Examination of Linearity of Time-series Data of Ocean Waves with Reference to Small Fishing Boats

Abstract

Studies of ocean waves have been developed by treating time-series data of ocean waves as linear stochastic processes (e.g., the spectral model proposed by Pierson and Moskowitz). However, they are based on the small amplitude wave theory, which presents limitations due to the wave height being sufficiently small compared with the wavelength, and the wavelength being sufficiently small compared with the water depth. In the above theory, the irregularity of ocean wave time-series data is due to the linear superposition of many component waves. Therefore, if the measured time-series data of ocean waves do not exhibit sufficient linearity, then an analysis based on the power spectrum density function cannot be reliable performed. A method to evaluate the linearity of measured ocean wave time-series data is discussed herein using phase-randomized surrogate data, and a linear wave is defined as a linear superposition of many component waves. Specifically, the geometric features of the reconstructed trajectories of the measured time-series data are quantified to evaluate the linearity.