# An Inter-Comparison Study of Multi- and DBS Lidar Measurements in Complex Terrain
## 3 Results and Discussion
### Horizontal Wind-Speed Statistics from the ML and Doppler Beam Swinging (DBS) Technique
#### 3.2.1 First-Order Statistics of the Horizontal Wind Speed
The deviation between \(\overline{V_{hidar}}\) and \(\overline{V_{thmast}}\) for the ML measurements is smaller than for the DBS system for most sectors and WindScanner combinations (Figure 6). Especially for the WindScanner combinations SW/SE/EE and SE/SW, the differences are small for all directions and only vary between approx. \(-2\%\) and \(2\%\). For the SE/EE combination, a relatively large positive deviation of  
Figure 6: (**a**) mean of the directional deviation in \(\overline{V_{h}}\) between the sonic and the different lidar configurations; (**b**) same as (**a**) but for the SE/EE combination with and without the correction for \(\overline{w}\); see text for details; periods during which \(\overline{V_{h}}\)\({}_{sonic}<4\) m\(\cdot\)s\({}^{-1}\) were excluded from the comparison to increase the comparability to other complex terrain measurements reported in the literature. Also, bins with n \(<5\) are not displayed; error bars denote \(\pm\) one standard deviation. the ML system in comparison to the sonic wind speed can be observed between approx. 350 and 25\({}^{\circ}\), which even exceeds the DBS-sonic deviations. This is likely due to the fact that within this range, the angle between the mean wind direction and the beam directions of SE and EE are large and the difference in beam directions is small (cf. [38]). This configuration leads to an increased error propagation in the estimation of \(u\) that largely dominates \(\overline{V}_{hidar}\)--i.e., the azimuth angles and flow direction are unfavourable for the retrieval of \(\overline{V}_{hidar}\). For flow angles which are directed in a more parallel manner to the orientation of the lidar beams, the error propagation for \(v\) is expected to be large. The effect on \(\overline{V}_{hidar}\), however, is then much smaller. A second effect which can affect the quality of the measurements of SE/EE combination is the relatively large elevation angle of the EE system compared to the other systems (Table 1). The assumption, \(\overline{w}=0\) m\(\cdot\)s\({}^{-1}\), thus results in a contamination of \(\overline{V}_{hidar}\) by \(\overline{w}\). Due to the low availability, an inclusion of the MA system which could correct for the influence of \(\overline{w}\) in the directional analysis was not possible. Therefore, a direction-dependent correction factor was calculated using \(\overline{w}_{sonic}\). Equation (3) is first solved using \(\overline{v}_{r~{}SE}\), \(\overline{v}_{r~{}EE}\) and \(\overline{w}_{sonic}\). In a second step, (3) is solved only using \(\overline{v}_{r~{}SE}\) and \(\overline{v}_{r~{}EE}\). The ratio of the two results is then applied as a correction factor to \(\overline{V}_{hidar}\). The correction reduces the deviations in the 350\({}^{\circ}\)-25\({}^{\circ}\) sector. The effect is, however, relatively small. Therefore, the assumption \(\overline{w}=0\) m\(\cdot\)s\({}^{-1}\) does not seem to be the main cause of the observed deviations. Some of the deviations between the sonic and the lidar measurements might also be caused by the flow distortion of the mast. However, we estimate this effect to be small (c.f. Section 2.4. ).