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CHEMICAL ENGINEERING TRANSACTIONS 
 

VOL. 61, 2017 

A publication of 

 

The Italian Association 
of Chemical Engineering 
Online at www.aidic.it/cet 

Guest Editors: Petar S Varbanov, Rongxin Su, Hon Loong Lam, Xia Liu, Jiří J Klemeš 
Copyright © 2017, AIDIC Servizi S.r.l. 

ISBN 978-88-95608-51-8; ISSN 2283-9216 

Correlation Analysis between Ozone and Other Atmosphere 

Characteristics 

Yuhan Dinga,*, Guohai Liua, Xianqi Guob, Congli Meia, Peisuo Yanga 
aJiangsu University, Zhenjiang, 212013, Jiangsu, China  
bPutuo Environmental Monitoring Station, Zhoushan, 316100, Zhejiang, China 

 yhding@ujs.edu.cn 

The correlation between ozone and other atmosphere characteristics is important for air pollution analysis. It is 

complicated to model and analyse. In this paper, a correlation analysis method based on neural network and 

mean impact value (NN-MIV) is proposed. In NN-MIV correlation analysis method, the external correlation of 

key variable (ozone) and auxiliary variables (other atmosphere characteristics) is calculated by MIV and 

internal correlation is calculated by NN. By this means, stable correlations are obtained. The correlation value 

shows that ozone is most related to NO2, followed by humidity, PM2.5, temperature and pressure. The 

correlation result is then analysed and some valuable conclusions are presented. Finally, an NN correlation 

model (or soft sensing model) of ozone is constructed by the 5 most correlated variables and a good soft 

sensing result is obtained. 

1. Introduction 

The tropospheric ozone is a severe secondary pollutant and a kind of greenhouse gas in the atmosphere. The 

tropospheric ozone is mainly produced by the photochemical reaction from the first pollutant, such as NOx, 

SO2 and volatile organic compound, emitted by motor vehicles and factories (Jenkin et al., 2000). With the 

increasing consumption of the mineral fuel, the emission of the first pollutant is increasing rapidly, resulting in 

the increasing of the ozone in the atmosphere. High density of the ozone will influence the human health and 

creature growth, bring serious harm to the ecosystem (Wang et al., 2001). 

Researches indicate that ozone is not only related to the other pollutant gas, but also the ultraviolet, 

atmosphere temperature, wind speed and inhalable particles (Sadanaga et al., 2017). Therefore, it is 

necessary to learn the correlation between these atmosphere characteristics (including the pollutant gases) 

and the ozone. Finding the correlation model is helpful to predict and control the air pollution (Sillman, 1999). 

There are quite a few researches reported in this area. For instance, Saitoa et al. (2002) studied the 

relationship between O3, and its precursors (NOx and NMHC), but they did not research the relationship 

between O3 and other atmosphere characteristics. Nishanth et al. (2014) analysed the correlation between O3 

and its precursors as well as investigated the influence of PM10 on surface O3. Santurtún et al. (2015) 

discussed the temporal variations of surface ozone concentrations and its link with atmospheric pattern. 

However, the analysis method is the simple classification and no numerical result of the relationship is 

presented.  

In this paper, a correlation analysis method based on neural network and mean impact value (NN-MIV) is 

proposed. In NN-MIV correlation analysis method, the external correlation of key variable (ozone) and 

auxiliary variables (other atmosphere characteristics) is calculated by MIV method (Sun et al., 2012) and 

internal correlation is calculated by NN method (Du Jardin et al., 2010). A stable correlation is established by 

combining the both methods. In the meantime, an NN correlation model (or soft sensing model) of ozone is 

constructed using the 5 most correlated variables. The soft sensing result is expected to be used as real 

measurement value in some special circumstances such as ozone sensor failure.  

                               
 
 

 

 
   

                                                  
DOI: 10.3303/CET1761289

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Please cite this article as: Ding Y., Liu G., Guo X., Mei C., Yang P., 2017, Correlation analysis between ozone and other atmosphere 
characteristics, Chemical Engineering Transactions, 61, 1747-1752  DOI:10.3303/CET1761289  

1747



2. Data source and analytical method 

The data used to analyse the correlation between the ozone concentration and atmosphere characteristics are 

collected from 2013 to 2015 with interval being 1 h in Donggang, Putuo, Zhoushan, China. As Zhoushan is an 

island city, the ozone and other atmosphere data are little affected by the industry and traffic of other cities, 

and the relation between ozone and another atmosphere variable is relatively stable and easy to research. 

The sampling equipment is on the top of a seven-story building in 29.57° North Latitude and 12.18° East 

Longitude. The collected data include SO2, NO2, CO, PM2.5, PM10, temperature (T), atmosphere pressure (P), 

humidity (H), wind speed (WS) and O3. Table 1 shows some typical data of each variable. 

Then the collected data are analysed and processed, forming several batches of valid data. After that, the 

correlation between variables can be researched. 

Table 1: Typical data 

O3 

(mg/m3) 

SO2 

(mg/m3) 

NO2 

(mg/m3) 

CO 

(mg/m3) 

PM2.5 

(mg/m3) 

PM10 

(mg/m3) 

T 

(℃) 

P 

(kPa) 

H 

(%) 

WS 

(m/s) 

135 9 11 0.9 27 38 10.183 101.896 65.177 0.464 

120 8 14 0.9 26 37 9.803 101.837 66.168 0.173 

109 7 17 0.9 25 36 9.54 101.766 65.144 0.121 

109 7 14 0.9 23 35 9.621 101.692 62.988 0.236 

109 6 12 0.9 24 36 9.468 101.695 64.764 0.166 

109 5 13 0.9 22 33 9.435 101.74 68.077 0.158 

81 6 40 1 25 39 9.86 101.795 69.415 0.159 

66 11 56 1.1 34 53 12.56 101.828 55.844 0.123 

84 12 39 0.9 27 42 14.557 101.877 52.767 0.256 

107 13 24 0.9 24 39 15.457 101.936 42.814 0.556 

3. NN-MIV correlation analysing method 

3.1 Mean impact value (MIV) correlation analysis 
Consider an independent input variable vector which contains p variables, observe it m times to get the 

variable space  1 2 mX x x x , and each dependent output variable corresponding to the sample point 

can be written as  1 2 mY y y y . Taking independent variable vector X including m samples as input, 

the corresponding output vector Y as output, an initial neural network is trained and saved. Give a 10 % 

increase and 10 % decrease to a single independent variable at one time. In this way, 2p ( 1,i p ) new 

variable spaces can be obtained.  

11 12 1

21 22 2

(1)

1 2

1 2

(1 10%) (1 10%) (1 10%)

m

m

i

i i im

p p pm

x x x

x x x

x x x

x x x

 
 
 
 

  
   

 
 
  

X  (1) 

11 12 1

21 22 2

(2)

1 2

1 2

(1 10%) (1 10%) (1 10%)

m

m

i

i i im

p p pm

x x x

x x x

x x x

x x x

 
 
 
 

  
   

 
 
  

X  (2) 

Take the newly-constructed variable spaces one by one as the input of the neural network model trained 

previously, and 2p groups of output vector are obtained through the network:  

1 2

(1) (1) (1) (1)

mi i i
y y y 
 i

Y  (3) 

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1 2

(2) (2) (2) (2)

mi i i i
y y y 
 

Y  (4) 

Each group is corresponding to the sample point whose i th  ( 1,2i p ) variable index is changed. 

Calculate the difference of Eq(3) and Eq(4) to obtain the impact value by the equation 
(1) ( 2)

i i i
IV Y Y   when 

the i-th variable indicator is changed. And the mean impact value can be calculated as following:  

1

( ) /
m

i i
j

MIV IV j m


  , 1,2,i p  (5) 

The symbol of 
i

MIV  indicates the contribution of the independent input variable to the dependent output 

variable, whose value represents a relation between the input variable and the output variable. Therefore, the 

correlation of 
i

x  and y  can be calculated as: 

M

1

i

i

p

i

i









MIV

MIV

 
(6) 

This method calculates the correlation of input variables to the output by the changes of external input, hence 

it can be defined as external correlation. 

3.2 Neural network (NN) correlation analysis 
The neural network (Souza et al., 2015) used in the method is a kind of single hidden layer feedforward neural 

network as shown in Figure 1. The structure of the NN can be described by the following expression: 

0 0
1 1

( )
q p

j ji i j
j i

y F   
 

    x  (7) 

In Eq(7), 
1 2

T

p
x x x x    , p refers to the number of input variables, ( 0,1, , )j j q   are the weights 

from hidden layer to output layer, 
0 1

( , , )
ji j j jp

     are the weights from input layer to hidden layer. Define 

0
1

p

j j ji i

k

Z x 


   , and Eq(7) can be transformed to 0
1

( )
q

j j
j

y F 


  Z . On the basis of neural interpretation 

diagram (NID) (Özesmi and Özesmi, 1999), the correlation of input variables can be calculated according to 

the correlation coefficient and the covariance and the correlation of input 
i

x  to hidden layer 
j

o  can be 

calculated as:  

( , )
, 1, , ; 1, ,

( )

j i

ji ji

j

Cov Z x
u j q i p

Var Z
    (8) 

and the correlation of hidden layer 
j

o  and the output y  can be calculated as:  

( ( ), )
, 1, ,

( )

j

j j

Cov F Z y
v j q

Var y
   (9) 

The overall correlation value of the i th  input 
i

x  and the output y  is:  

1

, 1, ,
q

i j ji
j

C v u i p


   (10) 

or: 

1

i

i
N n

i

i

C

C








 

(11) 

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w10

β0wj0

wq0

x1

xp

y

F(*)

βj

xi

wji

 

Figure 1: Single hidden layer feedforward neural network 

3.3 Variable selection method based on NN-MIV 
MIV correlation represents model's character on the changes over external input and the calculated 

correlation is the external one. Meanwhile, correlation analysing method based on NN calculate the correlation 

according to the weights from input layer to hidden layer and from hidden layer to output layer, hence this kind 

of correlation is called internal correlation. In order to make use of the advantages of both methods to obtain 

the most optimal correlation, the authors propose a neural network variable selection method based on MIV 

(NN-MIV), where the integrated correlation is defined as  

1
( , , )

i i i

T

NM M N p
C C C    (12) 

In normalized way, the overall integrated correlation of 
k

x  and output can be expressed as: 

1

i

i

i

NM

MN p

NM

i

C

C








 

(13) 

4. Experiment and discussion 

Based on the NN-MIV method proposed in the previous section, the authors researched the relationship 

between the ozone concentration (denoted as y) and other atmosphere characteristics, including SO2 

concentration, NO2 concentration, CO concentration, PM2.5 concentration, PM10 concentration, temperature T, 

atmosphere pressure P, humidity H, and wind speed WS (denoted as x1, x2, …, x9). 

First, a 9-15-1 feedforward neural network was constructed, with activated function of hidden layer neurons 

being “tansig” and the one of output layer being “purelin”. Then the NN was trained with Levenberg-Marquardt 

training algorithm (Lera and Pinzolas, 2002) for 500 times and the training error got less than 
4

10


. 

Based on the trained network, MIV correlation analysing method was applied to calculate the external 

correlation according to Eq(1) - Eq(6), and then NN correlation analysing method was applied to calculate the 

internal correlation according to Eq(7) - Eq(11). 

The integrated correlations were obtained according to Eq(12) and Eq(13). The correlation calculated is very 

stable, and only minor digit number varies, which does not change the correlation sequence as shown in 

Table 2. The calculated correlation values are also shown graphically in Figure 2.  

Table 2: The correlation between O3 and other variables 

Denotation x1 x2 x3 x4 x5 x6 x7 x8 x9 

Variable SO2 NO2 CO PM2.5 PM10 T P H WS 

Correlation 0.0072 0.50 0.011 0.079 0.015 0.045 0.040 0.28 0.016 

Sequence 9 1 8 3 7 4 5 2 6 

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Figure 2: The correlation graph between O3 and other variables 

From the table and figure, the relationship between ozone concentration O3 and other atmosphere variables 

has the following features: 

(1) O3 has the maximum correlation with NO2 and has small correlation with SO2 and CO, which indicates that 

O3 is transformed from NO2 by photochemical reaction, not SO2 and CO. 

(2) T, H, and P have high correlation with O3, indicating that the temperature, humidity and atmosphere 

pressure are all related to the transformation from NO2 to O3. Although T, H, P will not directly change NO2 to 

O3, they will influence the ultraviolet intensity which is the key factor to the photochemical reaction, which is 

reflected by the correlation between T, H, P and O3. 

(3) PM2.5 and PM10 also have relative high correlation with O3. It is because the extinction effect of the 

particles will decrease the sun radiation and influence the photochemical reaction level, and change the 

amount of O3 transformed from NO2. Since correlation between PM2.5 and O3 are bigger than PM10 and O3, we 

believe that the extinction effect of PM2.5 is greater than the one of PM10. 

(4) O3 is also related to WS. Since wind can take O3 to other place and bring it from other place, the O3 

concentration should have some relation to the wind speed. However, the distribution of O3 is very complex, 

and the relation is very complex, too. This complex relation will make the calculated correlation value varies, 

and lead to a result neither too big nor too small if the data scale is large, as appeared here in this paper. 

Furthermore, a 5-10-1 neural network structure was constructed by the 5 most correlated variables, which is 

the so-called NN soft sensing model. This soft sensing model was trained by the data of year 2013 and 2014, 

and tested by the data of year 2015. Figure 3 presents a period of time of soft sensing result. It can be seen 

from the figure that, the soft sensing model constructed by the correlation analysis can provide O3 soft sensing 

result close to the real data and it can be used as the real value in some special circumstances such as ozone 

sensor failure. 

 

Figure 3: Soft sensing result 

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5. Conclusion 

In this paper, an NN-MIV correlation analysing method is proposed to obtain the correlation between ozone 

concentration and other atmosphere characteristics. The method analyses the internal correlation by NN 

method and external correlation by MIV method and obtain a stable correlation value. The deep meaning of 

the correlation is then analysed and discussed. An NN soft sensing model is constructed by the 5 most 

correlated variables. Experimental result shows that this soft sensing model can provide a soft sensing result 

very close to the real data, indicating it can be used in some special circumstances to represent the real value 

such as ozone sensor failure. The relations between variables from different areas should be further 

developed and the variables from neighbouring area will be added to the soft sensing model to make the soft 

sensing result more accurate. 

Acknowledgments  

This work is supported by the Priority Academic Program Development of Jiangsu Higher Education 

Institutions (PAPD [2011]6), and Open Research Foundation of Key Laboratory of Modern Agricultural 

Equipment and Technology in Jiangsu University (NZ201301). 

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