## 1 Introduction  
The atmospheric boundary layer (ABL) height is an important factor in diluting pollutants emitted at the surface, in which layered pollutants vertically disperse through the action of turbulence. Accurate estimation of ABL diurnal variability is critical to predict pollutant concentrations by model computations [1; 2; 3; 4], especially for the ABL over urban environment, so-called the urban boundary layer [5; 6; 7]. The most common way to determine the boundary layer height (BLH) is by using vertical profiles of meteorological variables, such as the potential temperature, wind speed (WS), and bulk Richardson number (\(R_{lb}\)), which are generally obtained from radiosonde launches or aircraft observations [8]. However, radiosonde observations are usually infrequent and rarely made in central urban environments [9]. Mostly, radio soundings collected at rural sites nearby cities are used to assist in the analysis of the urban boundary layer [10; 11]. Particularly, spatial differences in daytime BLH have been reported due to various surface properties with different surface heat flux characteristics [12; 13]. Thus, the BLH estimated from radio soundings launched at rural sites is not representative of urban areas. Moreover, in the frame of the World Meteorological Organization (WMO), the radio soundings are launched only twice per day. In few other locations, i.e., during field campaigns and densified observation, radio-sounding are launched three times a day and therefore cannot capture the diurnal development of the urban boundary layer. In the last decades, remote sensing techniques and network of instruments became the most valuable and popular approach for detecting the nature of the atmosphere [14], particularly in the urban layer, because of their higher temporal resolutions, such as ceilometers [15; 16], sodars [17; 18], and lidars [1; 11]. The Doppler wind lidar is an optical active remote sensing instrument that became popular after the discovery of the CO\({}_{2}\) laser [19; 20]. Compared to other lidar types (e.g., elastic and Raman), Doppler wind lidar is the most suited for the investigation of the vertical wind structures, the development of the urban boundary layer [3; 19; 20; 21; 22; 23; 24; 25], and for validating numerical forecast models [26] as it has the capability to measure the 3D wind vector field with the maximum measurement range exceeding 10 km. For instance, the vertical velocity variance (\(\sigma_{w}^{2}\)), obtained from the 3D wind measurements, can be used to describe the turbulence intensity by the turbulence method, and the BLH can be defined. The urban mixing height was defined by using a threshold method (the so-called threshold method) as the height up to which \(\sigma_{w}^{2}>0.1\) m\({}^{2}\) s\({}^{-2}\) in London, UK [21]. A previous study pointed out that the threshold method provides a reliable height retrieval for convective boundary layer (CBL) with strong turbulence and unstable atmospheric stratification but is not recommended to determine the nocturnal boundary layer (NBL) height, when usually the turbulence is weak and often has \(\sigma_{w}^{2}<0.1\) m\({}^{2}\) s\({}^{-2}\)[27]. For another instance, a Doppler wind lidar was set in urban Beijing during the summer of 2015. Our previous study also evaluated a new improved version of the threshold method [28], to determine the NBL height, which defined the NBL top as the height at which \(\sigma_{w}^{2}\) decreases to 10% of its near-surface maximum after subtracting a background value [27]. Based on a case study under heavily polluted conditions (1-4 December 2016), we found that these two threshold methods in London and Beijing were both inaccurate in determining the NBL height [29]. The former was also proven wrong for severely polluted urban boundary layer conditions with weak turbulence during daytime in winter in Beijing. This might have been because of the lower urban BLH dropping below the minimum observable height (100 m) during the time of the NBL.