## 4 Results and Analyses
### Transport Trajectories in Different Seasons  
Based on the airflow backward trajectory clustering results in different seasons, combined with the hourly PM\({}_{2.5}\) concentration data, this paper analyzes the pollution characteristics of different transport trajectories. According to the second-level PM\({}_{2.5}\) concentration (75 ug/m\({}^{3}\)) in Ambient Air Quality Standards (GB 3905-2012), back-trajectories are classified into \"low polluted\" trajectories (\(<\)75 ug/m\({}^{3}\)) and \"polluted\" trajectories (75 ug/m\({}^{3}\)). The statistics for different types of trajectories are described in Table 1.  
Figure 3: Quarterly and monthly characteristics of PM\({}_{2.5}\) concentration in Weifang. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{3}{*}{**Season**} & \multirow{3}{*}{\begin{tabular}{c} **Trajectory** \\ **Cluster** \\ \end{tabular} } & \multirow{3}{*}{**Proportion (\%)**} & \multirow{3}{*}{\begin{tabular}{c} **Average** \\ **(\%/m3)** \\ \end{tabular} } & \multirow{3}{*}{\
\begin{tabular}{c} **Proportion of Seasonal** \\ **Total Polinted** \\ **Trajectories (\%)** \\ \end{tabular} } & \multirow{3}{*}{
\begin{tabular}{c} **Average** \\ **(\%/m3)** \\ \end{tabular} } \\ \hline \multirow{3}{*}{Spring} & 1 & 12.08 & 83.35 & 29.43 & 109.71 \\  & 2 & 45.36 & 69.63 & 31.55 & 99.46 \\  & 3 & 27.15 & 53.72 & 18.83 & 98.21 \\  & 4 & 15.41 & 76.64 & 20.20 & 111.62 \\  & All & & 70.83 & & 104.87 \\  & 1 & 34.06 & 41.50 & 12.04 & 89.41 \\  & 2 & 22.71 & 42.93 & 4.45 & 88.29 \\ \multirow{3}{*}{Summer} & 3 & 6.63 & 62.95 & 20.68 & 99.94 \\  & 4 & 21.16 & 68.16 & 43.19 & 94.13 \\  & 5 & 15.44 & 47.59 & 19.63 & 96.24 \\  & All & & 52.63 & & 94.92 \\  & 1 & 25.80 & 94.52 & 52.60 & 124.22 \\ \multirow{3}{*}{Autumn} & 2 & 74.20 & 66.53 & 47.40 & 116.84 \\  & All & & 80.53 & & 120.72 \\  & 1 & 37.11 & 148.08 & 55.72 & 158.08 \\ \multirow{3}{*}{Winter} & 2 & 62.89 & 82.99 & 44.28 & 114.11 \\  & All & & 115.54 & & 138.61 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Trajectory proportions and PM\({}_{2.5}\) concentrations based on all trajectories and pollution trajectories. Figure 4: Cluster mean back-trajectories in different seasons in Weifang from March 2015 to February 2016. 1. Pollution characteristics in spring The average PM\({}_{2.5}\) concentration of spring trajectories is 70.83 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\). The trajectory clusters in descending order are: \(2>3>4>1\). The airflow trajectories originating from the north (Inner Mongolia) have the highest average PM\({}_{2.5}\) concentrations, reaching 83.35 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\). This may be due to two reasons: one is that these airflows mainly come from the western arid regions of China, and, in spring, northwesterly winds easily blow loose topsoil and fine sand from dry surfaces to form sandstorms; the other reason is that these trajectories pass over the industrial areas in southern Hebei and easily transport local pollutants to Weifang City to form accumulation. Type 3 trajectories from the northwest are longer and have the lowest PM\({}_{2.5}\) concentration of 53.72 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\). This may due to two reasons: (1) these trajectories travel large distances at high wind speeds; and (2) they subsequently pass over regions with high vegetation cover and relatively low population density [41], such as Xilingol league in Inner Mongolia, Chengde City in northern Hebei, and waters of the Bohai Sea. Both the abovementioned cases may lead to low pollution transport and effective adsorption, diffusion, and dilution of pollutants. The average PM\({}_{2.5}\) concentration of the polluted trajectories is 104.87 \(\mathrm{\SIUnitSymbolMicro g}\)/m\({}^{3}\). In particular, Type 1 and 2 trajectories account for 29.43% and 31.55% of the total polluted trajectories, respectively.