Space-Time Extremes in Short-Crested Storm Seas

This study develops a stochastic approach to model short-crested stormy seas as random fields both in space and time. Defining a space-time extreme as the largest surface displacement over a given sea surface area during a storm, associated statistical properties are derived by means of the theory of Euler characteristics of random excursion sets in combination with the Equivalent Power Storm model. As a result, an analytical solution for the return period of space-time extremes is given. Subsequently, the relative validity of the new model and its predictions are explored by analyzing wave data retrieved from NOAA buoy 42003, located in the eastern part of the Gulf of Mexico, offshore Naples, Florida. The results indicate that, as the storm area increases under short-crested wave conditions, space-time extremes noticeably exceed the significant wave height of the most probable sea state in which they likely occur and that they also do not violate Stokes Miche-type upper limits on wave heights.