## 3 Results  
### Urban BLH  
The threshold method, based on the lidar data, was not able to yield the NBL height at all times throughout the measurement campaign, because the urban BLH (averaged in one hour) was too low (\(<\)100 m, not shown). This method was either available for the urban boundary layer retrievals under daytime heavy pollution conditions. Considering as a case study a red-alert pollution event (the air quality index reaches more than 300, which will last for at least three consecutive days) from 16 to 22 December (Figure 3), rarely the threshold method worked in determining the urban BLH during daytime with a small \(\sigma_{w}^{2}\), especially under heavily polluted conditions (daytime mean concentrations of PM\({}_{2.5}>200\) ug m\({}^{-3}\) on 18-21 December). In contrast, the \(Ri_{b}\) method successfully retrieved the NBL height and even the height of the polluted urban boundary layer during daytime, which shows reasonable results by reference to the change in \(\sigma_{w}^{2}\). Therefore, in our study, the NBL height was estimated by using the \(Ri_{b}\) method. Considering that the blind overlap lidar region was 100 m, the results of urban BLH from threshold method, which was lower than 150 m, were not considered. Note that the two methods are different, while both of them are based on similar physical parameters related to turbulence processes. Figure 2: Relationship between the urban boundary layer height (BLH) calculated by using the \(Ri_{b}\) method (\(Ri_{b}=0.25\)) with two different parameter values, \(b=0\) and \(b=100\) for convective boundary layer (CBL) (blue) and nocturnal boundary layer (NBL) (black), during December 2016 (a), and the time series values of BLH values from 16 December to 21 December 2016 (b), \(b=0\) (+) and \(b=100\) (dots). In case that only one method is available to retrieve the boundary layer height, that retrieved value is taken as reference. Instead, when the boundary layer height could be retrieved with the two methods, the intercomparison is shown in Figure 4. Combined with Figure 3, it was found that mostly the boundary layer height retrieved by the \(Ri_{b}\) method is higher with respect to the retrievals obtained with the threshold method, and the urban BLHs from threshold method is rather insensitive for urban BLH below about 200 m. The correlation is essentially nonexistent (\(r^{2}=0.16\)). Considering that the threshold method may underestimate the depth of mixing layer/the urban boundary layer under weak turbulence context [21, 23, 27], we use the threshold (200 m) of the definition of the onset of CBL [45] and the height of the meteorology tower (325 m) as the references to choose the different results as the real values. When the height could be retrieved from both the two methods, the urban BLHs retrieved from the \(Ri_{b}\) method was considered as reference (4% of the total values) if the urban BLHs from threshold method were lower than 200 m, and the averaged values were chosen if the urban BLHs from threshold method were larger than or equal to 200 m, and lower than 325 m (3% of the total values) (see Figure 4). About 1% of the urban BLHs retrievals from threshold method were higher than 325 m and also than the values from \(Ri_{b}\) method, which happened during the clean noon time with relatively larger turbulence. Thus, in this condition, the values from threshold method were considered credible and chosen as the real ones. In addition, through comparison against simulated urban BLH derived by three different BL parameterization schemes (Table S1 in supporting information) in Weather Research and Forecast (WRF) model, it is shown that similar diurnal patterns of urban BLH were captured by our present observation (See Figure S2 in supporting information), implying that the physical process of boundary layer evolution based on our observation is reasonable. While the biases are mainly related to different BLH definitions causing the divergence among different schemes [46].