## 4 Methods
### Data Filtering and Statistical Methods  
For the duration of the experiment, the Norwegian hindcast archive (NORA3) results never showed a wind speed exceeding 20 ms\({}^{-1}\). Thus, lidar measurements exceeding 20 ms\({}^{-1}\) were considered nonphysical and flagged as not a number (NaN). The NORA3 utilizes the HARMONIE-AROME numerical weather prediction model to offer a reanalysis of atmospheric data. This reanalysis features a spatial resolution of 3 km and a temporal resolution of 1 h [34]. Furthermore, three steps were taken to filter the data. Firstly, low-quality signals were discarded. To discard the low-quality signals, line-of-sight (LOS) velocities with carrier-to-noise ratios (CNRs) less than \(-23\) dB were excluded from the analysis. This threshold value is suggested by manufacturer and is chosen based on the analysis of [PERSON] et al. [35]. Figure 4: Impact of (**a**) rotational, (**b**) translational, and (**c**) combined motion on the observed LOS velocity (\(v_{r},o\)) and the retrieved velocity (\(\hat{u}\)) in the Cartesian reference frame. Secondly, the outliers were detected and discarded using the median absolute deviation (MAD) approach [36; 37]. Any observation (\(X\)) is considered an outlier if  
\[|X-M|>3\times\frac{M}{0.6745}, \tag{8}\]  
where \(M\) is the rolling median of all observations. The wind speeds measured by the WindCube V1 reference on 2011-08-17 at 85 m before (gray) and after (orange) applying the MAD filter are shown in Figure 5 as an example. This visualization illustrates the effectiveness of the MAD method in removing high spikes in the raw data. Yet, some spikes in wind speed are present in the time series of the WindCube V1 reference (see Figure 5 at 15:00 UTC). In the experiment log, it was reported that the WindCube V1 reference occasionally overestimated wind speed due to unresolved technical issues. This might be the reason for the presence of such erroneous spikes in the WindCube V1 reference data. These data were considered faulty and non-physical. To identify and discard these faulty data in the WindCube V1 reference data, the third step in filtering was taken. In this step, comparisons were made between the moving and reference lidar of each type, constraining the relative difference of their standard deviations to 70% to ensure measurement consistency. The relative standard deviation was defined as  
\[\Delta\sigma_{relative}=\frac{\sigma_{ref}}{\sigma_{moving}}-1, \tag{9}\]  
where \(\sigma_{ref}\) is the standard deviation of the WindCube V1 reference data and \(\sigma_{moving}\) is the standard deviation of the WindCube V1 moving data. The latter was considered as the base for the filtering. Using this measure, the data points of the WindCube V1 reference with a \(\Delta\sigma_{relative}\) exceeding 70% were excluded from analysis. This ensures that the standard deviation of the reference lidar does not exceed the standard deviation of the moving lidar by more than 70%. As in the ZephIR300 data, such inconsistency was not observed, only the first two steps were applied to the data. After filtering the data, all test cases which had data availability of less than 50% were discarded. Wind speeds at the two heights of 85 m and 145 m were then obtained from the lidars without motion correction. As an initial survey, the performance of the lidars was compared based on the baseline test cases. Later on, the lidars' performances based on the motion type were compared. The turbulence intensity (TI) estimate of lidars was calculated as  
\[\text{TI}=\frac{\sigma_{U}}{\overline{U}}, \tag{10}\]  
Figure 5: Comparison of wind speed on 2011-08-17 for the reference lidar before and after applying the MAD filter. Raw data are shown in gray and the filtered data are shown in orange. The median is shown as a dark-red dashed line, and the dotted gray lines represent the thresholds. where \(\sigma_{U}\) represents standard deviation of horizontal wind speed and \(\overline{U}\) represents the mean wind speed within the test time span.