## 2 Planar LiDAR Data
### Synthetic LiDAR Data  
A large-eddy simulation based on the parallelized large-eddy simulation model (PALM) [29] and with the actuator line approach (ACL) [30] was used to calculate numerical approximations of the reference wake flow field behind the National Renewable Energy Lab's 5-MW model wind turbine [31] with a rotor diameter (\(D\)) of 126 m. We decided to run this LES in an offshore environment since we did not plan to compare the real LiDAR data directly with the synthetic data. Furthermore, the simulation of the LiDAR measurement parameters is not affected by the choice between onshore or offshore conditions. The atmospheric conditions corresponded to a mean wind speed (\(u_{o}\)) of 8 m/s at a hub height of 92 m with an ambient turbulence intensity (\(I_{0}\)) of 5.8% at neutral stability. In these simulations, we used a 10-min time interval for the entire simulation, which therefore has a temporal resolution of 1 Hz and a spatial resolution of 10 m per grid cell in all three dimensions. The varied parameter for the parametric analysis was the measurement frequency (\(f_{s}\)) as a function of the angular velocities, \(\omega_{\phi}\) and \(\omega_{\theta}\). These parameters are listed in Table 1. Figure 2 shows that the spatial resolution of the measurement grid of the trajectories has a significant effect. To make this data comparable to actual LiDAR measurement campaigns, we chose reasonable and realistic scan durations and extended them to approach the upper physical limits of common commercial long-range LiDAR devices. We selected a total of 11 different angular velocities for each value of \(\omega_{\phi}\) and \(\omega_{\theta}\) and applied the accumulation time of \(\theta_{acc}\) = 200 ms at the sampling frequencies of 0.024 to 0.417 Hz. The effect on the number of scans for each scan type within a 10-min interval (N\({}_{\phi}\) and N\({}_{\theta}\)), the number of measurement points (\(n_{pnt}\)) for each scan type, the number of angular measurements per scan (\(n_{\phi}\) and \(n_{\theta}\)), the angular resolution (\(\mathcal{R}_{\phi}\) and \(\mathcal{R}_{\theta}\)), the scan duration (T\({}_{\phi}\) and T\({}_{\theta}\)), and the  
Figure 1: Illustration of cross-measurement trajectories. A horizontal PPI scan is shown in dark blue, and a vertical RHI scan is shown in pink. The wake volume is indicated in light blue. measurement-time efficiency (\(\eta_{m}\)), all as a percentage of the total measurement time within a 10-min interval, are listed in Table 1. The coordinate system and the wind-speed components, as they are used below, are defined in Figure 1.  
With the simulated measurement trajectories, we aimed to reproduce measurement points that are comparable to those in the measurement campaign and maintain the radial resolution of 7 m. The related choices result in an overlap of the pulses emitted by the LiDAR as 81.3% of the probe volume length of ~60 m. This resulted in the total number of radial ranges (\(n_{r}\)) being 180 at the radial distances of 1 to 1260 m. The point density of the Cartesian LES and the polar LiDAR measurement grid differ in the \(\chi\) direction because of the radial spread of the angular measurements, which is illustrated in Figure 2. Thus, numerical redundancies while interpolating within LES grid cells can only be prevented with an extremely finely discretised wind field and the necessary numerical and temporal capacities were not available within the scope of this study. Since the spatial resolution of the LES with 10 m per grid cell is coarser than the 7-m radial resolution of the LiDAR simulation, the permanent interpolation of the LES grid onto the LiDAR grid restricts our results to realistic behaviours. We expect that the standard deviation of the simulated LiDAR measurement will be lower than that of free-field measurements because of the interpolation from the polar to the Cartesian grid, but the main cause of this difference in the standard deviation is the much lower accumulation time of