## 5 Discussion  
Scanning LiDAR measurements must strike a compromise between temporal and spatial resolution. Since full-field measurements are usually very expensive, the scan parameters are usually chosen to minimize the scanning time. The greatest obstacle to the choice of effective scanning parameters is the limited availability of adequate validation measurements, so we used synthetic LiDAR data to verify the validity of parameter choices. This synthetic dataset raises questions about transferability and the extent to which the combination of a synthetic wind field and a LiDAR simulator can represent realistic characteristics of full-field LiDAR measurements. As discussed in Section 2.2, the lack of volume averaging in the scanning direction limits the direct transferability of synthetic data to step-and-stare LiDAR measurements. In most actual cases [21; 26; 33; 43; 46; 47; 48; 49; 50; 51], scanning measurements are taken on-the-fly to minimize the scanning time. This tendency implies that during the angular movement of the scanner head, backscattering is accumulated continuously, so the velocity measurements are averaged over the traversed volume of air. Real on-the-fly measurements will show a higher reduction in the standard deviation caused by this additional averaging. Though the data processing within a LiDAR system can be regarded as a non-linear signal process, we compensated for the effects of scanning-volume averaging with retrospective averaging. We considered this missing effect with a separate consideration of the mean and standard-deviation error at the centreline to representing the on-beam behaviour and planar error. \begin{table}
\begin{tabular}{l c c c|c c c} \hline \hline  & \multicolumn{2}{c|}{**PPI**} & \multicolumn{3}{c}{**RHI**} \\ \hline  & **Wake Region** & **Wake Centreline** & **Free Flow** & **Wake Region** & **Wake Centreline** & **Free Flow** \\ \hline \(\omega\) & \(5^{\circ}\)/s & \(5^{\circ}\)/s & \(5^{\circ}\)/s & \(5^{\circ}\)/s & \(5^{\circ}\)/s & \(3^{\circ}\)/s \\ \(\Pi\) & 16 & 18 & 9 & 14 & 16 & 7 \\ \(\epsilon_{\overline{u}}\) & 0.24\% & 0.15\% & 0.14\% & 0.20\% & 0.13\% & 0.40\% \\ \hline \(\omega\) & \(4^{\circ}\)/s & \(5^{\circ}\)/s & \(4^{\circ}\)/s & \(4^{\circ}\)/s & \(5^{\circ}\)/s & \(3^{\circ}\)/s \\ \(\Pi\) & 33 & 21 & 16 & 33 & 26 & 13 \\ \(\epsilon_{e_{u}}\) & 2.89\% & 0.60\% & 3.02\% & 2.79\% & 1.61\% & 4.53\% \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Combinations of \(\omega\) and \(\Pi\) that give local minima for different error regions in the PPI and RHI data. \begin{table}
\begin{tabular}{l c c c|c c c} \hline \hline  & \multicolumn{2}{c|}{**PPI**} & \multicolumn{3}{c}{**RHI**} \\ \hline  & **Wake Region** & **Wake Centreline** & **Free Flow** & **Wake Region** & **Wake Centreline** & **Free Flow** \\ \hline \(\omega\) & \(1^{\circ}\)/s & \(2^{\circ}\)/s & \(2^{\circ}\)/s & \(1^{\circ}\)/s & \(1^{\circ}\)/s & \(1^{\circ}\)/s \\ \(\Pi\) & 16 & 21 & 13 & 13 & 16 & 8 \\ \(\eta_{\overline{u}}\) & 35.5\% & 31.0\% & 36.9\% & 30.5\% & 31.2\% & 46.5\% \\ \hline \(\omega\) & \(1^{\circ}\)/s & \(1^{\circ}\)/s & \(1^{\circ}\)/s & \(1^{\circ}\)/s & \(1^{\circ}\)/s & \(1^{\circ}\)/s \\ \(\Pi\) & 33 & 42 & 37 & 67 & 60 & 26 \\ \(\eta_{e_{u}}\) & 42.8\% & 43.6\% & 45.6\% & 43.9\% & 42.0\% & 60.5\% \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Combinations of \(\omega\) and \(\Pi\) that optimize \(\eta_{\overline{u}}\) and \(\eta_{e_{u}}\) for different cases of PPI and RHI data. Optics and internal signal processing are also not considered in the LiDAR simulator, as described by [PERSON] et al. [34]. The calculated velocities have the typical device characteristics of one-dimensionality and beam-wise volume averaging, but no indication of the measurement quality, which is usually given by the carrier-to-noise ratio (CNR) or signal-to-noise ratio (SNR).