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Safety and Reliability

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

[+] Author and Article Information
Kevin Ewans

Shell International Exploration and Production, P.O. Box 60, 2280 AB Rijswijk, The Netherlandskevin.ewans@shell.com

Philip Jonathan

Shell Technology Centre Thornton, P.O. Box 1, Chester, Chesire CH1 3SH, UKphilip.jonathan@shell.com

J. Offshore Mech. Arct. Eng 130(4), 041604 (Oct 01, 2008) (8 pages) doi:10.1115/1.2960859 History: Received July 03, 2007; Revised October 22, 2007; Published October 01, 2008

## Abstract

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.

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Topics: Design , Storms , North Sea

## Figures

Figure 1

Estimated quantiles of HSsp as a function of storm peak direction aggregated over all locations. Nonexceedence probabilities are given on the right-hand side.

Figure 2

Estimated densities of HSsp over threshold aggregated over all locations. Thresholds of 3m, 6m, 9m, and 12m are used.

Figure 3

Rank correlations between corner and center locations. The top left illustrates interdependence on gray-scale (black=highest, white=lowest). The bottom right gives numeric values for rank correlations between pairs of locations.

Figure 4

Scatter plot of HSsp for NE location against SW. These locations give the lowest rank correlation between corner and center locations, but are nevertheless strongly interdependent.

Figure 5

Median differences (in degrees) between storm peak directions for corner and center locations. The top left illustrates difference on gray-scale (black=highest, white=lowest). The bottom right gives numeric values for median difference between pairs of locations.

Figure 6

Scatter plot of storm peak direction for NE location against SW. These locations give the largest median angular difference in storm peak direction from the corner and center locations, but are nevertheless strongly interdependent.

Figure 7

Median directional storm dissipation ρ as a function of HSsp. For any storm, ρ is the minimum reduction in HS (expressed as a fraction of HSsp) as a function of angular difference from the storm peak direction.

Figure 8

Variable threshold estimates for local quantiles q=0.2, q=0.5, and q=0.8. The median case is adopted.

Figure 9

Overall model fitting and prediction error as a function of λ. The optimal value for λ can be seen to be 3×10−5. Note that points corresponding to fitting and predictive performance for the constant model are superimposed on the right-hand side.

Figure 10

The optimal functional forms of γ and σ, with bootstrap 95% confidence bands

Figure 11

Sector HS100 characteristics for a sequence of 36 consecutive directional sectors, each of width 10deg, which partition [0,360), starting at 0deg

Figure 12

Optimal boundaries for four directional design sectors

Figure 13

Cumulative distribution functions for sector and omnidirectional HS100 using variable extremal threshold and directional model

Figure 14

Cumulative distribution functions for sector and omnidirectional HS100 using variable extremal threshold and direction-independent (constant) model

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