Statistical Analysis of Local Extrema in Rough Sea Surfaces Based on Computer Simulation

Abstract

   Introduction. Generalized extreme value (GEV) distributions represent a universal description of the limiting distribution of the normalized local maxima statistics for independent and identically distributed data series. Extreme value distributions are commonly classified into three different types representing different functional forms and thus varying in shape, also known as types I, II, and III. Thus, attribution of some observational data series to a particular type of its local maxima distribution, as well as fitting of the distribution parameters, provides certain information about the laws governing the underlying natural or technogenic process. Radar-based remote sensing techniques represent a ubiquitous tool for analyzing large patterns of the sea surface and determining the parameters of the waves. In turn, understanding the laws governing the extreme values in the rough sea surface obtained from their radar images followed by evaluation of their distribution parameters, depending on the wind speed and direction, as well as the presence of surface currents and swells, can be useful for predicting wave height.   Aim. Analysis of the functional forms governing the local extreme value distributions in a rough sea surface for the given wind and swell parameters based on computer simulations.   Materials and methods. For the rough sea surface simulated by an additive harmonic synthesis procedure, the local extreme value distribution was fitted using the least-mean-squares technique. The fitted parameters were then used for their classification according to the three predetermined types.   Results. Computer simulations of a rough sea surface with combined wind and swell waves were performed. It is shown that the distribution of local maxima in the absence of swell waves could be well approximated by theWeibull (type III GEV) distribution, with the parameters explicitly depending on the wind speed. At the same time, no significant dependence on the sea depth was observed. On the contrary, in the presence of additional swell waves, the distribution of local extrema could be rather attributed to the Fréchet (type II GEV) distribution, with the parameters additionally depending on the angle between the wind and swell waves.   Conclusion. The laws governing the distributions of local wave extrema in rough seas are in a good agreement with the theoretical GEV approximations, with the distribution parameters being deductible from the key features of the waves. This indicates the predictability of wave height extrema from sea surface measurements, which can be performed based on remote radar observations.