# 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
Only for very large \(k_{1}\) are the spectra for the \(u\) component of the DBS lidar and the sonic close together. For the \(u\) component, a local maximum can be observed around approx. \(k_{1}=10^{-1.8}\) m\({}^{-1}\). The \(v\) spectrum of the DBS lidar is higher than the sonic spectrum for the whole wave number range and a (smaller) second maximum can be observed around \(k_{1}=10^{-1.4}\) m\({}^{-1}\). For higher wave numbers, the spectra then quickly drop off. The exact shape of the measured spectra of a Windcube does not only depend on the atmospheric conditions and measurement heights, but will also vary with the flow direction towards the scanning geometry of the Windcube [10]. It is thus difficult to explain all features of the measured spectra. The strong positive deviations from the sonic spectra in this range are likely to be caused by the cross-contamination effects between \(\overline{u^{\prime 2}}\), \(\overline{v^{\prime 2}}\) and especially by the contamination of the horizontal variances by \(\overline{w^{\prime 2}}\). The short region where the spectra are almost horizontal at the high wavenumber  
Figure 8: Normalised spectra of \(u\) and \(v\). For (**a**) SW/SE/EE, (**b**) SW/SE and (**c**) Windcube v2 next to the mast; solid lines are the sonic spectra; dashed lines are the lidar spectra; sonic time series have been aggregated to 0.5 Hz (a and b) and 0.89 Hz before calculation of the spectra; only periods with \(\overline{u}_{sonic}>4\) m\(\cdot\)s\({}^{-1}\) and \(\overline{u^{\prime 2}}_{sonic}>0.2\) m\({}^{2}\cdot\)s\({}^{-2}\) were used in the spectral averaging; \(u_{s}\) is the friction velocity computed from the sonic anemometer measurements; the black line indicates the theoretical \(-2/3\) slope in the inertial subrange; n indicates the number of periods used for averaging. end is likely to be caused by the algorithm which derives the wind vector from the measurements of \(v_{r}\). In analogy with the internal software of the Windcube v2, in this paper the wind vector was calculated whenever a new measurement of \(v_{r}\) was available--i.e., at a frequency of approx. 0.89 Hz. One full rotation, however, takes five measurements of \(v_{r}\) and thus acts similarly to a moving average filter [41]. The relatively strong overestimation in the measured variances by the Windcube compared to some other studies using similar instruments (Windcube v1 and v2) [9; 19] is likely to be related to the great measurement height (188 m) and thus the large distance between the different beams. In parts, it might also be caused by a dominance of unstable conditions which are more frequent during the summer season and the inhomogeneous flow caused by the terrain complexity. In Table 3, we also provide the statistics for periods when \(\overline{u}_{sonic}>4\) m\(\cdot\)s\({}^{-1}\), as this filter criterion is often used in applications and studies in the wind-energy sector, thereby allowing a more direct comparison to other experiments. For the ML combinations SW/SE/EE, SW/SE and SE/EE, there is only a small change in the linear-regression statistics. For the Windcube v2 and the SW/EE, which have lower \(R^{2}\) values, \(R^{2}\) significantly improves after the application of the \(\overline{u}_{sonic}>4\) m\(\cdot\)s\({}^{-1}\) criterion.