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Copyright © 1995 Elsevier Science Ltd Printed in Great Britain. All rights reserved 1352-2310/96 $9.50 + 0.00

1352-2310(95) 00261-8

R E C E P T O R M O D E L I N G O F VOCs, CO, NOx, AND THC IN

TAIPEI

CHANG-CHUAN CHAN and CHIU-KUEI NIEN

National Taiwan University, College of Public Health, Institute of Occupational Medicine and Industrial Hygiene, Rm. 1447, No. I, Jen-Ai Rd., 1st See,, Taipei, Taiwan

and

J I N G - S H I A N G H W A N G

Institute of Statistical Science, Academia Sinica, Taipei 115, Taiwan

(First received 19 September 1994 and in final form 19 June 1995)

Abstract--An empirical receptor model based on Markov Chain Monte Carlo simulation was applied to one-year measurements of eight VOCs, CO, NOx, and THC collected in Taipei during 1993. Ambient monitoring data were measured at four monitoring stations in Taipei metropolitan. Among five VOC- based sources (motorcycles, catalyst passenger cars, non-catalyst passenger cars, diesel vehicles, and gasoline vapor), non-catalyst passenger cars had the greatest contributions to eight VOCs (53--61%; 90.0--220.3/tg m-a). Among seven sources based on CO--NO~THC emissions (catalyst and non-catalyst two-stroke motorcycles, four-stroke motorcycles, catalyst and non-catalyst passenger cars, diesel vehicles, and gasoline vapor), passenger cars had the greatest contributions to NOr (50q53%; 0.0~0.26 mgm-a), motorcycles had the greatest contributions to CO (70--76%; 0.81-4.97mgm -a) and gasoline vapor contributed substantially to THC (17-58%; 0.35--0.85mgm-a). Our empirical receptor models have successfully improved the estimation of source coefficients for VOCs, CO, NO~, and THC by partially solving the collinearity problems among various mobile source profiles. Such an improved methodology is useful for validating source inventory and managing air quality in metropolitan areas.

Key word index: Receptor model, Monte Carlo simulation, VOC, mobile sources, motorcycles.

~'I'RODUC~ON

The receptor modeling method has been applied to apportioning sources of particulate air pollutants suc- cessfully in several studies in the past (Miller et al., 1972; Kowalczyk et al., 1982; Dzubay et al., 1988). However, the receptor models based on chemical mass balance (CMB) were recently used to identify sources of non-methane hydrocarbons (NMHC) in Tokyo (Wadden et aL, 1986), Newark and Linden (Scheff and Klevs, 1987), Chicago (Scheff and Wad- den, 1993), and Detroit (Chung et al., 1994). Until now, no studies of receptor modeling on CO and NOx were reported. Such a time lag in the application of receptor modeling to gaseous air pollutants can be explained by several inherent constraints in CMB models. First, until recently, extensive field measure- ments of speciated volatile organic compounds (VOCs), such as benzene, toluene, and xylenes were not carried out. Formerly, all hydrocarbons were measured as a whole without speciation, and termed as total hydrocarbons (THC). Second, valid source profiles based on various gaseous air pollutants have

not been established yet. Third, there seemed to be a higher collinearity among various source profiles based on gaseous species. Last, the reactivity of gas- eous air pollutants may need to be taken into account in the models. Even though there is room for improve- ment for receptor models on gaseous air pollutants, we perceived it as a useful tool in helping to set air pollution control strategies. In Taipei, several studies have shown that mobile-related air pollutants, such as CO and VOC, are associated with the deterioration of air quality (Chan et al., 1993, 1994; Liu et al., 1994). The emission inventory also indicates that mobile sources, including motorcycles, gasoline cars and die- sel buses and trucks, may account for about 90% of CO, 60% of NOx, and 90% of THC emissions in Taipei (Taiwan EPA, 1993). These pollutants' emis- sion contributions from different vehicle categories, however, are not well documented because the emis- sion factors and vehicle mileage of motorcycles and cars are unavailable for mobile source modeling in Taipei. In order to have a comprehensive control strategy based on the priorities of emissions, the es- timation of emissions from various mobile sources 25

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26 CHANG-CHUAN CHAN et al. N 10 km FT

iaipei city~_~ ~ r

cs

)

Taipei county

Fig. 1. The locations of monitoring stations in Taipei metropolitan area.

in Taipei is needed. This study, therefore, applies a modified receptor model to apportioning gaseous air pollutants from various mobile sources in metropoli- tan areas of Taipei.

METHODS

Samplincl locations

The ambient concentrations of VOCs, CO, NO~, and THC are collected at four fixed-site monitoring stations in Taipei metropolitan area. One of them, the Taipei-Bridge station (TB), is located at the intersection of two main traffic routes in downtown Taipei. The TB site is designated as a "traffic monitoring station" by Taiwan EPA. The height of sampling inlet is around 3 m. The other three stations, the Chung-San (CS), the Fu-Ta (FT), and the Ku-Ting (KT), are all located in campus of respective schools (see Fig. 1). They are all designated as "ambient air quality monitoring sta- tions" by Taiwan EPA since their locations are not closely adjacent to any main traffic routes. The heights of the samp- ling inlets at these three stations are all around 12 m. One particular feature of these stations is that there is a big gasoline service station near the FT station.

Samplino schedule

One-year measurements of air pollutants in 1993 are used for modeling. The sampling frequency of VOCs is one samp- ling day per week for the first seven months and one samp-

ling day per month for the last three months. On each sampling day, two 12-hour samples (7:00 a.m. to 7:00 p.m. and 7:00 p.m. to 7:00 a.m.) are collected simultaneously at four stations. For NO~, CO and THC, hourly concentrations measured continuously at four monitoring stations in 1993 are used in receptor modeling calculation.

Samplino and analytical methods

The U.S., EPA TO 1 method is modified to collect and analyze the VOCs. The sampling system consists of a stain- less steel tube (178 mm x 5.2 mm ID) with 0.6 g Tenax-GC, and a low-flow sampling pump (Gilian Inc., Model LFS l13D). The sampling rate is adjusted at 50mimin -1 for a duration of 12 h. The VOCs collected in the Tenax-GC are first thermally desorbed and then analyzed by a high resolu- tion gas chromatography-mass spectrometry (GC/MS) tech- nique, Such a measuring method can quantify a total of eight VOCs, including benzene, heptane, heptene, toluene, ethyl- benzene, m/p-xylenes, o-xylene, and isopropyl benzene. The

details of sampling and analytical conditions and QA/QC procedures have been reported in a previous study (Chart et al., 1993). Ambient concentrations of NOx, CO, and THC

are continuously measured by standard instruments for am- bient air monitoring stations, which are a chemilumines- cence method for NO~, a non-disperse infra-red (NDIR) method for CO, and a flame ionization detection (FID) method for THC.

Empirical receptor model

Conventionally, the mathematical receptor models, such as chemical mass balance models (CMB), have a general

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form like this:

Y~=X/3, i = 1 , 2 . . . n (1) where Y~ denotes the ambient concentration vector of a set of m pollutants, 1/= (/3j, P2, ..., ~p) is a p-vector of total mass concentrations contributed by p individual sources, and X is the m x p matrix of source profiles. It is well recognized that solutions to this equation usually suffer by the problems of collinearity among source profiles and the negative/~.

Several mathematical techniques, such as non-negative least square routine,% have also been successfully demon- strated to solve such problems (Wang and Hopke, 1989). In this paper, we propose to apply the Bayesian statistical approaches to solve these problems. In doing so, we treat /~ as a vector of random variables in our model, rather than solving/~ directly from equation (1). Therefore, the feature of 1~ can be better described through statistical modeling of the modified CMB equation by the following form:

a(YO = a ( x # ) + ~ N(O, W )

W =

"-.

(2)

where Y~,X, and p have the same definitions as in equation (1). To simplify the modeling process, we need first to trans- form the raw data by a function, 0, in order to assure that the vector of errors, 8, is normally distributed. Accordingly, the choice of g is dependent on the characteristics of raw data. Besides that, we must always restrict/~ to be non-negative in our model because soarces cannot produce negative contri- butions to ambient measurements physically.

Given n measurements of Y~ in the model, the calculation of equation (2) becomes a problem of computing the poste- rior distributions of A~ and 61 through 6 , in a Bayesian framework. The posterior distribution is, therefore, directly proportional to the product of the likelihood function, ~'(Yl/J, 61 ... fi,,), and a prior density, p(/~, ~51 ... ~,), which can be expressed by the following equation:

I I ( ~ , 6 ~ ... 6 , ~ l y ) o c E ( y l B , 6 t ... 6 , ) ' p ( B , 6 1 ... 6 ~ (3) where

{1.

¢'(~, t~l ... tim) oc I W r "/2)exp - ~ ~ [ g ( Y , ) - g(Xfl)]' i=1 x W - 1 {-g(yi) _ ~',Xfl)] } ' l(o.®)(fl).

In our model, the prioL p(fl,ft ... 6,), is assumed to be non- informative. Under such an assumption, one simplified form of the non-informative prior, P(fl,~l ... 6,,,), is chosen to be proportional to t~]- ~ x --. x 6ff 1.

Equation (3) is expressed as a proportional form only because it is difficult to compute the normalization constant of the higher dimensional posterior distribution needed for an exact form either by traditional analytic or numerical methods in the equation. From a Bayesian approach, we can estimate features of the posterior indirectly by using the Markov Chain Monte, Carlo (MCMC) method to draw samples from the product of likelihood function and the prior. Due to its conceptual simplicity in simulation and the availability of calculatic,n algorithms, such as Gibbs Sampler and Metropolis algorithm, the M C M C method has been widely applied to several statistics-related fields, such as statistical physics, image process, and medicine (Smith and Roberts, 1993).

In our application, the M C M C method obtains chains of values as samples to mimic the posterior distributions, which

are generated from the Gibbs Sampler and Metropolis algo- rithm. To perform the MCMC simulation, a starting value is first assigned to the algorithms. After tens or hundreds of iterations, the chains will start to converge to the posterior. The chains of values are then taken as samples once the chains converge to the posterior. The details of this algo- rithra are described in the Appendix A.

We used all available measurements from the sampling days in our model fitting, which were about 38-53d for VOCs and 329-363 d for CO, NOr and THC at the four monitoring stations. As expected, the raw data of these measurements were not normally distributed. Therefore, we selected log as our g function in equatio n (3) to transform the raw data into approximate normal distribution. We then assigned 5000 iterations in our simulation in order to gener- ate enough samples for the description of/3. However, we found that the simulated chains converged very quickly after 100 iterations. Instead of using all generated samples in our model fitting, we selected only 500 samples systematically from 4900 simulated//values, (/pol,/~1o2, ... ,//sooo) for fur- ther calculation. Accordingly, we can estimate the distribu- tion of source contributions,//, from these 500 samples for individual air pollutants at each monitoring station.

We used three criteria to check the model's internal con- sistency in our fitting approach. First, we proposed to use the averaging r-square, ~ , in the following equation to estimate overall goodness-of-fitness of the empirical model.

1 " ( ~ - - y i ' l ) ' ( f t - - Y ~ ' l )

n i = t

where I?i = X~, ~is the average of these 500 samples of • ~ is the average ofm measured concentrations of Y, and I is an m x 1 vector of ones. The model is said to be better fitted if the ~ is greater. Second, the proportion of model-calculated mass in the actual measurements, % mass, should be close to 100%. A model is considered to be ill-fitted ff the deviation of % mass is too large. Usually, 25% overestimation or under- estimation is considered to be unacceptable. Third, the vari- ation in the simulated source coefficients should be within the acceptable range. A smaller variation indicates that a better model is obtained. We used the inter-quartile range (IQR) of source coefiicients, which is the range between 75th and 25th percentiles of the samples, as the index of such variation in the model.

Source profile development

As shown in Table 1, 12 source profiles based on VOCs, NO,, CO, and THC are constructed for tailpipe emissions of gasoline ears and motorcycles, diesel vehicles, and gasoline vapors. Five VOC-based source profiles are calculated from normalizing weight concentrations of 8 VOC species in emis- sions to 100%. We reduced three different motorcycles into one source profile because their VOC-based source profiles were very similar. We constructed another seven source profiles for NOx, CO, and THC by normalizing their weight concentrations in emissions to 100%. For NOx, CO, and THC, the source profiles are significantly different between two-stroke and four-stroke motorcycles. The tailpipe emis- sions of VOCs, NOx, CO, and THC for gasoline cars and motorcycles are obtained from a study on vehicle emissions tests by chassis dynamometer under standard driving cycles, conducted in Taiwan (Chan et al., 1994). The tailpipe emis- sions of VOCs for diesel vehicles reported by Seheffet al. and the emissions of NOx, CO, and THC reported by Palmer are used as surrogate emissions for diesel vehicles in Taiwan since the data of diesel emissions are currently unavailable in Taiwan (seheff et al., 1992; Palmer, 1993). Because the emis- sions of speeiated VOCs from gasoline vapor are unavailable in Taiwan, the source profiles reported by Sigsby et al. are adopted in the current study (Sigsby et al., 1987).

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28 CHANG-CHUAN CHAN et al.

Table 1. Twelve source profiles normalized to eight VOCs and CO-NOx-THC (wt%)

Compounds Motorcycles Car_NC Car_C Diesel Gasoline vapor

Benzene 20.3 18.4 21,2 22.1 4.9 Heptene 2.9 2 2,8 0 0 Heptane 9.5 9.8 13.7 5.1 3.8 Toluene 34.4 32.4 36.7 29.1 62.8 Ethylbenzene 10.1 8.9 6.7 4.9 3.9 m/p-Xylene 12.1 20.3 13.2 6.9 15.6 o-Xylene 9.3 7.7 5.2 17.7 6.4 Isopropyl benzene 1.4 0.5 0.5 14.3 2.7

2S-NC 2 S _ C 4S_NC Car_NC Car_C Diesel Gasoline vapor

CO 58 66 82 79 69 26 0

NOx 0 0 4 12 18 14 0

THC 41 34 14 9 13 59 100

2S_NC: Two-stroke motorcycle without catalytic converter. 2S_C: Two stroke motorcycle with catalytic converter.

4S-NC: Four-stroke motorcycle without catalytic converter. Car_NC: passenger car without catalytic con- verter.

Car_C: passenger car with catalytic converter.

RESULTS AND DISCUSSION

Ambient measurements of air pollutants

The average ambient concentrations of 8 VOCs, CO, NOt, and T H C over the sampling period in four monitoring stations are summarized in Table 2. Mean concentrations are 67.1 #gin -3 for benzene, 129.6 #g m -3 for toluene, 6.52 m g m - a for CO, 0.43 m g m - a for NOt, and 2.59 m g m -3 for THC at the TB station. The mean concentrations are about 17.3-23.2 # g m - 3 for benzene, 58.7-85.2/~gm -3 for toluene, 1.15-1.78 m g m - a for CO, 0.08--0.14mgm -3 for N O t , and 1.33-1.47 mg m - 3 for T H C at three ambient sampling stations (FT, CS, and KT). Apparently, the concentra- tions of all air pollutants are the highest at the traffic monitoring station (TB). The ambient measurements, however, show no significant differences among three ambient air monitoring stations. The ratios of ambi- ent concentrations between the traffic station and the ambient station are about 1.5-3.9 for 8 VOCs, 3.7-5.7 for CO, 3.1-5.4 for N O t , and 1.8-2.0 for THC. Obvi- ously, mobile sources seem to contribute a large amount of concentrations of these pollutants meas- ured at the traffic station.

Source coefficients for 8 VOCs

The five emission sources considered in modeling 8 VOCs are motorcycles, catalyst passenger ears and non-catalyst passenger cars, diesel vehicles, and gaso- line vapor. The mean and I Q R of the estimated source coefficients, and the simulation model's */.mass and r 2 are shown in Table 3. Overall, the model's internal consistency is reasonably good because r 2 values, 0.70-0.75, are moderately high and %mass, 73-89%, are close to 1 for four monitoring stations. The vari- ation of source coefficients tends to vary with the absolute values of estimated source coefficients. As

source coefficients become smaller, their relative vari- ations become larger. F o r example, the IQR/mean ratios are always less than 1 for the non-catalyst passenger cars, which is always the greatest contribu- tion source at all monitoring stations. In contrast, for the second largest contribution source, the motor- cycles, and other minor sources, their IQR/mean ratios are either very close to 1 or greater than 1.

Non-catalyst passenger cars are the greatest contri- bution sources to 8 VOCs among five mobile sources. They account for 53--61'/o mass concentrations of 8 VOCs measured at four monitoring stations, which are equal to 92.0--220.3/zg m - 3 . In contrast, catalyst passenger cars have relatively small contributions to 8 VOCs. The difference in source contributions be- tween these two car types is generally in agreement with the difference in vehicle numbers and emission factors between non-catalyst and catalyst cars in Taipei. It is estimated that less than 20% passenger cars are currently equipped with catalysts in Taipei because catalytic converters are only required for the 1991 model of domestically made and imported passenger cars. Moreover, the emission factors of eight VOCs for the two car types are quite different, differing by about a factor of two. Motorcycles are the second highest contribution sources for eight VOCs at the TB station, which contribute 30.8 #g m - 3 to total VOC mass concentrations. The high contributions from motorcycles at TB station are believed to be due to a relatively higher motorcycle traffic volume near the station where specific traffic lanes are designated for motorcycles. The contributions of gasoline vapor to eight VOCs are relatively higher at three ambient monitoring stations than the traffic station. This indi- cates that the importance of fugitive emissions in- creases as the contributions of tail-pipe emissions decrease. It is also understandable that diesel vehicles have the least contributions to eight VOCs in all

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0 O c , i r ~ ~ c , i ~ ( ' - , i , , ' 4 ~ " " '

~o

o g-- ~J o ed r~ t~ p~ e~ ¢q 8

..g

m o z

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30 CHANG-CHUAN CHAN et al. stations because the diesel engine's hydrocarbons

emissions consist of higher carbon numbers than the eight VOCs in this study.

Source coefficients for CO, NO~, and T H C

The source coefficients of CO, NO~, and THC for seven different mobile sources are shown in Table 4. Apparently, the overall performance of modeling CO, NOx, and THC is even better that of VOCs. The values, 0.774).98, are high and the %mass is close to 1. The %masses are about 97-100% for CO, 100-102% for NOx, and 93-101% for THC. The results of IQR/mean show that variation in modeling CO, NOx, and THC is comparable to modeling VOCs.

Most of the CO concentrations measured at four monitoring stations are contributed by three motor- cycle types and the non-catalyst cars. In total, they account for about 70% of CO's total mass concen- trations measured at four monitoring stations. The passenger cars account for another 20% of CO con- centrations, while the diesel emissions explain the other 1-5%. The differences in CO contributions among these three vehicle categories simply reflect the differences in their CO emission factors. On average, motorcycles' CO emission factors are about three times higher than passenger cars' (Chan et al., 1994). Comparing source contributions among motorcycles alone, we found that 2-stroke motorcycles' CO contri- butions are the greatest. At three ambient monitoring stations, two-stroke motorcycles' contributions are about 2.5-3 times that of four-stroke motorcycles. The differences in CO contributions between two- stroke and four-stroke motorcycles are generally in agreement with their differences in CO emission rates. As reported by Chan et al., a two-stroke motorcycle's CO emission rates are about twice that of a stroke motorcycle (Chan et al., 1995). However, we found equal CO contributions from two-stroke and four- stroke motorcycles at the TB station, whose contribu- tions are 39.4 and 39.9%, respectively. We believe this may simply reflect differences in traffic volumes be- tween two-stroke and four-stroke motorcycles near the TB station. The mean source contributions of CO in terms of mass concentrations are 0.59-2.37 mg m - 3 from two-stroke motorcycles, 0.22-2.60 mg m - 3 from four-stroke motorcycles and 0.26-1.46 mg m - ~ from passenger cars.

F o r NOx, passenger cars are the most important contributing sources, which account for 5 0 ~ 2 % of NOx concentrations measured at four stations. The second important sources for NOx are diesel vehicles at three ambient monitoring stations (25-42%) and four-stroke motorcycles at the TB station (30%). In contrast, two-stroke motorcycles have no significant contributions to NOx. Again, such comparisons can be explained by differences in emission factors among vehicles and variation in traffic volumes among monitoring stations. It is known that two-stroke motorcycles are low NO~ emitters and diesel cars are

high emitters (Chan et al., 1995). The mean source contributions of NOx in terms of mass concentrations are 0.05-0.27mgm -3 from passenger cars and 0.024).5 mg m - 3 from diesel cars.

For THC, gasoline vapor and two-stroke motor- cycles are two of the most important contributing sources, which account for 17-58% and 25-53% of THC concentrations measured at four monitoring stations, respectively. Gasoline vapor becomes an im- portant contributing source to THC because several light-chain hydrocarbons evaporate from the vehicu- lar gasoline tanks easily in the subtropical weather of Taiwan. Two-stroke motorcycles are another im- portant contributing source because of their high THC emission rates. On average, two-stroke motor- cycles' THC emission rates are about 3 ~ times higher than that of other vehicles (Chan et al., 1995). The source contributions of THC in terms of mass concen- trations are 0.38-0.85mgm -3 from gasoline vapor and 0.17-1.39 mg m - 3 from two-stroke motorcycles.

Model comparisons and limitations

The results of apportioning CO, NOx, or THC measurements to various motor vehicles have not been reported in the previous CMB receptor model- ing studies. The lack of reliable source profiles, which are based on CO, NOx, and THC emissions, is the main difficulty in modeling these pollutants. Although there are some CMB receptor modeling studies on VOCs, mobile sources are not further classified to various vehicle types in these studies. The high col- linearity of source profiles among mobile sources is one major problem for traditional CMB receptor models in apportioning mobile sources. F o r VOC- based source profiles in this study, there is a high collinearity among two-stroke motorcycles, four- stroke motorcycles and passenger cars because their condition indexes (CI) are greater than 30 in the regression collinearity diagnosis. Accordingly, the CMB7 model can only partition VOCs into two cat- egories, the gasoline vapor and the tailpipe emissions of all vehicles. Apparently, the calculation methodo- logy applied in our empirical receptor model is more robust toward coUinearity problems because it has successfully attributed contributions of VOCs, CO, NOx and THC to 5-7 different mobile sources. How- ever, the collinearity problems are still not fully solved by our approach because source coefficients' vari- ations are still relatively large for minor contributing sources in our models.

Traditional CMB models also often encounter the problem of overestimating or underestimating total source contributions. This is not found to be a serious problem for our empirical receptor models. F o r CO, NO~ and THC, their ambient concentrations at four monitoring stations are very close to the total emitted %mass by seven sources in Taipei metropolis. The ambient concentrations of VOCs at most monitoring stations except the FT station are also well explained by five sources considered in Taipei. Such modeling

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[..., "6 E % 00 I= c~ o~ I == ~J

z

[-, =1 0 r~3 " o ~ o ~

o

= ~ ~ o ~ . . . 0 0 0 . ~ . ~ , ~ ,.~ ,.o .,~ E "E

8

8

8

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32 CHANG-CHUAN CHAN et al. results are empirically plausible because there are

relatively fewer industrial or fugitive emission sources compared to mobile sources in Taipei. The VOC measurements at the F T station are significantly underestimated because our empirical model can only explain 73% of total mass concentrations. This im- plies that additional contributions to VOCs may be from emissions other than mobile sources near the F T station. However, a more accurate and comprehens- ive emission inventory of these pollutants in Taipei is needed in order to have a precise validation of the modeling results.

It has also been reported that variation in the hydrocarbon's photochemical reactivity is a problem in CMB receptor modeling for VOCs (Aronian et al., 1989) and PAHs (Li and Kaments, 1993). The measurements of pollutants need to be modified by individual pollutant's reactivity in order to meet mass conservation requirement in CMB models. The reac- tivity problem is believed not to be a major problem in our model for the following three reasons. First, the reactivities of eight VOCs are about the same except heptene. The experimental results of these VOCs' re- activity to OH radicals in the laboratory show that their reactivities are in the same order according to the reports of Atkinson (1986). Second, the distances between the ambient measurements and the emission sources at station are relatively short. Therefore, vari- ation of these air pollutants' half-lives may not have major effects on the modeling results. Third, the effect of meteorological variation on source patterns can also be neglected because one-year averaging meas- urements are used in our models. However, a more accurate and precise estimation of source contribu- tions can still be expected by including the reactivity of VOCs and the meteorological variation in our empirical models.

The representativeness of source profiles is deemed to be the major limitation of our empirical model. The real-world emission factors of mobile sources can be very different from the emission factors obtained from the dynamometer because the driving cycles and vehicular ages in the standard testing procedures may not be representative. Therefore, the mean con- tributions estimated by our empirical receptor model may overestimate the contributions from "clean vehicles" but underestimate the contributions from "dirty vehicles".

CONCLUSION

An empirical receptor model based on the Markov Chain Monte Carlo simulation has been successfully applied to apportioning the contributions of the am- bient measurements of eight VOCs, CO, NOx, and THC to six various mobile sources and one fugitive source in Taipei metropolitan. Non-catalyst passen- ger cars are found to be a major source of V O C s and NOx in Taipei. The other important source of NOx is

the diesel cars. The motorcycles, particularly the two- stroke motorcycles, are found to be a major source of CO and THC in Taipei. The gasoline vapor is found to be another major source of THC in Taipei. The source contributions estimated by our empirical re- ceptor models are generally in agreement with emis- sion factors and number of various motor vehicles in Taipei metropolitan. Our empirical receptor models are also more robust to the issues of VOC's reactivity and source profile's collinearity than traditional CMB models. This study successfully demonstrates that em- pirical receptor models can be applied to apportion- ing organic and inorganic air pollutants to various mobile sources in the metropolitan areas where their air pollution problem are mainly traffic related. The proposed receptor models are believed to be very useful for validating inventory of various emission sources or designing effective management programs of air quality controls.

Acknowledgements--We would like to thank the Taiwan Environmental Protection Agency (contract No. EPA-82- E4FI-08-23) for partially sponsoring this study. We would especially like to thank all auto companies which helped us carry out the emission tests.

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Wadden R. A., Uno I. and Wakamatsu S. (1986) Source discrimination of short-term hydrocarbon samples meas- ured aloft. Envir. Sci. Technol. 20, 473-483.

Wang D. and Hopke P. K. (1989) The use of constrained least squares to solve the chemical mass balance problem.

Atmospheric Environment 23, 2143-2150.

APPENDIX A: MARKOV CHAIN MONTE CARLO METHODS (MCMC)

We follow the notation of the M C M C methods used by Smith and Roberts (1993) to describe Gibbs sampler and Metropolis algorithms in this paper. The objective of using the M C M C in this study is to draw p-vector samples

0 = (01, 02, ..., 0p) from the distribution A(0), which is pro- portional to the product of a likelihood function and a prior. To serve such a purpose, we need to construct Markov chains from two well-established simulation procedures, the Gibbs sampler and the Metropolis algorithms. The system- atic form of the Gibbs sampler algorithm is used in the following two steps. The first step is to input one set of starting values 0 ° = (0 °, 0 ° . . . 0 °) arbitrarily to initiate the algorithm. In the second step, successively random drawings can be obtained from the full conditional distributions de- scribed in the following:

0~ from A(01 l0 ° . . . 0 °) 021 from A(02 101, 03 . . . 0 °) i o

0~ from A(0.10~, O2 ~, .... 0p_,).

By completing the above cycle once, we can get a transition from 0 ° = ( ~ , o°2 .. . . . 0~ °) to 01 = (0L 0~ . . . 0.'). Wherefore,

the iterations of this cycle, in turn, will produce a sequence, 0 °, 0 I, 0 2, ..., ff . . . which is a realization of a Markov chain. The key feature of this algorithm is that we only sample from one=dimensional distributions, which are per- formed by the Metropolis algorithm described in the follow- ing paragraph.

In generating a value for the next realized state from the current state realization O~ by the Metropolis algorithm, we can randomly draw O~ from the neighbor of 0~. and calculate the ratio of

A(0? i 0,i+ t, .... 0 j - l , ~ + 1 . . . 0r) ,+ t A(~ f 071 . . . 07-I, ~ + , . . . 0~)'

We then compare the ratio with a random number, which is drawn uniformly between 0 and 1. We will accept ~+ 1 __ 0~ if the ratio is greater than this random number. Otherwise, we will reject the value 0~', and set ~+ t = 0).

Therefore, the Markov chain of 0 °, 01, 02 . . . 0 t .. . . can be successfully constructed by using the Metropolis algo- rithms within the Gibbs sampler as explained in the previous discussions. When t is large enough, ff = ( ~ , 0~ .. . . . 0~,) will approximately reach the equilibrium distribution, A(0). In other words, the simulation will start to converge after cer- tain iterations. The chains of values after convergence, ac- cordingly, become available samples to mimic A(0).

數據

Fig.  1.  The locations  of monitoring stations  in Taipei metropolitan area.
Table 1.  Twelve source  profiles normalized  to eight  VOCs  and CO-NOx-THC  (wt%)

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