A penalised piecewise-linear model for non-stationary extreme value analysis of peaks over threshold

TL;DR

This paper introduces a flexible, penalised piecewise-linear model for non-stationary extreme value analysis of peaks over threshold, effectively capturing covariate effects like direction and season on storm peak significant wave heights.

Contribution

It develops a novel penalised piecewise-linear approach for modeling non-stationary extremes with covariates, optimizing predictive performance through cross-validation.

Findings

Effective modeling of storm peak significant wave height extremes.

Good predictive performance with a six-node triangulation.

Flexible representation of covariate effects at reasonable computational cost.

Abstract

Metocean extremes often vary systematically with covariates such as direction and season. In this work, we present non-stationary models for the size and rate of occurrence of peaks over threshold of metocean variables with respect to one- or two-dimensional covariates. The variation of model parameters with covariate is described using a piecewise-linear function in one or two dimensions defined with respect to pre-specified node locations on the covariate domain. Parameter roughness is regulated to provide optimal predictive performance, assessed using cross-validation, within a penalised likelihood framework for inference. Parameter uncertainty is quantified using bootstrap resampling. The models are used to estimate extremes of storm peak significant wave height with respect to direction and season for a site in the northern North Sea. A covariate representation based on a triangulation of the direction-season domain with six nodes gives good predictive performance. The penalised piecewise-linear framework provides a flexible representation of covariate effects at reasonable computational cost.