# 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
#### 3.2.2 Second-Order Statistics of the Horizontal Wind Vector Components  
This section presents the second-order statistics (variances and spectra) of the horizontal wind components \(u\) and \(v\). The second-order statics for the \(w\) component can be found in Section 3.1.2. (MA WindScanner). Figure 7 displays the scatter plots and linear-regression statistics for the different ML combinations and the DBS lidar when compared to the sonic measurements. The differences between the DBS and ML, but also among the different ML combinations, are quite large. Almost identical linear-regression statistics can be observed for the SW/SE/EE and SW/SE combinations (Figure 7a,b). The \(R^{2}\) values of the linear regression for \(\overline{u^{\prime 2}}\) and \(\overline{v^{\prime 2}}\) are similar to the statistics of \(\overline{v^{\prime 2}}\) (Table 2 and Figure 3). Also the slope indicates a similar underestimation of \(\overline{u^{\prime 2}}\) (and \(\overline{v^{\prime 2}}\)) of about 20%. Looking at the spectra of SW/SE/EE and SW/SE, one can clearly see the effects of line averaging which causes the reduction in \(\overline{u^{\prime 2}}\) and \(\overline{v^{\prime 2}}\) (Figure 8a,b). As for \(v_{r}\), an attenuation in the spectral density from approx. \(k_{1}=10^{-2}\) m\({}^{-1}\) for \(u\) and \(v\) can be observed. The line averaging effect thus also causes the reduced \(\overline{u^{\prime 2}}\) and \(\overline{v^{\prime 2}}\) in SW/SE/EE and SW/SE. The scatter in the inter-comparison between the SW/EE and SE/EE is larger than for SW/SE/EE and SW/SE and the slope of the linear regression shifts close to 1. One of the reasons for the increased scatter in the ML combinations using two WindScanners including the EE system might be that the EE system has an inclination angle which is not close to 0\({}^{\circ}\). In the wind-vector reconstruction for two scanners, the \(w\) component is assumed to be 0 m\(\cdot\)s\({}^{-1}\). Some of \(\overline{w^{\prime 2}}\) will thus contaminate the measurement of \(\overline{u^{\prime 2}}\) and \(\overline{v^{\prime 2}}\). Moreover, as discussed earlier, the direction of the flow in relation to the beam directions will also influence the error propagation for the individual components, especially if the angle between the beams is small [38]. In the experimental setup it is, however, difficult to separate these effects as they are likely to be correlated. This observation suggests that for the ML method, an adequate positioning of the lidar devices is even more important for measuring turbulence quantities than for the mean wind speed. In general, random measurement errors in the time series will always lead to an increased variance. Therefore, both the contamination by the \(w\) component and the unfavourable angles in the lidar combination lead to increased \(\overline{u^{\prime 2}}\) and \(\overline{v^{\prime 2}}\) in the lidar measurement. The slope values close to the 1:1 line are thus likely a result of the combination of these measurement errors and the line averaging, which act in opposing directions. Figure 7: Scatter plots of \(\overline{u^{\prime 2}}\) from different lidar configurations against the reference sonic at 188 m; (**a**) SE, SW and EE; (**b**) SE and SW; (**c**) SE and EE; (**d**) SW and EE; (**e**) Windcube v2 next to the mast; (**a–d**) are measurements from WindScanners in ML mode; the Wincube is operated in DBS mode. For ML combinations with only two beams, \(w=0\) m\(\cdot\)s\({}^{-1}\) is assumed in the wind-vector reconstruction; n indicates the number of value pairs displayed in the individual scatter plots. The comparison between the DBS system and the sonic indicates a clear overestimation of \(\overline{u^{\prime 2}}\) and \(\overline{v^{\prime 2}}\) by the DBS system (Figure 7e and Table 3). Also, the \(R^{2}\) values are lower than for all ML combinations. The spectra of the DBS system show a significant contamination of the variance measurements across almost the whole wavenumber range.