Distribution of Large Wave Heights

Abstract

The statistical distribution of zero‐crossing wave heights is considered within the context of a previous theory proposed by the writer some years ago. The underlying model, definitions, and assumptions are reexamined systematically to develop asymptotic approximations to the probability density, exceedance probability, and statistical moments of wave heights larger than the mean wave height. The asymptotic results have closed forms, and thus are easier to use in practical applications than the original theory, which requires numerical integration. Comparisons to empirical data are given to show that the present asymptotic theory produces the observed statistics of large wave heights faithfully to within 1%. Further, comparisons with other relevant theories also reveal that if one remains true to the theoretical definitions, then the present theory is the most accurate in predicting the exceedance distribution of large wave heights. Finally, the asymptotic theory is coupled with the statistics of wave periods to derive a theoretical expression for the joint distribution of large wave heights and associated periods. The predictive utility of this last result remains to be explored.