Modeling extreme values of processes observed at irregular time steps: Application to significant wave height

TL;DR

This paper extends the peaks over threshold method to irregularly sampled time series, enabling analysis of extreme wave heights from satellite data in the North Atlantic Ocean.

Contribution

It introduces a max-stable process-based approach with composite likelihood estimation for irregular time series extreme value analysis.

Findings

Method accurately describes extremal behavior in simulated data.

Successfully applied to satellite wave height data in North Atlantic.

Provides realistic estimates of extreme wave height properties.

Abstract

This work is motivated by the analysis of the extremal behavior of buoy and satellite data describing wave conditions in the North Atlantic Ocean. The available data sets consist of time series of significant wave height (Hs) with irregular time sampling. In such a situation, the usual statistical methods for analyzing extreme values cannot be used directly. The method proposed in this paper is an extension of the peaks over threshold (POT) method, where the distribution of a process above a high threshold is approximated by a max-stable process whose parameters are estimated by maximizing a composite likelihood function. The efficiency of the proposed method is assessed on an extensive set of simulated data. It is shown, in particular, that the method is able to describe the extremal behavior of several common time series models with regular or irregular time sampling. The method is then used to analyze Hs data in the North Atlantic Ocean. The results indicate that it is possible to derive realistic estimates of the extremal properties of Hs from satellite data, despite its complex space--time sampling.