## 3 Results and Discussions
### Transmission Path Characteristics  
To illuminate the influence of regional atmospheric transmission and its path characteristics on PM and pollution dynamics in Chenzhou City throughout the four seasons, this study employed the TrajStat software based on the HYSPLIT model. The analysis focused on Chenzhou City's coordinates (25.41\({}^{\circ}\) N, 113.06\({}^{\circ}\) E) at 0:00 h on 1 March 2022, with backward trajectory simulations commencing at 23:00 h on 28 February 2023. These trajectories delineate the air mass's transit path and direction, signifying the regions traversed en route to the simulation point. The transport distance serves as a metric for gauging the velocity of the air mass. Cluster analysis across various seasons yielded trajectory categories numbering 6, 4, 4, and 4, as depicted in Figure 7.  
Figure 7 shows the results of cluster analysis of backward trajectories in different seasons in Chenzhou City, which divide the air mass sources and transmission paths into different categories to reveal the potential regional sources and transmission characteristics of PM\({}_{2.5}\) pollution in each season. In spring (Figure 7a), cluster analysis obtained six major categories of trajectories, which represent different air mass sources and transmission paths. Each type of trajectory corresponds to a specific geographical area and transmission characteristics, and these paths may involve different pollution source areas, such as industrial areas, urban agglomerations or natural source areas. The air mass transmission path in spring may be more complex because spring is a transition period from the end of the winter heating period to the beginning of the summer high temperature period. Changes in meteorological conditions and human activities may lead to the diversity of pollution sources and transmission paths. The cluster analysis results of summer (Figure 7b) show that there are four major categories of trajectories. Compared with spring, there are fewer trajectory categories in summer, which may mean that the air mass sources and transmission paths in summer are relatively concentrated. High temperatures and strong vertical convection in summer may make pollutants diffuse more rapidly, thereby reducing the complexity of transmission paths. In addition, summer may be affected by specific directions (such as the southeast monsoon), which further affects the source and transmission path of air masses. There are also four major types of trajectories in autumn (Figure 7c). The meteorological conditions and human activities (such as agricultural burning and industrial production) in this season may lead to different transmission paths and potential source areas of PM\({}_{2.5}\) pollution. The trajectory categories in autumn may reflect the meteorological changes during the transition from summer to winter, as well as the transmission characteristics associated with the pollution source activities unique to autumn. The cluster analysis in winter also obtained four major types of trajectories (Figure 7d). Winter meteorological conditions, such as lower temperatures and weaker vertical convection, may lead to the accumulation of pollutants in the near-ground layer, thus affecting the transmission path of air masses. The beginning of the winter heating period also means an increase in pollution sources such as coal burning, which may be reflected in the trajectory clustering, because these pollution sources may have a significant impact on the transmission path and potential source area of PM\({}_{2.5}\). In summary, the cluster analysis results of different seasons in Figure 7 reveal the regional transmission characteristics of PM\({}_{2.5}\) pollution and the seasonal changes in potential source areas in Chenzhou City. Concurrently, quantitative statistical analyses were conducted utilizing the daily hourly concentrations of PM\({}_{2.5}\) throughout the study duration.