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Measurement-based estimates of extreme wave conditions for the Gulf of Mexico

During 2004 and 2005, four severe hurricanes - Ivan, Dennis, Katrina, and Rita - occurred in the Gulf of Mexico. These hurricanes created winds and waves that were close to or exceeded the calculated 100 years return period conditions. As a result, new estimates of extreme metocean conditions are needed for many offshore engineering applications. Recently, such estimates have been derived by Berek et al. (2007) using hindcast (modeled) data. In some regions of the Gulf, these new (proposed) estimates suggest a substantial increase, relative to the American Petroleum Institute's current estimates of the 100-year design conditions, the maximum wave heights increasing by as much as 6.4 m and the wind speeds by 5 m/s. We have therefore reexamined the problem and obtained additional estimates in the Gulf of Mexico using other methods. To overcome difficulties associated with synthetic data which can generally subject to modeling related errors, we use buoy data. At several locations, nearly 32 years of data are available. (According to a rule of thumb, extrapolations to three or four times the data length are appropriate). In the context of statistical modeling of extremes, the basic problem is ill-posed. Various difficulties and the need for multiple or even non-standard tools have been noted in the literature. Instead of the traditional methodology of using one or more distribution (e.g. Gumbel, Weibull, Frechet, etc.), we used the Generalized Extreme Value distribution, which eliminates the need for identifying the most appropriate distribution. Also, to increase the utility and value of possibly short datasets, we use the r-largest order statistic (instead of the annual maximum traditionally used). This approach is intended to make more efficient use of the data and to mitigate concerns about small dataset length. Using these methods, estimates of the significant wave heights and wind-speeds are derived for the Gulf of Mexico and compared with the estimates of Berek et al. (2007). Besides traditional statistical aspects, factors such as long-term trends in wave height changes must also be considered. In the literature, such trends have been noted off both US coasts. We estimate an average increase of 3.5 cm/year in the annual maximum significant wave heights; Komar and Allan (2007) give an estimate of 1.7 cm/year for the location of a buoy in the mid-Atlantic. Based on these our study has made initial attempts to include an appropriate ldquotrend parameterrdquo in the n-year return period calculation.