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Ocean Engineering

Modeling the Seasonality of Extreme Waves in the Gulf of Mexico

[+] Author and Article Information
Philip Jonathan

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

Kevin Ewans

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

J. Offshore Mech. Arct. Eng 133(2), 021104 (Dec 06, 2010) (9 pages) doi:10.1115/1.4002045 History: Received July 08, 2008; Revised October 28, 2009; Published December 06, 2010; Online December 06, 2010

Statistics of storm peaks over threshold depend typically on a number of covariates including location, season, and storm direction. Here, a nonhomogeneous Poisson model is adopted to characterize storm peak events with respect to season for two Gulf of Mexico locations. The behavior of storm peak significant wave height over threshold is characterized using a generalized Pareto model, the parameters of which vary smoothly with season using a Fourier form. The rate of occurrence of storm peaks is also modeled using a Poisson model with rate varying with season. A seasonally varying extreme value threshold is estimated independently. The degree of smoothness of extreme value shape and scale and the Poisson rate with season are regulated by roughness-penalized maximum likelihood; the optimal value of roughness is selected by cross validation. Despite the fact that only the peak significant wave height event for each storm is used for modeling, the influence of the whole period of a storm on design extremes for any seasonal interval is modeled using the concept of storm dissipation, providing a consistent means to estimate design criteria for arbitrary seasonal intervals. The characteristics of the 100 year storm peak significant wave height, estimated using the seasonal model, are examined and compared with those estimated ignoring seasonality.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Empirical density of storm peak events at location A. Darker shading represents higher density.

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Figure 2

Quantiles of HSsp by season at location A

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Figure 9

Extreme value shape γ and scale σ by season with a 50% variable threshold at location A

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Figure 10

Extreme value shape γ and scale σ by season with 50% and 80% variable thresholds at location A

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Figure 8

Overall GP model fitting and prediction error as a function of λ with a 50% variable threshold at location A

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Figure 7

Quantiles of HSsp by season at location B

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Figure 6

Empirical density of storm peak data at location B

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Figure 21

Cumulants for monthly and omniseasonal HS100 with 50% variable threshold at location B and the constant model

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Figure 20

Cumulants for monthly and omniseasonal HS100 with 50% variable threshold at location B and the seasonal model

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Figure 19

Cumulative distribution functions for monthly and omniseasonal HS100 with 50% variable threshold at location A for the constant model

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Figure 18

Cumulative distribution functions for monthly and omniseasonal HS100 with 50% variable threshold at location A for the seasonal model

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Figure 12

Overall Poisson model fitting and prediction error as a function of κ with a 50% variable threshold at location A

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Figure 11

Extreme value shape γ and scale σ by season with 50% and 80% variable thresholds at location B

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Figure 5

Variable extreme value threshold at location A. Thresholds set to omit 50% and 80% of values for a given seasonal degree.

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Figure 4

Conditional density of storm peaks over threshold at location A

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Figure 3

Quantiles of HSsp by direction at location A

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Figure 17

Cumulative distribution function for omniseasonal HS100 with 50% and 80% variable thresholds at location B for the seasonal and constant models

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Figure 16

Cumulative distribution function for omniseasonal HS100 with 50% and 80% variable thresholds at location A for the seasonal and constant models

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Figure 15

Estimated Poisson rate μ by season with 50% and 80% variable thresholds at location B

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Figure 14

Estimated Poisson rate μ by season with 50% and 80% variable thresholds at location A

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Figure 13

Storm counts (o) and estimated Poisson rate μ by season with a 50% variable threshold at location A. Rate is defined as the number of storms per location per seasonal degree per annum.

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