# 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  
For resource estimation in the wind industry, it is standard to use the scalar horizontal velocity (\(\overline{V_{h}}\)). This approach is also followed here. Although in many remote sensing applications it is common practice to work with the vector average of the wind velocity, publications concerning the accuracy  
Figure 4: Spectra of \(\
u_{r}\) measured by different WindScanners and the sonic anemometer when the wind direction was close to parallel (\(\pm 15^{\circ}\)) to the azimuth angle of the WindScanner (**a–c**); (**d**) spectra of the MA location and the \(w\) component of the sonic anemometer; sonic time series have been aggregated to 0.5 Hz before calculation of the spectra to account for the temporal averaging effect and the associated filter function \(\xi\left(k_{1}\right)\) ; the black line indicates the theoretical \(-2/3\)-slope in the inertial subrange; (**e**) spectral transfer function \(\left|\xi\right|^{-2}T_{\
u_{r}}\) derived from the average of the normalised spectra in (**a–c**); only periods with \(\overline{u}_{sonic}>4\) m\(\cdot\)s\({}^{-1}\) and \(\overline{u^{\prime 2}}_{sonic}>0.2\) m\({}^{2}\)\(\cdot\)s\({}^{-2}\) (SW, SE, EE), and \(\overline{w^{\prime 2}}_{sonic}>0.1\) m\({}^{2}\)\(\cdot\)s\({}^{-2}\) (MA) were used in the spectral averaging; n indicates the number of periods used for averaging. of lidars in complex terrain often use the scalar mean [4; 6]. While vector averaging produces slightly different numbers, the general patterns that can be observed remain the same and the differences are very small. The comparison of \(\overline{V_{h}}\) measurements of the ML combination using three lidars and the sonic reveals an excellent agreement between the two techniques as would be expected from the comparison of \(\overline{v_{r}}\) (Figure 5a). Also, the ML technique using two lidars and neglecting the vertical component in the vector reconstruction only produces marginally different results for the scanner combination SE/SW (Figure 5b). For the SW/EE combination, the scatter slightly increases and we can see a few points which significantly deviate from the linear relationship (Figure 5d). The observed differences between the different dual-lidar configurations are likely to be at least partly caused by the setup of the instruments. One characteristic which sets the different dual-lidar measurements apart is the difference in azimuth angle between the WindScanner beams. For SW/EE, the angle is smallest (43\({}^{\circ}\)) which causes the strongest error propagation from the radial wind speed onto the wind vector when solving Equation (3) (cf. [38]). The angle for SE/EE is slightly larger (49\({}^{\circ}\)) and the SE/SW combination has an angle difference of 88\({}^{\circ}\), which is close to the ideal 90\({}^{\circ}\). The DBS measurement with the Windcube v2 exhibits more scatter and the linear regression significantly deviates from 1:1 when compared to the sonic (Figure 5e). Especially for low wind speeds, an overestimation of the \(\overline{V_{hsonic}}\) by the DBS lidar can be observed. In general, the linear-regression statistics for the DBS lidar are similar to what has been reported at Rodeser Berg in earlier measurement campaigns [6] and are similar to what has been reported from other lidar-mast inter-comparisons in complex terrain [39] albeit significantly worse than in flat terrain (e.g., [1]). In contrast, the statistics for the ML combinations are similar to the results which we regularly observe during DBS lidar calibrations in flat and homogeneous terrain. The \"bump\" in the DBS data at low wind speeds might be associated with turbulence effects which are more important for low wind speeds. Moreover, thermal effects on the flow might create increased vertical velocities (relative to the horizontal wind speed) which are likely to spatially vary in the complex surroundings at Rodeser Berg.