  Models for extreme values accommodating non-stationarity have been amply
studied and evaluated from a parametric perspective. Whilst these models are
flexible, in the sense that many parametrizations can be explored, they assume
an asymptotic distribution as the proper fit to observations from the tail.
This paper provides a holistic approach to the modelling of non-stationary
extreme events by iterating between parametric and semi-parametric approaches,
thus providing an automatic procedure to estimate a moving threshold with
respect to a periodic covariate in circular data. By exploiting advantages and
mitigating pitfalls of each approach, a unified framework is provided as the
backbone for estimating extreme quantiles, including that of the $T$-year level
and finite right endpoint, which seeks to optimize bias-variance trade-off. To
this end, two tuning parameters related to the spread of peaks over threshold
are introduced. We provide guidance for applying the methodology to the
directional modelling of hindcast storm peak significant wave heights recorded
in the North Sea. Although the theoretical underpinning for adaptation of
well-known estimators in statistics of extremes to circular data is given in
some detail, the derivation of their asymptotic properties lays beyond the
scope of this paper. A bootstrap technique is implemented for obtaining
direction-driven confidence bounds in such a way as to account for the relevant
boundary restrictions with minimal sensitivity to initial point. This provides
a template for other applications where the analysis of directional extremes is
of importance.
