A factor analysis-multiple regression model for source apportionment of suspended particulate matter

Atmospheric Environment Vol. 24A, No. 8, pp. 2089 2097,-1990. Printed in Great Britain.

0004 6981/90 $3.00+0.00 Pergamon Press plc

A FACTOR A N A L Y S I S - M U L T I P L E REGRESSION M O D E L FOR SOURCE A P P O R T I O N M E N T OF S U S P E N D E D PARTICULATE

MATTER

SH1N'ICHI OKAMOTO

Tokyo University of Information Sciences, 1200-2 Yatocho, Chiba 280-01, Japan MASAYUKI HAYASHI Shibaura Institute of Technology, 307 Fukasaku, Omiya, Saitama, 330, Japan

and MASAOMI NAKAJIMA, YASUTAKA KAINUMA a n d KIYOSHIGE SHIOZAWA Waseda University, 3-4-1 Okubo, Shinjuku, Tokyo, 160, Japan (First received 15 December 1988 and in final.form 18 October 1989)

Abstract A factor analysis multiple regression (FA-MR) model has been used for a source apportionment study in the Tokyo metropolitan area. By a varimax rotated factor analysis, five source types could be identified: refuse incineration, soil and automobile, secondary particles, sea salt and steel mill. Quantitative estimations using the FA-MR model corresponded to the calculated contributing concentrations determined by using a weighted least-squares CMB model. However, the source type of refuse incineration identified by the FA-MR model was similar to that of biomass burning, rather than that produced by an incineration plant. The estimated contributions of sea salt and steel mill by the FA-MR model contained those of other sources, which have the same temporal variation of contributing concentrations. This symptom was caused by a multicollinearity problem. Although this result shows the limitation of the multivariate receptor model, it gives useful information concerning source types and their distribution by comparing with the results of the CMB model. In the Tokyo metropolitan area, the contributions from soil (including road dust), automobile, secondary particles and refuse incineration (biomass burning) were larger than industrial contributions: fuel oil combustion and steel mill. However, since vanadium is highly correlated with SO,2- and other secondary particle related elements, a major portion of secondary particles is considered to be related to fuel oil combustion. Key word index: Aerosols. chemical mass balance, factor analysis, multivariate analysis, receptor model, source apportionment.

INTRODUCTION Several extensive implementation plans have been carried out for SO 2 and NO:, in the T o k y o metropolitan area. However, no program based on a quantitative prediction for suspended particulate matter has been carried out in this area. In Japan, particulate matter under 10 #m has been defined as suspended particulate matter (SPM); SPM is measured by lowvolume air samplers, c o n t i n u o u s / ~ - r a y monitors, or continuous monitors of the light-scattering method with calibration by a filtration method, Though there were 38 SPM monitoring stations in Tokyo, only two stations recorded levels satisfying the environmental standards by 1986. The environmental standard for SPM is a daily average of 100 #g m - 3 with an hourly value of 200 pg m 3. Although air pollution control of S P M has become one of the most important issues, the contributing source types, distribution of these sources, and emission rates could not be clarified at present. Therefore, implementation

plans based on a diffusion model simulation are not effective. Considering this situation, the receptor model is useful for identifying the source type and estimating the contributing concentration for each emission source. Several types of mathematical models were used in the source apportionment study. For quantitative analyses, chemical mass balance (CMB) and multivariate models were developed. Factor analysis, target transformation factor analysis, and multiple regression are parts of the multivariate model. The advantages and disadvantages of the multivariate model have been discussed by Henry et al. (1984), Thurston and Lioy (1987) and Lowenthal and Rahn (1987). In the Tokyo metropolitan area, there have been no extensive investigations designed to produce a precise database for the chemical compositions of particulate matter at emission sources. Therefore, factor analysis-multiple regression ( F A - M R ) models seem to be useful. The purpose of this study was to identify the

2089

SHIN'ICHI OKAMOTOet al.

2090

contributing source types and to estimate the contributions of suspended particulate matter in the Tokyo metropolitan area. For this purpose we applied the F A - M R model to data obtained during the fall and early winter, a period during which the SPM concentration level is usually high.

FACTOR

ANALYSIS-MULTIPLEREGRESSION MODEL

The fundamental relation between the concentration at a receptor site and source information can be expressed as

contribution is not expressed by Equation (3). The absolute score method for the receptor model was introduced by Thurston and Spengler (1985). Since there is a mathematical model in the first place and the model for errors is taken into consideration, the factor analysis is preferred over the principle component analysis used in this study (Okamoto et al., 1987). Therefore, the absolute factor score (AFSjk) is used instead of the absolute principal component score (APCS) of Thurston and Spengler (1985). The procedures to.calculate the AFSs are the same as those for APCSs.

j where Cik is the concentration of element i in sample k and aij is the composition of element i of source j; the fractional abundance of element i in the j-th source profile, S~k is the contributing mass concentration (contribution) by the j-th source to sample k. The basic model for a factor analysis is of the form

Although the absolute factor score is proportional to the source contribution, the score is not in units of mass concentration. Thus, a transformation to mass concentration units is necessary in order to obtain the contribution quantitatively. These proportionality constants can be determined by a multiple regression analysis for estimating the mass concentration by using the absolute factor score as the predictor variable:

C~k = E ~ijSjk'~-~'ik,

Yk = ~ Zj(AFS)jk + Zo,

Cik = ~, aijSjk,

(1)

(2)

j

where, Ci~kis the normalized value of Cik (namely, the mean of CTk is 0 and the variance of CTk is 1), S}k is the factor score of the j-th common factor for the k-th sample, aij is the factor loading, and/~ik is the error or residual which is not explained by the common factors. It should also be mentioned that although both principal component analysis (PCA) and factor analysis (FA) are used for data reduction, some difference can be seen between PCA and FA, as follows: (i) although FA adopts a mathematical model involving data structure, PCA does not; (ii) PCA does not allow the presence of error variance; the error terms in FA are assumed to be uncorrelated with each other. More detailed descriptions for this difference were presented by Harris (1985) and others, In a familiar factor analysis, e.g. a varimax rotated factor analysis model, it is assumed that there is no correlation between the common factors, between the errors, and between the common factors and errors. If the same assumption is adopted in Equation (1), this equation becomes equivalent to that of the factor analysis model. This is the reason why the factor analysis model is often used in a source apportionment study (Henry et al., 1984; Thurston and Lioy, 1987). Comparing equations (1) and (2), the following relation can be obtained (Henry et al., 1984): ( s ~ - s 2 ~'/2

.

where, Yk is the mass concentration of sample k, and Zj is the partial regression coefficient. The value Z o is a regression constant (intercept) and has meaning as a source contribution, which could not be considered based on the above mentioned factors. The product of Zj and (AFS)jk is the estimated contribution (in mass concentration unit)of source j for sample k: S~k = Zj(AES)jk. (5) Considering a regression model for estimation of Cik,

Cik = ~ aijSjk + aio + Etik,

(6)

j the source composition a o can be obtained as a partial regression coefficient of the linear multiple regression Equation (6), where a~0 + e'i~are values corresponding to errors e~k in the factor analysis model. The factor loading of Equation (2) has been found to be equivalent to the normalized partial regression coefficient, by comparing Equations (2)and (6). The source composition, air, is derived by the following (Henry et al., 1984):

(Ci.--Ci.)22

1/2

ai~=ct~J (.~2 .~2~1/2 " "-J'--J-"

(7)

DATA During the period October-November 1986 aero-

Sik--;~. S~k -

(4)

J

(3)

-J" Although Equation (3) shows that the normalized value of the source contribution is equal to the value of the factor score, the origin of the absolute value of the

sols were collected at Waseda University (see Fig. 1). Samplers were set on the roof of an 18-storey buil.ding (about 60 m above the ground), which is located 200 m from Meiji-Dori Avenue (a "major circular road in Tokyo). Two sets of Shibata portable Hi-vol samplers were used to collect the total suspended particulate

Factor analysis-multiple regression model -

Saitama

'~ ...... •~ - . I,S~

Tokyo ~.2~j~ , , ~ , \-~ i ~

~"'--~ ....

j

Waseda ~,Univ .i 7 Nasn-Tokyo

]hiba ~ ~'~

i '

i "~ ~

' j

_ , 4 N

Kanagawa

¢

+ 0 t

5 km

~

~ Fig. 1. Map showing the sampling site and NASN-Tokyo monitoring station.

matter (TSP). Although no size-selective device was used with the samplers, the sampling site was so high that the content of large soil particles would be rather small. The sampling duration was 5.5 h. Sampling usually started at 9:00 and 15:00, except for rainy days. A total of 42 data were obtained during this period. Two samples were collected simultaneously: one on a Teflon filter (Toyo PF-1) for elemental analysis, the other on a quartz filter (Palleflex 2500 Q A S T ) for analyses of carbon and anions. Thirty elements were analyzed by instrumental neutron activation analysis (INAA). Cd, Pb, S and Si were analyzed by X-ray fluorescence (XRF); NH,~ by an indophenol method. SO ] - , N O 3 and C1- in sample on the quartz filter by ion chromatography (IC). These chemical analyses were performed at the Japanese Environment Sanitary Center (Otoshi, 1986). The total carbon was analyzed by combustion and measurements of the CO2 released (Sakamoto, 1986). These analyses were performed in cooperation with Saitama University. The average concentration and average I N A A analytical error for elements and ions are shown in Table 1. I N A A analytical errors were determined by the counting of the 7-ray spectrum. Additional data for gaseous pollutants were obtained at a monitoring station of the T o k y o Metropolitan Government. The National Air Sampling Network, N A S N - T o k y o station is located 800 m west of the Waseda University. Meteorologial data were obtained by T o k y o Observatory.

2091

Table 1. Average concentration and INAA analytical error for elements and ions in suspended particulate matter

Component

Average concentration (ng m -3)

INAA analytical error (%)

Number of ND* samples

0 0

Ag

6.3

7.7

AI As Ba

2000 4.1 25

2.9 8.3 48.6

36

Br Ca Ce CI Co Cr Cs

17 2700 2.2 6500 1.4 15 0.13

13.1 5.9 19.2 2.9 19.8 9.1 41.5

2 0 I 0 "~ 0 21

Fe Hf

2200 0.17

7.8 37.3

0 16

770 1.1 0.02 750 100 1400 10 17 0.36 1.6 0.12 0.18 200 11 1.6 370 3.1 170 1700 6400 780 3000 4600 6100 27,000 105,000

28.3 27.2 49.8 25.9 5.5 3.7 44.8 2.0 4.9 31.6 14.5 28.0 14.8 2.9 34.1 4.0 -

5 5 40 5 0 0 27 0 0 6 2 5 6 0 16 0 26 0 0 0 0 0 1 0 0 0

Cu

K La Lu Mg Mn Na Ni Sb Sc Se Sm Th Ti V W Zn Cd Pb S Si NH,~ C1NO3 SO 2C Mass

3100

3.3

--

--

0

0

ND*: Under the detection limit.

RESULTS

Factor analysis A varimax rotated factor analysis was applied to the elemental data. First, a principal factor analysis was carried out by replacing the estimated communality by a diagonal term of the correlation matrix. This estimated communality was obtained by an iteration m e t h o d ( T a n a k a et al., 1984). Next, a varimax rotation was carried out. Although data of 42 samples for 39 chemical components (elements and ions) were prepared, only 19 components were used, so as to avoid the Heywood case. In this screening, components which had many data under the detection limit were rejected. Also, two samples were rejected, since the values of these data were shown to be outliers for some elements. Finally, a data matrix of 40 samples by 19

2092

SH|N'ICHIOKAMOTOet al. Table 2. Varimax rotated factor loading and corresponding probable source type Variable

Factor 1

Factor 2

A1 As Br Ca Cr Fe Mn Na Sb Sc V Zn Pb Si NH2 C1NO 3 SOl C

0.267 0.688 0.681 0.291 0.293 0.286 0.647 0.067 0.837 0.100 0.420 0.721 0.837 0.411 0.268 0.485 0.203 0.551 0.598

Variance

4.972

Probable source type

Factor 3

Factor 4

Factor 5

0.812 0.501 0.234 0.664 0.364 0.655 0.260 0.211 0.198 0.882 0.409 0.283 0.210 0.760 0.220 0.101 0.362 0.144 0.447

0.320 0.332 0.417 0.378 0.411 0.295 0.088 0.140 0.282 0.095 0.654 0.391 0.302 0.352 0.815 -0.135 0.714 0.673 0.505

0.192 0.226 0.300 0.213 0.053 0.102 0.242 0.936 0.095 0.083 0.172 0.107 0.103 0.147 -0.007 0.726 -0.069 0.200 0.136

0.062 -0.081 0.168 0.262 0.682 0.606 0.496 0.028 0.067 0.280 0.303 0.417 0.284 0.082 0.090 0.131 0.182 0.208 0.169

4.175

3.597

1.850

1.753

Sea salt

Steel mill

Refuse Soil and incineration automobile

Secondary particles

Communality (factor 1-5) 0.874 0.892 0.811 0.783 0.855 0.976 0.799 0.945 0.834 0.882 0.892 0.938 0.927 0.898 0.792 0.808 0.721 0.860 0.860 16.347"

* Sum of communality.

components was used. The degree of freedom was not sufficient, but seemed to be within the permissible range (Henry et al., 1984). The factor loadings are shown in Table 2 with probable source types. In Table 2, factors with a variance greater than 1.0 are considered. The first factor shows high loadings for As, Br, Sb, Zn, Pb and C. These tracer elements indicate both refuse incineration and the associated open burning of industrial or domestic waste. However, this interpretation is not based on firm evidence, and further analysis is necessary (discussed in the latter section). The second factor seems to express soil particles, since it is correlated with A1, Ca, Fe, Sc and Si. These elements are usually found in crustal components. Moreover, this factor appears to have a weak correlation with N O 3 and carbon: it can, therefore, be estimated that the second factor is also associated with automobile exhaust, Since almost all gasoline-powered automobiles use unleaded gasoline, Pb is not a useful tracer element in Japan. The third factor depends upon N H ~ , N O 3 and SO 2 - . These are the predominant chemical components of secondary particles. In this third factor, the factor loading of V, which is a tracer element of oil combustion, also indicates a high value. It is suggested that a major origin of secondary particles is the sulfur dioxide produced by oil combustion, The fourth factor is highly loaded in Na and C1-. This is obviously sea salt. The fifth factor groups Cr, Fe, M n and Zn; its origin is probably steel mills and metal works, Next, the relationships between these factors and other variables which were gaseous pollutant concen-

trations at the N A S N - T o k y o station and meteorological observations at Tokyo meteorological observatory were investigated. The correlation coefficients among these variables are shown in Table 3. The first factor is correlated with C O (correlation coefficient r=0.412) and non-methane hydrocarbon N M H C (r=0.524). However, no correlation with N O (r = 0.295) can be seen at the significance level of p = 0.05. This result implies that the origin of this factor may not be automobiles but, rather, imperfect combustion of wastes. The second factor is most correlated with N O (r = 0.507). Since there were no major stationary sources near the receptor site, the concentration of N O for the most part represented automobile exhaust. This correlation seems to endorse the interpretation that the second factor corresponds to automobile exhaust. Since soil particles are also correlated with automobile exhaust, the resuspension of soil particles from road surfaces (road dust) plays an important role in the total quantity of soil particles for a site near a roadway. Estimation o f source contributions

The absolute factor score was calculated for each sample and for each identified factor. The contributing concentration for each sample was estimated by a multiple regression analysis using the absolute factor scores as predictor variables. The results are shown in Table 4. Since the scores are orthogonal to each'other, the normalized partial regression coefficient is consistent with the correlation coefficient between the mass (TSP) concentration and each contributing concentration. All of the partial regression coefficients are

Factor analysis-multiple regression model

2093

Table 3. Correlation coefficients between the factor scores and gaseous pollutant concentrations at NASN-Tokyo monitoring station and meteorological observations at Tokyo observatory Variable

Factor 1

Factor 2

Factor 3

Factor 4

Factor 5

SO 2 O., NO NO z NO:, CO NM HC CH 4 THC

0.275 -0.309 0.295 0.216 0.274 0.412 0.524 0.086 0.483

0.352 -0.023 0.507 0.384 0.470 0.399 0.356 0.222 0.310

0.573 -0.025 0.329 0.611 0.473 0.581 0.512 0.706 0.576

0.121 -0.600 - 0.068 0.034 -0.028 - 0.028 0.068 0.131 0.076

0.427 -0.119 0.351 0.377 0.375 0.318 0.372 0.15 I 0.357

Wind speed Temperature

t/.149 -0.054

-0.250 -0.135

-0.549 0.436

0.027 0.347

0.229 0.075

NMHC: Non-methane hydrocarbon. THC: Total hydrocarbon. Ox: Oxidant (KI methodl. When correlation coefficient is larger than 0.31, we can say that this correlation is meaningful at significance level p=0.05, because the degree of freedom is 38. Table 4. Results of multiple regression analysis Source of variation

Sum of squares

Degrees of freedom

Mean square

Fo

Due to regression Residual

82,676 4480

5 34

16,535 132

125"*

Total

87,156

39

Factor

Regression coefficient

Standard error

Normalized partial regression coefficient

25.0 24.5 28.9 7.2 6.5

1.88 1.90 1.94 1.87 1.83

0.52 0.50 0.58 0.15 0.14

(11 (2) (3) (4) t51

Refuse Soil and auto. Secondary Sea salt etc. Steel etc.

Constant

0.43

Fo 178"* 166"* 221"* 15.0"* 12.7"*

5.20

** 1% significance. meaningful at a significance level ot p--0.01. The multiple correlation coefficient is 0.97. The constant of the regression equation has meaning in that it represents the contributing concentration of an unidentifled source by factor analysis; since this constant is sufficiently small, this analysis seems to be satisfactory, This result shows that the contributions due to refuse incineration, soil (road dust) and automobile, as well as secondary particles are major portions of the particulate matter in the Tokyo metropolitan area A few negative contributions were calculated using Equation (5) for the following source types: steel mill, refuse incineration and secondary particles. However, since the absolute values of these negative contributions were small, these values were replaced by zero for the following calculations,

Estimation of source composition The estimated source composition calculated using Equation (7) is shown in Table 5. A relatively large

value of carbon content for all factors (source types) can be seen. Especially, the carbon content of the estimated composition of sea salt is 26%. Since, we intended to obtain the orthogonal factor in a varimax factor analysis, more than two contributions which were highly correlated, could not be estimated separately. In this factor analysis, the contributions of both sea salt and the anthropogenic sources located along the coastline could not be distinguished, since these two contributions have similar temporal variations. The total content of Na and C1 is 33%. This means that the ratio of sea salt in the imaginary source category, corresponding to the fourth factor, seems to be less than half. This problem is caused by multicollinearity and has already been pointed out by Henry (1985) and other researchers. Carbon is the most c o m m o n member in suspended particulate matter and its source is widely distributed. Therefore, we could not discriminate the carbon from the source categories which did not

2094

SHIN'ICHI OKAMOTOet al. Table 5. Estimated source matrix (unit: %) Component AI As Br Ca Cr Fe Mn Na Sb Sc V Zn Pb Si NH,~ CI NO 3 SO ] C

Refuse incineration

Soil (road dust) and automobile

1.076 0.006 0.027 1.443 0.010 1.120 0.234 0.186 0.034 0.000 0.010 0.656 0.329 5.431 0.401 4.685 2.989 6.666 33.712

3.381 0.004 0.010 3.399 0.013 2.649 0.097 0.610 0.008 0.001 0.010 0.266 0.086 10.370 0.341 1.008 5.496 1.797 26.002

Secondary particle 1.153 0.002 0.015 1.675 0.013 1.034 0.029 0.351 0.010 0.000 0.014 0.318 0.106 4.160 1.093 ( - 1.164) 9.401 7.287 25.475

release carbon particles. This problem seems to show the limitation of the multivariate analysis model based on correlation between elements. The estimated content of A1, Ca and Fe for the second factor (soil and automobile) is nearly half of the reference value of the soil composition (IPCAJ, 1986; Mizohata and Mamuro, 1979). Therefore, the composition of the second factor seems to be the total of soil (and road dust) and automobile (mainly diesel exhaust); the ratio of these source types seems to be about unity. The emission strength of a gasolinepowered automobile is very weak compared with that of a diesel automobile (JEA, 1987). Diesel exhaust consists mostly of elemental carbon; the carbon content is usually 50-90% (Yoshizumi, 1985; Mizohata, 1985). However, the carbon content of the second factor is 26 %. This may also be the reason why for the

Sea salt etc. 2.661 0.006 0.041 3.625 0.006 1.381 0.301 9.009 0.013 0.000 0.014 0.335 0.140 6.680 ( - 0.034) 24.127 ( - 3.502) 8.329 26.429

Steel mill etc. 0.935 ( - 0.002) 0.025 4.847 0.089 8.869 0.671 0.293 0.010 0.001 0.026 1.417 0.417 4.042 0.503 4.736 10.009 9.413 35.514

imaginary source type, the second factor, the ratio of diesel exhaust to soil particles is about unity. Comparison with C M B calculations

The contributing concentrations for each sample can be obtained by a chemical mass balance method. The usual weighted least-squares method was used. The inverse of the elemental concentration was used as the value of the weight coefficient. The source data used for C M B calculations are shown in Table 6. This source composition is much different from that listed in Table 5. One probable reason is given in the previous section, namely indiscrimination of highly correlated source categories. The compositions of both soil and road dust are so similar that C M B calculations using both source types may result in failure. The result of a factor analysis

Table 6. Source matrix for CMB calculation (unit: %)

Road dust AI Ca Fe K Mn Na V Pb C

6.8 6.9 7.4 0.97 0.14 1.1 0.019 0.012 4.7

Reference

Iitoyo (1987)

Sea salt 0.000030 1.2 0.000029 1.1 0.0000058 30.4 0.0000058 0.0000087 0

Steel mill 0 0.078 22.3 0 0.41 0 0.0092 1.09 0

Mizohata and Iitoyo Mamuro (1979) (1987)

Fuel oil 0.18 1.5 2.9 0.085 0.061 2.8 0.33 0.033 56.8 Iitoyo (1987)

Refuse 0.42 1.1 0.62 20 0.033 12 0.0027 1.7 8.4

Diesel 0.061 0.061 0.036 0.037 0.0012 0.015 0.00075 0.049 78

Mizohata and Mizohata Mamuro (1979) (1985)

Straw burning 0.12 0.54 0 3.7 0.030 0 0.00040 -0 55 Taniguchi et al. (1986)

Factor analysis-multiple regression model suggested that soil and automobiles were highly correlated. Therefore, the road dust was used as a sum of the two source types: soil and road dust. Since a multicollinearity also appeared between refuse incineration and straw burning, two trialcalculations were carried out for different cases. In one case, refuse incineration was used and straw burning was rejected. In the other case, refuse incineration was replaced by straw burning. Tentative CMB calculations were carried out by using average data instead of specific sample data. Plausible results were obtained for both cases. In the first case, the estimated contribution from refuse incineration was 3% and that of

100

r = 0.52

2095

unknown material was about 34%. In the second case, the estimated contribution of straw burning was 13% and that of unknown material was about 30%. These results show that the contribution of large incineration plants seems to be about 3% in the Tokyo metropolitan area; however, the contribution of an undefined source, which has a similar composition of the straw burning, is more than 10%. The calculated contribution of straw burning is close to the contribution of refuse incineration obtained by the FA-MR model. Since there is no agriculture land around the receptor site, straw burning does not take place near the receptor. Therefore, this result suggests that there

~.. 125 I

r = 0.59

E E II1

80

o~ 100

s0

75

:L

40

=:

•

•

•

• el,&'°° OoO~ .. 2C~-t . 0" " " 20

40

60

80

50

~~

25 "Oo~e . , .

100

10

• ..Oo

0

25

50

75

100

125

Soil and auto. (FA-MR) (p.g m -3) 30

r =0.71

r 20 E o~ ~" 15 E

I.

0~•

"~ ®

Refuse (FA-MR) (/Ag m -3)

25

•

r =0.98

E 24 o~ 3 ~ 18 oe

•

•

.e

•

~

12

5/,....o _ ..

8..' 0

. i~ S.

~ ,~1, •

5

10

15

20

25

Steel mill (FA-MR)(/Ag m -3) 100

*"

o=t °

•

6

12

18

24

Sea salt (FA-MR) (#g m -3)

r = 0.75

I

E

80

•

60

•

•

40 OC

=

e e

•

•

•

CO0

•

•

2c

Ooo% I

I

I

I

I

0

20

40

60

80

100

•

•

oo

Secondary particle (FA-MR) (p.g m -3)

Fig. 2. Comparison of the calculated contributions by FA-MR and CMB models.

3'0

2096

SHIN'ICHIOKAMOTOet al.

are some emission sources which have similar compositions to straw burning or refuse incineration, though more similar to straw burning. The carbon content of the estimated source composition for refuse incineration by the F A - M R model is about 30%. This value is larger than that of a modern incineration plant (5-10%), suggesting that this source type is correlated with an emission source involving imperfect combustion. This source type may represent an open burning of biomass (waste plants), including dead leaves, waste wood, paper and so on, or small-size domestic incinerators. Perhaps the composition of these sources may be similar to that of straw burning, CMB calculations were carried out for each sample by using the six source types: soil (using the composition data of road dust), steel mill, diesel exhaust, refuse incineration (using the composition data of straw burning), sea salt and fuel oil combustion. The average contributions for 40 samples are shown in Table 7, together with values derived using the F A - M R model. A scatter diagram for CMB and F A - M R calculations is given in Fig. 2. The consistency between the estimated contributions by F A - M R and CMB models can be seen in Fig. 2. This means that the interpretation of factor loading and the result of the F A - M R model may be correct. However, the result of this comparative study also shows the limitation of the F A - M R model as a method for quantitative estimations; the contributions of more than two source types which have a similar tendency cannot be separated. The estimated contributions due to steel mills by the CMB model are sometimes less than half that predicted using the F A - M R model. This result implies that there are many emission sources near a steel mill and that the temporal variation of these contributing concentrations at the receptor site are similar during the experimental period. The same tendency can be seen regarding sea salt. The ratio of the other sources, which cannot be separated from sea salt, is about 2/3 of the contribution corresponding to the fourth factor (identified as sea salt). This ratio is consistent with the value estimated by the calculated source composition (Table 5) in which the content of Na and CI in the source composition corresponding to the fourth factor is about 30%.

The unknown terms of the CMB model, which are obtained by subtracting the total of the estimated contributions from the observed mass concentration, are correlated with the estimated contributions of secondary particles by the F A - M R model. The correlation coefficient is 0.75. The averages of the unknown term of the CMB model and the secondary particles of the F A - M R model have almost the same value, about 32/~gm-3. The major part ofthe unknown term ofthe CMB model is considered to represent secondary particles. Therefore, the particulate matter for this monitoring program can be explained, to a large extent, in terms of the source types considered here.

CONCLUSIONS Since the concentration of suspended particulate matter is usually high in late fall and early winter in the Tokyo metropolitan area, a source apportionment study was conducted during the period October November 1986, at Waseda University, located in the central part of Tokyo. A factor analysis multiple regression (FA-MR) model was used for this study. The varimax rotated factor analysis was applied to the TSP data, and five source types were identified: refuse incineration, soil (road dust resuspension included) and automobile, secondary particles, sea salt and steel mill. A multiple regression analysis for a quantitative estimation of the contributing concentration was carried out by using the absolute factor scores as predictor variables. The results by the F A - M R model were compared with those by a weighted least-squares CMB model. The quantitative estimations by the F A - M R model corresponded to the calculated contributing concentrations by a weighted least-squares CMB model. However, the source type of refuse incineration identified by the F A - M R model was similar to biomass burning, rather than that produced by an incineration plant. The estimated contributions of sea salt and a steel mill by the F A - M R model contained those of other sources, which have the same temporal variation of the contributing concentration. This symptom was caused by a multicollinearity problem, showing the limitation of the multivariate receptor model. How-

Table 7. Average contributions for each emission source type by FA-MR and CMB models CMB calculations

(%)

FA-MR calculations

Soil (including road dust) Diesel exhaust Sea salt Steel mill Fuel oil Refuse (biomass burning) Unknown

23.8 23.0 3.4 4.9 1.6 12.7 30.6

Soil (including road dust) and automobile Sea salt, etc. Steel mill, etc. Fuel oil Refuseincineration Secondary particle

(%) 39.4 (37.8)* 10.3 (9.9) 5.4 (5.8) 14.0 (16.6) 30.3 (29.9)

*Numbers in parentheses mean the percentage in which negative contributions are replaced by zero.

Factor analysis-multiple regression model ever, useful information is simultaneously presented concerning the source types and their distributions. In the T o k y o metropolitan area, the contributions of soil (including road dust), automobile, secondary particles and refuse incineration (biomass burning) were larger than industrial contributions: fuel oil combustion and steel mills. However, since vanadium is highly correlated with S O ~ - and other secondary particle related elements, a major part of the secondary particles is considered to be related to fuel oil combustion. Acknowledgement--The carbon analysis was carried out at Saitama University by courtesy of Dr Sakamoto of Saitama University.

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