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

Nearly every known exceedance probability distribution applied to rogue waves has shown disagreement with its peers, suggesting that the underlying phenomenon may be too complex to grasp within a single distribution. In recent studies, this view has been supported by the realisation that there is no distribution suitable for wide ranges of sea states, even though distributions can perform well in a limited and small number of conditions. Towards the better quantitative assessment of rogue wave occurrence, the present work focuses on the apparent discrepancy among the majority of previous works. Furthermore, on the grounds of the uneven distribution of rogue waves found in North Sea observations, a new exceedance probability distribution for rogue waves is introduced. The proposed distribution is a geometrical composition of some of the most popular simple models for waves while introducing additional algebraic structures. The model also obeys empirical physical bounds obtained from the analysis of nearly 350,000 waves from storms recorded in North sea and supports the qualitative analysis of rogue wave occurrence based on the interaction among three sea state parameters