A penalised piecewise-linear model for non-stationary extreme value analysis of peaks over threshold. (1st January 2023) - Barlow, Anna Maria; Mackay, Ed; Eastoe, Emma; Jonathan, Philip
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. Highlights: Non-stationary model for extreme values of a variable with respect to covariates. Generalised Pareto scale and shape parameters modelled as piecewise-linear functions. Parameter variation penalised to obtain optimal predictive performance. Model is computationally efficient and sufficiently flexible to capture covariate effects. Open-source software available for model fitting.