Atmospheric Aerosol - American Chemical Society

2

The Application of Factor Analysis to Urban Aerosol Source Resolution

Downloaded by UNIV OF MICHIGAN ANN ARBOR on May 21, 2016 | http://pubs.acs.org Publication Date: October 13, 1981 | doi: 10.1021/bk-1981-0167.ch002

PHILIP Κ. HOPKE Institute for Environmental Studies, University of Illinois, Urbana, IL 61801

Among the multivariate statistical techniques that have been used as source-receptor models, factor analysis is the most widely employed. The basic objective of factor analysis is to allow the variation within a set of data to determine the number of independent causalities, i.e. sources of particles. It also permits the combination of the measured variables into new axes for the system that can be related to specific particle sources. The principles of factor analysis are reviewed and the principal components method is illustrated by the reanalysis of aerosol composition results from Charleston, West Virginia. An alternative approach to factor analysis, Target Transformation Factor Analysis, is introduced and its application to a subset of particle composition data from the Regional Air Pollution Study (RAPS) of St. Louis, Missouri is presented.

There has r e c e n t l y been a surge o f i n t e r e s t i n t h e development and a p p l i c a t i o n o f techniques t h a t permit the i d e n t i f i c a t i o n and q u a n t i t a t i v e apportionment o f sources o f urban a e r o s o l mass. Among these techniques a r e v a r i o u s forms o f a s t a t i s t i c a l method c a l l e d f a c t o r a n a l y s i s . S e v e r a l forms o f f a c t o r a n a l y s i s have been a p p l i e d t o the problem o f a e r o s o l source r e s o l u t i o n . These d i f f e r e n t forms p r o v i d e s e v e r a l d i f f e r e n t frameworks i n which t o examine a e r o s o l composition data and i n t e r p r e t i t i n terms o f source c o n t r i b u t i o n s . In an a e r o s o l sampling and a n a l y s i s program, a l a r g e number o f samples, n, a r e taken and analyzed f o r many elemental c o n c e n t r a t i o n s . Thus, a l a r g e matrix o f data i s o b t a i n e d . We can t h i n k o f p l o t t i n g the v a l u e s obtained i n a m u l t i d i m e n s i o n a l space. 0097-6156/81/0167-0021 $ 0 7 . 5 0 / 0 © 1981 American Chemical Society

Macias and Hopke; Atmospheric Aerosol ACS Symposium Series; American Chemical Society: Washington, DC, 1981.


22

ATMOSPHERIC

AEROSOL

I f we have determined m elements i n n samples, we could d i s p l a y these r e s u l t s as n p o i n t s i n an m-dimensional space. However, because some of the elements are emitted by the same source of p a r t i c l e s , t h e i r c o n c e n t r a t i o n s w i l l be r e l a t e d . To i l l u s t r a t e t h i s i d e a , suppose t h a t we have two sources of p a r t i c l e s , an i r o n foundry and automobile emissions, and that we measure three elemental c o n c e n t r a t i o n s , i r o n , l e a d , and bromine. I f we p l o t c o n c e n t r a t i o n s i n a t h r e e dimensional space, a p o i n t r e p r e s e n t s a sample as shown i n F i g u r e 1. In f a c t , the space necessary t o show a l l of the p o i n t s i s r e a l l y only two dimensional, s i n c e the amount of l e a d and bromine are d i r e c t l y interrelated. By a simple a x i s r o t a t i o n shown i n F i g u r e 2, i t can be seen t h a t a l l of the p o i n t s l i e i n a plane d e f i n e d by the i r o n a x i s and a l i n e t h a t d e f i n e s the lead-bromine r e l a t i o n s h i p . For more complex systems, f a c t o r a n a l y s i s w i l l help to i d e n t i f y the t r u e d i m e n s i o n a l i t y of the system being s t u d i e d and permit the d e t e r m i n a t i o n of these i n t e r e l e m e n t a l r e l a t i o n s h i p s . With t h i s i n f o r m a t i o n , i t i s then p o s s i b l e to determine the mass c o n t r i b u t i o n of the p a r t i c l e sources to the t o t a l observed mass.

Statistical

Background

In determining the q u a n t i t y of a p a r t i c u l a r element or compound i n a s p e c i f i c sample at a d e f i n i t e time, the i n v e s t i g a t o r has randomly removed a sample from a d i s t r i b u t i o n o f m a t e r i a l s present i n the environment. Then, by t a k i n g enough samples, the d i s t r i b u t i o n of that p a r t i c u l a r v a r i a b l e i n t h a t k i n d of sample can be d e s c r i b e d by s e v e r a l parameters commonly used f o r t h a t purpose i n c l u d i n g the mean value of the j t h v a r i a b l e n

\

= 1/n

Z

(1)

(x ) i i

j-l and

the second moment of the d i s t r i b u t i o n or the

2

s

n [ l / ( n - l ) | Z (x. j=l

=

1

1 J

- x,)

2

variance

(2)

3

where n i s the number of samples examined. The standard d e v i a t i o n i s simply the square r o o t of the sample v a r i a n c e . For some s t a t i s t i c a l procedures, i t i s necessary to remove the e f f e c t s of u s i n g d i f f e r e n t m e t r i c s i n d e s c r i b i n g the v a r i o u s v a r i a b l e s , so the v a r i a b l e s are put i n standard form. F i r s t , the d e v i a t i o n i s c a l c u l a t e d by s u b t r a c t i n g the mean value from each sample v a l u e .

d

x

x

ij = i j - j

(3)


Urban

Aerosol

Source

Resolution


HOPKE

Figure 2.

Artificial aerosol composition data after axes rotation


24

ATMOSPHERIC

The s t a n d a r d i z e d v a r i a b l e , z the d e v i a t i o n by the standard


X

AEROSOL

can be c a l c u l a t e d by d i v i d i n g deviation

X

ij

*" j

(4)

The s t a n d a r d i z e d value then has a mean v a l u e o f zero and a standard d e v i a t i o n o f u n i t y , and thus, a l l s t a n d a r d i z e d v a r i a b l e s have a mean v a l u e o f zero and a standard d e v i a t i o n o f 1. The i n i t i a l step i n the a n a l y s i s o f the data g e n e r a l l y r e q u i r e s the c a l c u l a t i o n o f a f u n c t i o n t h a t can i n d i c a t e the degrees o f i n t e r r e l a t i o n s h i p t h a t e x i s t w i t h i n the data. F u n c t i o n s e x i s t t h a t can p r o v i d e t h i s measure between e i t h e r the v a r i a b l e s when c a l c u l a t e d over a l l o f the samples or between t h e samples c a l c u l a t e d over the v a r i a b l e s . The most well-known o f these f u n c t i o n s i s the product-moment c o r r e l a t i o n coefficient. To be more p r e c i s e , t h i s f u n c t i o n should be r e f e r r e d t o as the c o r r e l a t i o n about the mean. The " c o r r e l a t i o n c o e f f i c i e n t " between two v a r i a b l e s , x.. n d x over a l l n samples i s g i v e n by a

E

=

ik

x

x

x

ir i>< kr k>

( MX..-X.)

utilizing

C

(x

k

2

M x

the s t a n d a r d i z e d

}

= ). A number of commonly used methods f o r determining the number of r e t a i n e d f a c t o r s have been reviewed (3)• In g e n e r a l the average e r r o r appears to be the most u s e f u l c r i t e r i o n where the number of f a c t o r s i s determined by the number t h a t are r e q u i r e d to reproduce the o r i g i n a l data w i t h i n the average root-mean-square u n c e r t a i n t y of the data. A f t e r the number of f a c t o r s have been determined, i t i s necessary t o i n t e r p r e t the f a c t o r s as p h y s i c a l l y r e a l s o u r c e s . For the a p p l i c a t i o n s o f t h i s approach to a e r o s o l source i d e n t i f i c a t i o n (4,6-10), the reduced s i z e matrix of e i g e n v e c t o r s was r o t a t e d i n such a way as to maximize the number of v a l u e s t h a t are zero or u n i t y . This rotation c r i t e r i o n , c a l l e d "simple s t r u c t u r e " i s d e s c r i b e d i n the appendix of r e f e r e n c e 4. A Varimax r o t a t i o n (21) i s o f t e n used t o achieve i t . However, simple s t r u c t u r e may not be the most u s e f u l c r i t e r i o n f o r environmental source r e s o l u t i o n s i n c e an element may be present i n an a e r o s o l sample because o f i t s emission by s e v e r a l sources. The v a r i a n c e should, t h e r e f o r e , be spread over s e v e r a l f a c t o r s r a t h e r than c o n c e n t r a t e d i n one. Prior Applications. The f i r s t a p p l i c a t i o n of t h i s t r a d i t i o n a l f a c t o r a n a l y s i s method was an attempt by B l i f f o r d and Meeker (6) t o i n t e r p r e t the elemental composition data obtained by the N a t i o n a l A i r Sampling Network(NASN) d u r i n g 1957-61 i n 30 U.S. c i t i e s . They employed a p r i n c i p a l components a n a l y s i s and Varimax r o t a t i o n as w e l l as a non-orthogonal r o t a t i o n . In both cases, they were not a b l e to e x t r a c t much i n t e r p r e t a b l e i n f o r m a t i o n from the data. S i n c e t h e r e i s a very wide v a r i e t y of sources of p a r t i c l e s i n 30 c i t i e s and o n l y 13 elements measured, i t i s not s u r p r i s i n g t h a t they were unable to p r o v i d e much s p e c i f i c i t y to t h e i r f a c t o r s . One i n t e r e s t i n g f a c t o r t h a t they d i d i d e n t i f y was a copper f a c t o r . They were unable to p r o v i d e a c o n v i n c i n g interpretation. I t i s l i k e l y t h a t t h i s f a c t o r r e p r e s e n t s the copper contamination from the brushes of the high volume a i r samples t h a t was subsequently found to be a common problem (_12). Hopke, et a l . (4) and Gaarenstroom, Perone, and Moyers (7) used the common f a c t o r a n a l y s i s approach i n t h e i r analyses of the Boston and Tucson area a e r o s o l composition, r e s p e c t i v e l y . In the Boston data, f o r 90 samples at a v a r i e t y of s i t e s , s i x common f a c t o r s were i d e n t i f i e d t h a t were i n t e r p r e t e d as s o i l , sea s a l t , o i l - f i r e d power p l a n t s , motor v e h i c l e s , r e f u s e i n c i n e r a t i o n and an unknown manganese-selenium source. The s i x f a c t o r s accounted f o r about 7&% o f the system v a r i a n c e . There was a l s o a high unique f a c t o r f o r bromine t h a t was i n t e r p r e t e d t o be f r e s h automobile exhaust. Large unique f a c t o r s f o r antimony and selenium were found. These f a c t o r s may p o s s i b l y r e p r e s e n t emission o f v o l a t i l e s p e c i e s whose c o n c e n t r a t i o n s do not covary with other elements emitted by the same source.



2.

HOPKE

Urban

Aerosol

Source

Resolution

29

In the study of Tucson ( 7 ) , a t each s i t e whole f i l t e r data were a n a l y z e d s e p a r a t e l y . They f i n d f a c t o r s t h a t are i d e n t i f i e d as s o i l , automotive, s e v e r a l secondary a e r o s o l s such as (NH^)pSO^ and s e v e r a l unknown f a c t o r s . They a l s o d i s c o v e r e d a f a c t o r t h a t r e p r e s e n t e d the v a r i a t i o n of elemental composition i n t h e i r a l i q u o t s of t h e i r neutron a c t i v a t i o n standard c o n t a i n i n g Na, Ca, K, Fe, Zn, and Mg. This f i n d i n g i l l u s t r a t e s one of the important uses of f a c t o r a n a l y s i s ; s c r e e n i n g the data f o r n o i s y v a r i a b l e s or a n a l y t i c a l a r t i f a c t s . Gatz (8) a p p l i e d a p r i n c i p a l components a n a l y s i s to a e r o s o l composition data f o r S t . L o u i s , Mo taken as p a r t of p r o j e c t METROMEX (13-14). Nearly 400 f i l t e r s c o l l e c t e d at 12 s i t e s were analyzed f o r up to 20 elements by ion-exchange x-ray f l u o r e s c e n c e . Gatz used a d d i t i o n a l parameters i n h i s a n a l y s i s i n c l u d i n g day of the week, mean wind speed, percent of time with the wind from NE, SE, SW, o r NW quadrants or v a r i a b l e , v e n t i l l a t i o n r a t e , r a i n amount and d u r a t i o n . At s e v e r a l s i t e s the i n c l u s i o n of wind data permitted the e x t r a c t i o n of a d d i t i o n a l f a c t o r s that allowed i d e n t i f i c a t i o n of s p e c i f i c p o i n t s o u r c e s . S i e v e r i n g and coworkers (£) have made e x t e n s i v e use of f a c t o r a n a l y s i s i n t h e i r i n t e r p r e t a t i o n of midlake a e r o s o l composition and d e p o s i t i o n data f o r Lake M i c h i g a n . S p e c i f i c Example . Lewis and Macias (J_0) have used a p r i n c i p a l components a n a l y s i s on s i z e f r a c t i o n a t e d a e r o s o l composition data from C h a r l e s t o n , West V i r g i n i a . They made the a n a l y s i s on both coarse and f i n e samples combined i n t o a s i n g l e data s e t and r e s o l v e d f o u r f a c t o r s : s o i l (with some automotive c o n t a m i n a t i o n ) , ammonium s u l f a t e , automotive e m i s s i o n s , and a mixed anthropogenic source. They were unable to s e p a r a t e a coal-combustion source d e s p i t e i t s apparent importance as i n d i c a t e d by a high average a r s e n i c c o n c e n t r a t i o n o f 26 ng/nr i n the fine fraction. However, they excluded a r s e n i c from the f a c t o r a n a l y s i s because of the i n c o n s i s t e n c i e s i n a r s e n i c v a l u e s obtained from f i v e s i m u l t a n e o u s l y o p e r a t i n g samplers. Because of the a b i l i t y o f f a c t o r a n a l y s i s to s o r t out the sources of v a r i a n c e , i t would be u s e f u l t o observe i f the sampling and a n a l y s i s v a r i a n c e c o u l d be separated from the v a r i a n c e r e s u l t i n g from source v a r i a t i o n . I t may be p o s s i b l e to o b t a i n a d d i t i o n a l i n f o r m a t i o n from the data o f Lewis and Macias by extending the a n a l y s i s t h a t they performed. A more complete r e s o l u t i o n of the sources might be p o s s i b l e i f the f i n e - and c o a r s e - s i z e d p a r t i c l e f r a c t i o n s are s e p a r a t e l y a n a l y z e d . A r e a n a l y s i s can be made s t a r t i n g from the c o r r e l a t i o n matrix they r e p o r t . The e i g e n v a l u e s f o r the separated f i n e and coarse f r a c t i o n s are g i v e n i n t a b l e 1. Lewis and Macias (JO) have used an a r b i t r a r y c u t o f f v a l u e of u n i t y to decide how many f a c t o r s to r e t a i n . C o n v i n c i n g arguments have been made a g a i n s t the use of t h i s c r i t e r i o n (J_5) and i t i s recommended t h a t i t not be adopted as the o n l y c r i t e r i o n employed. An a l t e r n a t i v e approach f o r s e l e c t i n g the number of r e t a i n e d f a c t o r s may be found by examing the p a r t i t i o n of v a r i a n c e a f t e r the o r t h o g o n a l rotation. I t can be argued t h a t a f a c t o r with a v a r i a n c e of l e s s than one c o n t a i n s l e s s i n f o r m a t i o n than d i d one of the o r i g i n a l v a r i a b l e s . However, s i n c e the o b j e c t i v e of the r o t a t i o n i s to r e d i s t r i b u t e the v a r i a n c e from the a r t i f i c i a l l y compressed s t a t e t h a t r e s u l t s from the m a t r i x d i a g o n a l i z a t i o n , i t appears to be u s e f u l to examine a number o f s o l u t i o n s with d i f f e r i n g numbers of r e t a i n e d f a c t o r s . The r o t a t e d s o l u t i o n s that c o n t a i n f a c t o r s with t o t a l v a r i a n c e l e s s than one can then be r e j e c t e d . For t h i s example, the f i n e f r a c t i o n r e s u l t s y i e l d


ATMOSPHERIC AEROSOL


30

e i g e n v a l u e s o f 7.35, 2.04, 1.28, 0.81, 0.49, and 0.39 f o r the f i r s t s i x factors. On the b a i s o f the e i g e n v a l u e o f one c r i t e r i o n , o n l y t h r e e f a c t o r s would be r e t a i n e d . However, i f the 4,5, and 6 f a c t o r s o l u t i o n s a r e examined a f t e r a Varimax r o t a t i o n , t h e v a r i a n c e s f o r the s i x f a c t o r s are 3.27, 3.06, 2.23, 2.11, 1.24, and 0.45. The s i x t h f a c t o r has no l o a d i n g above 0.42 and t h i s f a c t o r appears t o c o n t a i n no u s e f u l information. F o r f i v e f a c t o r s , a l l o f the f a c t o r s have a v a r i a n c e g r e a t e r than one and, t h e r e f o r e , t h i s s o l u t i o n was chosen. Five factors i s a l s o the c h o i c e f o r the coarse f r a c t i o n data as w e l l . The Varimax r o t a t e d r e s u l t s a r e presented i n Tables 2 and 3. For the f i n e f r a c t i o n , t h e f i r s t f a c t o r c l e a r l y r e p r e s e n t s (NH^^sOa as Lewis and Macias showed was a major c o n t r i b u t o r to the f i n e p a r t i c l e mass. The next f a c t o r i s s t r o n g l y a s s o c i a t e d with i r o n , c a l c i u m , and potassium and i s a t t r i b u t e d t o f i n e p a r t i c l e s o i l even though i t does have o n l y a moderate s i l i c o n l o a d i n g . The t h i r d f a c t o r has a h i g h e r s i l i c o n v a l u e and h i g h e r v a l u e s f o r z i n c , selenium and s t r o n t i u m . I f i t were simply a high z i n c f a c t o r , i t might have been a t t r i b u t a b l e to the z i n c contamination from the pump motor d e s c r i b e d by Lewis and Macias. S i n c e i t a l s o i n c l u d e s s i l i c o n , selenium and s t r o n t i u m , i t may r e p r e s e n t c o a l - f i r e d power p l a n t ash. The f o u r t h f a c t o r i s c l e a r l y automotive e m i s s i o n s . The low value f o r l e a d may a r i s e from the i n t e r f e r e n c e i n the l e a d d e t e r m i n a t i o n by t h e presence o f arsenic. The f i n a l f a c t o r has moderate l o a d i n g s f o r carbon and s t r o n t i u m and somewhat lower v a l u e s f o r s i l i c o n and l e a d . I t i s not c l e a r what type o f source t h i s f a c t o r r e p r e s e n t s although i t may i n d i c a t e an i n t e r f e r e n c e between the S r L x r a y with the S i K x r a y i n t e n s i t y t h a t has not been p r o p e r l y c a l c u l a t e d . For the coarse f r a c t i o n , t h e f i r s t f a c t o r c o n t a i n s the m a j o r i t y o f the v a r i a n c e and r e p r e s e n t s s o i l . There a r e h i g h l o a d i n g s f o r A l , S i , K, Ca, T i , Fe and S r . The second f a c t o r has high v a l u e s f o r bromine and lead. T h i s f a c t o r can be i d e n t i f i e d as motor v e h i c l e exhaust. I t does not have a l a r g e l o a d i n g f o r mass. I t would be expected t h a t most o f the motor v e h i c l e mass would be found i n the f i n e p a r t i c l e f r a c t i o n . The t h i r d f a c t o r has a high l o a d i n g f o r carbon, t h e f o u r t h a h i g h v a l u e f o r n i t r o g e n , and the f i f t h has a high value f o r s u l f u r . These f a c t o r s i n d i c a t e t h a t these elements do not covary with o t h e r elements. There are no c o r r e l a t i o n c o e f f i c i e n t s between these elements and any o f the o t h e r s t h a t a r e g r e a t e r than 0.33- The carbon f a c t o r shows a r e l a t i o n s h i p w i t h the t o t a l c o a r s e p a r t i c l e mass. The source o f the carbon f a c t o r i s not c l e a r . Carbonate l e v e l s would be expected t o be s m a l l and covary with c a l c i u m . Humic m a t e r i a l s i n s o i l s should vary w i t h the elements found i n the f i r s t f a c t o r . T h i s f a c t o r may account f o r p o l l e n s i n c e these samples were taken i n l a t e summer. Without a wider p r o f i l e o f elements, i t i s d i f f i c u l t t o be more s p e c i f i c . The n i t r o g e n and s u l f u r f a c t o r s may r e p r e s e n t the h i g h e r u n c e r t a i n t i e s i n these d e t e r m i n a t i o n s than f o r the f i n e p a r t i c l e f r a c t i o n where they were i n g r e a t e r abundance. Lewis and Macias i n d i c a t e t h a t t h e r e were d i f f i c u l t i e s i n the a n a l y s i s o f NH^ ,N0 " , and SOjj " because o f the s m a l l amounts p r e s e n t . The p o i n t made here i s t h a t care must be taken i n the a p p l i c a t i o n o f f a c t o r a n a l y s i s . +

T h i s form o f f a c t o r a n a l y s i s has the advantages o f being a b l e t o combine d i f f e r e n t types o f v a r i a b l e s i n the a n a l y s i s , o f i d e n t i f y i n g v a r i a n c e i n the data t h a t a r i s e s from sampling and/or a n a l y t i c a l procedure e r r o r s , and t o p r o v i d e a p r o s p e c t i v e o f the data without any a



1 2 3 4 5 6 7 8 9 10 11 12 13

Number

7.3539 2.0363 1.2792 .8093 .4911 .3865 .2176 .1925 .1031 .0847 .0283 .0167 .0009

Eigenvalue

Fine Fraction

56.57 15.66 9.84 6.23 3.78 2.97 1.67 1.48 .79 .65 .22 .13 .01

Percent of Total Variance

1 2 3 4 5 6 7 8 9 10 11 12 13

Number

8.0782 1.6549 1.4636 .7539 .4863 .1979 .1443 .0750 .0612 .0372 .0303 .0142 .0029

Eigenvalues

Coarse F r a c t i o n

Table 1. Eigenvalues f o r F a c t o r A n a l y s i s o f C o r r e l a t i o n M a t r i c e s o f Lewis and Macias(10)

62.14 12.73 11.26 5.80 3.74 1.52 1.11 .58 .47 .29 .23 .11 .02

Percent of T o t a l Variance



Variance

Mass C N Si S K Ca Fe Zn Se Br Sr Pb

Element

3.0683

.80401 .32538 .93182 .14505 .94296 .12131 .41555 .25148 .01888 .33974 .05867 .04830 .40661

1

3.0523

.53753 .38540 .09460 .53188 .20758 .75450 .75257 .93193 .21894 .39535 .10013 .01273 .24767

2

2.7330

.04317 .27853 .19196 .66091 .03713 .44304 .27398 .14420 .87835 .70750 .31768 .71226 .07840

3

1 .9721

.00595 .51289 .18688 .06791 .12538 .29126 .28949 .02478 .24047 .15974 .91986 .25545 .69987

4

Table 2. Orthogonally Rotated F a c t o r M a t r i x For Fine F r a c t i o n Aerosol

1.1439

.11566 .55826 .08505 .42558 .06226 .06142 .03917 .12719 -.03313 .19940 .03476 .61458 .43061

5


11.9697

.9506 .9067 .9562 .9265 .9532 .8689 .8995 .9693 .8787 .8376 .9617 .9528 .9081

Communality


.59072 .09152 .01945 .93172 .94557 -.13216 .94124 .80687 .92078 .92570 .39426 .89285 .45145

6.5355

Variance

1

Mass C N Al Si S K Ca Ti Fe Br Sr Pb

Element

2.1685

.24112 .07854 -.00751 .23120 .25601 .19330 .27771 .46949 .25257 .32771 .85928 .10506 .85422

2

1.5354

.65619 .95699 .14641 .18167 .12830 .10912 .09865 .18720 .10463 -.01863 .10428 .15669 .12101

3

1.1024

.21137 .09762 .97876 .04462 -.03498 -.12604 -.01809 -.13533 .04673 -.05571 .02940 .21470 -.01638

4

Table 3. Orthogonally Rotated F a c t o r Matrix For Coarse F r a c t i o n A e r o s o l

1.0951

-.21149 .18334 -.11491 -.05683 -.05162 .95375 -.00930 .09049 -.12433 -.08429 .22489 -.04084 .07036

5


12.4370

.9271 .9271 .9930 .9598 .9800 .9923 .9732 .9330 .9402 .9749 .9561 .8805 .9534

Communality

ATMOSPHERIC AEROSOL

Table 4.

Results


RAPS S t a t i o n 112,

of Dimensionality Tests J u l y and

August

Fine F r a c t i o n , J u l y 4th and

Factor 1 2 3 4 5 6 7 8 9

Eigenvalue 87. 4.9 2.0 0.2 0.1 0.04 0.02 0.02 0.01

1976

5th Excluded

Average Chi Square Exner % E r r o r 7.5 2.6 0.4 0.2 0.1 0.07 0.05 0.03 0.02

.304 .304 .070 .050 .037 .029 .023 .019 .015

197 197 123 98 73 69 69 67 53

Coarse F r a c t i o n

Factor 1 2 3 4 5 6 7 8 9

Eigenvalue 96. 2.4 0.6 0.29 0.19 0.07 0.03 0.02 0.01

Average Chi Square Exner % E r r o r 3.6 1.2 0.6 0.3 0.1 0.06 0.03 0.01 0.01

.216 .125 .089 .064 .040 .028 .019 .013 .009

73 50 45 41 35 33 28 23 22


2.

HOPKE

Urban

Aerosol

Source

Resolution

35

p r i o r i knowledge of the system under study. T h i s approach has the disadvantages of being unable to q u a n t i t a t i v e l y a p p o r t i o n the a e r o s o l mass among the v a r i o u s sources or to p r o v i d e the elemental c o n c e n t r a t i o n p r o f i l e s of the sources. In order to overcome these d i f f i c u l t i e s , an a l t e r n a t i v e approach to f a c t o r a n a l y s i s has been employed and w i l l subsequently be d e s c r i b e d .


Target T r a n s f o r m a t i o n F a c t o r A n a l y s i s Method D e s c r i p t i o n . By employing a d i f f e r e n t approach i t becomes p o s s i b l e to p r o v i d e a q u a n t i t a t i v e apportionment of a e r o s o l mass. The procedure d i f f e r s from t h a t used above i n s e v e r a l important ways. F i r s t , the c o r r e l a t i o n about the o r i g i n i s employed as the measure of interrelationship. Because the mean value i s no l o n g e r s u b t r a c t e d from the raw data v a l u e , i t i s p o s s i b l e to produce a r e s u l t i n the form o f e q u a t i o n 16. The second d i f f e r e n c e i s t h a t the c o r r e l a t i o n s between samples are c a l c u l a t e d r a t h e r than the c o r r e l a t i o n s between elements. In the terminology of Rozett and Peterson O ) , the c o r r e l a t i o n between elements would be an R a n a l y s i s while the c o r r e l a t i o n between samples would be a Q analysis. Thus, the a p p l i c a t i o n s of f a c t o r a n a l y s i s d i s c u s s e d above are R a n a l y s e s . Imbrie and Van Andel (J_6) and Miesch (J_7) have found Q-mode a n a l y s i s more u s e f u l f o r i n t e r p r e t i n g g e o l o g i c a l d a t a . Rozett and Peterson M ) compared the two methods f o r mass s p e c t r o m e t r i c data and concluded t h a t the Q-mode a n a l y s i s p r o v i d e d more s i g n i f i c a n t informtion. Thus, a Q-mode a n a l y s i s on the c o r r e l a t i o n about the o r i g i n m a t r i x f o r c o r r e l a t i o n s between samples has been made (18,19) f o r a e r o s o l composition data from Boston and S t . L o u i s . The matrix i s d i a g o n a l i z e d i n the same manner as d e s c r i b e d above. In the R-mode a n a l y s i s , the A m a t r i x i s obtained and the F m a t r i x i s c a l c u l a t e d from the data and the A m a t r i x . In the Q-mode a n a l y s i s the F m a t r i x i s i n i t i a l l y obtained and the A m a t r i x i s c a l c u l a t e d . A f t e r d i a g o n a l i z a t i o n , the number of f a c t o r s to be r e t a i n e d i s determined. The same problems of d e t e r m i n i n g the number of f a c t o r s t o r e t a i n are found i n t h i s model. An important area of a c t i v e r e s e a r c h i s the e x p l o r a t i o n o f more o b j e c t i v e methods of d e t e r m i n i n g the number o f f a c t o r s to be used. In order to i l l u s t r a t e t h i s procedure, an example o f the a n a l y s i s of a subset of data from the R e g i o n a l A i r P o l l u t i o n Study (RAPS) i s used. The s e t to be analyzed are the data from s i t e 112 ( F r a n c i s F i e l d on the Washington U n i v e r s i t y Campus) f o r the months o f J u l y and August, e x c l u d i n g J u l y 4 and 5. These samples are excluded because of h i g h contamination of s e v e r a l samples by the B i c e n t e n n i a l f i r e w o r k s d i s p l a y t h a t c o u l d be c l e a r l y d i s t i n g u i s h e d i n the data s e t . A f a c t o r has been i s o l a t e d f o r t h i s source even though i t o n l y impacts on t h r e e of the one hundred samples i n c l u d e d i n the a n a l y s i s . A more d e t a i l e d d e s c r i p t i o n of the data i s g i v e n by A l p e r t and Hopke (29). The t e s t s to determine the number of f a c t o r s t o r e t a i n are g i v e n i n t a b l e 4 f o r both the f i n e and coarse f r a c t i o n s . For the f i n e f r a c t i o n t h e r e appear to be three s t r o n g sources and two weaker ones. The coarse f r a c t i o n r e s u l t s do not g i v e a c l e a r i n d i c a t i o n o f the number of f a c t o r s and p a r a l l e l a n a l y s e s with 4 and 5 r e t a i n e d f a c t o r s were performed u n t i l i t was found t h a t 4 sources gave the best r e s u l t s . The major advantage of t h i s form of a n a l y s i s i s t h a t the data have r e t a i n e d t h e i r t r u e o r i g i n and the columns of the A m a t r i x can be a s s o c i a t e d with elemental p r o f i l e s of s p e c i f i c source t y p e s . The


ATMOSPHERIC AEROSOL

36

v e c t o r s obtained as a r e s u l t of the e i g e n v e c t o r a n a l y s i s are not directly interpretable. At t h i s p o i n t i t i s necessary t o r o t a t e the f a c t o r axes i n order to be able to a s s o c i a t e columns of the A m a t r i x w i t h s p e c i f i c source elemental c o n c e n t r a t i o n p r o f i l e s . This target t r a n s f o r m a t i o n r o t a t i o n was f i r s t developed by Malinowski and coworkers (20,21). A suggested source p r o f i l e i s p r o v i d e d and a l e a s t - s q u a r e s m i n i m i z a t i o n i s performed to r o t a t e a f a c t o r a x i s toward t h i s input t e s t vector. R e w r i t i n g equation 19 y i e l d s


X = ARR-'F

(20)

where AR c o n t a i n s r e p r e s e n t a t i o n s of the c o n c e n t r a t i o n p r o f i l e s of the r e a l sources and R~'F are the c o n t r i b u t i o n s of these sources to each sample. A r o t a t i o n v e c t o r , r , a column of matrix R, i s found by u s i n g a l e a s t - s q u a r e s f i t to a p o s s i b l e t e s t v e c t o r b. The v e c t o r may be c a l c u l a t e d by

r

= (A^A)-

1

A^b

(21)

where A i s the transpose of A and W i s a weighting m a t r i x . The weighting matrix W i s a d i a g o n a l matrix w i t h the d i a g o n a l terms being the elemental weights to be used i n t h i s l e a s t - s q u a r e s f i t . The elemental weights t h a t can be used are any t h a t r e p r e s e n t the s t a t i s t i c a l v a r i a t i o n or c o n f i d e n c e i n the elemental data, e.g., the i n v e r s e of the square of the average experimental e r r o r , the v a r i a n c e of the elemental c o n c e n t r a t i o n s i n the data s e t , o r the error-weighted v a r i a n c e of the elemental c o n c e n t r a t i o n s . I f there i s t o be no weighting, the d i a g o n a l terms are simply s e t equal t o one. D e t a i l s of the d e r i v a t i o n of equation 2 i s g i v e n by Malinowski and Howery (20). While t r y i n g to r e s o l v e which sources are present i n the data, one s t a r t s with an i n i t i a l guess of the elemental composition of the source material. T h i s c o n c e n t r a t i o n p r o f i l e i s then used as the t e s t v e c t o r , b, i n equation 21. From the r o t a t i o n v e c t o r and b, a p r e d i c t e d v e c t o r , b', can be c a l c u l a t e d . The e r r o r observed between the o r i g i n a l t e s t v e c t o r b and the p r e d i c t e d t e s t v e c t o r b' g i v e s an i n d i c a t i o n as t o whether the t e s t v e c t o r i s a reasonable r e p r e s e n t a t i o n of a f a c t o r . Then b' can be used as the new i n i t i a l t e s t v e c t o r b and a new p r e d i c t e d b " can be c a l c u l a t e d . Thus, the o r i g i n a l b has been r e f i n e d to a b t h a t b e t t e r r e p r e s e n t s the data. C o n t i n u i n g i n t h i s manner, one can i t e r a t e the i n i t i a l guess of b toward a b' t h a t i s much more r e p r e s e n t a t i v e of the s p e c i f i c sources f o r t h a t p a r t i c u l a r data s e t . One of the c l a i m s of f a c t o r a n a l y s i s i s t h a t a minimum of p r i o r knowledge i s r e q u i r e d , yet the t a r g e t t r a n s f o r m a t i o n r o t a t i o n begins with an i n i t i a l t e s t v e c t o r . The q u e s t i o n now a r i s e s , how good must the i n i t i a l t e s t v e c t o r be? Must the i n i t i a l v e c t o r be a c l o s e approximation to the r e s u l t b or can a simple i n i t i a l guess f o r b be used? To answer t h i s q u e s t i o n , Roscoe and Hopke (22) made a comparative study on a p r e v i o u s l y source r e s o l v e d s e t of g e o l o g i c a l data (23). They found that source composition p r o f i l e s c o u l d be developed by t h i s i t e r a t i v e process from simple i n i t i a l t e s t v e c t o r s t h a t c o n s i s t e d of zero values f o r a l l but one element and u n i t y f o r t h a t s i n g l e element. They obtained e x c e l l e n t agreement between the source p r o f i l e s developed by the t a r g e t t r a n s f o r m a t i o n r o t a t i o n (22) and those g i v e n by the



2.

HOPKE

Urban

Aerosol

Source

Resolution

37

e a r l i e r r e p o r t (23) as shown i n t a b l e 5. Thus, the input t e s t v e c t o r s s u p p l i e d appear t o speed the convergence but do not n e c e s s a r i l y s e t the f i n a l values. I t should be noted that i n many i n s t a n c e s the u l t i m a t e source p r o f i l e s a r e deduced from the simple v e c t o r s t h a t a r e unique f o r a s i n g l e element and not from other t e s t v e c t o r s . I t does not appear t h a t a p r i o r i knowledge of the d e t a i l e d source v e c t o r s f o r a p a r t i c u l a r study area a r e r e q u i r e d but f u r t h e r s t u d i e s o f t h i s q u e s t i o n a r e i n progress. For any o f the t e s t v e c t o r s , the nature o f the a n a l y s i s i s such t h a t the r e l a t i v e c o n c e n t r a t i o n s o f the elements a r e p r e d i c t e d , but the a b s o l u t e c o n c e n t r a t i o n s a r e n o t . I f the t o t a l mass o f the a e r o s o l sample has been measured, i t i s then p o s s i b l e t o determine a s e t o f s c a l i n g f a c t o r s . The F v a l u e s f o r a sample a r e r e l a t i v e measures o f the mass c o n t r i b u t i o n o f each source t o that sample and, t h e r e f o r e , the F v a l u e s should sum t o the t o t a l mass i f they have been p r o p e r l y s c a l e d . The c o n c e n t r a t i o n o f an element can be r e w r i t t e n as

P

P

a

ik

such that the mass o f the j t h sample i s g i v e n by

M.

s

E b F k

(23)

k j

The c o l l e c t i o n o f measured M. v a l u e s and the c a l c u l a t e d F^. v a l u e s can then be used i n a m u l t i p l e r e g r e s s i o n a n a l y s i s t o determine the b^ v a l u e s . This a n a l y s i s provides several t e s t s . F i r s t , no c o n c e n t r a t i o n value, ( a / b ) , should be g r e a t e r than 100$. The sum o f these values over the m elements should be

w

X

o

> H

£


2.

HOPKE

Urban

Aerosol

Source

39

Resolution

Table 6. Refined Source P r o f i l e s . (mg/g) RAPS S t a t i o n 112, J u l y and August 1976 Fine F r a c t i o n , J u l y 4 t h and 5th Excluded

Element Al Si S CI K Ca Ti Mn Fe Ni Cu Zn Se Br Sr Ba Pb

Motor Vehicle 5. 0.0 0.02 2.4 1.4 11. 0.0 0.0 0.0 0.08 0.6 0.8 0.1 30. 0.09 0.7 107.

Sulfate

Flyash/ Soil

Paint

1.1 1.9 240. 1.1 1.6 0.0 0.7 0.0 1.1 0.04 0.01 0.0 0.1 0.03 0.01 0.05 6.5

53. 130. 19. 0.0 15. 16. 2.5 0.7 36. 0.042 0.0 0.0 0.001 2.5 0.15 0.07 5.

0.0 0.0 6. 4.6 5.7 34. 110. 4.8 90. 0.011 0.0 3.7 0.2 0.0 0.1 28. 0.0

Refuse 0.0 7. 0.0 22. 48. 1.2 0.0 8.6 36. 0.7 8.7 65. 0.2 0.05 0.005 0.5 46.


ATMOSPHERIC AEROSOL

40

motor v e h i c l e exhaust w i l l vary from c i t y to c i t y and i s dependent on the r a t i o o f leaded g a s o l i n e to unleaded and diesel-powered v e h i c l e s . The c a l c u l a t e d source p r o f i l e f o r the r e f u s e f a c t o r , w i t h high c o n c e n t r a t i o n s of c h l o r i n e , z i n c , and l e a d , i s s i m i l a r to t h a t measured by Greenberg and coworkers(25) f o r the N i c o s i a M u n i c i p a l I n c i n e r a t o r near Chicago. However, Greenberg et a l found t h a t c h l o r i n e , z i n c , and l e a d c o n c e n t r a t i o n s of 27% 11%, and 7%, r e s p e c t i v e l y . In the present study, the c h l o r i n e c o n c e n t r a t i o n i s only 2% and the z i n c and l e a d c o n c e n t r a t i o n s are h a l f those found by Greenberg. The lower c a l c u l a t e d c o n c e n t r a t i o n s may r e s u l t from the combining of both r e f u s e - i n c i n e r a t o r and l e a d / z i n c - s m e l t e r emissions i n t o a s i n g l e f a c t o r . In the paint-pigment component, the t i t a n i u m and i r o n c o n c e n t r a t i o n s are s i m i l a r to those c a l c u l a t e d by Dzubay (27). The nature of the c a l c u l a t e d s o i l / f l y a s h f a c t o r i s more l i k e t h a t of c o a l f l y a s h than s o i l , though the a b s o l u t e c o n c e n t r a t i o n s of the major elements are l e s s than those r e p o r t e d by Gladney (20) and F i s h e r , e t a l . (29) f o r c o a l flyash. Because of the s i m i l a r i t y of t h e i r elemental p r o f i l e s , d i f f e r e n t i a t i n g s o i l and c o a l f l y a s h i s a problem o f t e n encountered i n a e r o s o l source r e s o l u t i o n s . Coal f l y a s h emissions are expected t o c o n t r i b u t e more to the f i n e f r a c t i o n while c r u s t a l m a t e r i a l should be found i n the coarse f r a c t i o n . Thus, we conclude t h a t t h i s f a c t o r i s p r i m a r i l y the r e s u l t of c o a l - b u r n i n g power p l a n t emissions. Reliable data f o r elements, such as a r s e n i c , would be needed t o c l e a r l y d i f f e r e n t i a t e the c o n t r i b u t i o n s of s o i l and c o a l f l y a s h .


9

For the coarse f r a c t i o n , the t a r g e t t r a n s f o r m a t i o n i n d i c a t e d the presence of a s u l f a t e f a c t o r , a paint-pigment f a c t o r , and two c r u s t a l f a c t o r s ; an a l u m i n o - s i l i c a t e type and a limestone or cement source. In an e a r l i e r f a c t o r a n a l y t i c a l study of a e r o s o l sources i n the S t . L o u i s a r e a , Gatz (8) found the element calcium to be a s s o c i a t e d with o t h e r than c r u s t a l sources. The high calcium l o a d i n g at one s i t e was a t t r i b u t e d to cement p l a n t s i n the sampling a r e a . Kowalczyk (30) r e p o r t s f i n d i n g a potassium to calcium r a t i o of 0.8 i n plume a e r o s o l s c o l l e c t e d over a cement p l a n t near Washington, D. C. The uniqueness t e s t f o r calcium shows no s t r o n g c o r r e l a t i o n between c a l c i u m and potassium, i n d i c a t i n g the o r i g i n s of the source are probably c r u s t a l . The r e f i n e d source p r o f i l e s t h a t best reproduced the coarse f r a c t i o n are l i s t e d i n t a b l e 7. The c a l c u l a t e d p r o f i l e s of the two c r u s t a l components f o l l o w those of Mason (3]_), though the calcium c o n c e n t r a t i o n o f 20% i n the limestone f a c t o r i s l e s s than the r e p o r t e d v a l u e . The p a i n t pigment p r o f i l e s t r o n g l y resembles t h a t c a l c u l a t e d f o r the f i n e - f r a c t i o n data. The only major d i f f e r e n c e i s t h a t u n l i k e the f i n e f r a c t i o n , the c o a r s e - f r a c t i o n p r o f i l e does not a s s o c i a t e barium with the paint-pigment f a c t o r . The c a l c u l a t e d s u l f u r c o n c e n t r a t i o n i n the c o a r s e - f r a c t i o n s u l f a t e f a c t o r i s much l e s s than t h a t i n the f i n e - f r a c t i o n and there are s i z a b l e c o n c e n t r a t i o n s of elements such as aluminum, i r o n , and l e a d not found i n the f i n e - f r a c t i o n p r o f i l e . The o r i g i n of t h i s f a c t o r i s not c l e a r although as d e s c r i b e d e a r l i e r a p o s s i b l e e x p l a n a t i o n i s that a s m a l l p a r t of the s u l f a t e p a r t i c l e s i n the f i n e f r a c t i o n ended up i n the coarse samples. Table 8 summarizes the average elemental c o n c e n t r a t i o n s along with the average observed c o n c e n t r a t i o n s f o r the f i n e f r a c t i o n . The major elements, A l , S i , S, K, Ca, Fe, and Pb are f i t very c l o s e l y . The o v e r a l l f i t f o r the remaining elements i s a l s o f a i r l y good. However, the average p o i n t - b y - p o i n t e r r o r s i n the reproduced data range up t o a v a l u e of 350% f o r barium. Note t h a t d e s p i t e the l a r g e p o i n t - b y - p o i n t



2.

HOPKE

Urban

Aerosol

Source

Resolution

41

T a b l e 7. R e f i n e d S o u r c e P r o f i l e s . (mg/g) RAPS S t a t i o n 112, J u l y and A u g u s t 1976 Coarse F r a c t i o n Element Al Si S CI K Ca Ti Mn Fe Ni Cu Zn Se Br Sr Ba Pb

Soil 71. 274. 4.9 1.4 19. 40. 0.0 0.8 40. 0.01 0.0 0.0 0.01 0.5 0.2 0.6 1.5

L i m e s t one 30. 150. 0.0 16. 15. 188. 1.5 1.6 34. 0.2 0.6 4.2 0.02 3.1 0.3 0.7 11.

Sulfate 28. 0.0 90. 3.6 9.3 0.08 0.0 1. 43. 0.2 0.9 4.3 0.13 3.8 0.2 0.4 13.

Paint 5. 0.0 37. 6.9 0.0 25. 128. 1.2 65. 0.06 0.0 0.3 0.001 1.3 0.1 3.2 6.7



23. 0.0 0.09 11. 6. 49. 0.0 0.0 0.0 0.4 2.6 3.6 0.4 135. 0.4 3.1 480.

Motor Vehicle

21. 36. 4570. 21. 30. 0.0 12. 0.0 21. 0.8 0.2 0.0 2.1 0.5 0.2 0.9 120.

Sulfate 170. 420. 62. 0.0 49. 52. 8. 2.3 120. 0.1 0.0 0.0 0.0 8.2 0.5 0.2 16.

0.0 0.0 2. 2.0 2.4 14. 46. 2.0 37. 0.0 0.0 1.5 0.1 0.0 0.1 12. 0.0

Flyash/ Soil Paint 0.0 9. 0.0 27. 60. 1.5 0.0 11. 45. 0.9 11. 81. 0.2 0.1 0.0 0.6 57.

Refuse 230 470 4630 61 150 120 66 15 220 2.1 14 86 2.8 140 1.2 16 680

Total Predicted

Average point-by-point

error i n p r e d i c t e d and measured

data.

U n c e r t a i n t y i s the standard d e v i a t i o n of the mean value.

Al Si S CI K Ca Ti Mn Fe Ni Cu Zn Se Br Sr Ba Pb

Element

Fine F r a c t i o n

Samples From J u l y 4 t h and 5th Excluded

Table 8. Summary of Mass C o n t r i b u t i o n s . (ng/m ) RAPS S t a t i o n 112, J u l y and August 1976

200 + 24 450 + 59 4360 + 320 80 + 9 150 + 9 110 + 10 64 + 13 17+3 220 + 19 2.2 + 0.2 15 + 2 75 + 8 2.7 + 0.2 132 + 8 1.1 + 0.1 15+4 720 + 53

Total* Observed


29 15 7 163 28 53 260 122 15 106 210 77 89 27 88 353 6

Average % Error

2.

HOPKE

Urban

Aerosol

Source

Resolution

43


e r r o r , the average p r e d i c t e d and observed c o n c e n t r a t i o n s are very c l o s e , 16 and 15 ng/m r e s p e c t i v e l y . The d i s p a r i t y i s , i n p a r t , due t o the tendency of the t a r g e t t r a n s f o r m a t i o n r o t a t i o n to produce p r o f i l e s t h a t r e p r e s e n t the average composition of each source. Thus, even though the average f i t f o r barium i s very good, the p o i n t - b y - p o i n t e r r o r i n d i c a t e s t h a t t h i s element has not been w e l l reproduced. The problem i s compounded by the l a r g e number of v a l u e s below d e t e c t i o n l i m i t s f o r many of the l e s s abundant elements. The presence of source components t h a t are not r e s o l v e d can l e a d to the u n d e r p r e d i c t i o n of elements. Table 9 summarizes the mass c o n t r i b u t i o n s f o r the coarse f r a c t i o n . Here, a l l the elements are f i t w e l l . A comparison of the p r e d i c t e d and measured masses f o r each sample i s another i n d i c a t o r o f the q u a l i t y of f i t produced by the t a r g e t transformation. The average d e v i a t i o n s i n the mass p r e d i c t i o n s were 16$ f o r the f i n e - f r a c t i o n data and 12% f o r the c o a r s e . The very good f i t to the mass p r e d i c t i o n s i n d i c a t e s t h a t most of the undetermined elements such as carbon and n i t r o g e n c o r r e l a t e f a i r l y c l o s e l y with the measured elements. F i g u r e 3 summarizes the average mass c o n t r i b u t i o n f o r each source to the t o t a l measured sample mass. The low percentage of unaccounted sample mass i s expected i n t h i s type of a n a l y s i s s i n c e the r e g r e s s i o n f i t c a l c u l a t e s s c a l i n g f a c t o r s so as t o minimize the o v e r a l l d i f f e r e n c e between the measured and p r e d i c t e d sample mass. However, p o s s i b l e u n c e r t a i n t i e s i n the s c a l i n g f a c t o r s of the l e s s important s o u r c e s , i . e. r e f u s e , paint-pigment, and f l y a s h , c o u l d r e s u l t i n l a r g e u n c e r t a i n t i e s i n the c a l c u l a t e d c o n c e n t r a t i o n s of these s o u r c e s . Secondary s u l f a t e a e r o s o l p a r t i c l e s account f o r 64% o f the mags of the f i n e - f r a c t i o n data, an average c o n c e n t r a t i o n of about 19 g/m^. Motor v e h i c l e emissions account f o r another 15%. The measured l e a d c o n c e n t r a t i o n i s d i v i d e d among the r e f u s e and motor v e h i c l e f a c t o r s . Here the l e a d c o n t r i b u t i o n i s 70% from motor v e h i c l e emissions and 10% from r e f u s e i n c i n e r a t o r s . In the coarse f r a c t i o n , the two c r u s t a l components account f o r 80% o f the t o t a l mass. T h i s approach has c l e a r l y allowed the r e s o l u t i o n of the sources with r e s u l t s t h a t appear to be very c o m p e t i t i v e to the chemical mass balance method. However, i t was not necessary t o make i n i t i a l assumptions r e g a r d i n g the number of p a r t i c l e sources or t h e i r elemental composition. A d d i t i o n a l s t u d i e s need to be made to t e s t the accuracy and p r e c i s i o n w i t h which such r e s o l u t i o n s can be made.

Conclusions I t i s c l e a r t h a t s e v e r a l forms of f a c t o r a n a l y s i s can be very u s e f u l i n the i n t e r p r e t a t i o n of a e r o s o l composition data. The t r a d i t i o n a l forms of f a c t o r a n a l y s i s t h a t are widely a v a i l a b l e permit the i d e n t i f i c a t i o n of sources, the s c r e e n i n g of data f o r n o i s y r e s u l t s , and the i d e n t i f i c a t i o n of i n t e r f e r e n c e s or a n a l y t i c a l procedure problems. I t i s important, however, t h a t new users of these techniques take the time to develop a l i t t l e understanding of the s t r e n g t h s and l i m i t a t i o n s of them. I t i s very easy to employ a standard s t a t i s t i c a l package with



1365. 5266. 94. 27. 365. 769. 0.0 15. 769. 0.2 0.0 0.0 0.2 8.8 3.8 11. 29.

Al Si S CI K Ca Ti Mn Fe Ni Cu zn Se Br Sr Ba Pb

Average

111. 0.0 356. 14. 37. 0.3 0.0 4.0 168. 0.8 3.6 17. 0.5 15. 0.7 1.4 52.

Sulfate 125. 0.0 92. 17. 0.0 62. 320. 3.0 162. 0.1 0.0 0.7 0.0 3.2 0.3 8.0 17.

Paint

Fraction

1760 6630 543 200 540 2540 330 37 1410 3.2 9.4 56 0.9 55 7.2 27 197

Total Predicted

error i n predicted

a

1840 + 180 6400 + 580 490 + 32 210 + 213 540 + 50 2380 + 141 300 + 43 39 + 4 1470 + 158 3.6 + 0.4 8.9 + 0.8 56+6 0.7 + 0.04 51+3 7.9 + 0.8 27+3 193 + 11

Total Observed

data.

value. and m e a s u r e d

i s t h e s t a n d a r d d e v i a t i o n o f t h e mean

272. 1359. 0.0 145. 136. 1703. 14. 15. 308. 2.0 5.8 38. 0.2 28. 2.4 6.3 100.

Limestone

point-by-point

Uncertainty

Soil

Element

Coarse

T a b l e 9. Summary o f Mass C o n t r i b u t i o n s , (ng/nr) RAPS S t a t i o n 1 1 2 , J u l y and A u g u s t 1976

12 4 35 72 9 8 107 37 11 155 149 126 154 51 21 53 47

"1 b Average % Error



2.

HOPKE

Urban Aerosol

Source

45

Resolution

Figure 3. Average percent contribution of each source to the total average mass. The data are the fine- ((left) average mass = 29A fxg/m ) and coarse-fraction (fright,) average mass = 32.5 jxg/m ) samples from RAPS Station 112 for July and August 1976. 3

3


ATMOSPHERIC AEROSOL


46

standard options without understanding the e x p l i c i t and i m p l i c i t assumptions that have thus been made. A new form of f a c t o r a n a l y s i s has been a p p l i e d to a e r o s o l source r e s o l u t i o n . I t r e q u i r e s that v a r i a b l e s that are not l i n e a r l y a d d i t i v e p r o p e r t i e s of the system be excluded. However, i t i s p o s s i b l e to i d e n t i f y the number of sources, t h e i r elemental composition and the amount of mass they c o n t r i b u t e to the ambient a e r o s o l . A major l i m i t a t i o n to the method i s the q u a l i t y of data. P a r t i c u l a r l y i f the r e g r e s s i o n approach i s to be used to determine s c a l i n g f a c t o r s , the t o t a l sample mass must be measured. A l s o the elemental a n a l y s i s should be s u f f i c i e n t l y complete to account f o r a r e l a t i v e l y high f r a c t i o n of the t o t a l mass observed i f a f a c t o r a n a l y s i s i s to be performed such t h a t c o n t r o l s t r a t e g i e s could be based on i t s r e s u l t s . Although i t appears that an e x c e l l e n t f i t to the S t . Louis data was obtained without the measurement of carbon or n i t r o g e n , i t would seem l i k e l y t h a t there i s a strong r e l a t i o n s h i p between N and S as (NH^pSOn and t h a t most of the carbon i n the summer months i s s t r o n g l y c o r r e l a t e d with other elements such as l e a d . The r e s u l t s of Macias and Chu (32) demonstrate that there i s a very s t r o n g c o r r e l a t i o n between elemental carbon and both l e a d and bromine i n S t . L o u i s . Large sources of u n c o r r e l a t e d carbon would l e a d to much poorer q u a l i t y r e s u l t s . I t i s , t h e r e f o r e , important i n the planning new a i r sampling programs to i n c l u d e the requirements of the endpoint s t a t i s t i c a l a n a l y s i s so that the f i n a l source r e s o l u t i o n w i l l have v a l i d i t y .

Acknowledgements I would l i k e to acknowledge the c o n t r i b u t i o n s of Daniel A l p e r t and Bradley Roscoe i n the development and c o n t i n u i n g e x p l o r a t i o n of f a c t o r a n a l y s i s . T h i s work has been supported i n part by the U n i v e r s i t y of I l l i n o i s Campus Research Board, the U. S. Environmental P r o t e c t i o n Agency (Contracts D6004NAEX and 68-02-3449 and Grant R808229) and the U. S. Department of Energy (Contract DE-AC02-80EV10403.A000).

Literature Cited 1.

Rozett, R. W.; Petersen, E. M. Methods of Factor Analysis of Mass Spectra, Anal. Chem., 1975, 47, 1301.

2.

Rozett, R. W.; Petersen, E. M. Classification of Compounds by the Factor Analysis of their Mass Spectra, Anal. Chem., 1976, 48, 817.



2.

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Aerosol

Source

Resolution

47

3.

Duewer, D. L . ; Kowalski, B. R.; Fasching, J . L. Improving the Reliability of Factor Analysis of Chemical Data by Utilizing the Measured Analytical Uncertainty, Anal. Chem., 1976, 48, 2002.

4.

Hopke, P. K.; Gladney, E. S.; Gordon, G. E . ; Zoller, W. H.; Jones, A. G. The Use of Multivariate Analysis to Identify Sources of Selected Elements in the Boston Urban Aerosol, Atmospheric Environ., 1976, 10, 1015.

5.

Cattell, R. B. "Handbook of Multivariate Experimental Psychology", Rand McNally: Chicago, 1966; 174.

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Blifford, J r . , I. H.; Meeker, G. O. A Factor Analysis Model of Large Scale Pollution, Atmospheric Environ., 1967 1, 147.

7.

Gaarenstroom, P. D.; Perone, S. P.; Moyers, J . L. Application of Pattern Recognition and Factor Analysis for Characterization of Atmospheric Particulate Composition in Southwest Desert Atmosphere, Environ. Sci. Technol., 1977, 11, 795.

8.

Gatz, D. F. Identification of Aerosol Sources in the St. Louis Area Using Factor Analysis, J . Appl. Met., 1978, 17, 600.

9.

Sievering, H.; Dave, M.; Dolske, D.; McCoy, P. Trace Element Concentrations over Mid-Lake Michigan as a Function of Meteorology and Source Region, Atmospheric Environ., 1980, 14, 39.

10. Lewis, C. W.; Macias, E. S. Composition of Size-Fractionated Aerosol in Charleston, West Virginia, Atmospheric Environ., 1980, 14, 185. 11. Kaiser, H. F. Computer Program for Varimax Rotation in Factor Analysis, Educational and Psychological Measurement, 1959, 19, 413. 12. Hoffman G. L . ; Duce, R. A. Copper Contamination of Atmospheric Particulate Samples Collected with Gelman Hurricane Samples, Environ. Sci. Technol., 1971, 5, 1134. 13. Changnon, S. A.; Huff, R. A.; Schickedenz, P. T.; Vogel, J . L. Summary of METROMEX, Volume 1: Weather Anomalies and Impacts, Illinois State Water Survey Bulletin 62, Urbana, IL, 1977. 14. Ackerman, B., et al.. Summary of METROMEX, Volume 2: Causes of Precipitation Anomalies, Illinois State Water Survey Bulletin 63, Urbana, IL, 1978. 15. Kaiser, H. F . ; Hunka, S. Some Empirical Results with Guttmans Stronger Lower Bound for the Number of Common Factors, Educational and Psychological Measurement, 1973, 33, 99.

American Chemical Society Library 1155 St. N. Aerosol W. Macias and Hopke;16th Atmospheric ACS Symposium Series; Washington, American Chemical Society: Washington, DC, 1981. D. C. 20036

48

ATMOSPHERIC AEROSOL

16. Imbrie, J.; Van Andel, T. H. Vector Analysis of Heavy-Mineral Data, Geological Soc. Amer. Bull., 1964, 75, 1131. 17. Miesch, A. T. Q-Mode Factor Analysis of Geochemical and Petrologic Data Matrices with Constant Row-Sums, U. S. Geological Survey Professional Paper 574-G, Washington, 1976.


18. Alpert D. J.; Hopke, P. K. A Quantitative Determination of Sources in the Boston Urban Aerosol, Atmospheric Environ., 1980, 14, . 19. Alpert, D. J.; Hopke, P. K. A Determination of the Sources of Airborne Particles Collected During the Regional Air Pollution Study, Atmospheric Environ., in press, 1981. 20. Malinowski E. R.; Howery, D. G. "Factor Analysis in Chemistry", John Wiley & Sons, Inc.: New York, 1980. 21. Weiner, P. H.; Malinowski, E. R.; Levinstone, A. R. Factor Analysis of Solvent Shifts in Proton Magnetic Resonance, J. Phys. Chem., 1970, 74, 4537. 22. Roscoe, Β. Α.; Hopke, P. K. Comparison of Weighted and Unweighted Target Transformation Rotations in Factor Analysis, Computers and Chemistry, in press. 23. Bowman, H. R.; Asaro, F . ; Perlman, I. On the Uniformity of Composition in Obsidians and Evidence for Magnetic Mixing, J. Geology, 1973, 81, 312. 24. Rheingrover, S. W. A Statistical Model for Titanium Pollution Transport and Dispersion in the Atmosphere of Saint Louis, M.S. Thesis, Florida State University, 1977. 25. Greenberg, R. R,; Gordon, G. E . ; Zoller, W. H. Composition of Particles from the Nicosia Municipal Incinerator, Environ. Sci. Technol., 1978, 12, 1329. 26. Dzubay, T. G.; Stevens, R. K.; Richards, L. W. Composition of Aerosols over Los Angeles Freeways, Atmospheric Environ, 1979, 13, 653. 27. Dzubay, T. G. Chemical Element Balance Method Applied to Dichotomous Sampler Data, Annals Ν. Y. Acad. Sci., 1980, 338, 126. 28. Gladney, E. S. Trace Elemental Emissions from Coal-Fired Power Plants: A Study of the Chalk Point Electric Generating Station, Ph.D Thesis, University of Maryland, 1974. 29. Fisher, G. L . ; Crisp, C. E . ; Hays, T. L. Carbonaceous Particles in Coal Fly Ash. In Proceedings of the Conference on Carbonaceous Particles in the Atmosphere, Lawrence Berkeley Laboratory Report LBL-9037, CONF-7803131, UC-11, 1978.


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30. Kowalczyk, G. S. Concentration and Sources of Elements on Washington, D. C. Atmospheric Particles, Ph.D Thesis, University of Maryland, 1979. 31. Mason, B. "Principles of Geochemistry"; John Wiley & Sons, Inc.: New York, 1966.


32. Macias, E.S.; Chu, L . S . , Urban Aerosol Carbon - Primary or Secondary?, in Chemical Composition of the Atmospheric Aerosol: Source/Air Quality Relationships, E.S. Macias and P.K. Hopke, Eds., A.C.S. Symposium Series, 1981.

RECEIVED April 10, 1981.


Atmospheric Aerosol - American Chemical Society

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