## 6 Conclusions  
This paper has presented a space-time conversion method for long-range planar LiDAR data, which achieves temporal interpolation that reflects reasonable approximations of fluid-dynamic processes. This method allowed us to retrospectively improve the temporal resolution of successive scans and to synchronise the scans with measurements collected with different time stamps. This method corrects for time shifts within a scan by applying a sinusoidal weighted average of forward- and backward-propagated wind fields taken from different completed scans, which fills in the unmeasured flow behaviour. We used synthetic LiDAR data generated by a numerical simulator and in an LES wind-turbine wake flow field to evaluate the method in terms of the mean wind speed and standard deviation. A parametric study of \(11\) scanning velocities for both PPI and RHI scans was then carried out for a test case with an ambient wind speed of \(u_{0}=8\) m/s and a turbulence intensity of \(I_{0}=5.8\) %. Using a total of 2334 scans, we revealed how the mapping error in the LiDAR measurements is affected by the angular-scan velocity. This error is temporal in nature at low scanning speeds and shifts to a spatial error at high scanning speeds. The optimal scanning speed is determined by the turbulence intensity and the corresponding spatial variability in the wind-turbine wake. Analysis of 11 different scan velocities showed that, with the careful selection of typical measurement parameters, the compromise between temporal and spatial resolution is well balanced. In the specific test case we considered, the optimal measurements are taken with slower scan speeds and higher spatial resolutions. The use of wind-field propagation increased the volume of synthetic LiDAR data by a factor of 2.4 to 40, allowing synchronisation with the LES reference data. This synchronization led to an improvement of the structural mapping, in terms of both the mean wind speed and the standard deviation. The interpolation method can be used with various configurations of interpolation steps between two scans, so it can serve as a universal tool for increasing the temporal resolution of planar LiDAR measurements with a minimal increase in statistical errors. This interpolation is particularly useful for the analysis and comparison of wake measurements, for which some wake characteristics might be correlated with data of finer temporal resolution recorded external to the wind turbine, such as load data. In addition to synchronising the data from complex measurement campaigns taken with various LiDAR devices and sensors, the possibility of temporal up-sampling allows for easier processing. In the test case discussed above, the maximum reduction of the error of the mean wind speed was 30.5% and the standard-deviation error was reduced by 42%. The following videos are available online at [[https://zenodo.org/record/2635033#.XK3C0](https://zenodo.org/record/2635033#.XK3C0) qIRWUK]([https://zenodo.org/record/2635033#.XK3C0](https://zenodo.org/record/2635033#.XK3C0) qIRWUK): Video S1: Visualisation of up-sampled horizontal wind-speed data and the wind speed error in comparison to the LES reference for different angular velocities. The red line indicates the scanning laser beam. Video S2: Visualisation of up-sampled vertical wind-speed data and the wind speed error in comparison to the LES reference for different angular velocities. The red line indicates the scanning laser beam. This study was done as a part of [PERSON]'s doctoral studies supervised by [PERSON] [PERSON] conducted the research work and wrote the paper. [PERSON] supervised the research work, advised about the structure of the paper and supplied review and editing.