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 $HS$ over threshold is modeled using a generalized 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-penalized maximum likelihood, the optimal value of roughness selected by cross-validation. The characteristics of a $100-year$ storm peak $HS$⁠, estimated using the directional model, differ from those estimated when ignoring the directionality of storms. In particular, the extreme right-hand tail of omnidirectional $HS100$ 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 modeling, 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 omnidirectional storm peak $HS$ nonexceedence probability of 0.5. We suggest a risk-cost criterion, which minimizes design cost for a given omnidirectional design specification, as an objective basis for optimal selection of directional criteria.