## Materials and Methods
### Methods  
#### Estimation of Urban BLH  
Based on radiosonde data, the \(Ri_{b}\) method is widely used, as it is a reliable method to determine both the CBL and SBL [38]. Compared with the methodology based on detecting the altitude where there is a sharp change in the temperature and RH profiles, the \(Ri_{b}\) method has been found to be more effective, as shown in [39]. The WS and T at 15 levels provided by the 325-m tower make this method available in our study under the condition of BLH \(<\) 300 m. The definition of \(Ri_{b}\) was given as [40]:  
\[Ri_{b}(z)=\frac{\frac{\delta}{\theta_{\text{cs}}}(\theta_{\text{tr}}-\theta_{ \text{rs}})(z-z_{s})}{\left(u_{z}-u_{s}\right)^{2}+\left(v_{z}-v_{s}\right)^{2 }+bu^{*2}}, \tag{1}\]  
where \(z\) is height (m), \(g\) is the gravity acceleration constant (m s\({}^{-2}\)), \(\theta_{v}\) is the virtual potential temperature (K), \(u\) and \(v\) are the horizontal components of WS (m s\({}^{-1}\)), and \(u^{*}\) is the surface friction velocity (m s\({}^{-1}\)). In addition, \(z_{s}\) is the height of the lower boundary (m), and \(b\) is an empirical coefficient. According to [40], \(z_{s}\) can be set to 20 m or 40 m, and \(b\) can be set to 100 m. The \(Ri_{b}\) method defines the BLH as the height at which the \(Ri_{b}\) reaches the critical threshold value of 0.25 (the vertical change of \(Ri_{b}\) is shown in Figure S1). It is noted that a strong correlation [correlation coefficient (\(r\)), \(r\) = 0.83] between the BLH derived with \(z_{s}\) = 20 m and \(z_{s}\) = 40 m. In this paper, we choose \(z_{s}\) = 20 m.  
In many previous studies, \(b\) was set to 0 because of the unknown value of \(u^{*}\), as in the experiments [41; 42; 43]. In our study, \(u^{*}\) can be calculated as \(\left(\overline{u^{*}w^{*}}^{2}+\overline{v^{*}w^{*}}^{2}\right)^{1/4}\) by using the sonic anemometer (streamwise \(u\), cross-stream \(v\), and vertical velocities \(w\)). As shown in Figure 2, combining the time series of the results with \(b\) = 100 and \(b\) = 0 and their one-to-one plot, the sensitivity of the estimation of BLH to the effect of surface friction was studied. Generally, the BLH values computed with \(b\) = 100 are larger than those with \(b\) = 0, and the \(r\) is just 0.76, which indicates the surface friction effect cannot be ignored. Particularly, the different values in daytime (from sunrise to sunset), in blue, during a red-alert pollution event (17-21 December), reached to about 100 m, with the BLH lower than 150 m for \(b\) = 0 but larger than 250 m for \(b\) = 100. This suggests that, in a steadily polluted urban boundary layer with weak buoyancy destruction and shear production during daytime, the surface friction effect plays an important role in the development of the urban boundary layer.  
[PERSON] et al. [44] also found that the surface friction effect had a significant impact on the calculation of BLH, especially for the height of the SBL. Therefore, \(b=100\) was used in our study.  
The standard deviation (\(\sigma_{w}\)) of the 30-min vertical velocity was calculated by using the measurements from Doppler wind lidar. The threshold method of \(\sigma_{w}^{2}>0.1\) m\({}^{2}\) s\({}^{-2}\) derived by [13], as mentioned in the Introduction, was used to calculate urban BLH based on the lidar.