# Quantification and Correction of Wave-Induced Turbulence Intensity Bias for a Floating LIDAR System
###### Abstract  
Floating LIDAR systems (FLS) are a cost-effective way of surveying the wind energy potential of an offshore area. However, as turbulence intensity estimates are strongly affected by wave-induced buoy motion, it is essential to correct them. In this study, we quantify the turbulence intensity measurement error of a WindCube v2\({}^{\text{\textregistered}}\) mounted on a 12-ton anchored buoy as a function of met-ocean conditions, and we construct a subsequently applied correction method suitable for 10-min wind LIDAR data storage. To this end, we build a model to simulate the effect of buoyancy movements on the LIDAR's wind measurements. We first apply the model to understand the mechanisms responsible for the wind LIDAR measurement error. The effect of the buoy's rotational and translational motions on the radial wind speed measurements of the individual beams is first studied. Second, the temporality induced by the LIDAR operation is taken into account; the effect of motion subsampling and the interaction between the different measurement beam positions. From this model, a correction method is developed and successfully applied to a 13-week experimental campaign conducted off the shores of Fecamp (Normandie, France) involving the buoy-mounted WindCube v2\({}^{\text{\textregistered}}\) compared with cup anemometers from a met mast and a fixed WindCube v2\({}^{\text{\textregistered}}\) on a platform. The correction improves the linear regression against the fixed LIDAR turbulence intensity measurements, shifting the offset from \(\sim\)0.03 to \(\sim\)0.005 without post-processing the remaining peaks. osurmurm  
2021132973313  
estimate of a commercial continuous-wave (CW) or pulsed profiler wind LIDAR is generally as accurate as that provided by cup or sonic anemometers [9]. However, wind LIDARs are not an established technology for accurately measuring atmospheric turbulence. Both CW and pulsed profiler LIDARs show a significant measurement bias, compared to the reference instruments [10], which depends on boundary layer stability and measurement altitude. The main errors induced by profiler technology are: Spatial averaging due to the large measurement volume [11], cross-contamination between the different components of the velocity vector [12; 13] and low temporal sampling rate of the measurement [14]. Despite these systematic biases, profiler wind LIDARs are very practical devices because of their ease of installation and relocation, and their ability to provide a reasonable estimation of atmospheric boundary layer behavior in a wide range of applications. In offshore applications, a large part of the planet is hardly accessible for fixed platforms due to the extreme depth of the oceans and the required financial investment for the deployment of this type of installation. A wind LIDAR mounted on a buoy is a commercially viable tool for investigating the atmospheric behavior in oceanic areas. We refer to this set-up as floating LIDAR system (FLS). The sea-induced motion of a FLS is highly dependent on the dynamic response of the buoy to wave behavior. The shape, weight and anchorage of the buoy have a significant influence on the motion experienced by the wind LIDAR. The buoy's motion has six degrees of freedom: Three are translational (surge, sway, heave) and three are rotational (roll, pitch, yaw). The six degrees of wave-induced motion of the buoy each affect the LIDAR Doppler measurements in their own way. Generally, wave motion introduces a bias of the order of 1-2% in the measurement of the 10-min averaged velocity vector by a profiler FLS [15]. In contrast, the turbulence intensity measurement is heavily impacted by sea motion, whether it be pulsed or CW technology [16; 17]. Wave-induced buoy motion tends to add variability to the Doppler measurements. Therefore, a 10-min turbulence intensity estimate from the floating LIDAR is generally overestimated compared to the reference measurement.