The new crown virus was discovered at the end of 2019, and since then there have been endless discussions about the new crown. Because of severe air pollution in winter, humans are at higher risk of contracting the new crown (Naqvi et al., 2021). Therefore, more scholars have focused their research on the impact of air and climate on COVID-19 (Linares et al., 2021), NO₂, PM_2.5, PM10, O₃ are directly proportional to the incidence and mortality of COVID-19 (Montse and Domingo José, 2022). Weather has become an important factor in determining the disease (Khurram et al., 2002). Temperature plays an important role in slowing down the spread of COVID-19 (Najaf Iqbal et al., 2020). The performance of the new crown varies in different environments (Shahzad et al., 2021). However, the harsh environment will always increase the incidence and mortality of new coronary pneumonia (Fareed et al., 2020). In order to control the development of the epidemic, the lockdown period has been continuously extended, and the new crown epidemic has therefore been partially controlled. During the COVID-19 lockdown, air quality has been significantly improved (Pandey et al., 2021; Raffaele et al., 2021). The reduction in personal travel and economic activities provides researchers with an opportunity to objectively evaluate air pollutants (Adam et al., 2021). The main pollutants of air quality can be determined by the changes in the concentration of pollutants before and after the epidemic is blocked (Xu et al., 2021). Thierno et al. (2021) used the atmospheric simulation data set method to analyze the changes in air pollution emissions during the epidemic. Found that the concentration of air pollutants dropped significantly during the blockade (Maji et al., 2021). According to environmental data released by NASA and ESA, it is found that pollution in many places has been reduced to 30% (Muhammad et al., 2020). For the quantitative analysis of air pollutants. Many scholars used a variety of methods to measure the air quality during the blockade, such as satellite data (Fatemeh and Alihsan, 2021), double-difference models (Yumin et al., 2021), and machine learning algorithms (Wei et al., 2021). However, since the outbreak of the new crown epidemic, there are fewer air pollutant data available to study, resulting in inaccurate prediction results of some models. The gray fractional cumulative GM(1,1) model (FGM(1,1) model) is extremely effective in short-term prediction (Wu et al., 2013). Therefore, this paper will use the FGM(1,1) model to predict the extremely polluted air quality in China to analyze the impact of the lockdown of the COVID-19 epidemic on air quality.

The concentration of air pollutants reflects the overall air quality at a specific time and place. In recent years, China has taken a variety of measures to deal with air pollution, and air quality has improved significantly. However, at this stage, China is still facing the pressure of extremely polluted air quality. Especially in summer, ozone has become the primary factor leading to excessive air quality in some cities, especially in key areas such as the Beijing-Tianjin-Hebei and surrounding areas, the Yangtze River Delta, the Fen-Wei Plain, and the junction of Jiangsu, Anhui, Shandong, and Henan. The scope of air pollution prevention and control strengthened supervision and designated assistance areas expanded from key areas such as Beijing-Tianjin-Hebei to non-key areas such as Jiangsu, Anhui, Shandong, Henan, etc. The target is summer ozone pollution. The increasing trend of ozone pollution is very obvious, and in some cities ozone even exceeds PM_2.5 as the primary pollutant. This shows that the control of extremely polluted air quality is imminent.

The Beijing-Tianjin-Hebei region is at the heart of China, with one of the largest economies in the country but also the most serious air quality problems. The industrial structure of Shanghai in the Yangtze River Delta is relatively balanced and the industrial industry is relatively developed, but the air quality is relatively poor. Shanxi Province and Shaanxi Province, the key areas of the Fen-Wei Plain, are rich in resources, and the continuous demand for resource extraction activities has deteriorated air quality. Structural problems are prominent in the junction area of Jiangsu, Anhui, Shandong and Henan. The development of steel and petrochemical industry leads to large basic emissions of air pollutants in this area, and it is relatively difficult to control them. The detailed geographical location is shown in Figure 1. However, air quality management is not achieved overnight. It requires long-term planning and collaborative governance Forecasting the annual average air index concentration from 2021 to 2025 can provide technical support for future air quality management of local governments.

The annual average concentration of inhalable particulate matter (PM_2.5) and the annual average 90% quantile concentration of 8-hour ozone (8-h O₃) are selected as predictive indicators. The indicators data are from the Air Quality Assessment Report VIII (CSSPKU, 2021), Table 1; Table 2. The current air quality data depends on a new standard (GB 3095-2012) published in 2012. The PM_2.5 values were mandatorily included in this new standard for the first time. Only a few sets of annual data are available. Due to the limited amount of data, the effect of other forecasting methods is not obvious. Therefore, the grey forecasting theory can deal with the forecasting problem of limited samples. The high-precision FGM(1,1) model is used to predict the annual average concentrations of PM_2.5 and 8-h O₃ from 2021 to 2025 in seven provinces and three cities.

Given a non-negative time series X ( 0 ) = { x ( 0 ) ( 1 ) , x ( 0 ) ( 2 ) , ⋯ , x ( 0 ) ( n ) } , the FGM(1,1) modelling process is as follows:

Step 1: By using x ( r ) = ∑ i = 1 k C k − i + r − 1 k − i x ( 0 ) ( i ) , the r -order accumulation sequence is

where C r − 1 0 = 1 , C k k + 1 = 1 , C k − − i + r − 1 k − i = ( k − i + r − 1 ) ( k − i + r − 2 ) ⋯ ( r + 1 ) r ( k − i ) ! (2)

The original time series has been represented by superscription ( 0 ) . The r -order accumulation time series has been represented by superscription ( r ) .

Step 2: For the r -order accumulation sequence X ( r ) , the first-order differential equation with one variable (i.e., the FGM(1,1) model) can be expressed as below:

Because the least squares estimate minimizes the sum of the squared residuals, the parameters are obtained by using the least squares. The unknown parameters a ^ , b ^ can be solved by using the following formulas: [ a ^ b ^ ] = ( B T B ) − 1 B T Y (5)

where Y = [ x ( r ) ( 2 ) − x ( r ) ( 1 ) x ( r ) ( 3 ) − x ( r ) ( 2 ) ⋮ x ( r ) ( n ) − x ( r ) ( n − 1 ) ] , B = [ − 0.5 ( x ( r ) ( 1 ) + x ( r ) ( 2 ) )                     1 − 0.5 ( x ( r ) ( 2 ) + x ( r ) ( 3 ) )                   1 ⋮ − 0.5 ( x ( r ) ( n − 1 ) + x ( r ) ( n ) )     1 ] (6)

Step 3: Inputting a ^ , b ^ into the time response function

Take Beijing as an example. The data from 2015 to 2020 are taken as the sample set. The traditional GM(1,1) model and the FGM(1,1) model are established respectively. The FGM(1,1) modelling process is as follows.

The average annual concentration of PM_2.5 is X ( 0 ) = , { 1179.1 , 186.7 , 124.5 , 129.1 , 98.3 , 94.4 }

The optimal fractional order found by the particle swarm algorithm (PSO) is 0.39, The 0.39-order accumulation sequence is X ( 0.39 ) = , { 179.1 , 256.2072 , 245.1979 , 266.1071 , 254.495 , 256.4708 }

The unknown parameters a ^ , b ^ can be solved by the following formulas: [ a ^ b ^ ] = ( B T B ) − 1 B T Y = [ 1.955093832 500.2563372 ] (10)

where Y = [ 77.1072 − 11.0093 20.90924 − 11.6121 1.975759 ] , B = [ − 217.654 1 − 250.703 1 − 255.653 1 − 260.301 1 − 255.483 1 ] (11)

Then, the time response function is x ^ ( r ) ( k + 1 ) = [ 179 . 1 − 500.2563372 1.955093832 ] e − 1.955093832 k + 500.2563372 1.955093832 (12)

Can get X ^ ( 0 . 39 ) = { 245.01,254.33 , 255.66,255.84 , 255.87,255.87 , 255.87 , 255.87 , 255.87 , 255.87 , 255.87 }

The Predictive Sequence is X ^ ( 1 ) = { 179.10 , 175.50 , 137.98 , 116.43 , 103.33 , 94.40 , 87.77 , 82.57 , 78.34 , 74.80 , 71.77 }

The fitting results of annual average concentration of PM_2.5 in Beijing are shown in Table 3. The MAPE of the FGM(1,1) model is significantly lower than that of the traditional GM(1,1) model. The result of the FGM(1,1) model with the best score is obtained through PSO on MaltlabR 2018b. In this order, the MAPE is the smallest and the fitting accuracy is higher. In addition, the Wilcoxon signed rank test is widely used to determine the importance of the superiority of a predictive model (Xiangmei Meng et al., 2021). According to the above literature, the prediction accuracy of FGM(1,1) model and traditional GM(1,1) model is consistent with the fitting results of Beijing PM_2.5 concentration. Wilcoxon signed rank test and 0.05 significance level 1 test show that the FGM(1,1) model is significantly better than the traditional GM(1,1) model. Therefore, it is effective to use FGM(1,1) model to predict Beijing PM_2.5 concentration.

The forecast results of the annual average concentration of PM_2.5 in Beijing are listed in Table 4.

Similarly, the 8-hour ozone (8-h O₃) annual average 90% quantile concentration is also limited. Grey prediction theory is also applicable. In order to obtain higher-precision prediction values, the FGM(1,1) model is used to predict these indicators. Therefore, the annual average concentrations of inhalable particulate matter (PM_2.5) and 8-h O₃ in Beijing, Tianjin, and Shanghai from 2021 to 2025 are predicted by the FGM(1,1) model, respectively.

Figure 2 shows the changing trends of air indicators in Beijing, Tianjin, and Shanghai. Obviously, the annual average concentrations of PM_2.5 and 8-h O₃ in the three cities are decreasing and the ranges are different. Among these indicators, the annual average PM_2.5 concentration in 2020–2025 will exceed 50 μ g / m 3 but not exceed 115 μ g / m 3 . These three cities will have mild pollution in the next 5 years. However, in 2024 and 2025, the annual average concentration of PM_2.5 in the three cities will not exceed 75 μ g / m 3 . Air quality will return to a good state under long-term control. Compared with the annual average concentration of PM_2.5, the annual average concentration of 8-h O₃ has continued to decrease. However, as of 2025, its concentration will still exceed the national secondary standard limit of 160 μ g / m 3 . The 8-h O₃ concentration in Tianjin has decreased by less than 10 μ g / m 3 , and the annual average 8-h O₃ concentration in 2025 will be 214.28 μ g / m 3 , which is the highest among the three cities. The air situation in Tianjin is still severe, and comprehensive improvement of air quality is still necessary.

Using similar methods, predict the annual average concentrations of PM_2.5 and 8-h O₃ in Shanxi, Hebei, Henan, Shandong, Jiangsu, Shaanxi and Anhui provinces respectively.

The change trends of air indicators in Shanxi, Hebei, Henan and Shandong provinces are shown in Figure 3. It can be seen from the figure that the downward trend of annual average PM_2.5 concentration is basically the same in the four provinces, and the trend of annual average concentration of 8-h O₃ varies. The annual average concentration of PM_2.5 declines rapidly and steadily from 2020 to 2025, which is better than the performance of the above three cities. In 2025, the annual average concentration of PM_2.5 in the three provinces except Shandong is less than 50 μ g / m 3 . The air quality continues to improve substantially and becomes good. However, the forecast of the annual average concentration of PM_2.5 in Shandong province has performed poorly. It will still be lightly polluted in 2023, and will only slightly enter a state of good air quality in 2024–2025. The predicted performance of the annual average concentration of 8-h O₃ is far inferior to the annual average concentration of PM_2.5. Although the four provinces have a clear downward trend, they will still exceed the national secondary standard limit 160 μ g / m 3 in 2025. However, the annual average concentration of 8-h O₃ in Shanxi and Shandong provinces only dropped by 11 μ g / m 3 and 14 μ g / m 3 . The annual 8-h O₃ concentration in Hebei and Henan provinces has declined steadily. Moreover, the annual average concentration of 8-h O₃ in Henan province will be 167.70 μ g / m 3 in 2025. The value is very close to the national secondary standard limit. If it drops by this amount, it is entirely possible that it will be less than 160 μ g / m 3 in 2026, that is, the ozone concentration will reach the standard.

The change trends of air indicators in Jiangsu, Shanxi and Anhui provinces are shown in Figure 4. From the figure, it can be seen that the annual average concentration of PM_2.5 and 8-h O₃ in Anhui Province has dropped significantly. The annual average concentration of PM_2.5 and 8-h O₃ in Jiangsu Province declined relatively slowly. The raw data of air quality indicators in Jiangsu, Shanxi and Anhui provinces are better than the other three cities and four provinces. By 2025, only Anhui province’s annual average concentration of PM_2.5 will fall below 50 μ g / m 3 . In addition, the annual average concentration of PM_2.5 in Jiangsu province is 72.06 μ g / m 3 and will reach 75 μ g / m 3 . At this time, the air quality is close to light pollution. The prediction of the annual average concentration of 8-h O₃ is relatively good. Among them, Shanxi province will be 161.53 μ g / m 3 in 2025, which is close to the national secondary standard limit. It is expected that the ozone concentration will reach the standard in 2026. The ozone concentration in Anhui province will reach the standard in 2023 and the annual average concentration of 8-h O₃ will be 146.02 μ g / m 3 in 2025. Although the ozone concentration in Jiangsu province has declined slowly, the average annual 8-h O₃ concentration in 2025 will be 169.25 μ g / m 3 . It is extremely hopeful that the ozone concentration will reach the standard in 2027. Although the air quality prediction indexes of Jiangsu province, Shanxi province and Anhui province have performed well. However, relevant government departments must not relax their air governance easily.

Based on the above prediction results, it can be known that the lockdown of the COVID-19 will have a continuous impact on China’s extreme air pollution. That is, the annual average concentration of PM_2.5 in China will continue to decrease under lockdown, which is the same as the results of Shakoor et al. (2020) and (Yumin et al., 2021) research. However, the annual average concentration of O₃ will increase first and then decrease, which is the same as the results of the study by (Wei et al., 2021).

The reason for the decrease in the concentration of extreme air pollutants is inseparable from the national policy control, such as coal-to-gas, loose coal management, ultra-low emissions from coal combustion, and energy-saving transformation (Lifu et al., 2018). Another important aspect is that after the outbreak of the COVID-19, China has actively adopted strict and comprehensive prevention and control measures. The whole society suspends work and production, and all employees are isolated at home (Hsiang et al., 2020). The simultaneous suspension of industry and construction has led to a sharp reduction in inhalable particulate matter. At the same time, home isolation restricts residents’ traffic and travel, which sharply reduces the pollutants emitted by fuel vehicles. The lockdown of the epidemic has accelerated the reduction in the annual average concentration of PM_2.5. However, the annual average concentration of PM_2.5 in some cities did not decrease significantly. It is necessary to consider the shortage of epidemic prevention materials during the epidemic. Medical material production enterprises resumed work ahead of schedule and started production at full capacity. (http://finance.people.com.cn/n1/2020/0131/c1004-31565804.html)No inspection of medical rescue vehicles (http://www.baiduhl.com/z/2019/10/17/8 0405.html). However, after the reduction of PM_2.5, there is no barrier of haze, and sunlight can penetrate the air more easily. Although ultraviolet light is not directly related to killing viruses (Farooq et al., 2021), it provides more energy for surface ozone. So while the PM_2.5 concentration is reduced, ozone pollution is further aggravated (Li et al., 2019). This also indirectly proves the research conclusions of Shahzad et al. (2021). That is, there is a significant interaction between PM_2.5 in air quality and ozone and the transmission of new coronary pneumonia. Ozone is the main factor that increases the spread of the COVID-19 (Sarwar et al., 2021), and the harsh environment will increase the death rate of the new crown virus (Fareed et al., 2020). Most ozone is produced by secondary conversion of anthropogenic NOX (nitrogen oxides) and VOCs (volatile organic compounds) under high-temperature light conditions. NASA researchers found that NO₂ first dropped sharply in Wuhan in a short period of time. At the same time, the NO₂ concentration in four metropolitan areas has declined (Cai et al., 2021). NO₂ mainly comes from toxic gases emitted by motor vehicles, power plants and industrial facilities. During the period of the epidemic blockade, the emissions of these toxic gases will be reduced, which will reduce the concentration of ozone. This is also in line with the above-mentioned prediction results.