Analysis of air quality changes during the COVID-19 in Wuhan city based on Over-standard multiples method and Gray relational analysis


 To study air quality changes during the COVID-19. This paper introduced the Over-standard multiples method and Gray relational analysis to study the individual and overall change trends of pollutants in Wuhan during the same period in the past seven years. The result shows that the concentrations of SO2 and O3 increased but still meet the standard. However, the pandemic promoted a decrease in PM2.5, PM10, and NO2 concentrations, but it had just reached the standard or even exceeded the standard. This article discussed the feasibility of using Gray relational analysis to analyze pollutants exceeding the standard from an overall perspective and provided new ideas for future research.


Introduction
In December 2019, unknown pneumonia patients appeared in Wuhan. The study found that it was caused by a new coronavirus. World Health Organization (WHO) named the new coronavirus-infected pneumonia as COVID-19. Nowadays, it has spread globally and presents a pandemic trend. (https://www.who.int/). To control the pandemic, many countries carried out isolation blockade which reduces people's social activities and prompted companies to stop production. These have a directly in uence on air quality. On the contrary, air pollutants can also affect virus transmission even some health issues (Brandt et al. 2020; Ciencewicki and Jaspers 2007). Hence, it is pretty essential to study air quality changes during the COVID-19 pandemic. Similarly, (Kerimray et al. 2020) indicated the concentrations of NO 2 , PM 2.5 , and CO reduced obviously.
But the concentrations of O 3 , benzene, and toluene were higher than those before lockdown in Almaty. In the above study, scholars have applied a variety of research methods, such as utilizing the cokriging method in ArcGIS, applying the WRF-CAMx modeling system, analyzing pollutants concentrations changes directly, and so on. However, few scholars have applied the Gray relational analysis (GRA) to analyze the changes in air quality during the pandemic.
Not only the trend of air quality changes but also the situation of excess air pollutants is worthy of attention. Analyzing the situation of exceeding air pollutants can help staff nd the degree of pollution directly and improve air quality more e ciently. Considering that the basic idea of GRA is to re ect the degree of correlation between systems by calculating the gray relational degrees (GRD) between systems, this paper intended to apply GRA to calculate the GRD between the actual concentration of air pollutants and the concentration limit sequence which re ects the situation of exceeding air pollutants, and then discussed the changes in pollutant concentration during the COVID-19. Furthermore, to prove the feasibility of GRA, this paper introduced an Over-standard multiples method (OSM) to analyze the exceeding standard situation and changing trend in the six monitoring pollutants while found that the main pollutants are PM 2.5 and PM 10 (PM). And then, this paper utilized GRA to analyze the concentration changes of PM and compared it with the result of OSM. The results showed that it is feasible to use GRA to analyze the changing trend of air pollutants and the exceeding standard situation. This paper not only analyzes the changes in air quality during the pandemic but also provides new ideas for analyzing the overall changes in the pollutants exceeding the standard.

Statistics date
The period analyzed in this article is the rst two months of the pandemic. However, it was during the Spring Festival (SF). Generally, people's behavior during the Spring Festival has strong stage characteristics. People's trip frequency and the possibility of setting off recrackers will increase.
Companies will stop production. These staged behaviors during SF will affect air quality to some extent.
Aiming to avoid the impact on the analysis, this article took the Chinese New Year's Eve (NYE) as a breakpoint, and regarded the two months corresponding to the 15 days before and after the NYE's calendar date in the past seven years as the same period.

Statistical data and reference standard
The air quality assessment project discussed in this article is PM 2.5 , PM 10   To analyze the speci c situation of each pollutants and provide a reference basis for verifying the results of GRA, this article introduced the method of over-standard multiples. The OSM is the ratio of the over-standard concentration and the concentration limit. The OSM re ects the degree of overcontamination of pollutants. The calculation formula is as follows: In Eq. (1), ω k represents the kth pollutant's OSM. R k represents the kth pollutant's actual concentration and L k is the kth pollutant's reference standard for concentration limit.

Gray relational analysis
Gray relational analysis is part of the gray system theory (Morán et al. 2006) and can be used to describe the degree of correlation or similarity between systems. With applying to small sample size (≥4), GRA is more widely used. The main steps are as follows: 1) Establish the original data matrix and dimensionless it.
2) Select a sequence that can be regarded as a comparison standard, called the reference sequence. The sequence of other evaluated objects is called the comparison sequence.
3) Calculate the GRD between the comparison sequence and the reference sequence, which directly re ects the correlation degree between them.
The greater the GRD, the stronger the correlation, that is, the higher the similarity.

Analysis of exceeding the standard of air pollutants in Wuhan
It can be seen from equation 1 that the OSM not only re ects whether the pollutant exceeds the standard but also re ects the degree of the pollutant exceeding the standard. When the OSM is positive, it means the pollutant is over-standard. When it is negative, it means that the pollutant meets the requirements and does not exceed the standard. The greater the OSM, the greater the degree of pollutants exceeding the standard. Applying the collected sample data to calculate the OSM of the corresponding air pollutants in Wuhan, the results are shown in Figure 1. PM 2.5 , PM 10 , SO 2 , and NO 2 , As shown in Figure 1, analysis of the overall change trend revealed that the OSM of most of the pollutants have decreased compared with 2014, that is, the concentration of pollutants has dropped. Compared with last year, the OSM of O 3 in the rst month and the SO 2 and O 3 in the second month have increased, but it is still negative, which means that although the concentration of these pollutants has increased this year, but still meet the standards. The OSM of CO is reduced and remains negative, that is, the concentration of CO is still in compliance with the standard. The OSM of NO 2 has decreased, that is, the concentration has decreased, and in the past two years, there has been a tendency to transition to the standard state. As for PM 10 and PM 2.5 , although their OSM decreased, they only showed a positive value in February 2020. Over the past seven years, the OSM of PM 10 and PM 2.5 has been relatively large, which means that the main pollutant in Wuhan is PM 10 and PM 2.5 (PM). Hence, this article focuses on the GRA of PM.

Grey correlation analysis of air quality in Wuhan
To explore the feasibility of applying GRA to analyze the change of air pollutant concentration, this paper conducted a grey correlation analysis on the concentration change of the main pollutants-PM in Wuhan.
In this article, regarding the concentration limits as a reference sequence, and the pollutant concentrations on the statistics date as comparative sequences, the GRD of them directly re ects the air quality. The greater the GRD, the better the air quality. This article takes PM as an example for GRA, and the results are shown in Figure 2.
As shown in Figure 2, according to the change trends of GRD, it is found that the GRD of PM has increased signi cantly compared with 2014. Comparing with last year, the situation is the same. These trends are consistent with the results of OSM analysis, which shows that it is feasible to apply GRA to analyze the change trend of pollutants Discussion And Conclusions (1) In terms of methods, the OSM can not only show the trends of pollutant concentration changes but also intuitively show the degree of pollutants exceeding the standard.
(2) When GRA is used to analyze the changing trend of pollutant concentration from an overall perspective, the analysis result is good for a single whole.
(3) From the perspective of pollutant concentrations, during the COVID-19 pandemic, the concentrations of O 3 and SO 2 mainly showed an upward trend, especially in the second month, that is, after the lockdown. The increase in O 3 concentration could be due to the decrease in PM and NOx (Sharma et al. 2020). Although some enterprises stopped production in the second month, considering the increase in SO 2 concentration mainly related to industrial emissions in China (Wang. and Huang. 2015), it may be that the sharp increase in shipments of medical products and medical wastes led to an increase in SO 2 concentration. Of course, there may be meteorological reasons, this article does not do an in-depth discussion (4) According to the result of GRA, the situation of pollutants exceeding the standard had improved. However, it should be noted that although the concentrations of PM 2.5 and PM 10 had decreased, it is still close to or even exceeded the limits.
(5) During the epidemic, the main pollutant in Wuhan was still PM, which has not changed in the same period in the past seven years.
(6) some scholars have pointed out that when the society fully resumes and the economy recovers, the improvement in air quality will not last forever, or even worse than before the pandemic (Quirin 2020; Wang and Su 2020). Hence, scholars should learn from the experiences during the pandemic and formulate environmental protection measures suitable for normal implementation.