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.

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The Statistical Distributions of SO2, NO2 and PM10 Concentrations in Xi’an,

China

Jiang Xue 1, Shunxi Deng 1, Ning Liu 1, Binggang Shen 2

1 Chang’an University, Xi’an, China2 Shaanxi Institute of Environmental Sciences and Technology Xi’an, China

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

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IntroductionIn 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 SO2, NO2 and PM10 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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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

5

1

2

3

5 67

4

Cao Tan

Switch Factory

West Gaoxin Zone

Municipal Stadium

Xingqing District

Xiao Zhai

Textile City

N

5公里

Fig1. The locations of the monitoring

sites in Xi’an

Data sources

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(a) SO2

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0 300 600 900 1200days

SO

2 d

aily

ave

rage

con

cent

rati

on,

mg/

m3

AAQS (secondarystandard), 24-hour

0.15 mg/m3

Fig.2. The variability of daily average concentration for each air pollutant with time. (a) SO2 (b) NO2 (c) PM10,

from 1 January 2006 to 31 December 2008.

The variability of daily average concentration of air pollutants with time

Basic statistics SO2 NO2 PM10

N (number of observations)

1096 1096 1095

Missing 0 0 1

Zero values 0 0 0

Maximum 0.2406 0.1052 0.3728

Minimum 0.0114 0.0116 0.0346

Mean 0.0507 0.0416 0.1260

Median 0.0404 0.0413 0.1188

SD 0.0309 0.0137 0.0535

Variance 0.0010 0.0002 0.0029

Skewness 1.9311 0.4700 1.4609

Percentiles

25 0.0288 0.0319 0.0912

50 0.0404 0.0413 0.1188

75 0.0649 0.0498 0.1443

Table 1 Summary of the basic statistics

Note: the unit are mg/m3.

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(c) PM10

0.00

0.10

0.20

0.30

0.40

0 300 600 900 1200

days

PM1

0 da

ily

aver

age

conc

entr

atio

n, m

g/m3

AAQS (secondarystandard), 24-hour

0.15 mg/m3

(b) NO2

0.00

0.04

0.08

0.12

0 300 600 900 1200days

NO

2 d

aily

ave

rage

con

cent

rati

on, m

g/m3

AAQS (secondarystandard), 24-hour

0.08 mg/m3

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 SO2, 0.82% for NO2 and 20.73% for PM10. 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 PM10 is significantly higher than SO2 and NO2.

So, PM10 has become a major air pollutant in Xi’an.

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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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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：

|)()(|max 0 xFxFD nn

k

i i

ii

np

npn

1

22 )(

nn

xFxFiA

n

i

inoio

1

12 )]}(1ln[)(){ln12(

2

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The identification of the best distribution model

TypesSO2 NO2 PM10

KS AD χ2 KS AD χ2 KS AD χ2

Lognormal 0.042(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 6 0.046(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 5 0.047(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 Value 0.049(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-Logistic 0.053(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. Gaussian 0.069(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)

Gamma 0.082(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)

Beta 0.082(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)

Weibull 0.085(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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The most appropriate statistical distribution models for the daily average concentration of SO2, NO2 and

PM10 were Pearson 6, Extreme Value and Log-Logistic

distributions, respectively (Fig.3).

Histogram Pearson 6 (4P)

SO2 concentration, mg/m30.20.150.10.05

Pro

babili

ty d

ensity f

unction

0.36

0.32

0.28

0.24

0.2

0.16

0.12

0.08

0.04

0

(a) SO2

Mean = 0.0514 mg/m3

S.dev = 0.0390 mg/m3

Histogram Gen. Extreme Value

NO2 concentration, mg/m30.10.080.060.040.02

Pro

babili

ty d

ensity f

unction

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

Histogram Log-Logistic (3P)

PM10 concentration, mg/m30.360.320.280.240.20.160.120.080.04

Pro

babili

ty d

ensity f

unction

0.26

0.24

0.22

0.2

0.18

0.16

0.14

0.12

0.1

0.08

0.06

0.04

0.02

0

Mean = 0.0416 mg/m3

S.dev = 0.0135 mg/m3

Mean = 0.1268 mg/m3

S.dev = 0.0574 mg/m3

(a) NO2

(a) PM10

Fig.3. The best distribution models of three air pollutant concentrations: (a) SO2 (b) NO2 (c) PM10.

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Parameter estimation The commonly methods of parameter estimation are th

e 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:

n

iix xfL

1

)|()(

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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

SO2 Pearson 6α=10.774   β=3.4853 σ=0.00989   θ=0.00847

NO2 Extreme Value σ=0.01268 θ=0.03626 k=-0.17945

PM10 Log-Logistic α=4.506 σ=0.1178 θ=-0.00114

Table 3 The estimated values of parameters

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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 cs (i.e. the values of the AAQS), E{c} is the mean concentration of the actual distribution and cb is the background concentration.

{ } { }

{ }S

b

E c E cR

E c c

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Table 4 The emission reduction

Air pollutants

The best distribution models

E{c}s ( mg/m3)

E{c}( mg/m3)

R(%)

PM10 Log-Logistic 0.100 0.1268 21.1

NO2 Extreme Value 0.040 0.0416 3.8

SO2 Pearson 6 0.060 0.0514 -16.7Note: when estimating the emission reduction in this study, cb is neglected in the rollback equati

on.

Therefore, the emission source reductions of SO2, NO2 and PM10

concentrations to meet the AAQS are -16.7%, 3.8% and 21.1%, respectively.

It means that the annual average SO2 concentration meets to the

AAQS without requiring further mitigation and with an environmental capacity of 16.7% in future, while control of PM10

and NO2 emission sources in Xi’an should be increased in order to

reduce the concentration and meet the AAQS.

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Thank you very much!