Airborne soil material accounts for the majority of the mass of suspended atmospheric particulate matter in both urban (80%)and rural (50%)locations in southern Arizona. Over a dozen of the 28 chemical species monitored in this program can be attributed either entirely or to a large extent (a majority) to the airborne crustal material. The urban activities are apparently a source for every chemical species measured in this program. For several nonsoil species, however, the urban source is small relative to nonurban sources. The acid-base nature of the atmospheric gases and aerosols is apparently largely responsible for defining sulfate speciation and the gas-particle distribution of volatile acid-base species. Meteorological parameters are probably most important in defining the concentration and fluctuation of various species suspended in the desert atmosphere. These meteorological effects are, however, quite complicated, and improved sampling and evaluation methodologies for quantitatively evaluating these relationships are required.
Acknowledgment We thank the Board of Directors of the Research Ranch for permitting us to locate our samplers there and Larry Michel, Director of the Research Ranch, for collecting our samples. Literature Cited (1) Friedlander, S . K., Enuiron. Sci. Technol., 7, 235 (1973).
(2) John, W., Kaifer, R., Rahn, K., Wesolowski,J. J.,Atmos. Enuiron., 7, 107 (1973).
(3) Gladney, E. S., Zoller, W. H., Jones, A. G., Gordon, G. E., Enuiron. Sci. Technol., 8,551 (1974). (4) Kneip, T. J., Eisenbrid, M., Strehlow, C. D., Freudenthal, P. C., J. Air Pollut. Control Assoc., 20,144 (1970). (5) Harrison, P. R., Rahn, K., Dams, R., Robbins, J. A., Winchester, J. W., Brar, S. S., Nelson, D. M., ibid., 21,563 (1971). (6) Hardy, K. A., Ahselsson, R., Nelson, J. W., Winchester, J. W., Enuiron. Sci. Technol., 10,176 (1976). (7) Hoffman, G. L., Duce, R. A., Hoffman, E. J.,J. Geophys. Res., 77, 5322 (1972). (8) Zoller, W. H., Gladney, E. S., Duce, R. A., Science, 183, 198 (1974). (9) Gaarenstroom, P. D., Perone, S. P., Moyers, J. L., Enuiron. Sci. Technol., 11,795 (1977). (10) Ranweiler, L. E., Moyers, J. L., ibid., 8, 152 (1974). (11) Rommers, P. J., Visser, J., Analyst, 94,653 (1969). (12) Kamphake, L. J., Hannah, S. A., Cohen, J. M., Water Res., 1, 205 (1967). (13) “1973 Annual Book of ASTM Standards”, Part 23, pp 426-27, American Society for Testing and Materials, Philadelphia, Pa., 1973. (14) Moyers, J. L., “The Identification and Analysis of Urban Air Quality Patterns”, EPRI Tech. Rept., Nov. 1976. (15) Fisher, R. A., “Statistical Methods for Research Workers”, p 356, Hafner, New York, N.Y., 1958. (16) Friend, J. P., Recent Adu. Air Pollut. Control, 70 (137), 267 (1974). (17) Junge, C. E., “Air Chemistry and Radioactivity”, p 173, Academic Press, New York. N.Y.. 1963. (18) Dennis, B. L., Wilson, G. W., Moyers, J. L., Anal. Chim. Acta, 86,27 (1976). (19) Taylor, S . R., Geochim. Cosmochim. Acta, 28,1273 (1964).
Received for review May 25, 1976. Accepted March 16, 1977. Work supported by the Arizona Mining Association and the Electric Power Research Institute (RP438-1).
Application of Pattern Recognition and Factor Analysis for Characterization of Atmospheric Particulate Composition in Southwest Desert Atmosphere Phillip D. Gaarenstroom and Sam P. Perone’ Department of Chemistry, Purdue University, W. Lafayette, Ind. 47907
Jarvis L. Moyers University Analytical Center, University of Arizona, Tucson, Ariz. 85721
Measurements made of the composition of atmospheric particulate matter collected in the greater Tucson, Ariz., area are examined by use of pattern recognition and factor analysis. Cluster analysis shows Si, Ti, Cs, Li, Rb, Al, K, Fe, Ca, Mg, Na, Mn, Sr, Co, and Cr to be primarily of soil origin. Factor analysis is used to separate the variance of the data base into a small number of factors. Examination of these factors suggests that it is possible to interpret their chemical and physical significance in terms of sources, source strength, and gasto-particle conversion processes. The results suggest that NH: and SO,“-distributions can be explained by a diffuse area-wide gas-to-particle conversion process which produces these species in a chemically combined state. The species NOT, Zn, Cu, Ni, and Cd would appear to result from multiple processes (sources). Relative to a remote desert location, all elements measured in this study show an enrichment in urban particulates, with P b being the most enriched (1300%) and SO:-, NH:, Zn, Cu, and Cd among the least enriched (150%). These data evaluation techniques show great potential for helping to reduce the dimensionality and explaining the complicated problems associated with atmospheric chemistry and air quality investigations.
A previous paper ( I ) has described the atmospheric sampling and analysis program of the University Analytical Center at the University of Arizona. To gain a maximum of information from the data, a number of multivariate statistical methods, which have been found useful with increasing frequency in numerous widely divergent areas, were utilized. Multivariate techniques provide insight into the interrelationships among the chemical species. A primary objective of this sampling, analysis, and evaluation program is to identify processes which influence the concentration and distribution of atmospheric particulate species. These processes can include sources for various species and chemical and physical changes responsible for species generation or removal. The sampling program was conducted from December 1973 through December 1974. Twenty-four-hour, high-vol samples were collected a t 11locations in and around the Tucson area during that period. Twenty-four species were monitored: total particulate mass, NH:, SO,’-, NO,, Si, Ti, Cs, Li, Rb, Al, Zn, K, Fe, Ca, Mg, Na, Pb, Cu, Mn, Sr, Ni, Co, Cr, and Cd. Most of the locations are within the city of Tucson, but several stations are located outside the city in an effort to provide background information (i.e., nonurban) about the southwest desert aerosol population. Figure 1 locates the sampling staVolume l l , Number 8, August 1977
795
tions in relation to Tucson. Station 11,which is 50 miles from the city, shows the smallest influence from the urban plume and localized activities ( I ) . There are 40-65 samples taken a t each location for which all of the measurements were available. (For a more detailed description of the sampling and analysis program, see ref. 1 .) Results and Discussion Table I contains the means and relative standard deviations of the species sampled a t two different locations. Location 2 is an urban location at which the most samples were collected. Location 11 is an outlying desert (background) location as
9 !a
UTUCSON 3 5
'is M I L E S '
t
11
Figure 1. Location of 11 sampling stations
Table 1. Megn Concentrations, Relative Standard Deviations ( s / X ) , and Ratios of Means for Location 2 (Urban) and Location 11 (Outlying) Location 2 Feature
Pb
Ca K Sr
Mg Li Rb Si AI Mn
Na Fe Mass Ti
cs co NO, Ni NH: Zn
so:Cd Cr
cu 796
Mean Pg/ma
0.72 4.9 2.5 0.019 0.93 0.0046 0.011 18.0 5.4 0.054 1.2 2.8 101.0 0.37 0.0013 0.0018 1.8 0.0058 1.2 0.16 5.0 0.0022 0.0038 0.13
Location 11 s/i
Mean, wg/m3
s/i
Ratlo
0.68 0.59 0.64 0.54 0.69 0.91 0.68 0.62 0.53 0.65 0.64 0.69 0.56 0.65 0.68 0.86 0.44 0.54 1.21 0.72 1.03 1.51 0.70 0.60
0.055 0.79 0.42 0.0035 0.18 0.0009 0.0025 4.1 1.3 0.013 0.29 0.68 28.0 0.12 0.0004 0.0006 0.74 0.0030 0.70 0.099 3.4 0.0015 0.0028 0.093
0.96 0.60 0.66 0.85 0.78 0.77 0.66 0.67 0.60 0.72 0.76 0.59 0.49 0.80 1.oo 0.77 0.53 0.83 1.06 0.50 0.73 1.15 0.63 0.67
13.1 6.2 5.8 5.4 5.3 5.2 4.4 4.4 4.3 4.3 4.3 4.1 3.6 3.1 3.0 2.9 2.5 1.9 1.6 1.6 1.5 1.5 1.4 1.4
EnvironmentalScience & Technology
identified in Figure 1. Also listed is the urban/background ratio of the means of each measurement, using only those days for which sampling was done at both locations. This ratio provides information on which species are the most enriched in the city relative to the desert background. Not surprisingly, lead is the most enriched element in the city. It is to be noted that all of the enrichment ratios exceed 1.0, which suggests the city as a source for all of the monitored species. However, some species are only slightly enriched within the city, relative to the background. For these species (NHZ, SO,"-, Zn, Cd, Cr, Cu), the apparent Tucson source may be minor (approximately half) compared to a nonurban source. Reference 1 contains the correlation matrices of the monitored species for locations 2 and 11. Examination of each correlation matrix suggests the existence of groups of species with mutually high correlations. Very likely, each species in any one of these groups arises from similar sources or from similar chemical and physical transformation processes in the atmosphere. Pattern recognition methods were used to locate these clusters of species, as described below. Pattern Recognition. Pattern recognition has been applied to a variety of chemical problems. It has been used to identify the presence or absence of functional groups from mass spectra ( 2 ) ,from nuclear magnetic resonance data (31, and from infrared spectra ( 4 ) ;to identify structure/activity relationships ( 5 ) ;and for other problems (6). Pattern recognition was used in a pollution study of lake sediments (7).The method of pattern recognition employed in this study is known as cluster analysis (also called unsupervised learning). Two complementary cluster analysis techniques were used, nonlinear mapping and hierarchical clustering. Nonlinear mapping is a display technique which allows human recognition of clusters but may suffer from mapping errors. Mapping errors do not occur in the hierarchical clustering technique, but the algorithms employed have difficulty separating odd-shaped clusters. Nonlinear Mapping (8,9). This mapping technique plots n-dimensional points in 2-dimensions and attempts to preserve structure by minimizing the differences between the n -space and the corresponding 2-space interpoint distances. The scheme is iterative and is halted when the mapping error, E , of the N points appears to converge.
The d,, symbol designates the distance between points i and j in n-space, and d,,* is the corresponding distance in 2space. Since chemical species are to be clustered based on their correlation coefficients, the distance between two species was defined as d,, = 1 - rLJ,where rll is the correlation coefficient between species i and j . The measure behaves as a distance in that, for two perfectly correlated species, the measure equals zero. In this study negative correlations are infrequent and of small magnitude. All the information contained in a nonlinear mapping is found in the interpoint distances. The two coordinate axes have no physical significance. Nonlinear mappings of the species from the urban and outlying locations, 2 and 11,respectively, are shown in Figures 2A and 2B. At the urban location there is clustering of the species Co, Cs, Rb, Li, Mn, Ti, Si, Al, Sr, Cr, Mg, Fe, K, Na, and Ca. These elements are probably of a crustal origin. Note that the total mass is also in this cluster which is not surprising since the species having the greatest concentrations-Si, Al, and Ca-are in this cluster. From Table I, the soil elements are the most enriched species in the city except for Pb. Because of the enriched quantities, the soil particulates can be considered to result primarily from various urban activities.
Except for NH: and SO,"-, the remaining species (Ni, NO;, Cd, Cu, NH:, SO:-, Pb, and Zn) are well separated from the soil cluster and from each other. Separation suggests different sources and/or different chemical and physical cycles in the atmosphere. The high degree of correlation between NH: and SO:- is probably explained by the chemical combination of these species in the atmosphere (10).This combination results from acid-base processes after SO2 is oxidized to H2SO4 (11). In contrast to the urban location, the soil cluster is more dispersed at the outlying location. The reduced concentrations of these elements may be allowing the effects of minor sources (such as a marine source) to be visible. Six nonsoil species (Cu, Cd, Pb, Zn, NH:, and SO:-) show greater correlation at the outlying location, perhaps reflecting similar particle size and transport behavior. For the four metals a common source might also contribute in part to the observed correlation. Hierarchical Clustering (12, 13). Hierarchical clustering initially considers each entity as a separate cluster. Then the clusters are joined one at a time according to an agglomerative algorithm, until all the entities are joined into a single cluster. The results of a hierarchical clustering are displayed in a dendogram-a diagram of the clusters existing at each level of clustering.
2
CORRELRTION PLOT LDCRTION
CU
Figures 3A and 3B are dendograms resulting from the hierarchical clustering of the species at locations 2 and 11, respectively. The same distance measure was used in this clustering as in the nonlinear mappings. The soil species are very evident by their tight clustering. Ni exhibits a behavior intermediate between soil and nonsoil, indicating that a portion of the Ni concentration may have a soil origin. A matrix of correlations among the locations provides information about both the locations and the species that is used to construct the matrix. Table I1 contains correlation matrices among locations using NH: and A1 features. NH: and SO;show the same behavior in that all interlocation correlations are very high. This behavior is expected and consistent with the suggested chemical oxidation and acid-base processes responsible for generating particulate NH: and SO:- on an area-wide basis. A1 is typical of all the soil elements. Correlations among the urban locations are seen, but the outlying location is obviously different. NO;, Ni, Zn, Cd, Cu, and P b have lower interlocation correlations, probably because they are influenced by localized urban sources (e.g., for Pb, traffic patterns may account for these lower correlations). Factor Analysis. The pattern recognition techniques condense the information present in the correlation matrices and present it graphically. This form allows general trends to be viewed more efficiently. However, nothing is learned from use of these techniques which would not have been observed in a careful study of the matrices which noted sets of species with mutually high correlations and similar behavior. It would be very desirable to have a model which explains the behavior of each chemical species in terms of the physical and chemical influences on that species in the atmosphere. Determining the number of major influences and identifying them will require a more sophisticated analysis and are the objectives of the remainder of this paper.
AB
co cs
Figure 2A.
1
Nonlinear map of features at location 2
I L
I l l I
I I I h r35-l I l-z?t-A 1
CD LH PB N $ N I II
CORRELRTION PLOT LOCRTlON
Figure 3A.
CR
SR
Figure 28.
1
Nonlinear map of features at location 11
C O C S CR K
FE MG NR CR R B T I R L SI SR L I M N MS
Dendogram showing clustering of features at location 2
n
1
co NR
I
I'A
NR H I CO CR R L
Figure 38.
Dendogram showing clustering of features at location 11 Volume 1 1 , Number 8, August 1977
797
There are several reasons why factor analysis may be useful in testing the atmospheric particulate data. Since it is not possible to change experimentally the values of the variables, the researcher must rely on natural variations and use a statistical method to deduce the interrelationships among the variables. This is a common problem in the natural and social sciences and has led to many multivariate analysis methods. Factor analysis has particularly found use in the psychological and political sciences. The common reference works are written by researchers in those fields ( 1 4 , 1 5 ) .Several applications of factor analysis to pollution problems have been published (7, 16). These works have used factor analysis to identify or confirm the presence of pollution sources. Related eigenvector analysis techniques have been used in a study of meteorological effects on air pollution (17, 18). The introduction of particulates into the atmosphere from a number of different point and area sources fits the factor analysis model of a variable being a weighted sum of factor values. It is not the purpose of this paper to describe computationally how to perform a factor analysis. Programs are available as part of statistical packages at computing centers. Alternatively, it may be more convenient to write the necessary programs for use on a laboratory computer as was done with this work. A description of the factor analysis model, some implicit assumptions, and limitations of the technique will be offered here. In the factor analysis model each variable (zJ)is expressed as a linear combination of m factors (Fi’s) common to all variables and a unique factor ( U j ) . The factors are hypothetical variables chosen so that the correlations among the observed variables can be reproduced as well as possible by only a few factors.
zJ = a,lF1
+ a,zFz + - + almFm + d,U,
(2)
The coefficients in the above equation are called loadings. We use an orthogonal factor analysis model which means that the factors are orthogonal to one another and the loadings are also
Table II. lnterlocation Correlations of NH; and AI 1
2
3
4
5
8
9
6
7
10
1.00 0.63 0.76 0.61 0.96 0.73
1.00 0.94 0.90 0.87 0.82
1.00 0.90 1.00 0.95 0.77 1.00 0.83 0.71 0.76 1.00
1.00 0.51 0.27 0.75 0.31
1.00 0.78 1.00 0.61 0.42 1.00 0.21 0.17 0.40 1.00
11
NH: 1 2 3 4 5 6 7 8 9 10 11
1.00 0.93 0.91 0.94 0.86 0.86 0.93 0.93 0.93 0.92 0.81
1 2 3 4 5 6 7 8 9 10 11
1.00 0.90 0.49 0.69 0.74 0.88 0.80 0.65 0.46 0.94 0.54
1.00 0.93 0.96 0.88 0.91 0.94 0.96 0.90 0.94 0.76
1.00 0.96 0.93 0.88 0.93 0.92 0.91 0.92 0.86
1.00 0.90 0.71 0.95 0.94 0.88 0.97 0.85
1.00 0.86 0.92 0.88 0.94 0.89 0.75
AI
798
1.00 0.56 0.78 0.80 0.78 0.71 0.67 0.51 0.92 0.48
1.00 0.64 0.68 0.42 0.41 0.73 0.53 0.52 0.20
1.00 0.76 0.68 0.45 0.76 0.65 0.71 0.31
1.00 0.75 0.60 0.76 0.63 0.81 0.38
1.00 0.87 0.70 0.47 0.92 0.28
Environmental Science & Technology
correlation coefficients between the observed variable and the factor. By noting which species have high loadings on a particular factor, it may be possible to assign a physical interpretation to that factor. The factor analysis computes the values of the loadings starting with the correlation matrix of the observed species. The values of the factors themselves for each sampling day were not computed. Several assumptions are implicit in the use of factor analysis for the atmospheric particulate study. All the major influences on particulate composition should be reflected in the correlation matrix. It is further assumed that the major influences are different enough in their effects on the correlation matrix to produce factors which represent only one influence, not combinations of several influences. One limitation of factor analysis lies in the interpretation of factors. Interpretations are based on the magnitudes of the loadings but also rely on previous knowledge and common sense. Of the factors resolved in this study, some were expected, some were unanticipated but interpretable, and others represent unknown influences. Rotation. The factors were rotated using the orthogonal varimax rotation (14). The purpose of rotation is to point a factor a t a cluster of variables so the factor may be easier to interpret. The algorithm will tend to cause loadings to be either high or low with few medium loadings. The loadings of the rotated six-factor solutions of locations 2 and 11are found in Table 111. Co and Cs were omitted from the analysis because there was too much uncertainty in these measurements. The Co values were near the detection limit, and there were contamination problems with Cs measurements. A measure of adequacy of a factor analysis solution is whether the factors can reproduce the observed correlation matrix. For the six-factor solution of location 2, the average difference between an observed correlation and a reproduced correlation is 0.01, and the maximum difference is 0.06. Five to eight factors are needed to adequately reproduce the correlation matrices of each location. The “Fraction of Total Variance” row of Table I11 shows that most of the variance of the standardized variables is contained in just a few dimensions. The six-factor solution contains 84% of the total variance. By examining the loadings of the corresponding factors and recalling that a loading is a correlation coefficient between a variable and a factor, it is possible to interpret the factors. Most of the factors can be interpreted as resulting from physical and chemical sources of particulates. The first factor of location 2 has high loadings from Na, K, Fe, Ca, Mg, Rb, Sr, Al, total mass, Ti, Si, Li, Mn, and Cr. The variance that is common to these species is due to their source, the soil. In the factor analysis of any of the locations, this apparent soil factor always appears first with high loadings for these same elements. Ni shows variable loadings on this factor at the different locations. The variability of Ni loading on this factor is consistent with the previous suggestion that atmospheric Ni concentrations result from both a soil and nonsoil source. At several locations Zn also shows some loading on the soil factor. The loadings of Cr, Na, and K are reduced a t location 11.The reduced quantities of particulates from the soil source have allowed variance from more minor sources to be visible. Factor 2 of location 2 has high loadings from SO$-, NH:, and Cu. Pb, Zn, and possibly a few other species have some variance in this direction. The factor analyses of other locations always have high NH: and SO:- loadings on the second factor. Locations which are outlying or at the edge of the city, such as 1,3,5,9, and 11,have 5-7 high loadings on this factor from among the features SO;-, NH:, Pb, Cu, Zn, NO,, Cd, and Ni. The urban locations 6 , 7 , and 10 have high loadings from
only NH: and S O f . Since the interlocation correlations suggest that NH: and SO:- are produced on a diffuse areawide basis, it is inferred that factor 2 corresponds to a background well-mixed aerosol from nonlocal sources. This explains why outlying locations have more species loaded on this factor, since local sources a t these locations are absent or of minor importance. The third factor of location 2 has a high loading from Zn and medium loadings from K, Ca, Na, Fe, and Mg. A factor like this is present a t nearly every location although it is not necessarily the third factor. At several locations the loadings from all six species are nearly the same. There may be a source which introduces quantities of these six elements into the atmosphere. It is curious, however, that in the chemical analysis procedure, when a sample is divided into aliquots for analysis, one of the aliquots is diluted and analyzed for just these six species ( I ) . This could explain why Na, Ca, K, Fe, and Mg are more tightly clustered than the other soil elements in the nonlinear map and the dendogram. Zn does not cluster with these species because its origin is from other sources, but the factor analysis can separate the common variation of the elements in this aliquot. This factor is not visible in location 11 because there are other nonsoil sources. Identification of the aliquot dilution factor illustrates the power of the factor analysis technique. It is doubtful that examination of pairwise relationships would have separated this small common variance from the much larger physical source variance. A multivariate approach is called for in these situations. Cd is the major contributor to factor 4 of location 2. Species having intermediate loadings are Ni, NO,, and Zn. At outlying locations Cd is loaded only on the distant source factor (factor 2). At all urban locations Cd has a high loading on a factor with other high or intermediate loadings from the set of NO:, Ni, Zn, Cu, and Pb. This may suggest that this factor is due to a high-temperature or combustion process since these elements
Table 111. Factor Analysis Loadings-Rotated
have been identified as being enriched in power plant fly ash (19,20). This factor is not visible at the outlying location. Factor 5 of location 2 is loaded from P b and NO,. This is unique for the particular location considered since these species are usually found on separate factors with no other high loadings, or on the distant source factor if the location is outlying. A Pb-loaded factor would reflect the automotive source, while a NO;-loaded factor would reflect a source which is unique for NO,, possibly an area source in which locally produced NO, is converted to particulate NO, in the atmosphere. The reason for the apparent convergence of these two factors at location 2 is unknown. At location 11,NO, is found alone on factor 6, and P b is among the species loaded on factor 2. These loadings happen to be negative, but this has no physical significance. The factor could be redefined with an opposite sign, and in fact at some other locations these factors do have positive loadings. Factor 6 at location 2 has no high loadings but contains intermediate loadings from Cr, Ni, and Cu. These three elements appear together loaded on factors at other locations as well, and may be from some common but unknown source. Factor 3 of location 11has loadings from Ni and Cr also. Quite possibly, this factor reflects mining activity in the area. Na is the only species with a high loading on factor 4 of location 11. Only location 5 has a similar factor. This may be variation from the marine source which is not visible at urban locations due to the higher Na concentration. A few factors appear at locations other than locations 2 and 11.A factor with loadings from Li, Mn, Cr, and Cu is present at eight locations (sometimes one of these elements is missing). Five locations have a factor whose only high loading is Rb. Table IV lists the observed significant factors for all of the locations and the proposed sources of variation. These may correspond to physical sources, chemical processes, contamination. or measurement variance.
Six-Factor Solutions
Location 2
Zn Pb cu Cd NH:
s0:NOT Ni Cr Li Mn Sr AI Si Rb Ti Mass Na Mg Fe Ca K
Location 11
1
2
3
4
5
6
0.05 0.02 -0.04 0.02 -0.02 -0.03 0.17 0.51 0.84 0.94 0.94 0.94 0.97 0.99 0.88 0.96 0.84 0.79 0.92 0.89 0.85 0.86
0.25 0.38 0.67 0.13 0.86 0.92 0.17 0.17 0.01 -0.04 -0.07 -0.06 -0.05 -0.03 0.03 -0.05 0.12 -0.07 0.01 -0.04 0.05 -0.01
0.73 0.12 -0.00 0.15 0.14 0.11 0.02 0.13 0.11 -0.04 -0.06 -0.01 -0.03 -0.02 -0.16 -0.08 0.05 0.41 0.29 0.40 0.42 0.45
0.33 0.05 0.16 0.61 0.09 0.03 0.30 0.34 0.21 0.10 0.10 0.07 0.00 0.05 0.18 0.03 -0.05 -0.06 -0.03 -0.08 -0.07 -0.08
-0.03 -0.75 -0.06 -0.20 -0.22 -0.18 -0.62 -0.16 0.06 -0.05 -0.03 -0.13 -0.07 -0.01 -0.15 0.05 -0.04 -0.34 -0.00 -0.11 -0.09 -0.18
0.03 0.05 0.39 0.04 -0.15 -0.02 0.00 0.39 0.32 0.20 0.22 0.05 -0.00 -0.05 -0.02 -0.16 -0.25 0.17 0.11 -0.04 -0.09 0.02
0.53
0.11
0.07
0.04
0.06
Communallty
0.71 0.73 0.64 0.46 0.84 0.90 0.53 0.60 0.87 0.94 0.95 0.91 0.96 0.98 0.86 0.96 0.79 0.94 0.94 0.97 0.92 0.97
Communality
1
2
3
4
5
6
0.20 0.12 0.01 0.04 -0.05 -0.02 0.32 0.01 0.35 0.82 0.86 0.76 0.95 0.87 0.90 0.81 0.73 0.39 0.69 0.95 0.91 0.37
0.73 0.90 0.91 0.90 0.59 0.73 0.03 0.21 0.02 -0.06 0.02 -0.11 0.05 0.06 0.11 -0.18 0.22 0.03
0.25 0.06 -0.10 -0.12 0.16 0.08 -0.07 -0.17 0.26 -0.48 -0.45 -0.51 0.06 -0.19 -0.05 -0.06 -0.00 -0.76 -0.43 -0.17 0.07 -0.08
0.16 0.15 -0.02 -0.00 0.66 0.51 0.11 -0.06 0.13 0.16 0.13 0.18 0.14 0.07 -0.05 -0.11 0.41 -0.05 0.32 0.01 0.23 0.62
0.14 -0.17 0.07 0.1 1 -0.35 -0.38 -0.68 0.12 -0.18 0.00 -0.00 0.12 -0.17 -0.12 0.21 -0.05 -0.13 -0.07 0.05 -0.08 -0.13 -0.02
0.90 0.92 0.88 0.85 0.93 0.95 0.58 0.87 0.66 0.96 0.97 0.89 0.95 0.83 0.87 0.72 0.77 0.75
0.16 0.16 0.10
-0.46 0.22 -0.20 -0.12 0.04 -0.05 0.03 -0.88 -0.65 -0.15 -0.12 -0.09 -0.02 -0.13 -0.08 -0.11 0.03 0.06 -0.28 -0.12 0.10 -0.04
0.19
0.08
0.08
0.07
0.04
0.84
Fraction of total variance 0.03 0.84 0.38
-0.03
0.85 0.98 0.94 0.54
Volume 11, Number 8, August 1977
799
Table IV. Element Loadings on Individual Factors and Possible Explanations for Factor Significance 1
2
3
Elements, major loading
Mass, AI, Ti, Si, Sr, NH’, Rb, Li, Mn, Ca, K, SO!-, Fe, Mg, Na, Cr Cu
Zn
(Minor loading)
(Ni, Zn)
(Mg, Na, Fe, Ca,
Physical or Soil chemical Large particle significance
(Ni, Cd, Zn, Pb, NO,) Distant and/or diffuse source Small
4
Pb
5
NO,
6
7
8
9
Cd
(Zn, Ni, Cu, Pb, NO:)
10
Na
(Li, Mn, Cr, Cu)
(Ni, Cr, (Rb) CUI
K) Common aliquot dilution variance
Auto- Gas-par- Unknown (may motive ticle have combustion conand/or version transport significance)
Urban only may Mining Un- Backsuggest signature activity kno- ground wn only of one or more urban sources Marine source?
particles GaS-
particle conversion
Conclusions
Literature Cited (1) Moyers, J. L., Ranweiller, L. E., Hopf, S. B., Korte, N. E., Enuiron.
The multivariate approach to data analysis appears to be particularly useful for studies of atmospheric aerosols. Many observations reported here could not have been made without the aid of these powerful methods. For example, the solid element cluster, ammonium and sulfate correlation, partial soil character of Ni, and the diversity of Pb, Zn, Cu, Cd, and NO, behavior were observations that were made by simple pairwise comparison of variables (correlation coefficients). These observations were also evident from the factor analysis. However, the factor analysis went even further in resolving a number of hypothetical variables which contained portions of the variance that is common to a t least several of the species. Interpretation of these factors by the researcher is then the most critical part. These factors may correspond to known physical sources, chemical processes in the atmosphere, common attributes of the chemical analysis procedure, or some unknown cause. From these studies it is suggested that improved sampling and analysis strategies can be designed to study specific processes (chemical and physical) responsibile for defining the distribution and behavior of trace species in the atmosphere. The application of these (and similar) evaluation techniques may provide an important new dimension in our ability to understand and quantitatively define the effects various sources and processes may have on the composition and distribution of species in the atmosphere. Work is currently under way to improve both the data base and the techniques for studying such data.
Sci. Technol., 11,789 (1977). (2) Varmuza, K., Rotter, H., Krenmayr, P., Chromatographia, 7,522 (1974). (3) Wilkins, C. L., Williams, R. C., Brunner, T. R., McCombie, P. J., J. Am. Chem. Soc., 96,4182 (1974). (4) Liddell, R. W., Jurs, P. C., Anal. Chem., 46,2126 (1974). (5) Kowalski, B. R., Bender, C. F., J . Am. Chem. SOC., 96, 916 (1974). (6) Kowalski, B. R., Anal. Chem., 47, 1152A (1975). (7) Hopke, P. K., J . Enuiron. Sci. Health, A l l (6), 367 (1976). (8) Sammon, J . W., IEEE Trans. Comput., C-18,401 (1969). (9) Fukunga, K., “Introduction to Statistical Pattern Recognition”, Chap. 10, Academic Press, New York, N.Y., 1972. (10) Junge, C. E., “Air Chemistry and Radioactivity”, Academic Press, New York, N.Y., 1963. (11) Keesee, R. G., Hopf, S. B., Moyers, J. L., “The Distribution and Characteristics of Particulate Sulfates in the Southwest Desert Atmosphere”, Proceedings of International Conference on Environmental Sensing and Assessment, Paper 23-6, Sept. 1975. (12) Everitt, B., “Cluster Analysis”, Halsted Press, 1974. (13) Duran, B. S., Odell, P. L., “Cluster Analysis Survey”, Springer-Verlag, 1974. (14) Harmon, H. H., “Modern Factor Analysis”, 2nd ed., Univ. of Chicago Press, Chicago, Ill., 1967. (15) Rummel, R. J., “Applied Factor Analysis”, Northwestern Univ. Press, 1970. (16) Blifford, I. H., Meeker, G. O., Atmos. Environ., 1,147 (1967). (17) Peterson, J. T., ibid., 4,501 (1970). (18) Peterson, J. T., ibid., 6,433 (1972). (19) Kaakinen, J. W., Jorden, R. M., Luwasani, M. H., West, R. E., Enuiron. Sci. Technol., 9,862 (1975). (20) Klein, D. H., Aunden, A. W., et al., ibid., p 973.’
Acknowledgment The authors thank Marty Pichler for his contributions to setting up the data base for the Purdue computer system.
Received for reuieu: May 25, 1976. Accepted March 16, 1977. Work supported by National Science Foundation Grant No. MPS74-12762, Office of Naval Research Contract No. NOOO14-75-C-0874,and by the Electric Power Research Institute RP438-1.
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