## 3 Results
### Validation of the Derived Wind  
#### 3.2.1 Different Quality Control Methods  
Figure 8 shows the comparison between the wind speeds derived using the optimized method (\(WS_{\text{lidar}}\)) and those measured by meteorological tower (\(WS_{\text{tower}}\)). The wind speeds derived at two heights (10 m and 70 m) using the radial wind speed from VAD scans at two elevation angles (10\({}^{\circ}\) and 30\({}^{\circ}\)) at two distinct sites, i.e., within the wind farm (S3) and upwind of the wind farm (S1), are shown. Wind speed derived from the optimized method are in good agreement with those measured by the meteorological tower, with a linear regression slope between 0.991 and 1.069, and a coefficient of determination exceeding 0.932. The volume of usable data is greater than 75% (the total data volume used for comparison during the study period is 1277 pairs). Figure 8: Comparison of observations from the meteorological tower with the (**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; (**c**) 70 m wind speed derived using VAD scans with a 10\({}^{\circ}\) elevation angle at S3; (**d**) 70 m wind speed derived using VAD scans with a 30\({}^{\circ}\) elevation angle at S3. The color bar gives information on the number of observations per 0.2 m/s wind speed intervals, and N refers to the number of data pairs. Figure 7: Frequency distribution of wind speed (**a**) and wind direction (**b**) at 70 m AGL. Table 1 gives the statistical results from the comparison of wind speeds derived using the optimized and traditional methods at different observation sites and heights against those measured by the meteorological tower. The significance of the difference between the results from the traditional and the optimized methods are tested using the Kolmogorov-Smirnov test, and the results are indicated in the last column in Table 1. Within the wind farm (S3), the optimized method significantly enhances the accuracy of the derived wind speed at 10 m and 70 m (significant at \(\alpha=0.05\)) for the 10-degree elevation angle, and at 70 m (significant at \(\alpha=0.01\)) for the 30-degree elevation angle. The results from the optimized method exhibit better R\({}^{2}\) values compared to those from the traditional method, particularly within the wind farm (S3) where the wind field is more complex. The statistics of our inversion results are better than similar studies by [PERSON] (R\({}^{2}\) = 0.956 at h = 74 m) using combined filtering [33], and by [PERSON] [34] using dynamic data filtering (R\({}^{2}\) = 0.85 at h = 41.5 m) and static standard deviation filtering (R\({}^{2}\) = 0.83 at h = 41.5 m). The optimized method also gives lower MAE and RMSE. The above results indicate that the optimized method is effective for deriving wind speed in complex wind environments, for example, within wind farms. Similar to the wind speed analysis, Figure 9 presents the scatter plots that compare the wind directions derived using VAD scans (\(WD_{\text{lidar}}\)) with different elevation angles (10\({}^{\circ}\) and 30\({}^{\circ}\)) against those from tower measurements (\(WD_{\text{tower}}\)). Results from the optimized and the traditional methods at different heights (10 m and 70 m) and different sites (S1 and S3) are compared. Table 2 shows the statistical results. Similarly, the wind direction obtained by both the traditional and the optimized methods show good correlations with observations from the meteorological tower. At 70 m, the derived wind directions using optimized methods are better than those in a similar study carried out by [PERSON] et al. (R\({}^{2}\) = 0.947 at h = 78 m) [22]. The optimized method improves the wind direction inversion when compared to the traditional method, as evidenced by the significant increase in the coefficient of determination. In the subsequent sections, we will focus our analysis on the effects of the proposed optimized method on wind speed inversions.