## 3 Results
### Validation of the Derived Wind
#### 3.2.2 Different Weather Conditions  
Previous studies have demonstrated that Lidar can not only detect signals scattered by aerosols but also capture background signals. Daytime background signals, primarily composed of direct or scattered light, are more intense than nighttime signals, predominantly originating from the moon and artificial light sources [35]. Therefore, considering the influence of background signals is essential when analyzing factors that affect the derived wind speed and direction. Additionally, atmospheric hydmeetors, such as clouds and raindrops, cause signal attenuation through particulate scattering, leading to a decrease in _CNR_. In the following, the performances of the optimized and traditional methods are compared under clear and cloudy conditions and during the day and night. The clear-sky index (CSI) has been used in previous studies to distinguish clear skies from cloudy conditions [36; 37; 38]. [PERSON] et al. [39] compared CSI with ceilometer readings and noted a high correlation. In this study, the longwave downward radiation (LDR) data from the four-component radiometer at S3 and air temperature and humidity data from the meteorological tower are used to calculate the CSI following [PERSON] and [PERSON] [34]:  
\[CSI=\frac{\in_{A}}{\in_{AC}}, \tag{15}\]  
\[\in_{A}=\frac{LDR}{\sigma_{S}T^{4}}, \tag{16}\]  
\[\in_{AC}=\in_{AD}+(k+2\sigma_{S})\Big{(}\frac{e}{T}\Big{)}^{1/8}, \tag{17}\]  
where \(\sigma_{S}\) is the Stephen--Boltzmann constant, T is the air temperature (K), \(\in_{A}\) is the apparent emittance of the sky, \(\in_{AC}\) is the empirical apparent cloud-free emittance, \(\in_{AD}\) represents the altitude-dependent clear-sky emittance of a completely dry atmosphere. In Equation (17), \(e\) is the water vapor pressure (Pa), and \(k\) is a position coefficient of determination. The water vapor pressure \(e\) is calculated from the relative humidity using the following equations:  
\[e=\frac{RH}{100}e_{s}, \tag{18}\]  
\[e_{s}=6.1121 exp\Big{(}\frac{17.502t}{t+240.97}\Big{)}, \tag{19}\]  
where \(RH\) is the relative humidity (%), \(e_{s}\) is the saturated water vapor pressure (hPa), \(t\) is the air temperature (\({}^{\circ}\)C). The coefficient \(k\) is location-dependent and determined by fitting \(\in_{A}\) and \(e/T\) (Figure 11) using Equation (17) [33]. Figure 10: Comparison of wind speed derived using the traditional and the optimized methods with those measured by meteorological tower. (**a**) 10 m wind speed derived using VAD scans with a 10\({}^{\circ}\) elevation angle at S3; (**b**) 10 m wind speed derived using VAD scans with a 10\({}^{\circ}\) elevation angle at S1. A clear-sky index exceeding 1 suggests cloud presence, whereas a CSI of 1 or below indicates a cloud-free condition. During the study period, there are a total of 1277 half-hourly observations, of which 375 are cloudy (212 of which are daytime observations and 163 of which are nighttime observations) and 902 are clear (431 of which are daytime and 471 of which are nighttime observations). Table 3 shows the statistical results for the comparison of the derived wind speeds (using the optimized and the traditional methods) with those measured by the meteorological tower under cloudy and clear sky conditions. Despite the reduced data availability, the optimized method outperforms the traditional method in the coefficient of determination (R\({}^{2}\)), root mean square error (RMSE), and mean absolute error (MAE). Under cloudy conditions, the R\({}^{2}\) for the optimized method (0.925 during the day (07: 00-18: 30) and 0.932 during the night (19: 00-06: 30)) exceed those of the traditional method (0.813 during the day and 0.905 during the night). Thus, the wind speed derived using the optimized method is more accurate. In addition, the optimized method consistently gives lower RMSE and MAE than the traditional method, especially under cloudy conditions.