How Should We Combine Long and Short Term Wave Height Distributions?

Estimating the maximum wave or crest height that will occur in a long return interval is one of the fundamental problems for ocean engineers. Long time series of individual wave heights are not available. The calculations must start with measured or hindcast time series of significant wave heights. An extreme value distribution is fit to that data. The resulting long term distribution is then combined with a short term distribution for the individual heights. This study is concerned with finding the most accurate methods for that calculation. The basic tool is the Borgman integral, but it has been applied in many different ways. Theoretical derivations do not clearly indicate which method is most accurate, and time series of measurements long enough for accurate tests do not exist. These problems were circumvented in this study by constructing very long simulated time series with known distributions. Both initial value and storm based methods were tested. The correct method of calculation depends on what question is being asked. The distribution of the maximum wave heights in a six hour interval is different than the distribution of the maxima of all of the waves. The distribution of the maxima in a storm is different than the distribution of the maxima in an interval. We believe that the finding the maximum in a storm is the most appropriate question for ocean engineering design. The Tromans and Vanderschuren (1995, Proc. Offshore Tech. Conf., OTC 7683) method accurately matches the results from our storm simulations.