Impact of Errors in Buoy Measurements on Nonlinear Fourier Spectra

The nonlinear Fourier transform (NFT) has been recently used to analyze the measured rogue waves in shallow water (Teutsch et al., Nat. Hazards Earth Syst. Sci., 2023). When analyzing field measurement data from the buoy, measurement errors are unavoidable due to various factors. The drag forces on the buoy can e.g. result in low-frequency measurement noise (Ashton and Johanning, Ocean Eng., 2015), while the sensors employed on the buoy are limited in bandwidth and contribute noise themselves (Yurovsky and Dulov, Ocean Eng., 2020). It is still uncertain how the noise generated during the buoy measurement influences the nonlinear Fourier spectrum computed by the NFT. In this study, we discuss the impact of measurement errors on the nonlinear Fourier spectrum of water waves. We first generate random-phase time series from typical wave spectra such as the Pierson-Moskowitz (PM) spectrum for various significant wave heights. We will then artificially incorporate measurement errors into the generated time series. The impact of the errors is studied by comparing the nonlinear Fourier transforms of the time series with and without measurement errors.