## 3 Results
### Urban BLH
The aerosol scattering coefficient method probably defines the RL as the stable NBL [49; 50; 51]. Thus, attention should be given when comparing aerosol- and turbulence-derived urban BLHs [52], especially when evaluating results from model computations. Nonetheless, the aerosol scattering method provides a useful reference for the RL and NBL, which can help provide an indication of the change of the whole ABL. To reduce the impact of the diurnal change in meteorological parameters on the urban BLH, the values were averaged for daytime and nighttime. The daily mean urban BLH was in the range of 130-536 m and 64-268 m during daytime and nighttime, with monthly averaged values of 278 m and 152 m, respectively. During the heavily polluted event, the daytime mean urban BLH decreased to \(<\)200 m. The lowest BLH during daytime occurred on 18 December, with the lowest WS (0.46 m s\({}^{-1}\)) at the 8-m level and notably poor turbulent activity (\(H\) = 15.16 W m\({}^{-2}\), \(u^{*}\) = 0.12 m s\({}^{-1}\) and TKE/m = 0.11 m\({}^{2}\) s\({}^{-2}\) at the 47-m level), at which the corresponding daily mean urban BLH during nighttime was only 65 m. The correlation coefficients were calculated between the urban BLH and WS, \(H\) and turbulence parameters (\(u^{*}\) and TKE/m), which were 0.6, 0.6, 0.6, and 0.5 during daytime, and 0.6, 0.2, 0.6, and 0.5 at nighttime, respectively. The correlation coefficient between BLH and DSR was 0.6 during daytime. All these above results indicate WS greatly contributed to the change in urban BLH during both daytime and nighttime, because of its direct positive effects on \(H\), \(u^{*}\) and TKE. For instance, on 17  
Figure 5: Diurnal cycles of urban BLH derived from threshold method combined with the Richardson number method (**a**), PM\({}_{2.5}\) concentration (**b**), \(H\) and DSR (**c**), and turbulent parameters, TKE and \(u^{*}\) (**d**). The cloud fraction is marked as red crosses (cloudy) and black crosses (clear). December 2016, weak high-pressure system is to the southeast of Beijing, resulting in southwesterly prevailing weak winds over Beijing (Figure S3). This will induce a weak mixing with lower BLH (Figure 5). In contrast, on 22 December 2016, under the confluence of the high pressure system and the low pressure system (Figure S3), there is a northwest jet in the boundary layer over Beijing, leading to a higher wind speed and strong mixing with higher BLH (Figure 5). Previous studies demonstrated that pollutant aerosol concentration is directly linked to the urban BLH in Beijing [53; 54]. In our study, the correlation coefficient between urban BLH and PM\({}_{2.5}\) concentration was \(-0.7\) for daytime (at 0.05 significance level) but only \(-0.5\) for nighttime (at 0.05 level significance). This relatively weak correlation for nighttime may have resulted from the small variation range of the BLH during most nights. In addition, as shown in Figure 6, a shallow urban BLH under polluted conditions was usually accompanied by high RH, suggesting that such a humid and shallow BLH favored the accumulation of PM\({}_{2.5}\). This fact agrees with previous study results in which the generation and transformation of secondary aerosols were found to be significant during humid conditions, leading to an increase of PM\({}_{2.5}\) concentrations and the resultant occurrence of severe air pollution episodes [55; 56]. The daytime urban boundary layer was clean (PM\({}_{2.5}\) < 50 \(\mu\)m\({}^{-3}\)) once the daily mean urban BLH reached 300 m or above. For nighttime, when the urban BLH was higher than 200 m, the concentration of PM\({}_{2.5}\) was mostly lower than 100 \(\mu\)g m\({}^{-3}\). Meanwhile, it should be noted that for some shallow nighttime urban BLHs (e.g., 9-10 December), defined as urban BLH < 150 m, concentrations of PM\({}_{2.5}\) were lower than for others, partly explainable by the lower RH, which implies the level of pollution can be attributed to a humid or dry urban boundary layer.