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Research Papers: Ocean Engineering

Estimation of Storm Peak and Intrastorm Directional–Seasonal Design Conditions in the North Sea

[+] Author and Article Information
Graham Feld

Shell Projects & Technology,
Aberdeen AB12 3FY, UK
e-mail: graham.feld@shell.com

David Randell

Shell Projects & Technology,
Manchester M22 0RR, UK
e-mail: david.randell@shell.com

Yanyun Wu

Shell Projects & Technology,
Manchester M22 0RR, UK
e-mail: yanyun.wu@shell.com

Kevin Ewans

Sarawak Shell Bhd,
Kuala Lumpur 50450, Malaysia
e-mail: kevin.ewans@shell.com

Philip Jonathan

Shell Projects & Technology,
Manchester M22 0RR, UK
e-mail: philip.jonathan@shell.com

Contributed by the Ocean, Offshore, and Arctic Engineering Division of ASME for publication in the JOURNAL OF OFFSHORE MECHANICS AND ARCTIC ENGINEERING. Manuscript received April 23, 2014; final manuscript received January 15, 2015; published online February 10, 2015. Assoc. Editor: Arvid Naess.

J. Offshore Mech. Arct. Eng 137(2), 021102 (Apr 01, 2015) (15 pages) Paper No: OMAE-14-1048; doi: 10.1115/1.4029639 History: Received April 23, 2014; Revised January 15, 2015; Online February 10, 2015

Specification of realistic environmental design conditions for marine structures is of fundamental importance to their reliability over time. Design conditions for extreme waves and storm severities are typically estimated by extreme value analysis of time series of measured or hindcast significant wave height, HS. This analysis is complicated by two effects. First, HS exhibits temporal dependence. Second, the characteristics of HSsp are nonstationary with respect to multiple covariates, particularly wave direction, and season. We develop directional–seasonal design values for storm peak significant wave height (HSsp) by estimation of, and simulation under a nonstationary extreme value model for HSsp. Design values for significant wave height (HS) are estimated by simulating storm trajectories of HS consistent with the simulated storm peak events. Design distributions for individual maximum wave height (Hmax) are estimated by marginalization using the known conditional distribution for Hmax given HS. Particular attention is paid to the assessment of model bias and quantification of model parameter and design value uncertainty using bootstrap resampling. We also outline existing work on extension to estimation of maximum crest elevation and total extreme water level.

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Figures

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Fig. 1

Storm peak significant wave height HSsp on storm direction θsp (upper panel) and storm season φsp (lower panel)

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Fig. 2

Empirical quantiles of storm peak significant wave height, HSsp by storm direction, θsp, and storm season, φsp. Panel titles indicate quantile nonexceedance probability. Empty bins are colored white.

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Fig. 3

Storm trajectories of significant wave height, HS, on wave direction θ for 30 randomly chosen storm events (in different colors (or grayscales)). A circle marks the start of each intrastorm trajectory.

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Fig. 4

Directional–seasonal parameter plot for extreme value threshold, ψ, corresponding to nonexceedance probability 0.5 of HSsp. The upper panel shows the bootstrap median threshold on storm peak direction, θsp, and storm peak season, φsp. The lower panels show 12 monthly directional thresholds in terms of bootstrap median (solid) and 95% bootstrap uncertainty band (dashed).

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Fig. 5

Directional–seasonal parameter plot for rate of threshold exceedance, ρ×104, of HSsp. The upper panel shows the bootstrap median rate on θsp and φsp. The lower panels show 12 monthly directional rates in terms of bootstrap median (solid) and 95% bootstrap uncertainty band (dashed). Unit of rate ρ is number of occurrences per annum per directional–seasonal covariate bin.

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Fig. 6

Directional–seasonal parameter plot for GP shape, ξ. The upper panel shows the bootstrap median shape on θsp and φsp. The lower panels show 12 monthly directional shapes in terms of bootstrap median (solid) and 95% bootstrap uncertainty band (dashed).

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Fig. 7

Directional–seasonal parameter plot for GP scale, σ. The upper panel shows the bootstrap median scale on θsp and φsp. The lower panels show 12 monthly directional scales in terms of bootstrap median (solid) and 95% bootstrap uncertainty band (dashed).

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Fig. 12

Directional–seasonal return value plot for 100-year maximum wave height, Hmax100. The upper panel shows omnidirectional return values on wave season, φ, in terms of monthly median (solid black), most-probable (dot-dashed black), 2.5‰ and 97.5‰ (both dashed black), and the corresponding omnidirectional omniseasonal estimates (in red (or gray), common to Fig. 11). The lower panels show seasonal return values for directional octants in terms of median (solid), most-probable (dot-dashed), and 2.5‰ and 97.5‰ (both dashed). The corresponding omniseasonal estimates are also shown (in red (or gray)).

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Fig. 13

Validation of directional–seasonal model for storm peak significant wave height, HSsp, by comparison of CDFs for original storm peak sample with those from 1000 sample realizations under the model corresponding to the same time period as the original sample. The upper panel shows the omnidirectional omniseasonal CDF for the original sample (red (or gray)), the corresponding median from simulation (solid black), together with 2.5‰ and 97.5‰ from simulation (both dashed). The lower panels compare 12 monthly CDFs in the same way. Titles for plots, in brackets following the month name, are the numbers of actual and simulated events in each month.

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Fig. 14

Validation of directional–seasonal model for significant wave height, HS, by comparison of CDFs for original sample with those from 1000 sample realizations under the model (incorporating intrastorm evolution of HS) corresponding to the same time period as the original sample. The upper panel shows the omnidirectional omniseasonal CDF for the original sample (red (or gray)), the corresponding median from simulation (solid black), together with 2.5‰ and 97.5‰ from simulation (both dashed). The lower panels compare 12 monthly CDFs in the same way. Titles for plots, in brackets following the month name, are the numbers of actual and simulated events (in each month).

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Fig. 8

CDFs for 100-year storm peak significant wave height, HS100 from simulation under the directional–seasonal model, incorporating uncertainty in parameter estimation using bootstrap resampling. Upper panel shows CDFs for directional octants and lower panel for months of year. The common omnidirectional omniseasonal CDF is shown in both panels (in black).

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Fig. 9

Directional–seasonal return value plot for 100-year significant wave height, HS100. The upper panel shows omniseasonal return values on wave direction, θ, in terms of directional octant median (solid black), most-probable (dot-dashed black), 2.5‰ and 97.5‰ (both dashed black), and the corresponding omnidirectional omniseasonal estimates (in red (or gray), common to Fig. 10). The lower panels show 12 monthly directional octant return values (in black) in terms of median (solid), most-probable (dot-dashed), 2.5‰ and 97.5‰ (both dashed). The corresponding omnidirectional estimates are also shown (in red (or gray)).

Grahic Jump Location
Fig. 10

Directional–seasonal return value plot for 100-year significant wave height, HS100. The upper panel shows omnidirectional return values on wave season, φ, in terms of monthly median (solid black), most-probable (dot-dashed black), 2.5‰ and 97.5‰ (both dashed black), and the corresponding omnidirectional omniseasonal estimates (in red (or gray), common to Fig. 9). The lower panels show seasonal return values for directional octants in terms of median (solid), most-probable (dot-dashed), and 2.5‰ and 97.5‰ (both dashed). The corresponding omniseasonal estimates are also shown (in red (or gray)).

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Fig. 11

Directional–seasonal return value plot for 100-year maximum wave height, Hmax100. The upper panel shows omniseasonal return values on wave direction θ, in terms of directional octant median (solid black), most-probable (dot-dashed black), 2.5‰ and 97.5‰ (both dashed black), and the corresponding omnidirectional omniseasonal estimates (in red (or gray), common to Fig. 12). The lower panels show 12 monthly directional octant return values (in black) in terms of median (solid), most-probable (dot-dashed), and 2.5‰ and 97.5‰ (both dashed). The corresponding omnidirectional estimates are also shown (in red (or gray)).

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