## 3 Data and Methodology
### Methodology  
(1) HYSPLIT model  
The Hybrid Single-Particle Lagrangian Integrated Trajectory (HYSPLIT) model established by the Air Resources Laboratory of the National Oceanic and Atmospheric Administration (NOAA) is used in this paper to analyze sources and transport trajectories of air pollutants [29; 30]. This model gives highly accurate and temporally continuous simulation results and has been widely used in research on the transport and diffusion of various pollutants in different areas. The HYSPLIT model is divided into two parts: the backward transport model and the forward diffusion model, which solve problems concerning sources and sinks, respectively. In this paper, the backward transport model of the HYSPLIT model is employed to simulate 72-h backward airflow transport trajectories near the ground surface in Weifang during the period of interest. The characteristics of the airflow movements in the study area are thereby reflected. (2) Trajectory clustering analysis  
Trajectory clustering analysis, a multivariate statistical analyses technique, was used to divide the trajectory data into several classes or clusters. Data in the same class or cluster share a higher degree of similarity, whereas those in different classes or clusters vary more significantly [31]. This paper uses TraiStat, a plugin of MeteoInfo; this plugin can view, query, and cluster trajectories and includes two clustering methods: Euclidean distance and angle distance. Because this paper aims to determine the direction from which the air masses that reach the site have originated, the angle distance clustering method is utilized to cluster airflow trajectories. The angle distance is often used to define the mean angle between the two trajectories, which varies between 0 and \(\pi\). The details of the angle distance clustering method can be found in the work of [PERSON] and [PERSON] (1995) [32]. (3) Potential source contribution function (PSCF)  
The PSCF model is a simple method that links residence time in upwind areas with high concentrations through a conditional probability field [33]. This method can identify pollutant sources by analyzing airflow trajectories and a given threshold [34; 35]. It can be calculated as follows:  
\[PSCF_{ij}=\frac{n_{ij}}{N_{ij}} \tag{1}\]  
where \(N_{ij}\) is the total number of airflow trajectories' endpoints that fall in the _ij_th grid and \(n_{ij}\) is the total number of airflow trajectories' endpoints for which the measured PM\({}_{2.5}\) concentration exceeds a given threshold in the same grid. In this study, the 24-h average Grade II standard PM\({}_{2.5}\) concentration (75 \(\mu\)g/m\({}^{3}\)) in ambient air quality standards of China (GB3095-2012) was selected as the threshold value [26]. The trajectories were calculated hourly. Studies have demonstrated that great uncertainty exists in the calculation result when \(N_{ij}\) is extremely small. To eliminate this uncertainty, an arbitrary weight function, \(W_{ij}\), was applied when the number of the endpoints in a particular cell was less than three times the average number of endpoints for each cell [36; 37]. \[WPSCF_{ij}=W_{ij}\times PSCF_{ij} \tag{2}\]  
\[W_{ij}=\left\{ \begin{array}{ll}1.00&N_{ij}>80\\ 0.70&20<N_{ij}\leq 80\\ 0.42&10<N_{ij}\leq 20\\ 0.05&0<N_{ij}\leq 10\end{array} \right. \tag{3}\](4)  
Concentration weighted trajectory (CWT)  
The CWT method first computes the weighted concentrations of trajectories and then obtains the weighted concentrations of grids [38]. The calculation formula of the CWT method is given as follows:  
\[CWT_{ij}=\frac{\sum_{k=1}^{N}C_{k}\tau_{ijk}}{\sum_{k=1}^{N}\tau_{ijk}} \tag{4}\]  
where \(CWT_{ij}\) is the weighted average concentration of grid _ij_; N is the total number of trajectories; \(k\) denotes a trajectory; \(C_{k}\) is the PM\({}_{2.5}\) concentration of trajectory k when it passes through grid _ij_, which can be calculated by the HYSPLIT model; and \(\tau_{ijk}\) is the duration in which trajectory \(k\) stays in grid _ij_[39; 40].