## 3 Methodology and Data Sources
### Contributions of Straw Open Burning Sources  
The contributions to urban PM\({}_{2.5}\) from SOB sources can be calculated using the TSSTMB model. According to the results shown in Figure 10, we discovered that during the three severe PEs, the contribution of the horizontal transport of SOB sources to the urban PM\({}_{2.5}\) level was more obvious than the contribution during the heavy PE.  
In the first PM\({}_{2.5}\) increase period of PE I, the sharp elevation of urban PM\({}_{2.5}\) concentration was closely related to the rapid increase in the share of SOB sources. Especially from 19:00 to 21:00 on 16 November 2020, the percentage of PM\({}_{2.5}\) contribution from SOB was significantly larger, reaching up to 47% with an hourly average contribution of 44 \(\upmu\)g m\({}^{-3}\), and the urban PM\({}_{2.5}\) concentration increased by 144% simultaneously. Unexpectedly, the latter two occurred under the meteorological conditions of precipitation in the city, as shown in Figure 6. Moreover, no SOB fire spots were identified on the corresponding HTPs. This implies that the increasing urban PM\({}_{2.5}\) concentration in the middle-to-late stages was possibly related to local sources. Overall, the total contribution of SOB as regional sources to PE I was 352 \(\upmu\)g m\({}^{-3}\), which accounted for 7% of the accumulated urban PM\({}_{2.5}\) concentration.  
The temporal variation in contribution from SOB has a similar trend to the fluctuating urban PM\({}_{2.5}\) concentration during PE II and PE III. The total contributions of SOB sources during PE II and PE III were 872 and 1224 \(\upmu\)g m\({}^{-3}\), respectively, which were 27% and 23% of the corresponding urban accumulated pollution levels. The contribution during the early-increase processes was more significant than the late one. The hourly and stage-average contributions from the SOB sources to urban PM\({}_{2.5}\) pollution levels during PE II and PE III are presented in Table S2. During the first and second increases in PE II, the hourly average contribution from SOB was 116 and 35 \(\upmu\)g m\({}^{-3}\), accounting for 50% and 9.8% of the corresponding urban PM\({}_{2.5}\) level. The proportions of SOB contribution were 38% and 8.0% during the first two and third increases in PE III, and the average contributions were 59 and 9.4 \(\upmu\)g m\({}^{-3}\), respectively. This seemed to indicate that primary pollutants from SOB  
Figure 9: Bivariate polar plots of PM\({}_{2.5}\) during, and for several hours before and after, PEs, based on urban ground-monitoring data of hourly PM\({}_{2.5}\) concentration, wind speed, and wind direction.  
sources played a more important role in the early stage in the evolution of haze episodes characterized by bimodal or multimodal distribution, and the later peak was not only related to the primary pollutants but also ascribed to the formation of secondary aerosols. This is consistent with the results reported by [PERSON] et al. (2020) [50].  
It is interesting that the contribution from SOB during PE IV was low, despite the burning area of the identified SOB fire spots being nearly twice that of PE I. The total contribution from SOB sources during PE IV was 4.9 \(\upmu\)g m\({}^{-3}\), which accounted for 0.31% of the urban cumulative PM\({}_{2.5}\) concentration. This is because of the higher PBLH on the transport pathways of SOB sources and the long transport distance so that the particulate matter produced by straw burning was fully diffused and diluted before flowing to urban areas.  
Our results are consistent with other studies and also indicate that straw open burning is the major source of PM, especially during the heavy pollution periods in autumn and spring over Northeast China [51]; a significant portion of the polluted days during the post-harvest season was related to straw burning [52].