# 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
#### 4.3.1 Study of Wave-Induced TI Experimental Error  
The operating principle of the profiler LIDAR technology induces a bias in the turbulence intensity measurement compared to anemometers [9]. In the open sea conditions of Fecamp, the regression line on the non-normalized data from the fixed LIDAR follows the equation: \(y_{fixed}=1.004x+0.002,\ R^{2}=0.869\) (Figure 12a). The TI measurement of the fixed LIDAR is on average similar to that of the anemometer. However, the dispersion of the points is very large. This divergence is due to the difference in technology and to the low measurement altitude (54.8 m relative to MSL, i.e., about 40 m from the fixed LIDAR) that affects the LIDAR measurement accuracy [20]. In the case of the floating LIDAR, the effect of wave motion induces a much larger error (Figure 12b). The regression line on the non-normalized data follows the equation: \(y_{FLS}=1.083x+0.029,\ R^{2}=0.523\). The slope is close to unity, but the value at the origin is non-zero, which means that buoyancy motion introduces an offset of the order of +0.03. The dispersion of the points is also accentuated by the wave motion. We conclude that the wave-induced error is much greater than the technological error from the LIDAR when compared to a cup anemometer. In the remainder of this section, we compare the floating LIDAR measurements with the fixed LIDAR measurements in order to evaluate the effect of waves with equivalent technology. From the wind, wave and atmospheric data used to select the 13 weeks out of the overall measurement campaign (Section 3.2), we performed a parametric study correlating the met-ocean conditions with the floating LIDAR turbulence intensity measurement error. The most highly correlated data with the floating LIDAR measurement error is the wave period (Figure 13a), which is itself closely correlated with both wave height (Figure 13b) and wind speed. In Figure 13a, we observe that for any average wave period within a 30-min interval, the mean error in the TI measurement is always significant (>0.01). Therefore, low wave periods induce sufficient motion to the WINDSEA_02 buoy to have a substantial impact on the LIDAR turbulence intensity measurement. We note that this result is highly dependent on the dynamic response of the buoy to waves, for example, the buoy used in [PERSON] et al. [17] experiences a weaker response to low waves. We also note that, in our case, very low wave heights are filtered out by the \(V_{hor}>2\) m/s condition. Figure 12: Linear regression of turbulence intensity measurements by the fixed **(a)** and floating **(b)** LIDARs in comparison with the cup anemometer measurements, at altitude 54.8 m. The ticks are normalized by the anemometer mean TI from all the 10-min samples. We now analyze in detail the floating LIDAR measurement error during the Fecamp campaign. By studying the origin of the wind in the reference frame of the LIDAR (and the buoy) (Figure 14a), we can observe that the dominant component of the wind is coming from the east. Furthermore, in our previous study (Section 4.2.3), we observed that the dominant motions in the LIDAR measurement error in rough seas are tilt and heave. Thus, the tilt motion whose axis is perpendicular to the wind source (the roll) is the dominant rotational motion in the turbulence intensity measurement error. Figure 14b confirms this trend: It shows a very strong correlation between roll, mean wind speed and the floating LIDAR measurement error. The trend is less apparent for translational movements because the components involved in the heave motion are affected by the rotation of the buoy. This macroscopic method allows us to understand a part of the behavior of the floating LIDAR measurements. However, a mathematical model is mandatory in order to take into account all the geometrical effects and their mutual interactions. Figure 14: Study of the dominant phenomenon in the turbulence intensity measurement error of the floating LIDAR on the Fécamp site.