Quantifying PM2.5 Variations via Meteorological Factors

Several statistical indicators, including correlation coefficient ( $R$ ), root mean square error ( $RMSE$ ), mean bias ( $MB$ ), general error ( $GE$ ), mean fractional bias ( $MFB$ ), and mean fractional error ( $MFE$ ) were used to evaluate the simulation results. The indicators were defined as follows: $$R=\frac{{{\displaystyle \sum }}_{i=1}^N\left(X_i-\overline{X}\right)\left(Y_i-\overline{Y}\right)}{\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(X_i-\overline{X}\right)}^2}\sqrt{{{\displaystyle \sum }}_{i=1}^N{\left(Y_i-\overline{Y}\right)}^2}},$$
$$RMSE=\sqrt{\frac{{{\displaystyle \sum }}_{i=1}^N{\left(X_i-Y_i\right)}^2}{N}},$$
$$MB=\frac{{{\displaystyle \sum }}_{i=1}^N\left(X_i-Y_i\right)}{N},$$
$$GE=\frac{{{\displaystyle \sum }}_{i=1}^N\left|X_i-Y_i\right|}{N},$$
$$MFB=\frac{1}{N}{{\displaystyle \sum }}_{i=1}^N\frac{\left(X_i-Y_i\right)}{\left(X_i/2+Y_i\right)}\times 100\%,$$
$$MFE=\frac{1}{N}{{\displaystyle \sum }}_{i=1}^N\frac{\left|X_i-Y_i\right|}{\left(X_i/2+Y_i\right)}\times 100\%,$$
where $X_i$ and $Y_i$ represent the simulated and observed values, respectively. The indicator of $R$ with a value closer to 1, or $MB$ with a value closer to 0, or $RMSE$ and $GE$ with smaller values indicate a better simulation effect [49 (link)].
In order to quantify the effects of meteorological elements on PM_2.5 variations induced by the underlying surface of “water networks”, multiple linear regression is adopted to quantify the contribution of meteorological factors to the change in air pollutants by using the software MATLAB (https://ww2.mathworks.cn/, accessed on 7 February 2023).