## 4 Results
### Time-Resolution Improvement  
To evaluate the effects of increasing the temporal resolution of the synthetic LiDAR data, we first propagated the LiDAR scan backwards and forwards using the wind-field propagation method described in Section 3.2 to obtain a mixed and closed space-time conversion. Then, we compared the propagated scans with the reference LES wind field. We corrected the scan-containing time error and synchronised the propagated data with the LES time data. In this subsection, we first discuss the effect of the propagation on the temporally averaged values, like the mean value and the standard deviation, before we address the dynamic behaviour. The following results are based on the averages of the optimal time steps achieved in Section 4.3. For the results herein, we used \(\Pi_{\phi}=16\) as the number of interpolation steps for the PPI data and \(\Pi_{\phi}=~{}14\) for the RHI data. The influence of \(\Pi_{\phi,\theta}\) is discussed in Section 4.3. We present all the RHI-related results in Appendix C.  
Figure 10 illustrates the averaged wind speed (\(\overline{u}\)) of the propagated PPI data, which are analogous to the original PPI data shown in Figure 7. As with the original LiDAR scan discussed in Section 4.1, no significant differences in the mean wind speeds of the wake appear. When considering the differences from the LES data (Figures 10d-fj,k and 11d-fj,k, the same deviation structures occur independently of the angular velocity, even though the structures become coarser because of angular quantisation at faster sampling rates. Compared with Figure 7a,b,d,e, in which individual flow artefacts that are caused by the very low number of samples appear, the artefacts in the propagated data in Figure 10a,b,d,e are smoothed into the flow direction and are much more like the LES reference data. With propagation and synchronisation with the LES time steps, the number of scans is increased by  
a factor of 2.4 to 40 within the 10-min time period. Depending on the scanning speed, the structural representation of the flow field is significantly improved. For the angular velocities, \(\omega_{\phi}=1^{\circ}/\mathrm{s}\) and \(\omega_{\phi}=5^{\circ}/\mathrm{s}\) (Figure 10a,b,d,e), propagation artefacts are clearly visible at the extremes of the measurement domain around \(\chi D^{-1}=10\). In those cases, the interpolation time (\(\mathrm{T}_{\phi}\)) and the propagation domain create a mixture of wind speeds with boundary conditions in combination with the mean flow velocity, and this blending manifests as a reduction of wind speed. These artefacts can also be seen in the visualisation of the standard deviation of the wind speed shown in Figure 11a,b,d,e, which are no longer detectable if \(\omega_{\phi}>~{}5^{\circ}/\mathrm{s}\). The effect of the quantisation of the measurement area by individual angular measurements, which is also remarked upon in Sections 4.1 and 4.3, is not compensated for by wind-field propagation and is still visible if \(\omega_{\phi}\geq 8^{\circ}/\mathrm{s}\) (Figure 11c,f-h,j,k). Figure 10: Visualisation of the normalised 10-min averaged wind-speed component (\(\overline{u}\)) of the propagated PPI data and (**d-f,j,k**) the corresponding flow deviations (\(\varepsilon_{\overline{u}}\)) in comparison to (**i**) the normalised 10-min averaged wind-speed component (\(\overline{u}\)) of the LES data. To address the dynamic effects of wind-field propagation and to reveal a holistic understanding of the dynamic behaviour, the reader should refer to the supplementary information of video S1 for horizontal slices and video S2 for vertical slices. Videos S1 and S2 show the main wind-speed components (\(u\)) of the propagated LiDAR data and deviations from the LES reference for different angular velocities, which are analogous to the data in Figure 7. As the angular velocity increases, flow structures are represented with decreasing accuracy because of the decreasing point density of the polar grid.