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

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