## 4 Results  
### Simulated Dual-Doppler Lidar Measurement Scenarios  
In Figure 6a, the absolute value of the 10 min horizontal wind speed at hub height over the LES-simulated wind field is shown. Absolute error plots of this wind speed are depicted in Figure 6b,c for the volume scan scenario and the single elevation scan scenario, corresponding to case 1 and 3 in Table 1, respectively. Grid points are only included when there was at least one measurement from each of the lidars available locally. The absolute error patterns of the two different scenarios both show similar significant errors of up to 1 m\(\cdot\)s\({}^{-1}\) on the boundaries of the wake. These are characterised by large velocity gradients, which are smoothed by the averaging of the single lidar line-of-sight measurements over their probe volumes, the weighted averaging of the measurements over the circular area with radius of influence, taking into account measurements from different heights and the temporal averaging. Figure 5: Sketch of the selected dual-Doppler lidar PPI scan scenario setup in “alpha ventus”. Figure 6: Plots of the mean absolute horizontal wind speed: (**a**) large eddy simulation (LES) at hub height; (**b**) absolute error of the volume scan (case 1); (**c**) absolute error of the single elevation scan (case 3) and the wind direction: (**d**) LES at hub height; (**e**) absolute error of the volume scan (case 1); and (**f**) absolute error of the single elevation scan (case 3). For each of the considered cases listed in Table 1, the mean average error on the absolute wind speed (\(MAE\)) is calculated from the corresponding absolute error plots (see Figure 6b,c). This enables the assessment of different combinations of lidar placement, different PPI scan scenarios and the effect of the continuity correction. Based on the \(MAE\), the most favourable scanning scenario is the single elevation scan. The best lidar configuration in this case is using lidar 2 and 3 (see Figure 3). The continuity equation always has a positive influence, but the improvement is largest for the least favourable combination of lidar locations. Namely, in the case of combining lidars 1 and 3, a part of the measurements from both lidars lie on the same line-of-sight (\(\Delta\chi\approx 180^{\circ}\)) and are therefore linearly dependent. The 2D wind field description is completed by the wind direction, which is represented by Figure 6d for the LES. Again, the absolute error on the wind direction can be seen in Figure 6e,f for the two aforementioned scenarios. Note that westerly wind is described as a relative angle \(\theta=0^{\circ}\) here. It can be observed that the flow is locally deflected with up to \(\pm 15^{\circ}\) as it passes the wind turbine rotor and then gradually aligns with the initial wind direction further downstream. For both measurement scenarios, the deflection around the wind turbine is captured well. However, local errors can be noticed on the absolute error plots in Figure 6e,f, caused mainly by two reasons: the first issue is the intrinsically heterogeneous measurement distribution of the radial scan pattern of the lidars. Second, the average height at which measurements were taken causes a problem. Especially for the volume scan scenario, these two effects are entangled. Figure 7a,b show the measurement distribution, i.e., the number of measurements \(K\) taken into account per grid point, for the two respective scenarios. Figure 7c,d illustrate the average offset from hub height of the measurement set for each grid point. The measurement distribution of the single elevation scan corresponds to the radial scanning pattern. Since the lidars are both located to the west, the distribution becomes less dense when progressing radially outward, i.e., from west to east. The measurement distribution of the volume scan is relatively heterogeneous due to the combination of multiple, partly overlapping PPI scans.