The Effect of Directionality on Northern North Sea Extreme Wave Design Criteria

The characteristics of hindcast data for extreme storms at a Northern North Sea location are shown to depend on storm direction, reflecting storm strength and fetch variability. Storm peak H_S over threshold is modelled using a generalised Pareto distribution, the parameters of which are allowed to vary smoothly with direction using a Fourier form. A directionally-varying extreme value threshold is incorporated. The degree of smoothness of extreme value shape and scale with direction is regulated by roughness-penalised maximum likelihood; the optimal value of roughness selected by cross-validation. The characteristics of 100-year storm peak H_S, estimated using the directional model differ from those estimated when ignoring the directionality of storms. In particular, the extreme right hand tail of omnidirectional H_S100 is longer using the directional model, indicating in this case that ignoring directionality causes underestimation of design criteria. Although storm peak data alone are used for extreme value modelling, the influence of a storm, in directional design sectors other than that containing its storm peak direction, is incorporated by estimating the storm’s directional dissipation directly from the data. An automated approach to selection of directional design sectors is described. Directional design criteria are developed using three different approaches, all consistent with an omni-directional storm peak H_S non-exceedence probability of 0.5. We suggest a risk-cost criterion, which minimises design cost for a given omni-directional design specification, as an objective basis for optimal selection of directional criteria.