## 2 Materials and Methods
### Data Processing  
In the first step, the raw 1 s DBS data of the Windcube v1 had to be de-spiked and filtered due to highly variable data quality, in particular in the case of the wls65. Time periods with strongly variable Carrier-to-Noise Ratios (CNR) were removed from the dataset by filtering for time periods without a registered wiper count. The CNR fluctuations occurred also for levels above \(-23\) dB, which are typically accepted for reliable measurements by the manufacturer. As the remaining raw wind data still included single non-physical spikes, an advanced de-spiking routine was developed and applied. Spikes were detected as outliers if located outside of four standard deviation (4\(\sigma\)) based on a 15 min averaging interval. Since the data were partly collected in highly turbulent wake conditions, we kept measurements exceeding 4\(\sigma\), if the exceedance persisted over more than 15 consecutive measurements. After repeating this algorithm four times, the performance of the de-spiking routine was manually checked for each measurement day. A more detailed description of the detected data quality issues and the de-spiking algorithm can be found in [PERSON] [22]. After the de-spiking, we turned the coordinate frame into the meteorological convention and additionally filtered the DBS data for independent wind vectors to avoid the misleading oversampling of wind vectors in their retrieval algorithm. Using only every 4 th retrieved wind vector leads to an independently sampled time series, compared to the original time series, where one LOS measurement is used up to four times in the wind vector retrieval process. By filtering the data to use only independent wind vectors, the potential effects of cross-contamination described by [PERSON] et al. [23] can be avoided. Therefore, every 4 th wind vector was taken into account, leading to a sampling interval of 4 s, as described by [PERSON] et al. [14]. After filtering the data, spectral energy densities were calculated for one- and four-hour periods in the later presented composites and case studies, respectively. Following [PERSON] et al. [14], we linearly \begin{table}
\begin{tabular}{l c c c} \hline \hline \multirow{2}{*}{**Instrument**} & **Shadow** & **Distance (D)** & **Direction (\({}^{\circ}\))** \\  & **Mast Shadow** & **0** & **180** \\ \hline
**M3** & WT5 & 3.5 & 315 \\  & WT6 & **2.5** & **31** \\  & WT7 & 5.4 & 71 \\  & WT8 & 9.0 & 81 \\  & WT9 & 12.7 & 85 \\ \hline
**wls67** & M3 & 0.8 & 357 \\  & WT5 & 4.2 & 322 \\  & WT6 & **3.2** & **23** \\  & WT7 & 5.7 & 63 \\  & WT8 & 9.1 & 76 \\  & WT9 & 12.8 & 81 \\ \hline
**wls37** & WT 5 & 5.2 & 260 \\  & **WT6** & **1.8** & **228** \\  & WT7 & 2.9 & 123 \\  & WT8 & 6.6 & 107 \\  & WT9 & 10.3 & 103 \\ \hline
**wls65** & WT 5 & 6.7 & 252 \\  & **WT6** & **3.5** & **227** \\  & WT7 & 3.0 & 156 \\  & WT8 & 5.9 & 121 \\  & WT9 & 9.5 & 111 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Location of the three Windcubes v1 used in this study with respect to expected wakes of the different Wind Turbines (WT5 to WT9) and the Met-mast (M3). The table presents the distance to the corresponding obstacle in rotor Diameters (D) related to the most affected wind direction. The information related to Wind Turbine Number 6 is highlighted in bold letters. interpolated the data on a regular time grid and turned the coordinate system into the mean wind direction before calculating the spectral energy density \(S(f)\) (Equation (1)). \[S(f)=\frac{2*|F(f)|^{2}}{\Delta f}\] with \[F(f)=\frac{1}{N}\sum_{k=0}^{N-1}(k\Delta t)*e^{2\pi f/k\Delta t} \tag{1}\]  
\(S(f)\) is the one-sided power spectrum as a function of frequency \(f\). It is estimated by splitting the analyzed period up into 20 blocks. A discrete Fourier transform \(F(f)\), with time represented as a whole-number multiple \(k\) of the sampling rate \(\Delta t\), is applied on each block, and the results are averaged over all samples in the block. Each block is smoothed with a Hanning window to suppress spectral leakage effects.