Second-order hydrodynamic loads can induce motions at the natural frequencies of a floating wind turbine. These resonant responses are highly dependent on the hydrodynamic damping, which is mostly introduced by viscous effects. Numerically, these viscous effects are often represented by a Morison drag term with relative velocity, which introduces forcing, sea state-dependent linear damping and amplitude-dependent quadratic damping. Recent literature shows that calibration of the Morison drag coefficients to decay tests is not sufficient to achieve an accurate response in the numerical models. In addition, calibration of the drag coefficient alone changes both forcing and damping. Hence, following common practice, additional damping terms are needed, which require calibration against operating conditions. In this study, we apply Operational Modal Analysis (OMA) to wave basin results for the TetraSpar floater of Stiesdal Offshore Technologies. The floater was tested at scale 1:60 with the DTU 10MW reference wind turbine, both in the semi and spar configurations. We identify the linearized damping ratio in surge and pitch for different environmental conditions and investigate its dependency on the sea state and the motion amplitude. Our preliminary results show that the damping of the pitch mode follows increasing trends with significant wave height and motion amplitude, whereas the damping in surge presents a less clear tendency. This is linked to the larger damping level, smaller natural frequency and larger OMA uncertainty for surge. The paper concludes with a discussion of the dependency of OMA estimates on the amount of data and its processing.