Analysis of Global and Key PM2.5 Dynamic Mode Decomposition Based on the Koopman Method

Understanding the spatiotemporal dynamics of atmospheric PM2.5 concentration is highly challenging due to its evolution processes have complex and nonlinear patterns. Traditional mode decomposition methods struggle to accurately capture the mode features of PM2.5 concentrations. In this study, we utilized the global linearization capabilities of the Koopman method to analyze the hourly and daily spatiotemporal processes of PM2.5 concentration in the Beijing–Tianjin–Hebei (BTH) region from 2019 to 2021. This approach decomposes the data into the superposition of different spatial modes, revealing their hierarchical spatiotemporal structure and reconstructing the dynamic processes. The results show that PM2.5 concentrations exhibit high-frequency cycles of 12 and 24 h, as well as low-frequency cycles of 124 and 353 days, while also revealing spatiotemporal modes of growth, recession, and oscillation. The superposition of these modes enables the reconstruction of spatiotemporal dynamics with a mean absolute percentage error (MAPE) of only 0.6%. Unlike empirical mode decomposition (EMD), Koopman mode decomposition (KMD) method avoids mode aliasing and provides a clearer identification of global and key modes compared to wavelet analysis. These findings underscore the effectiveness of KMD method in analyzing and reconstructing the spatiotemporal dynamics of PM2.5 concentration, offering new insights into the understanding and reconstruction of other complex spatiotemporal phenomena.