## 2 Planar LiDAR Data
### Measurement Trajectories  
During the measurement campaign, we were fortunately able to position two long-range LiDAR devices on a single nacelle. At first, the measurement campaign in Brusow was intended for the improvement of commercial measurements, but instead aimed at a specific investigation of wake deflections caused by specific yaw misalignments. For this purpose, one device was used for horizontal plan position indicator (PPI) scans and the other was used for vertical range height indicator (RHI) scans. This combination of scans forms two unsynchronised perpendicular measurement planes in the downstream direction, which sliced the wake in horizontal and vertical directions, as illustrated in Figure 1. The installation of the LiDAR on the nacelle offers the advantage of reducing the measurement elevation for the horizontal scans relative to that of ground-based scans, and avoiding obstacles when adjusting the scan orientation to align with the direction of the wind.  
Planar trajectories are executed either by fixing the elevation angle of the scanner (\(\theta\)) and continuously changing the azimuth angle (\(\phi\)) (PPI) or by fixing the azimuthal scanner orientation while varying the elevation angle (RHI). PPI scans are typically executed with a full 360\({}^{\circ}\) azimuth range, and RHI scans are typically executed with a full 180\({}^{\circ}\) elevation range. In the configuration used in the present study, we performed only sectoral scan patterns, which we refer to as PPI and RHI below for the sake of readability. Since only sectors were measured, the scanning head requires some reset time (\(t_{r}\)) to return to its initial position. As no previous such measurements or studies about nacelle-based wake measurements were available, the scanning parameters used in the 2015 measurement campaign were not chosen specifically for certain atmospheric conditions, but they were instead chosen for their potential use as universal settings for volumetric nacelle-based wake measurements.  
The structure of the LiDAR devices dictates that the measurement data is given in a spherical coordinate system that has the typical characteristics of a polar grid, in which the planar point density decreases as the measurement distance increases. The measurement grid is determined by the radial measurement points along the laser beam and the accumulation time due to the angular velocity in relation to the total opening angles, \(\Delta\phi\) and \(\Delta\theta\). In the measurement trajectories that are actually executed, the total opening angles are defined symmetrically as:  
\[\Delta\phi=|\phi_{2}-\phi_{1}|, \tag{2}\]  
\[\Delta\theta=|\theta_{2}-\theta_{1}|. \tag{3}\]  
Measurement points were set in the radial direction in a range of 50 m to 1150 m at intervals of 7 m. During the measurements, we tested various accumulation times and found that \(\theta_{acc}\) = 200 ms strikes a good compromise between the backscattering intensity and temporal resolution. The initial configuration for the angular speeds, \(\omega_{\phi}\) and \(\omega_{\theta}\), was set to \(2^{\circ}/\)s, with total opening angles, \(\Delta\phi\) and \(\Delta\theta\), of \(40^{\circ}\). These settings yielded angular resolutions, \(\mathcal{R}_{\phi}\) and \(\mathcal{R}_{\theta}\), of \(0.4^{\circ}\).