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Chang’an University The Statistical Distributions of SO 2, NO 2 and PM 10 Concentrations in Xi’an, China Jiang Xue 1, Shunxi Deng 1, Ning Liu 1, Binggang Shen 2 1 Chang’an University, Xi’an, China 2 Shaanxi Institute of Environmental Sciences and Technology Xi’an, China Chang’an University

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Xi’an, is one of four world- famous ancient cities

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Chang’an University Introduction In this work, the time series data of three conventional air pollutants concentrations in recent years were taken and analyzed. The purpose is to determine the best distribution models for SO 2, NO 2 and PM 10 concentrations and to estimate the required emission reduction to meet the ambient air quality standard (AAQS), through fitting the daily average concentration data to the several used commonly distribution functions.

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Chang’an University The data were taken over a three-year period from 1 January 2006 to 31 December 2008, the time series data of three air pollutants were measured at seven ambient monitoring stations in Xi’an. The detailed locations of these stations are shown in Fig.1 Fig1. The locations of the monitoring sites in Xi’an Data sources

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Chang’an University Fig.2. The variability of daily average concentration for each air pollutant with time. (a) SO 2 (b) NO 2 (c) PM 10, from 1 January 2006 to 31 December The variability of daily average concentration of air pollutants with time Basic statisticsSO 2 NO 2 PM 10 N (number of observations) Missing001 Zero values000 Maximum Minimum Mean Median SD Variance Skewness Percentiles Table 1 Summary of the basic statistics Note: the unit are mg/m 3.

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Chang’an University The daily average concentrations of three pollutants have strongly seasonal variability from these figures. Fig.2 also shows the exceedance of three air pollutants, and the probabilities of exceeding the secondary standard of AAQS are 1.09% for SO 2, 0.82% for NO 2 and 20.73% for PM 10. This means that the number of days exceeding the AAQS for three air pollutants in a year are 4, 3 and 76, respectively. The probability of exceedance for PM 10 is significantly higher than SO 2 and NO 2. So, PM 10 has become a major air pollutant in Xi’an.

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Chang’an University Distribution models used in representing air pollutant concentrations In this study, the following distributions are chosen to fit the concentration data, they are Lognormal, Gamma, Inverse Gaussian, Log-logistic, Beta, Pearson 5, Pearson 6, Weibull and Extreme value distributions.

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Chang’an University Goodness-of-fit tests The goodness-of-fit tests are used to determine the most appropriate statistical distribution model of air pollutant concentrations, including KS test, AD test, PCC test and Chi-squared test. KS test ： AD test ： test ：

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Chang’an University The identification of the best distribution model Types SO 2 NO 2 PM 10 KSADχ2χ2 KSADχ2χ2 KSADχ2χ2 Lognormal0.042(1)3.66(3)53.4(3)0.029(4)1.03(3)17.0(6)0.059(4)3.80(4)70.8(4) Pearson (2)3.04(2)43.0(1)0.029(6)1.03(4)17.0(7)0.069(6)4.95(6)73.2(6) Pearson (3)2.99(1)44.3(2)0.029(3)1.01(2)15.3(4)0.056(3)3.44(3)59.8(2) Extreme Value0.049(4)5.48(5)67.0(4)0.027(1)1.00(1)15.2(3)0.052(2)3.35(2)61.4(3) Log-Logistic0.053(5)4.83(4)74.1(5)0.032(7)1.48(8)18.4(8)0.041(1)2.15(1)44.9(1) Inv. Gaussian0.069(6)8.89(6)95.7(6)0.060(9)8.46(9)54.9(9)0.062(5)4.91(5)80.7(8) Gamma0.082(7)11.52(7)98.9(7)0.029(5)1.09(5)15.0(2)0.069(7)4.97(7)72.7(5) Beta0.082(8)11.54(8)98.9(8)0.028(2)1.15(6)16.6(5)0.070(8)5.17(8)76.4(7) Weibull0.085(9)15.80(9)168.6(9)0.033(8)1.38(7)14.7(1)0.088(9)9.77(9)104.1(9) Table 2 The results of goodness-of-fit tests Note: The number in parentheses is the results of goodness-of-fit tests; red font corresponding distribution is the best distribution model under the different goodness-of-fit tests.

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Chang’an University The most appropriate statistical distribution models for the daily average concentration of SO 2, NO 2 and PM 10 were Pearson 6, Extreme Value and Log-Logistic distributions, respectively (Fig.3). (a) SO 2 Mean = mg/m 3 S.dev = mg/m 3 Mean = mg/m 3 S.dev = mg/m 3 Mean = mg/m 3 S.dev = mg/m 3 (a) NO 2 (a) PM 10 Fig.3. The best distribution models of three air pollutant concentrations: (a) SO 2 (b) NO 2 (c) PM 10.

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Chang’an University Parameter estimation The commonly methods of parameter estimation are the maximum likelihood estimator (MLE), the least square estimator (LSE), the method of quantiles (MoQ) and the method of moments (MoM). MoM is more widely used and MLE provides the best estimate of the parameters (Lynn, D.A., 1974). In the study, MLE was used, it is defined as:

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Chang’an University The estimated values of parameters for the best distribution model of air pollutants are shown in Table 3. Air pollutants The best distribution models Parameters SO 2 Pearson 6 α= β= σ= θ= NO 2 Extreme Valueσ= θ= k= PM 10 Log-Logistic α=4.506 σ= θ= Table 3 The estimated values of parameters

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Chang’an University Estimating the emission source reduction in Xi’an After determining the most appropriate distribution model for air pollutant concentrations, the emission source reduction R (%) required to meet the AAQS can be predicted from a rollback equation: where E{c} s is the expected concentration of distribution when the extreme value equals c s (i.e. the values of the AAQS), E{c} is the mean concentration of the actual distribution and c b is the background concentration.

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Chang’an University Table 4 The emission reduction Air pollutants The best distribution models E{c} s ( mg/m 3 ) E{c} ( mg/m 3 ) R (%) PM 10 Log-Logistic NO 2 Extreme Value SO 2 Pearson Note: when estimating the emission reduction in this study, c b is neglected in the rollback equation. Therefore, the emission source reductions of SO 2, NO 2 and PM 10 concentrations to meet the AAQS are -16.7%, 3.8% and 21.1%, respectively. It means that the annual average SO 2 concentration meets to the AAQS without requiring further mitigation and with an environmental capacity of 16.7% in future, while control of PM 10 and NO 2 emission sources in Xi’an should be increased in order to reduce the concentration and meet the AAQS.

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Chang’an University Thank you very much!

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