We present a stochastic model of sea storms to predict the maximum height of the wave surface over a given area during storms. To do so, we exploit the theory of Euler Characteristics of random excursion sets combined with a generalization of Boccotti's equivalent triangular storm model (Boccotti, 2000) that describes an actual storm history in the form of a generic power law (Fedele and Arena, 2010). An analytical solution for the return period of extreme wave events over a given area and the associated statistical properties are given. We then assess the relative validity of the new model and its predictions by analyzing wave measurements retrieved from NOAA-NODC buoys moored offshore of the Atlantic and Pacific coasts.
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