## 2 Materials and Methods
### Data Processing
\(N\) is the number of all samples in the analyzed period. In order to avoid rigorous data interpolation, \(S(f)\) was only calculated for periods where fewer than five data points were missing. To illustrate the performance of the spectral energy density retrievals and their differences between the data filtering methods, we show and compare power spectra from LiDAR DBS and sonic anemometer measurements during a free-stream and a wake case (Figures 2 and 3). The comparison is based on the energy spectra of the three stream-wise wind components u (along-wind), v (cross-wind) and w (vertical) and the Turbulence Kinetic Energy (TKE) calculated from sonic anemometer measurements and DBS data processed with different techniques. Figure 2: Energy spectra of four hours on 4 March 2014 during free stream conditions (\(dir_{mean}=240^{\circ}\)) of the along-wind (**a**), cross-wind (**b**) and vertical component (**c**) and TKE (**d**). Black colors show data from the sonic anemometer, and blue and grey colors show Windcube wls67 data, all at 108 m. The dashed line indicates the \(-2/3\) Kolmogorov slope. In the free-stream case, we analyzed a 4 h period from 19 to 23 UTC on 4 March 2014, which was characterized by south-westerly winds turning from 230\({}^{\circ}\) to 250\({}^{\circ}\) with wind speeds of around 5 m\(\cdot\)s\({}^{-1}\). The unprocessed DBS data, shown in light gray, underestimate the turbulence spectra compared to the sonic measurements, which was already found and discussed by [PERSON] et al. (2014) (Figures 2 and 3). Similar to [PERSON] et al. (2016), the drop in energy for frequencies above 0.1 Hz can be related to probe volume averaging. Following [PERSON] et al. (2014), we averaged all four wind vectors retrieved during one complete measurement cycle, illustrated in dark grey, which filters even more energy out of the flow compared to the unprocessed and sonic data. Finally, we show the spectrum of independent wind vectors, by only taking every fourth DBS measurement, in blue, with the same energy levels as the sonic measurements in the stream-wise wind component and the TKE estimate. Both the sonic and the processed DBS data show an energy decay parallel to the Kolmogorov \(-\)2/3 slope. The v- and w-components show, in contrast, distinct differences from the sonic spectra. In the w-component, differences occur both with respect to the overall energy level, which is clearly underestimated by the LiDAR measurements, and the slope of the spectra towards higher frequencies. This behavior is related to the limitations arising from the Windcube v1 measurement setup with only 4 beams, the fact that the vertical wind component is not measured directly and that the probe volume averaging has a larger effect in the vertical, filtering out small-scale turbulence, which is typical for the vertical wind component. In the v-component, energy spectral densities are slightly overestimated  
Figure 3: Energy spectra of four hours on 1 March 2014 during wake conditions (\(dir_{mean}=60^{\circ}\)) of the along-wind (**a**), cross-wind (**b**) and vertical component (**c**) and TKE (**d**). Black and blue colors show wake data from the sonic anemometer and Windcube wls67 at 108 m. The dashed line indicates the \(-\)2/3 Kolmogorov slope. by the LiDAR. One possible error source for the different performance between the v-spectra and the u-spectra is the LiDAR measurement geometry. Dependent on the prevailing wind direction, one of the wind components can be derived from two beams perpendicular to the main flow. Measuring radial velocities with an angle to the mean flow leads to measurement errors, since only parts of the aerosol movements are captured. The larger the angle between the prevailing wind direction and the LOS measurement, the bigger the error. [PERSON] and [PERSON] (2015) give the increased contribution of the spectral tensor component \(\Phi_{2}2(k)\) as the wave number \(k\) goes to 0 as an explanation for the increased spectral energy, but conclude that further research needs to be done.