## 3 Results
### Urban BLH
More details of BLH simulations are available in the study of [46]. Figure 3: Velocity variance, \(\sigma_{w}^{2}\) (m\({}^{2}\) s\({}^{-2}\)), calculated from the Doppler wind lidar data. Derived boundary layer depths, based on the threshold method (grey dots) and \(Ri_{b}\) method (red dots). It should be noted that the blank part of the \(\sigma_{w}^{2}\) can be attributed to a technical failure on 16 December, and the different range spans on different days may mainly depending on the aerosol concentration. Figure 5 shows the hourly urban BLHs during the whole month (1-31 December), as well as the meteorological conditions [WS, downward shortwave radiation (DSR), \(H\), cloud fraction, and PM\({}_{2.5}\) concentrations]. Considering that \(H\) was found to account for a much larger amount of the net radiation (40%) than the latent heat flux (10%) during this study period over Beijing, only \(H\) was shown to represent the heat transfer intensity in this paper. Generally, during this observational period, the urban BLH was positively linked to the near surface WS at all the 15 levels (e.g., \(r\) = 0.3 and \(r\) = 0.2 for 8 m and 320 m, respectively), and the largest correlation coefficient, \(r\) =0.4, was occurred at 47 m and 65 m, and then decreasing with the increasing height. The Urban BLH was also positively linked to DSR (\(r\) = 0.6), \(H\) (\(r\) = 0.5), \(u^{*}\) (\(r\)=0.5), and TKE/m (\(r\) = 0.5), but negatively linked to the PM\({}_{2.5}\) concentrations (\(r\) = -0.4). A high urban BLH occurred on strong, windy days with a large amount of solar radiation (e.g., 5 December and 23 December). Note that, for very clean windy days with very low aerosols concentration and strong wind as shown in Figure 5b (e.g., 5 December, 8 December, 15 December, and 22 December), the lidar signals showed a low signal-to-noise, resulting in not available data, because the heterodyne Doppler wind lidar technique using an infrared laser source relies on the presence of aerosols [21; 27], leading to discontinuous observations as shown in Figure 5a. The maximum urban BLH during the whole winter month was 1000 m, accompanied by the maximum DSR, approximately 480.7 W m\({}^{-2}\), on 23 December, which is half that reported on clear days during summer in Beijing by using the threshold method [27]. For a heavily polluted urban boundary layer with weak wind, e.g., 4 December, 18-21 December and 31 December, the maximum urban BLH ranged from 260-300 m, and that of DSR from 240-390 W m\({}^{-2}\), during daytime. For the NBL, the heights were mostly around or lower than 200 m, and even lower than 100 m during the heavily polluted conditions. Figure 4: Comparison of the boundary layer depths calculated using \(Ri_{b}\) and threshold methods from 1 to 31 December 2016. Dashed lines: 200 m (definition of the onset of the convective boundary layer) and 325 m (the height of the meteorology tower). Based on the retrieved vertical distribution of the aerosol extinction coefficient from a Mie-elastic backscatter polarization lidar (AGHJ-1-LIDAR) developed by Anhui Institute of Optics and Fine Mechanics (AIOFM) also located at the IAP site, the maximum retrieved urban BLH during daytime on 19 and 20 December was 350 m and 300 m in [31], respectively, which is similar to our results (300 m and 278 m). Note, however, that the urban BLH during the early morning was 500 m for these two days but 250 m and 300 m at night in [31], and about 200 m during the early morning on 19 December and 400 m at night on 20 December in [11] by using the same method as [31]. However, urban BLHs were mostly lower than 100 m and exhibited little change during the whole of nighttime (i.e., stable NBL, as shown in Figure S1) in our study. It was found that the stable NBL usually was accompanied by the temperature inversion near the surface during heavily polluted episodes, e.g., during 2-5 December, 16-22 December in [47]. It is important to note that a stable NBL is often coupled with a residual layer (RL) [48].