## 2 Materials and Methods
### Data Processing
In the wake case, the period from 00 to 04 UTC on 1 March 2014 is dominated by north-easterly winds turning from 50\({}^{\circ}\) to 80\({}^{\circ}\) with a wind speed of around 9 m\(\cdot\)s\({}^{-1}\). Both measurement methods show a distinct maximum in the spectra of the wind components at around 0.03 Hz and a broader, but still increased level of variance in the TKE spectra. While the level of variance is underestimated for the w-component and at the low frequency end of the u-spectrum, the different datasets seem to agree very well in the TKE spectra. The unprocessed and average DBS data show the same features as discussed during the free-stream condition with an energy drop for frequencies larger than 0.1 Hz. The fact that the v-component seems to be better represented than the u-component in the wake case, can be related to the prevailing wind direction, as the accuracy of the DBS data is dependent on the beam positions relative to the wind direction. Additionally, the position of the LiDAR in the wake is also related to the prevailing wind direction, as sometimes one LOS measurement could be outside the wake, while others are still inside the wake. It should, however, be pointed out that the two measurement systems seem to produce very similar and reproducible spectral energy densities in these free-stream conditions. This provides confidence that qualitative and quantitative estimates of wake effects based on Windcube v1 measurements are possible and justified. A more detailed analysis of these wake spectra is presented in Section 3 and discussed in the context of other studies in Section 4. In the further analysis of the energy spectra, we also separate the dataset for different atmospheric stability conditions. This turned out to be not straight-forward, as the only available on-site stability information is from temperature difference measurements between 37 m and 10 m at the met-mast. Due to the lack of co-located wind speed measurements at the same heights, the Richardson number cannot be calculated. For the determination of the Obukhov length, necessary to determine the stability parameter z/L, additional heat flux measurements would be required, which were not stored for the sonic anemometers on this met-mast. We therefore had to derive a proxy for the atmospheric stability based on the 10-minute average temperature difference measurements described above. Assuming a dry adiabatic lapse rate, the local change in temperature over a 27 m height interval should under neutral conditions result in a temperature difference of \(-0.27\) K. Analyzing the temperature difference measurements revealed an offset compared to the theoretical value, which indicates calibration issues. Therefore, we aimed to find an empirical estimate of the measured adiabatic lapse rate that represents the local conditions on site. To do so, we selected night time conditions with high wind speeds (\(>\)15 m\(\cdot\)s\({}^{-1}\)) to ensure neutral conditions. Additionally, we adapted the indicators for stable and unstable conditions to fit the whole dataset by analyzing the observed temperature difference distribution over the prevailing wind speeds at 108 m. The resulting stability proxy is presented in Table 2. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Stability Class** & **Temperature Difference** & **Data Share** & **Average Wind Speed at 108 m** \\ \hline stable & \(dT>0.03\) & 27\% & 9.1 m\(\cdot\)s\({}^{-1}\) \\ neutral & \(-0.26\leq dT\leq 0.03\) & 55\% & 9.8 m\(\cdot\)s\({}^{-1}\) \\ unstable & \(dT<-0.26\) & 18\% & 8.9 m\(\cdot\)s\({}^{-1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Definition of the stability criteria.