  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.
