## 3 Methodology and Data Sources
### Hourly Transport Pathways and Straw Open Burning Sources  
Based on hourly backward trajectories with arrival times at hourly intervals, the HTPs and HWFGs during each PE were reconstructed. The spatial distribution of the SOB sources and their inflow time into the city, identified using HTPs and HWFGs, are presented in Figures 7 and 8. From the spatial distribution of the identified SOB sources and their HTPs, we can judge the inflow direction of SOB-caused PM\({}_{2.5}\). In addition, based on the urban ground-monitoring data of hourly PM\({}_{2.5}\) concentration, wind speed, and wind direction, bivariate polar plots of PM\({}_{2.5}\) were plotted to indicate the direction of potential sources [48; 49], as shown in Figure 9.  
Figure 6: Hourly variations in PM\({}_{2.5}\) concentrations, PBLH, wind speed, and relative humidity for Changchun during each PE (time format: yyyy-mm-dd hh). The identified SOB sources of PE I were distributed on the HTPs of only the first sharp increase period of PM\({}_{2.5}\), and the burning area of SOB fire spots was 1.57 ha. This indicated that the air mass carrying SOB-caused PM\({}_{2.5}\) flowed into the city successively during the first sharp increase in PM\({}_{2.5}\), and the inflow direction was between south and southwest. From the bivariate polar plot of PM\({}_{2.5}\) during 16-18 November 2020, based on urban ground-monitoring data, high PM\({}_{2.5}\) concentrations could also be observed at a wind speed of 4-7 m/s when the wind direction was between the south and the southwest. During PE II, the identified SOB sources were found on the HTPs of the bimodal PM\({}_{2.5}\) increase period, and the burning activity was significant, with hotspot areas up to 20.42 ha. The inflow of the air mass carrying SOB-caused PM\({}_{2.5}\) was mainly between northwest and northeast. According to the bivariate polar plot of PM\({}_{2.5}\) during 7-8 April 2021, a high PM\({}_{2.5}\) level could also be identified when the wind speed was 4-6 m/s in the northwest-northeast direction. On the HTPs of all three PM\({}_{2.5}\) increase periods of PE III, the identified SOB sources were distributed. The burning area of these SOB fire spots on the transport pathways was 9.02 ha. The inflow direction of air mass was between southeast and southwest. From the bivariate polar plot of PM\({}_{2.5}\) during 9-10 April 2021, high PM\({}_{2.5}\) concentrations could also be observed from the southeast-south wind direction when the wind speed was 3-5 m/s, and medium PM\({}_{2.5}\) concentrations were recorded from the southwestern wind direction when the wind speed was \(>\)5 m/s. On the HTPs of the PM\({}_{2.5}\) increase period of PE IV, the burning area of the identified SOB sources was 2.84 ha. The inflow of the air mass carrying SOB-caused PM\({}_{2.5}\) was mainly from the southeast to the south. According to the bivariate polar plot of PM\({}_{2.5}\) during 20-21 April 2021, a high PM\({}_{2.5}\) level was recorded at a wind speed of 3-4 m/s when the wind direction was from the southeast and south. Figure 7: The inflow time into the city of the PM\({}_{2.5}\) from identified straw open burning sources. The above results demonstrate that the inflow time and direction of the SOB sources identified using HTPs and HWFGs are consistent with (within the range of) the occurrence time and wind direction of the high PM\({}_{2.5}\) level recorded using urban ground-monitoring data; this indicates the reliability of HTP and HWFG reconstruction using backward trajectories. Moreover, no SOB sources were found on the HTPs of some PM\({}_{2.5}\) sharp increase periods, such as the second and third increase during PE I; these high PM\({}_{2.5}\) levels were probably due to local emission activities. Furthermore, due to the long-range transport of regional sources and the complexity of wind-field variation, the orientation of SOB fire spots in rural areas relative to urban areas is not necessarily the inflow direction of the air mass carrying SOB-caused PM\({}_{2.5}\).