## 1 Introduction  
Accurate offshore wind condition observations are essential for proper wind resource assessment during wind farm planning and design. These observations are also critical for optimizing wind farm operation and control. It is also crucial for the characterization of appropriate weather windows required for marine operations related to turbine installation, maintenance, and repair in the marine environment. Yet, wind observations at offshore sites are sparse, leaving the characterization of the flow field in and around offshore wind farms as one of the big challenges for its future large-scale deployment [1]. Traditionally, mast-mounted anemometers have been used for corresponding measurements such as, e.g., the German FINO research platforms in the North and Baltic seas [2], or the Ilmujden mast off the Dutch coast [3]. Such mast-based measurements are, however, very expensive, logistically demanding, and restricted to a single location and thus lack flexibility. In addition, masts are infeasible for acquiring wind speed data over the rotor disc of modern wind turbines, now exceeding 250 m [4]. Wind lidars have emerged as a reliable and cost-effective alternative to conventional meteorological masts for comprehensive wind field monitoring [5, 6]. They have specific advantages, in particular offshore, where met masts cannot be deployed in a cost-effectiveway [7]. Consequently, lidar systems have been deployed offshore in diverse setups, depending on the corresponding measurement goals, including mounting on wind turbine nacelles [8; 9; 10], on fixed platforms like research platforms, electrical sub-stations or bottom-fixed turbines [11; 12; 13], and on dynamic platforms such as vessels or buoys [14; 15; 16; 17; 18]. When positioned on static platforms, such lidars effectively reach altitudes aligning with the size of modern turbines. However, their placement is again stationary and constrained to the foundation location. Therefore, deploying wind lidars on dynamic platforms, such as ships, can be a promising solution to overcome the limitations associated with their static counterparts [14; 19; 20; 21; 22]. The deployment of wind profiling lidars on a floating platform causes inevitable challenges related to motion-induced errors in the retrieval of wind speed and direction [17; 23; 24; 25; 26; 27]. The corresponding floating lidar systems (FLS) are exposed to wave-induced rotational and, in particular for ship-mounted systems, also considerable translational motion. The latter ones (heave, surge, and sway) directly superimpose artificial relative speeds, while the angular motions (pitch, roll, and yaw) are constantly altering the measurement geometry and thus affecting and complicating the wind field reconstruction required to derive horizontal wind speed and direction from multiple line-of-sight (LOS) readings. The amplitude of the resulting motion-induced errors depends on the lidar type (pulsed vs. continuous wave); the chosen measurement geometry and sampling frequency; the speed, frequency, and amplitude of the applied motion; and the chosen averaging interval [27]. Previous research has shown that the motion-induced errors in 10 min mean wind speed only range from 1% to 2% [14], as the effects of the random motion by the waves with periods in the order of 0.1 Hz are averaged out. Thus, 10 min average wind retrievals from FLS might provide sufficient accuracy for, e.g., resource assessment, even without any motion correction. The quality in the derivation of other important design parameters, such as the turbulence intensity (TI), defined as the standard deviation of the instantaneous wind measurements divided by the mean value, will in contrast be highly affected by the motion. Consequently, proper measures for motion compensation or motion correction are required to correct motion-induced errors on the instantaneous wind measurements.