The Rayleigh-Haring-Tayfun distribution of wave heights in deep water

Abstract

Regarding wave statistics, nearly every known exceeding probability distribution applied to rogue waves has showndisagreement with its peers. More often than not, models and experiments have shown a fair agreement with theRayleigh distribution whereas others show that the latter underpredicts extreme heights by almost one order of magnitude. Virtually all previous results seem to be microcosms, special cases of the underlying essence of this phenomenon.The present work focuses on the apparent contradiction among the majority of previous works. Based on the issueof strong uneven distribution of rogue waves found in Stansell (2004), a new exceeding probability distribution forrogue waves and the analysis of their uneven occurrence is conceived. The proposed distribution is a geometricalcomposition of the most popular models for wave records (Longuet-Higgins, 1952; Haring et al., 1976; Tayfun, 1980)with additional algebraic structures. The suggested distribution also obeys empirical physical bounds obtained fromthe analysis of nearly 350,000 waves from storms recorded in North sea and supports the qualitative likelihood ofappearance interpretation based on the symbiosis among three sea state parameters.