# An Inter-Comparison Study of Multi- and DBS Lidar Measurements in Complex Terrain
## 3 Results and Discussion
### Radial Velocity Components
#### 3.1.2 Second-Order Statistics  
For the locations SE, SW and EE, the linear-regression statistics between \(\overline{\
u^{\prime 2}_{\mathit{r} lidar}}\) (measured by the WindScanners) and the respective variance derived from the projection of the sonic measurement onto the direction of the respective WindScanner beam (\(\overline{\
u^{\prime 2}_{\mathit{r}sonic}}\)) are very similar (Table 2). The slope indicates a significant underestimation of \(\overline{\
u^{\prime 2}_{\mathit{r}sonic}}\) by the WindScanner measurements. This is likely to be due to the relatively large probe volume. In contrast, the slope of the linear regression for the MA system is significantly closer to 1. Here, the smaller range gate size seems to more than compensate for the smaller turbulent length scales which are usually found for \(w\). \(R^{2}\) is similar for all systems. The values are slightly worse than for the first-order statistics, except for the MA location, where \(R^{2}\) is slightly higher. The reduced values in \(R^{2}\) are probably partly caused by the reduced range of the observed variances when compared to the mean values. Another reason for the increased scatter is due to the fact that line averaging does not necessarily scale linearly with the observed variance. It is rather direction dependent on and selective of small wavenumbers. This makes the attenuation dependent on the form of \(\varPhi_{ij}\left(\mathbf{k}\right)\) (9), which varies with atmospheric conditions--i.e., under stable conditions, a larger portion of the variance will be contained in small eddies as opposed to under unstable conditions. Also, since a finite time interval is used (10 min), some scatter will be introduced by the stochastic distribution of the eddy sizes in the individual period. To further investigate the probe-volume averaging effect on \(\overline{\
u^{\prime 2}_{\mathit{r} lidar}}\) periods with wind directions close to parallel (\(\pm 15^{\circ}\)) to the azimuth angle of the individual WindScanner beams, SE, SW and EE were selected. The spectral filter function defined by (7) and (10) was applied to \(\upsilon_{\mathit{r} sonic}\) (Figure 3). The application of the filter function to the sonic data brings the slope of the linear regression between \(\overline{\
u^{\prime 2}_{\mathit{r}sonic}}\) and \(\overline{\
u^{\prime 2}_{\mathit{r} lidar}}\) closer to unity and slightly improves \(R^{2}\) for all systems. Interestingly, this improvement is also observed for the EE system, which has quite a large inclination angle into the atmosphere (\(\theta=22.3^{\circ}\)). A comparison of the average spectra of \(\upsilon_{\mathit{r}}\) of the sonic and WindScanner measurements reveals a clear spectral attenuation for SE, SW and EE spectra from approx. \(k_{1}>10^{-2}\)\(m^{-1}\) (Figure 4a-c). In contrast to the other systems, the spectrum of MA does not exhibit a clear spectral attenuation, which again is likely to be due to the smaller probe volume. Instead, the spectral energy at the high wavenumber tail for MA is actually higher than for the reference sonic. This behaviour can also be observed for the SW system (Figure 4c). Also \(T_{\upsilon_{\mathit{r}}}\) starts to increase at approx. \(k_{1}>10^{-1}\) m\({}^{-1}\) for all systems (Figure 4e). This effect becomes worse if measurements with small variances are included (data not shown) and is likely to be attributed to instrumental noise. The theoretical considerations