## 3 Methodology and Data Sources
### Reconstruction of Hourly Transport Pathways and Wind-Field Grids
#### 3.3.2 Plotting Hourly Transport Pathways and Wind-Field Grids  
Referring to the infinite-division idea of differentiation in mathematics, there are countless suppositional trajectories with short intervals of arrival time, evenly distributed between two backward trajectories of 1 h intervals of arrival time, calculated using TrajStat. If an emission source is located in the zone between two adjacent backward trajectories of 1 h intervals of arrival time, an air parcel passing through that zone indicates that particulate matter from the source is likely to be collected and transported along the trajectory to the receptor city and contributes to the corresponding hourly average pollutant concentrations of the city. In this study, the zone between two adjacent backward trajectories of 1 h intervals of arrival time is defined as an hourly transport pathway (HTP), which shows the geographic origin of regional sources most associated with hourly average concentrations of the receptor city. Then, we gridded the HTP and calculated the time when the air mass passed a specific grid to determine the spatiotemporal distribution of the wind field during the PE. The required steps for plotting the hourly wind-field grid (HWFG) are as follows:  
(1) Pre-processing trajectory data: As mentioned previously, the back-trajectory data have an attribute column representing the arrival time of the air mass. Hourly backward trajectories whose arrival times were in accordance with the time of the PEs were selected by attribute from the monthly backward trajectory file. Taking PE II in Section 4 as an example, hourly backward trajectories with hourly arrival times from 17:00 on 7 April to 7:00 on 8 April (Figure 2(b)) were selected from the April 2021 backward trajectory data (Figure 2(a)). (2) Reconstructing HTPs: To avoid spatial overlap, the trajectories were divided into several groups, which were calculated in the same way in the subsequent process and are shown in separate panels. The trajectories in Figure 3c, whose arrival time is from 17:00 to 23:00 on 7 April, is one of the groups during PE II, denoted as PE III. The zone between the two adjacent backward trajectories is the HTP. For example, the zone between the backward trajectories with the arrival time of 20:00 on 7 April and 21:00 on 7 April in Figure 3c is an HTP, and it is the geographic area most strongly associated with the regional  
Figure 3: Schematic of reconstructing hourly transport pathways and wind-field grids. Note: (**a**): Hourly backward trajectories with hourly arrival times of April 2021; (**b**): Hourly backward trajectories with hourly arrival times from 17:00 on 7 April to 7:00 on 8 April; (**c**): Hourly backward trajectories with hourly arrival times from 17:00 to 23:00 on 7 April; (**d**): Pathway lines indicating the geographic position of a moving air mass at the same moment as the pathway time; (**e**): Spatiotemporal distribution of the wind-field grids, for example, the air mass arriving at receptor city at 21:00–22:00 on 7 April 2021 was distributed in the region of the blue grid at 6:00–7:00 on 7 April 2021.  
sources and which contributed to the hourly average concentration from 20:00 to 21:00 on 7 April in Changchun. (3) Calculating pathway time and estimating the pathway line: According to the arrival time and backward hours of each trajectory, the time of each backward trajectory segment endpoint can be calculated, and it is defined as the pathway time. We connected the segment endpoints with the same pathway time to obtain a line (Figure 3d), which is defined as a pathway line indicating the geographic position of a moving air mass at the same moment as the pathway time. (4) Reconstructing HWFGs: The grids intersected by backward trajectories and the pathway lines are the spatiotemporal distribution of the wind field (Figure 3e).