A Non-Parametric, Data-Driven Approach to Despiking Ocean Surface Wave Time Series

We propose a methodology for despiking ocean surface wave time series based on a Bayesian approach to data-driven learning known as Gaussian process (GP) regression. We show that GP regression can be used for both robust detection of erroneous measurements and interpolation over missing values, while also obtaining a measure of the uncertainty associated with these operations. In comparison with a recent dynamical phase space-based despiking method, our data-driven approach is here shown to lead to improved wave signal correlation and spectral tail consistency, although at a significant increase in computational cost. Our results suggest that GP regression is thus especially suited for offline quality control requiring robust noise detection and replacement, where the subsequent analysis of the despiked data is sensitive to the accidental removal of extreme or rare events such as abnormal or rogue waves. We assess our methodology on measurements from an array of four collocated 5-Hz laser altimeters during a much-studied storm event in the North Sea covering a wide range of sea states.