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Models for extreme values accommodating non-stationarity have been amplystudied and evaluated from a parametric perspective. Whilst these models areflexible, in the sense that many parametrizations can be explored, they assumean asymptotic distribution as the proper fit to observations from the tail.This paper provides a holistic approach to the modelling of non-stationaryextreme events by iterating between parametric and semi-parametric approaches,thus providing an automatic procedure to estimate a moving threshold withrespect to a periodic covariate in circular data. By exploiting advantages andmitigating pitfalls of each approach, a unified framework is provided as thebackbone for estimating extreme quantiles, including that of the $T$-year leveland finite right endpoint, which seeks to optimize bias-variance trade-off. Tothis end, two tuning parameters related to the spread of peaks over thresholdare introduced. We provide guidance for applying the methodology to thedirectional modelling of hindcast storm peak significant wave heights recordedin the North Sea. Although the theoretical underpinning for adaptation ofwell-known estimators in statistics of extremes to circular data is given insome detail, the derivation of their asymptotic properties lays beyond thescope of this paper. A bootstrap technique is implemented for obtainingdirection-driven confidence bounds in such a way as to account for the relevantboundary restrictions with minimal sensitivity to initial point. This providesa template for other applications where the analysis of directional extremes isof importance.

Modelling non-stationary extremes of storm severity: a tale of two approaches