Asymptotic wave-height distributions and conditional statistics

Asymptotic forms of two theoretical distributions developed relatively recently by Stansell et al. (2004) and Zheng et al. (2006) are compared to Boccotti's asymptotic theory (Boccotti, 2000) describing the heights of large waves and the conditional statistics h(1/n) the mean of the largest 1/n fraction of wave heights. In particular, h(1/3) commonly referred to as the significant wave height h(s), is of theoretical and practical importance. The conventional Rayleigh distribution is known to over-predict h(1/n), for n >= 3. The present comparisons with empirical statistics derived from linear simulations indicate that whereas Boccotti's asymptotic distribution describes large wave heights and h(1/n) for n >= 3 quite accurately, with typical errors being within +/- 1% of simulations, the asymptotic forms of Stansell et al. and Zheng et al. distributions significantly over-predict them just as the Rayleigh distribution does. Further comparisons also show that an empirical regression formulated by Goda & Kudaka (2007) describes h(s) also quite accurately.