# 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  
The floating LIDAR measurement of a component of the horizontal wind is calculated from the radial speed measurements of two opposite rays. Thus, the horizontal speed is calculated from the measurement of the four non-vertical rays. As the radial velocities are measured alternately, they do not experience the same motion. At the scale of a 10-min measurement, each ray experiences a different subsampling of the LIDAR motion. In this section, we consider sinusoidal tilt, yaw and heave motions. The heave was chosen to represent the effect of translational velocity as it is the component with the greatest impact on the horizontal velocity measurement [16]. As in the WindCube v2(r) operation, we compute the lidar measurement statistics from the recorded data from each _LOS_ measurement. We normalize the velocities and standard deviations evaluated throughout this section by the incident horizontal wind speed \(V_{hor_{0}}\). All the simulations in this section are carried out under similar wind conditions (\(V_{hor_{0}}=8,W_{dir}=90^{\circ}\)). Figure 9: Example of the subsampling and averaging effect on the radial wind speed measurement of beam A described in Section 4.2.2 subjected to a sinusoidal tilt \(T\) of amplitude \(a_{tilt}=10^{\circ}\). The radial wind speed measured by the ray (in blue) is normalized by the value measured in a motionless case \(V_{r_{0}}\). Different periods of tilt are evaluated: P = 1 s (**a**), 2 s (**b**), 4 s (**c**), 8 s (**d**), 10 s (**e**), 40 s (**f**). The tilt motion is displayed (in grey), the scale of the motion is displayed on the right hand side of the figures. Figure 10 and Figure 11 show the influence of the period of the sinusoidal motion, and the direction of the initial beam in the model, respectively. The mean horizontal velocities and standard deviations are compared. Since the incident horizontal velocity is turbulence-free, the calculated standard deviation is entirely induced by the motion. The effect of the initial direction of the laser beam is evaluated at the period having the greatest impact on the LIDAR measurement, called resonance period. We discuss all the figures according to the type of motion: tilt, yaw and heave. Finally, we study the dominant effects on the LIDAR error as a function of sea conditions. We start with the tilt motion, it is applied in the axis perpendicular to the incident wind direction (i.e., roll for \(W_{dir}=90^{\circ}\)). The average horizontal velocity measurement (Figure 10a) evaluated by the model is either smaller or greater than the incident horizontal wind speed \(V_{hor_{0}}\) as a function of the tilt period. The error induced by an extreme motion (\(a_{tilt}=10^{\circ}\)) is up to 1 to 2% at the resonance period \(P_{tilt}=4\) s, the initial direction of the measurement beam in the model strongly influences the magnitude of this error (Figure 11a). Figure 10: Influence of the period of a sinusoidal motion on the mean horizontal velocity and its standard deviation estimated by the model and normalized by the incident horizontal velocity \(V_{hor_{0}}\). The periods having the greatest impact on the LIDAR measurement, called resonance period, are specified. (**a,b**) LIDAR subjected to a sinusoidal tilt motion for an incident wind along the component perpendicular to the axis of rotation. (**c,d**) LIDAR subjected to a sinusoidal yaw motion. (**e,f**) LIDAR subjected to a sinusoidal heave motion. The standard deviation of the horizontal velocity (Figure 11b) fluctuates with the period and amplitude of the motion, reaching its maximum value at the resonance period \(P_{tilt}=4\) s. The order of magnitude of the TI induced by an extreme motion is 0.2 at the resonance period. The standard deviation of the horizontal velocity is only slightly influenced by the initial direction of the beam (Figure 11b). Now, we study the effect of yaw motion. It has a similar influence on all the 4 non-vertical beams.