## 5 Results
### Discussion of the Observed Motion-Induced Errors  
[PERSON] and [PERSON] [27] showed that the tilt of lidars can cause degrees of error varying from no error to very large errors in measurements depending on factors such as the lidar's sampling frequency (the frequency of completing a VAD scan \(f_{s}\)), the amplitude of the motion, the presence of wind shear, and the wind direction. It is important to note that their study defines roll and pitch motions as the tilt of the lidar in the along-wind and crosswind directions, respectively. We, however, define the tilt rotations according to the geographic coordinate system. Consequently, we do not anticipate the roll rotation in the absence of wind shear to result in zero error and pitch to cause the highest errors as demonstrated in [27]. Nevertheless, we can explain our findings in light of their simulation results by considering both roll and pitch test cases as the tilt of the lidar, which may or may not correspond to the along-wind rotation. If the \(f_{0}<f_{s}\), the scanning cone is tilted completely in one cycle of motion, and hence the scanning geometry can be considered frozen, maintaining a consistent scanning geometry. Consequently, here test cases with \(f_{0}=0.1,0.2\) Hz are considered slow tilts for the ZephIR 300 with \(f_{s}=1\) Hz and the error is expected to increase only with increasing amplitude [27]. We expect test case 22 to result in lower errors compared to tests 23 and 12 (due to increased amplitude) of around 1.5%, and test 51 to cause the highest error of around 2%, based on Figure 6 in [27]. For WindCube V1 with \(f_{s}=0.25\) Hz, tilts with an \(f_{0}\) between 0.1 and 0.2 Hz are anticipated to cause higher errors, as \(f_{0}\approx f_{s}\). For instance, test 11 with \(A_{0}=15^{\circ}\) and \(f_{0}=0.2\) Hz as well as test 23 are expected to result in the highest errors, around 4% [27]. This aligns closely with the APE values measured by the WindCube V1 in our observations (see Figure 7). However, at 145 m, the APE is considerably higher, likely due to system differences which are even present in the absence of motion (baseline test cases). Furthermore, the presence of wind shear is expected to cause a tilted lidar to underestimate wind speed [27]. In all of our test cases with roll motion, wind shear is evident, particularly in tests 22 and 23. This explains the underestimation of mean wind speed measured by the moving lidars for both types. Regarding the yaw motion, [PERSON] and [PERSON] [27] have only explored the effect of slow yaw motion on lidars, finding it to be negligible. This is consistent with the behavior observed in the ZephIR 300 during our experiment with \(f_{s}=1\) Hz and yaw motion frequencies ranging from 0.025 to 0.2 Hz. However, the WindCube V1, with its lower sampling frequency (\(f_{s}=0.25\) Hz), might exhibit greater errors due to yaw rotation. This is because the lidar's sampling points and the corresponding azimuth angles on the VAD disc are altered by yaw motion at a frequency similar to \(f_{s}\). Assuming no initial phase shift between the beam and yaw rotation, when the beam swings to the azimuth angle \(\alpha_{1}=90^{\circ}\), the actual angle is offset by \(39^{\circ}\) due to yaw motion, resulting in \(\alpha^{\prime}_{1}=90^{\circ}+39^{\circ}\). Similarly, when the beam swings to \(180^{\circ}\), the sampling point will be at \(\alpha^{\prime}_{2}=\alpha^{\prime}_{1}+90^{\circ}\). The yaw angle subsequently decreases as part of its oscillatory motion while the beam also swings to \(270^{\circ}\), resulting in \(\alpha^{\prime}_{3}=\alpha^{\prime}_{2}+90^{\circ}-39^{\circ}\), as shown in Figure 8. Thus, during high-frequency yaw motion, the beams can become very close together at certain time steps, resulting in higher uncertainty and erroneous measurements. We can also observe this in the WindCube V1 data during test cases 20, 48, and 19, with frequencies of 0.2, 0.15, and 0.1 Hz, respectively (see Figure 7).