# Reducing the Uncertainty of Lidar Measurements in Complex Terrain Using a Linear Model Approach
## 3 Results
### Wind Speed Comparisons  
In this subsection the results of the different wind field reconstruction method compared to the cup anemometer are presented. The results of the statistical parameters of the OLS are summarized in Table 2.  
**SWE Scanner**: Figure 8 shows the results of the comparison between the SWE Scanner and the cup anemometer installed at 100 m using the _CLS_ and _PRESS_ methods. The results show very similar results for the methods and locations which are investigated. The parameter offset differs by up to 0.4 m\(\cdot\)s\({}^{-1}\) between the results and the slope changes by 0.04 between the lowest and the highest value. \(R^{2}\) is similar with values between 0.94 and 0.95. It is noticeable that the results with _PRESS_ (Figure 8b,d) have larger offsets and slopes than the _CLS_ method ( Figure 8a,c). These 10 min lidar data contain the point combinations that had the highest \(R^{2}\) in time  
Figure 7: Results of the projection of the _USA_ onto the five lidar beam normal vectors. Each polar plot represents a combination of azimuth-elevation angles of the laser beam. The positions of the plots correspond to the azimuth angle of the scanner laser beam: the upper left graph is equivalent to the azimuth angle at 288\({}^{\circ}\), the lower left graph is equivalent to 216\({}^{\circ}\), the middle graphic is the vertical measurement, etc. The axes of the graphs are rotated in the respective angles of the laser beam direction. The azimuth is the wind direction from the met mast. The distance of the point from the origin corresponds to horizontal wind speed (8, 12, 16 mper s). The absolute differences between met mast and lidar (\(\overline{\mu}_{usa}\cdot\overline{\mu}_{lidar}-\overline{\
u}_{los,j}\)) are represented in colour and the size of points shows the relative differences between met mast and lidar. Positive absolute differences are marked in red, very small differences (magnitude \(<\) 0.001) are shown in grey, and negative differences in blue. step \(t\), which should reduce the effect of outliers. However, this does not lead to an improvement in the agreement between lidar and mast. The investigated wind speed range in this case was range 0-20 m\(\cdot\)s\({}^{-1}\). Data are most frequent in the lower range (up to 10 m\(\cdot\)s\({}^{-1}\)), where the 5-95 th quantile range of the data is large compared to that seen in the more sporadic wind speeds over 15 m\(\cdot\)s\({}^{-1}\). The same comparison was also made using data from the SWE scanner at the second measurement location near the foot of the met mast. For brevity these results are not shown here. Results at this second (closer) site deviate more from the met mast at low wind speeds than at the first (further) site. At speeds greater than 8.8 m\(\cdot\)s\({}^{-1}\), the deviations are smaller compared to position one. These results suggest that the improvement in agreement between the lidar and the met mast are due to the measurement method, not the different locations. **Galion:** The results from the Galion system are shown in Figure 9. For the _CLS_ method all 18 trajectory points were used for the evaluation. A multiple overdetermined system of equations has to be solved. This lidar and method shows a better agreement between the lidar measurements and the met mast than the SWE Scanner measurements (Figure 9a; offset 0.018 m\(\cdot\)s\({}^{-1}\), slope 1.033, \(R^{2}\) 0.974). Figure 8: Correlation between SWE Scanner and the cup anemometer at 100 m above ground. The black dots represent the 10 min data points, the black line is the regression line, and the blue lines are the 5 th and 95 th quantiles. The trajectory of the Galion lidar consists of three identical trajectories with different half opening angles \(\phi\). In order to check whether there is an influence of the opening angle on the measuring quality, the three trajectories were examined and evaluated separately (Figure 9b-d).