

M D

0 1

0.1

0 1

0 2

0 2

0.2

0 3 0 3 0 3 0 4 0 4 0 4 0 5 0 5 0 5 0 7 0 7 0 7 S D

1.2

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Gr ad= _{M / C}

0 3 5 6

0 3 0 0

0 2 7 7

0.2 67

0 2 6 6 0 2 6 8

0 2 7 0 0 2 5 2

0 2₅9

0.265

0.2 7 3

0 2 5 0

0 2 6 3

0 2 7 2

0.2 4 5

0 2 5 0 0 2 6 4

0 2 4 6

0 0 1 8

0. 0 1 9

0 0 2 1

0 0 1 9

0 0 2 2

0 0 2 4

0 0 2 4

0. 0 2 2

0 0 2 2

0.0 2 4

0 0 2 6

0 0 1 9

0. 0 2 5

0.0 2 5

0 0 1 7

0 0 2 3

0 0 2 2

Ac c o rdin_g to the s e r e s u lt s, the be st ( + 50 % de viatio n fr om grad ie nt of u nity

)

e sti mate of

b

^„ is obtain ed w he n the fol lowing siz e d istributio ns a r e u s ed;

M

e a n D iamete r Std. De viatio n Gr adie nt =

M

/ C R ^

0 4 1.2 0.50 3 0.70 0

0.3 1.2 0.50 9 0.6 42

0 2 1.5 0 577 0.6 54

0.5 1.2 0 6 0 6 0.7 12

0.2 1.2 0.68 4 0 53 3

0 1 1.8 0.686 0.640

0.2 1.8 0.7 2 4 0.7 16

0 4 1.5 0 7 5 1 0.73 8

0.7 1.2 0.9 6 4 0 76 6

0.5 1.5 0.9 7 0 0 7 46

0.5 1.5 0.970 0.7 4 6

0 4 L 8 1.323 0.743

The be st e stimate ₍ + 5 0 % de viatio n fr om gr ad ie nt of u nit_y

)

of b

^^ ^ v alu e s c a n be

obtain ed u sin_g the fol lowin_g the siz e d istri butio n s :

M

e a n D iamete r Std. De v iatio n Gr ad ie nt =

M

/ C R ^

0.4 1.2 0.5 0 2 0.701

0.3 1.2 0.5 0 8 0

.64 4

0.2 1.5 0 5 7 8 0 6 5 6

0.5 1.2 0.5 8 0 0.7 34

0.3 1.5 0.6 0 8 0.712

0.1 1.8 0.6 8 8 0.64 1

0.2 1.2 0.6 8 9 0

.5 3 5

0.2 1.8 0 7 2 9 0.7 15

0.4 1.5 0 75 9 0.7 3 6

0.7 1.2 0.9 8 3 0.7 51

0.5 1.5 0.9 8 9 0.7 43

0.3 1.8 0.9 9 2 0

.7 30

0. 1 1.5 1.0 0 5 0.50 5

0.4 1.8 1.3 6 6 0.7 3 8

T he _gr ad ie nt v alu e s c alc ulated fo r b

5.2 D I S C U SS I ON:

5.2. 1 The Abs o rp ti o n Co e

ff

icien t:

T he R^ v alu e s fo r b

^^^ a r e mu ch low e r tha n the R v alu e s fo r b^^ a nd b^ ^ ^, T h is ind ic ate s

that w e ha v e be e n mu ch m o r e s u c c e s sful in e stimatin_g b

^ ^ , a nd b^ ^ ^ , v alu e s tha n b^i, ^

v alu es. T he low R

^

a nd gr ad ie nt v alu es fo r b ^^^ m

a_{y b}e du e to the r aw data, spe ci fi c al ly

the "E leme nt al Ca rbo n

M

a s s "

u s edin es ti matin_g the b

^^^ . To fu rthe r in v e stigate th is

po s si b i l it_{y p l}ots o f

M

e a s u r ed Zj

^^, v e r s u s "

E lemental Ca rbo n

M

a s s" w e r e made fo r

I

M

PR O V E a nd E F P V N data s ets r e s_pec tiv el y

(

s e e F i_gu r e 1 a nd F i gu r e 2

)

. Fi gu r e 1

show s a _gr adie nt v alu e o f 0.3 6 9 a nd a R

^

v alu e of 0.4 2 2.

F_{i g}ure 1. Co m pa riso n of Babs vs. E C lVI

y = 0 36 86x

(

I M P R O V E Da_ta Set

₎

R'

= 0 42 1 6

0 4 0 6 0 8

Mea s u r ed E C U {fig lm^₎

F i gu r e 2 show s a _gr adie nt v alu e of 0.0 9 0 a nd a R v alue of 0.0 31.

F igu r e 2. Co m

pa ris o n of B_abs vs E C M

y = o 08 99x _{(E F P V N D}ata Set

₎

R^ = _{0 03 1 3}

_ 0 3

^

0.25

\

0 2

i 0 15

£ 0 1

S 0 0 5

0 0.05 0 1 0 15 0 2 0 25 0 3 0 35 0 4

Mea s u red E C M(n g /m')

T he s e v alu e s a r e c e rtainl_y in the vicinit_y of the _gr adie nt a nd the R^ v alu e s obtain ed for

me a s u r ed v e r s u s c alc ulated b^^^ v alu e s. T h is r e s ult sho ul d n ot c ome a s a s u rpris e a s the

M

ie-A R

E S pr o_gr am rel ie s he a v i l y o n " Eleme ntal Ca rbo n

M

ass

"

to c alc ulate the b ^abs

v alu e.

In a r e c e n t a rticle in A tmo s_{p h}e ric En vir o nme nt, Huff ma n (19 9 6

)

shows a si m i la r tr e n d

with the l i g ht abs o rb in_g a e r o s ol

(

eleme ntal c a rbo n ma s s in o u r stud y

)

a nd the mea s u red

i>

„j„ in sp ite of the fa c t that the site s cho s e n fo r h is study we r e in the we ste r n Un ited

Stated r athe r tha n the Ea st. He su

gge sts that c o ntr a r_y to c ommo n bel ief, the r e a s o n

beh ind this is the wa_y the a v ai lab le c a rbo n dat a is inte r_pr eted in the I

M

PRO V E s_ystem

T he I

M

P R OVE s_ystem u s e_{s t}he rmal o_ptic al r ef le cta n c e

(

T O R

)

an al ysis to _pr o v i de 8

c a rbo n me a s u r eme nts w h ich r e_pr e s e nt amo u nts of ca rbo n e v olv ed at suc c e_{s s}iv _{e s t}e_ps in

tem_pe r atu r e. In the data ba s e o r

ga nic c a rbo n me a sur e_men_ts a re _{g i}ven a s 0 1, 0 2, 0 3, and

0 4. T he 0 1a nd 0 2 repres en t the low tem per atu r e o r

r e_pr e s e nt h i g h tem pe r atu r e o r_ga nic c a rbo n . Eleme ntal c a rbo n is s e

pa r ated into E l, E 2,

a nd E 3. T he E l a nd E 2 r epr ese nt the low tem pe r atu r e eleme ntal c a rbo n a nd E3

r e_pr e s e nts the h i g h tem_pe r atu r e eleme ntal c a rbo n . T he r e is als o a v alu e g iv e n fo r

p yr o l yz ed c a rbo n (P) betwe e n the o r_ga nic a nd the eleme ntal c a rbo n me a s u r eme nts In the

I

M

P R OVE data s_y stem a nd in o u r stud_y the li_ght abs o rbin_g c a rbo n, L A C (eleme ntal

c a rbo n ma s s, EC

M

in o u r study) is c alc ulated a s the s um of the E l, E 2, a nd E 3 min u s the

p yr ol yz ed c a rbo n

(

P

)

Howe v e r, a c c o rding to Huf f ma n th is is a n u nde r

-_{e s}tim_ati_{o n}

of the

LA C a nd he su_gge sts an alte r n ativ e c alc ulatio n method w he r e the l i_ght absorb in_{g p}a rts of

the h i_gh tem pe r atu r e o r_ga nic c a rbo n

(

0 4

)

a nd the _pyr ol yz ed c a rbo n is in c o r_po r ated in the

L A C c alc u la tio n. In h is stud y

, Huffma n show s that by u sing h is e stimatio n of LA C a o n e

to o n e r elatio n sh i_{p b}etw e e n L A C a nd me a s u r ed abs o r_ptio n c o eff icie nt is _po s si b le

A c c o rd in_g to h is stud y LA C sho ul d be c alc ulated u sin_gthe fol lowin_{g f}o rmula_;

LA C = _{0 4} + E l + E 2 - 0

.2 P

r athe r tha n L A C = _{E l} + E 2 + E 3- P

W

_e b_el i_{e v e} th_at th i_s m_od i f i_{c a}ti_{o n} t_o th_{e e}l_em

e ntal

c a rbo n ma s s in o u r stud y w o ul d _gr e atl_y i m pr o v e the e sti matio n of the &

^^^

v alu e s.

H owe v e r , du e to ti me c o n str aints th is mod ifi c atio n c o ul d n ot be c om pleted befo r e the

c om p letio n of th is the sis.

T he abo v e obs e r v ation s fo r c e u s to c o n si de r the ef fe c t of the b

^^^ v alu e o n the v alu e of

&_{„ ,} . T he b

^^ , v alu e is giv e n by;

K. ,

= _b

T he r efo r e, the pr ob lems e xpe rie n c ed w ith the b

^^^ a r e in cluded in the b^ ^ , . H owe v e r, the

wei g ht of the b

^^^ is about 2 0 pe r c e nt in IM P RO V E data w h ile o nl y abo ut 10 pe r c e nt in

E F P V N data. T h is ind ic ate s that altho u

g h we a r e n ot able to e stimate b

^^^ v alu e s wel l,

we c a n still e stimate b

^^ v alu e s quite w el l a s a ma

j

o rity of b^^ , v alu e s a r e mainl y

de_pe nde nt o n the v alu e of the b

^^ ^ , .

5.2.3 E

ff

e ct o

f

S ize D istr i butio n o n Esti mating Ex tinctio n and Sc at te ring

Co e

f f

icien ts :

Ba s ed o n the r e s ults obtain ed fr om the stud_y, the r e is n o cle a r ind ic atio n of a ny o n e

pa rtic ula r siz e _{d i}stributio n a s the be st to e stimate b

^ ^ ^ ,

a n_{d b}

^ ^ ^ v alu e s. Howe v e r, whe n

p lots of gr ad ie nt v e r s u s me a n d iamet er a r e a n al yz ed it is _po s si b le to s a_y that siz e

d istri butio n s of me a n diamete r betwe e n 0.2 to 0.4 w ith sta nda rd de v iatio n s of 1.2 a nd 1.5

giv e r e a s o n ab l_{y g}o o_de sti mate s

₍

with± 50 pe r c e nt de via_tio n fr om gr ad ie nt of u nit_y

)

of

both c o eff icie nts fo r both data s ets. T h is fa ct is il lu s tr ated in F i gur e s 3 a nd 4 for the

7 0

6 5

6 0 5 5

5 0

4 5 4 0 3 5

3 0

2 5 2 0

1 5

1 0

0 5

0 0

0 0

7 0 6 5

1 0

0 5

0 0

0 0

F i gu r e 3. Gr ad ie nt of be xt v s. Me a n D ia me te r

(

I M P R O V E Data Set

)

JL

^

_M

-3 e

HiiH

-\ }

-5^

t r

x S U = 1

n

0 1 0 2 0 3 0 4 0 5 0 6 0 7

Me a n d iamete r, dg (^m )

F i_gu r e 4. Gr ad ie nt of b_{s c at} v s . Me a n D iam ete r

(

I M P ROV E Data Set

)

-i i

-i r

-^ e

^ e

-t i¬

l l

0 1 0 2 0 3 0 4 0 5 06 0 7

7 0 65 6 0 5 5 5 0 4 5 4 0 3 5 3 0 2 5 2 0 1 5 1 0 05 00

7 0 6 5 6 0 5 5 5 0 4 5 4 0 3 5 30 2 5 2 0 15 1 0 05 00

F i gu r e 5. Gr ad ie n t o f be xt v s. Me a n D iam ete r

(

E F PV N Data Set

)

-^ h -_{£ J}

-0 1 0 2 0 3 0 4 0 5 0 6

Me a n Diamete r, dg(^m)

F i_gu r e 6. G r ad ie nt o f b_{s c at} v s . Me a n D iam ete r

(

E F PV N Data Set

₎

-m

0 1 0 2 0 3 0 4 0 5 06

Me a n D iamete r,d g(^m)

^ 1

□ S D = _{1 5}

0 7

♦ S D= 1 2

d S D= 1 5

>k SD = 1 8

-I ]

07

T he s e siz e d istri butio n s

(

me a n d iamete r 0.2 to 0 4 a nd sta nda rd de viatio n 1.2 to 1.5) a r e

with in the a c c umulatio n mode, wh ich is ac cept ed t o be predom in antl y respo nsi b le fo r the

ex tin c tio n of li_ght in the atmos_pher e It is als o hel p ful _{t o p}oint o ut that du rin_g sho rt te rm

mea su r ed simi la r siz e d istr ibu tion _pa r ame te r s (Z ha n_g, et al , 1 9 9 4, S loan e, at al , 1 9 9 1,

W

a_{g g}o n e e r, et al., 19 81

)

. In a ny c a se, it ap pe a rs that a s long a s a pa rtic ulate siz e

distri butio n lie s w ithin the r a n_ge me a n d iamete r 0.2 to 0 4 |j,m a nd the sta nda rd de v iatio n

5.2.4 Othe r F a cto r s tha t

M

ay E

f f

e ct Ac c u r a cy o

f

the Estimate s o

f

the Co e

f f

icie n ts :

Fol low in_g the s e _pr el imin a r_y r e s ults, it wa s de ci ded to fu rthe r a n alyz e the I

M

P R OV E data

r e s ults fo r the siz e d istributio n of me a n d iamete r 0.3 [im a nd sta nda rd de viatio n 1.5. T his

siz e d istributio n a nd data s et w e r e cho s e n a s it r e s ulted in clo s e e sti mate s ₍Gr adie n t =

0.9 17) of the me a s u r ed s c at te ringc o ef f icie nts a nd the I

M

P R OV E data s et c o ntain ed mo r e

points fo r in v e st_{i g}atio n tha n the E F PV N data ba s e. T h is an alysis wo ul d pr o v i de a cha n c e

to s tud y the ef fe cts of fa cto r s o the r tha n siz e d istri butio n in e sti matin_g the e xtin ctio n,

s c at te rin_g, a nd abs o rptio n c o ef fi cie nts T he c rite ria u s ed to s epa r ate the data a nd

c o r r e s_po nd in_{g g}r ad ie nt a nd c o r r elatio n c o efficie nt v alu e s a r e _giv e n below:

Gr ad ie nt=

M

_{/ C R}^

Relativ e Humid it_y < 70 % 1 018 0.8 63

Relativ e Hum i d it_y > 7 0 % 0.78 5 0.7 97

T otal A er o s ol M a s s < 1_{0 p g} 1.0 7 2 0.9 9 0

10 ^ g <Total A e r o s ol

M

a s s < 2 0 ^i_g 0.8 7 1 0.3 8 2

To tal Aer o s ol

M

ass > 2 0 \x_g 0.9 3 5 0.5 3 6

Su_{l f}u r

M

a s s < 1 _}X_g 0.97 8 0.0 64

1 _^i_g < Sul fu r

M

a s s < 2 |J,g 0.832 0.2 37

Sulfu r

M

a s s > 2 _fi_g 0 9 3 9 0.61 3

Lo c atio n :

G. Smok y Mts. N P 1.0 04 0.8 61

M

am moth Ca v e NP 0.5 94 0.828

Ac ad ia N P 0 6 8 7 0.4 9 4

Dol l y Sods

W

il de r n e s s 0.8 07 0.8 01

As it c a n be s e e n fr om the abo v e r e s ults al l the fa cto r s _pr o vi de si m i la r _gr ad ie nts. T he

onl y n otic e ab le d i f fe r e n c e is _{g i}v e n b y d i f fe rent lo c atio n s. For instance,

"

M

am_mo th Cave

N P" _gr adie nt is the fu rthe rmo st fr om the o v e r a_{l l g}r ad ie nt. H owe v e r

+ _{5 0 p}e r c e nt ma r_{g i}n A ls o , it is impo rta nt to point o ut that th is pa rtic ula r lo c atio n ha s the

fewe st data _points in the I

M

PROV E data s et. The r efo r e, it is als o n ot po s si b le to

dete rm in e whethe r lo c atio n is in fa ct a n i m po rta nt fa cto r fo r o u r c alc u latio n s to e stimate

5.3 Re s u lts an d D is c u s sio n fo r the

M

o d i f ied In pu t Data

C

o n tain in g

No A

m m

o n iu

m

M

as s :

To _pr o vi de a n in si g ht into the ef fect of the am mo nium m a s s o n e sti mated e xtinc tio n ,

s c at te rin_g, a nd abs o rption c o ef f icient s the input data u s ed in the

M

ie -AR E

S pr o_gr am ha v e

be e n modi f ied. T he prin cipal cha nge in the a s s umptio n s a nd c alc ulatio n s u s ed fo r this

stu_{d y w} a s that the ammo nium ma s s w a s n ot c alc ulated a nd thu s w a s n ot in c luded in the

in_put dat a to the

M

ie-A R E S

pr o_gr am. T he cha nge s to the a s s um ptio n s a n d c alculatio n s

u s ed to c r e ate the o ri g in al in_put data c o ntainin_g the ammo nium ma s s a r e _giv e n below:

a) Or _ga nic Ca rbo n

M

a s s

(

O C

M

₎ is _giv e n b_y;

O C

M

= _TC

M

- _EC

M

T he s ame a s s um ptio n s a s the o rigin al in_put data w ith am mo nium ma s s a r e

v al i d in th is c a s e .

b₎ Sul fate

M

a s s ₍SO_^

M )

is _giv e n b_{y ;}

S 0

^

M

= ₃

_{

_S

_M

₎

T he s ame a s s um ptio ns a s the o ri_gin al in _put data w ith a_mmo nium ma s s a r e

v ali d in th is c a s e.

c₎ In e rt

M

a s s ₍/

M

)is _{g i}v e n _{b y;}

IM = T A

M

- _{S O}

In e rt ma s s is a s s umed to be c a rbo n ma s s a nd a n_y othe r fr a ctio n of the total

a e r o s ol ma ss una c c o u nted fo r b y the s ul fa te ma s s.

d

₎

I f I

M

is _gr e ate r tha n z e r o , r e al

{

R I R

)

a nd i magin a ry

(

/ ?/ /

)

r efr a ctiv e indic e s

a r e _{g i}v e n b_y;

R 1R = \5

-I

M

- _EC

_U

I

M

(

EC

M

2

V

I

M

R I I

I

M

T he s ame a s s um_ptio n s a s the o ri g in al in_put data w ith am mo nium ma s s a r e

v al i d in th is c a se.

In e rt De n sit_y, p_, , is giv e n by;

_ f I

M

- EC

M

- O C

M

\ f E C

M

+ O C

M

' ~

\ I

M

J \ I

M

The s ame as sum_ptio n s a s the o ri g in al in_put data w ith am mo nium ma s s a r e

v al i d in this c a s e

5.3.1 Re s u lts

f

o r I

M

P R O V E Data

(

w itho u t the A m monium

M

a s s

)

:

Tab le 3 shows the s um ma r_y of the c_alc ulated gr a_{d i}e nt a nd R^ v alu e_s f_or e a c h siz e

distr i butio n u s ed in e sti matin_g b

^„ , b

9

ammo nium ma s s). T he R v alu e s fo r b

^ ^ ^ r a nge fr om 0.8 2 2 to 0.8 4 0, w hi le the gr ad ie nt

v alu e s r a n _ge fr om 0.5 6 5 to 3.075. T he R

^

v alu e s fo r b

^ ^ ^, r a nge fr om 0.78 9 to 0.81 8

,

w h i le the _gr adie nt v alu e s r a n_ge fr om 0 8 06 to 3.3 3 3. T he R

'

v alu e s fo r &

^^^ r a nge fr om

0.4 20 to 0.626, w hi le the gr adie nt v alu e s r a nge fr om 1 254 to 198 0

Ac c o rdin _g to the s e r e s ults, the be st ( + 50 % de viatio n fr om gr ad ie nt o f u nity) e sti m ate of

b_{^ ^ ,} is obtain ed whe n the follow in_g siz e d istri butio n s a r e u s ed:

M

e a n D iamete r Std. De v iatio n Gr ad ie nt =

M

/ C R

~

0.4 1.2 0.5 6 5 0.8 3 3

0.3 1.2 0.57 0 0.8 37

0.2 1.5 0 6 5 6 0.8 3 8

0.5 1.2 0.6 6 6 0.829

0.3 1 5 0 6 93 0.8 3 3

0. 1 1.8 0.7 7 6 0.8 3 7

0.2 1.2 0.7 9 8 0.840

0.2 1.8 0 8 3 0 0 8 3 5

0.4 1.5 0.8 7 3 0.8 3 2

0.3 1.8 1.13 6 0.8 3 3

0.5 1.5 1.14 5 0 8 3 0

0. 1 1.5 1.182 0.840