Estimating the parameters of ocean wave spectra

TL;DR

This paper introduces a statistical method, the de-biased Whittle likelihood, for more accurate and precise estimation of spectral parameters of wind-generated ocean waves, outperforming existing techniques and addressing practical implementation issues.

Contribution

It applies the de-biased Whittle likelihood to ocean wave spectra, demonstrating improved parameter recovery and uncertainty estimation over traditional methods.

Findings

Outperforms least squares fitting in accuracy and precision

Provides a practical approach for uncertainty estimation

Successfully applied to real-world wave data from New Zealand

Abstract

Wind-generated waves are often treated as stochastic processes. There is particular interest in their spectral density functions, which are often expressed in some parametric form. Such spectral density functions are used as inputs when modelling structural response or other engineering concerns. Therefore, accurate and precise recovery of the parameters of such a form, from observed wave records, is important. Current techniques are known to struggle with recovering certain parameters, especially the peak enhancement factor and spectral tail decay. We introduce an approach from the statistical literature, known as the de-biased Whittle likelihood, and address some practical concerns regarding its implementation in the context of wind-generated waves. We demonstrate, through numerical simulation, that the de-biased Whittle likelihood outperforms current techniques, such as least squares fitting, both in terms of accuracy and precision of the recovered parameters. We also provide a method for estimating the uncertainty of parameter estimates. We perform an example analysis on a data-set recorded off the coast of New Zealand, to illustrate some of the extra practical concerns that arise when estimating the parameters of spectra from observed data.