## 5 Discussion
In a real device, the variations in the CNR or SNR and the resulting fluctuations in the wind speed after filtering tend to reduce the data availability [26], which is also not reproduced in the simulation. The test case discussed above therefore represents an idealisation of the measurements in every respect, so it naturally draws attention to the peculiarities of real LiDAR measurements. The results given above are based on the projection of the LOS velocities in the main wind direction that was described in Section 3.1. The assumption of homogeneity in the projection affects the accuracy of the representation of the wind-speed statistics, especially in areas where the assumption does not apply (in the near-wake region (\(\chi D^{-1}\leq 3\))). Further, the calculation of the standard deviation from the projected time series of LOS velocities introduces some error due to the non-linear dependency of the standard deviation of the LOS velocities (\(\sigma_{\theta_{\text{LOS}}}\)) on the standard deviations of the main wind-speed components (\(\sigma_{u}\), \(\sigma_{v}\), \(\sigma_{w}\)). From Figures 8 and 11, one can see that the error in the standard deviation from deviations in the measurement angle (\(\phi^{\prime}\
eq 0\) and \(\theta^{\prime}\
eq 0\)) in the main flow direction is marginal compared to the error of the standard deviation due to the spatial and temporal quantisation. Otherwise, a clear trend in the error versus the measuring angle would be apparent in Figures 8 and 11. This statement only applies to the present test case since the difference in the angles of the measurement and the main wind direction (\(\phi^{\prime},\theta^{\prime}\)) are very small because of the nacelle-based measurement setup. We are aware that the projection error increases with increasing \(\phi^{\prime}\) and \(\theta^{\prime}\), but we cannot isolate this effect within the scope of this paper. We do assume that this source of error will have more of an effect if the scanned area is not aligned with the main wind direction, which is confirmed in Fuertes and [PERSON] [27] for ground-based measurements. For these reasons, we cannot claim that transfer to real data will results in the same degree of improvement in the mapping accuracy. The basis of data with which this study was conducted is too limited. To consider the general transferability of the propagation method discussed above, more flow situations with variable atmospheric conditions will need to be investigated analogously. These could be combined into a database that would give optimal measurement parameters for a range of atmospheric conditions. When improving temporal resolution, the space-time conversion proposed above will introduce some error. The results in Section 4.3 indicate that this numerical error increases along with the number of interpolations and will produce the minimal mapping error with some combinations of scan parameters. In the present study, we were not able to determine the extent to which the improvement in the mapping accuracy is due to the statistical correlation described in Equation (1). Regardless of the requirement of statistical independence imposed by Equation (1), we saw an improvement in the mapping quality of the mean values. The improvement in the standard deviation should be considered more critically and will be analysed again in a future study. A reasonable approach might consider, first, the ratio of the LiDAR accumulation time to the temporal resolution of the LES and, second, the nature of the step-and-stare measurement method. Further studies should evaluate the extent to which improvements to the standard deviation achieved with the wind-field propagation method satisfy turbulence characteristics, or whether this improvement is merely coincidental.