## 5 Results
### Applying Motion Correction  
Among the various test cases, test 11 with pitch motion was selected for the application of motion correction due to its high data quality, data availability, and consistency. In this specific test case, the system underwent sinusoidal rotation along the N-S axis with  
Figure 8: Top view of one VAD scan for WindCube V1 and the beam’s corresponding azimuth angle. \(\alpha\) shows the position of beam when there is no motion (gray) and \(\alpha^{\prime}\) shows the beam position when exposed to yaw motion with a frequency similar to beam swinging frequency (red). \(A_{0}=15^{\circ}\) and a \(f_{0}=0.2\) Hz. In this test case, the correlations between the moving and reference ZephIR 300 lidars are less than 0.75 and less than 0.50 for the WindCube V1 lidars (Figure 7c,d). Also, the TI of the moving WindCube V1 at both heights is noticeably higher than that of the reference lidar, as seen in Figure 6c,d. This TI overestimation was observed in all the pitch test cases for the WindCube V1. We applied motion correction to the entire test dataset. To illustrate the effect of this correction, we present a 15 min slice of the wind speed time series in Figure 9. In Figure 9a, the WindCube V1 reference and the uncorrected moving WindCube V1 are shown. Panel b displays the ZephIR 300 reference and the uncorrected moving ZephIR 300 data at the same time slice. The corrected moving WindCube V1 data alongside their reference are shown in panel c, and panel d illustrates the corrected moving ZephIR 300 data with their reference. The moving WindCube V1 exhibits larger errors in the range of 1 to 2 ms\({}^{-1}\) before applying motion correction. However, after applying motion correction, the error is substantially reduced (Figure 9a,c). For the ZephIR 300 in Figure 9b, the variation is less pronounced, with an error of approximately 1 ms\({}^{-1}\). Nonetheless, the motion correction considerably reduces the error, aligning the measurements of the moving lidar with those of the reference lidar in Figure 9d. This can also be observed in further detail in Figure 10. The error between the moving and reference lidars before compensation is more broadly distributed, with a wider histogram for the WindCube V1 Figure 10a compared to the ZephIR 300 Figure 10b. However, after applying motion correction, this distribution becomes narrower Figure 10c,d, and the standard deviation of the errors decreases for both lidars. The scatter plot of wind speed measurements in this test case also highlights the effectiveness of motion correction in reducing data dispersion. Prior to applying motion correction, the moving lidars' wind speed measurements have noticeable scatter when compared to the reference lidars, in particular with increasing overall wind speed values (Figure 11a,b). After applying motion correction, there is a marked reduction in data scatter. The measurements cluster more closely around the 1:1 line, and the slope of the Deming regression line becomes closer to one (see Figure 11c,d). These results indicate a substantial improvement in the accuracy of wind speed measurements after applying the motion correction to the FLS data. Figure 9: Comparison of wind speed time series before and after motion correction in a 15 min time slice for test 11. (**a**) WindCube V1 reference (purple) vs. WindCube V1 moving before compensation (light green), (**b**) ZephIR 300 reference (orange) vs. ZephIR 300 moving before compensation (light blue), (**c**) WindCube V1 reference (purple) vs. WindCube V1 moving after compensation (dark green), and (**d**) ZephIR 300 reference (orange) vs. ZephIR 300 moving after compensation (dark blue) (Courtesy of [PERSON] [38]). Figure 11: Wind speed scatter plot before and after motion correction for test 11.