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Natural Hazards and Earth System Sciences An interactive open-access journal of the European Geosciences Union
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Volume 11, issue 5
Nat. Hazards Earth Syst. Sci., 11, 1437–1446, 2011
https://doi.org/10.5194/nhess-11-1437-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

Special issue: Extreme and rogue waves

Nat. Hazards Earth Syst. Sci., 11, 1437–1446, 2011
https://doi.org/10.5194/nhess-11-1437-2011
© Author(s) 2011. This work is distributed under
the Creative Commons Attribution 3.0 License.

Research article 18 May 2011

Research article | 18 May 2011

Dynamical and statistical explanations of observed occurrence rates of rogue waves

J. Gemmrich and C. Garrett J. Gemmrich and C. Garrett
  • Department of Physics and Astronomy, University of Victoria, Victoria, BC V8W 3P6, Canada

Abstract. Extreme surface waves occur in the tail of the probability distribution. Their occurrence rate can be displayed effectively by plotting ln(–ln P), where P is the probability of the wave or crest height exceeding a particular value, against the logarithm of that value. A Weibull distribution of the exceedance probability, as proposed in a standard model, then becomes a straight line. Earlier North Sea data from an oil platform suggest a curved plot, with a higher occurrence rate of extreme wave and crest heights than predicted by the standard model. The curvature is not accounted for by second order corrections, non-stationarity, or Benjamin-Feir instability, though all of these do lead to an increase in the exceedance probability. Simulations for deep water waves suggest that, if the waves are steep, the curvature may be explained by including up to fourth order Stokes corrections. Finally, the use of extreme value theory in fitting exceedance probabilities is shown to be inappropriate, as its application requires that not just N, but also lnN, be large, where N is the number of waves in a data block. This is unlikely to be adequately satisfied.

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