*5.1. Correlation Analysis between Traditional Method Inversion Results and Haze Concentration*

This experiment used traditional methods to analyze the correlation between the inversion data of MOD02-1 km in Beijing in 2014 and the PM2.5 concentration of ground monitoring stations in Beijing. The result is shown in Figure 6, where (a–d) represents the results of the four seasons.

**Figure 6.** Linear regression between Aerosol Optical Depth (AOD) and PM2.5 (**a**) The inversion in spring; (**b**) The inversion in summer; (**c**) The inversion in fall; (**d**) The inversion in winter.

From the results, the highest correlation coefficient is in the spring inversion, which reaches a high level of 0.86, followed by winter and autumn, and the worst in summer. All of the correlation coefficients are above 0.5, indicating a strong correlation between AOD and PM2.5 concentration, considering their non-linear relationship and complex dynamics.

We also performed a linear fit to the inversion results of AOD in the whole year of 2014, as shown in Figure 7. The y-intercept *a*<sup>0</sup> is 45.85, the slope *a*<sup>1</sup> is 50.79, and the correlation coefficient R is 0.59. Compared with the results of the four seasons, the correlation coefficient of the linear fit for the whole year is 30% lower than that of the spring. We think this is because the four seasons have different factors, such as different climatic characteristics, industrial activities, and gas emissions caused by heating demand, which contribute to the correlation between AOD and PM2.5 concentration. Therefore, we conclude that studying the correlation performance of AOD and PM2.5 according to the season division can provide a more accurate basis for analysis.

**Figure 7.** Overall linear regression between AOD and PM2.5 in 2014.

Figure 7 shows that we can train the processed data through the neural network method to approximate the coupling relationship between the mapping relation and the linear relation to achieve the inversion classification method.
