Transcript Chang`an University

Chang’an University
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, China
2 Shaanxi Institute of Environmental
Sciences and Technology Xi’an, China
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Xi’an, is one of four worldfamous ancient cities
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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 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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Data sources


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.
N
1 Cao Tan
Switch Factory
xpy
Ring E
The detailed locations of
these stations are shown in
Fig.1
Fig1. The locations
of the monitoring
sites in Xi’an
5公里
2
Xingqing District
5
6
7
Municipal Stadium
Textile City
3
5
West Gaoxin Zone
4
Xiao Zhai
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The variability of daily average concentration of
air pollutants with time
(a) SO2
Table 1 Summary of the basic statistics
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
25
0.0288
0.0319
0.0912
50
0.0404
0.0413
0.1188
75
0.0649
0.0498
0.1443
Percentiles
Note: the unit are mg/m3.
AAQS (secondary
standard), 24-hour
3
SO2
SO2 daily average concentration, mg/m
Basic statistics
0.30
0.25
0.15 mg/m3
0.20
0.15
0.10
0.05
0.00
0
300
600
days
900
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.
1200
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(b) NO2
0.12
AAQS (secondary
standard), 24-hour
NO2 daily average concentration, mg/m
3
The daily average concentrations
of three pollutants have strongly
seasonal variability from these
figures.
3
0.08 mg/m
0.08
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.
0.04
0.00
0
300
600
days
900
1200
(c) PM 10
0.40
PM 10 daily average concentration, mg/m
3
AAQS (secondary
standard), 24-hour
0.15 mg/m3
0.30
The probability of exceedance for
PM10 is significantly higher than
SO2 and NO2.
0.20
0.10
So, PM10 has become a major air
pollutant in Xi’an.
0.00
0
300
600
days
900
1200
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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： Dn  max | Fn ( x)  F0 ( x) |
(2i  1){ln Fo ( xi )  ln[ 1  Fo ( xn i 1 )]}
n
AD test： A  
n
i 1
n
2
2
(
n

np
)
2
i
2

 i
  test：
npi
i 1
k
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The identification of the best distribution model
Table 2 The results of goodness-of-fit tests
SO2
Types
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)
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).
0.26
Mean = 0.0514 mg/m3
0.18
Mean = 0.0416 mg/m3
0.32
mg/m3
0.16
mg/m3
Probability density function
S.dev = 0.0390
0.28
0.24
0.2
0.16
0.12
Probability density function
0.36
0.14
0.12
0.1
0.08
0.06
S.dev = 0.0135
0.24
Mean = 0.1268 mg/m3
0.22
S.dev = 0.0574 mg/m3
0.2
0.18
0.16
0.14
0.12
0.1
0.08
0.06
0.08
0.04
0.04
0.02
0
0.04
0.02
0
0
0.05
0.1
0.15
0.2
0.02
0.04
SO2 concentration, mg/m3
Histogram
Pearson 6 (4P)
(a) SO2
0.06
0.08
NO2 concentration, mg/m3
Histogram
Gen. Extreme Value
(a) NO2
0.1
0.04
0.08
0.12
0.16
0.2
0.24
0.28
0.32
PM10 concentration, mg/m3
Histogram
Log-Logistic (3P)
(a) PM10
Fig.3. The best distribution models of three air pollutant concentrations: (a) SO2 (b)
NO2 (c) PM10.
0.36
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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:
n
L( )   f x ( xi |  )
i 1
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The
estimated values of parameters for the best
distribution model of air pollutants are shown in Table 3.
Table 3
The estimated values of parameters
Air
pollutants
The best
distribution models
Parameters
SO2
Pearson 6
α=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
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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:
E{c}  E{c}S
R
E{c}  cb
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.
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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
-16.7
Note: when estimating the emission reduction in this study, cb is neglected in the rollback
equation.
 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!