# Quantification and Correction of Wave-Induced Turbulence Intensity Bias for a Floating LIDAR System
## 4 Results and Discussion
### Theoretical Impact of Buoy Movements on the FLS Horizontal Velocity Estimates
#### 4.2.5 Influence of a 10-min Sinusoidal Motion on the Measurement of the Entire LIDAR
However, the difference in the timing of evaluations introduces a compositional effect between the subsampling encountered by each ray. The average horizontal velocity measurement evaluated by the model (Figure 10c) is always lower than the horizontal incident wind speed \(V_{hor_{0}}\). The underestimation for a yaw at resonance periods (\(P_{yaw}=3\) s & 8 s) and amplitude \(a_{yaw}=40^{\circ}\) is of the order of 10%. The standard deviation of the horizontal velocity (Figure 10d) varies with the period and amplitude of the sinusoidal motion, its maximum value being encountered at the resonance period \(P_{yaw}=3\) s. The order of magnitude of the motion-induced TI for a tilt amplitude \(a_{yaw}=40^{\circ}\) is about 0.05 at the resonance periods. The initial direction of the beam in the model has little influence on the horizontal velocity measurement of the floating LIDAR in the case of yaw motion (Figure 11c,d). And we specify that the case studied here of a yaw of high amplitude evolving at high frequency was not encountered in our experimental study (Section 4.1). The measured yaw from the  
Figure 11: Influence of direction of the initial beam within the model on the mean horizontal wind speed and its standard deviation estimated by the model and normalized by the incident horizontal speed \(V_{hor_{0}}\). (**a,b**) LIDAR subjected to a sinusoidal tilting motion of period \(P_{tilt}=4\) s for an incident wind along the component perpendicular to the rotation axis. (**c,d**) LIDAR subjected to a sinusoidal yaw motion of period \(P_{yaw}=3\) s. (**e,f**) LIDAR subjected to a sinusoidal leave motion of period \(P_{future}=4\) s.  
WINDSEA_02 buoy shows a high amplitude/low frequency in calm sea conditions and a low amplitude/high frequency in rough sea conditions. Now, we focus of the effect of heave. The translational movements of the buoy appear as an added component to the velocity vector measured by the LIDAR. The difference in the temporality of the evaluations introduces a compositional effect between the subsamples encountered by the rays. The average horizontal velocity measurement (Figure 10e) evaluated by the model is always higher than the horizontal incident wind speed \(V_{horo}\). The overestimation for a heave at resonance period (\(P_{heave}=4\) s) and amplitude \(a_{heave}=1\) m/s is of the order of 1%, the initial direction of the ray strongly influences the magnitude of this error (Figure 11e). The standard deviation of the horizontal velocity (Figure 10f) varies with the period and amplitude of the sinusoidal motion, the maximum value is encountered at the resonance period. The order of magnitude of the motion-induced TI for a tilt amplitude \(a_{heave}=1\) m/s is 0.15 at the resonance period. The initial direction of the beam has little effect on the standard deviation of the horizontal velocity estimated by the model (Figure 11f). Now, we want to assess the motions with the greatest impact on the LIDAR measurement in different sea conditions. The horizontal wind speed measured by a LIDAR subjected to a tilt, yaw or heave motion depends on the period of the motion. Resonance periods are observed for each of these phenomena. Each of the observed resonance period are close to the time required for the LIDAR to perform a _LOS_ measurement for each of its beams (\(\sim\)4 s). The initial direction of the measuring beam also has an influence on the average value of the horizontal velocity for tilt and heave. In the context of our turbulence intensity measurement correction method presented in Section 3.1, we note that the default choice of the first measuring ray influences the value of \(\overline{V_{hor}}\). The standard deviation of the horizontal velocity is only slightly influenced by the initial direction of the ray. However, this quantity is by definition linked to the average horizontal velocity. We shall study the order of magnitude of the motion-induced bias on the LIDAR measurement as a function of the sea conditions presented in Section 4.1.