In the present work, return periods of various level values of significant wave height in the Gulf of Mexico are given. The predictions are based on a new method for nonstationary extreme-value calculations that have recently been published. This enhanced method exploits efficiently the nonstationary modeling of wind or wave time series and a new definition of return period using the MEan Number of Upcrossings of the level value x* (MENU method). The whole procedure is applied to long-term measurements of wave height in the Gulf of Mexico. Two kinds of data have been used: long-term time series of buoy measurements, and satellite altimeter data. Measured time series are incomplete and a novel procedure for filling in of missing values is applied before proceeding with the extreme-value calculations. Results are compared with several variants of traditional methods, giving more realistic estimates than the traditional predictions. This is in accordance with the results of other methods that take also into account the dependence structure of the examined time series.

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