Evaluation of wave extremes occurring in short-crested sea states is the research topic of this doctoral thesis. Short-crestedness is the typical condition in sea storms. In fact, engineering practice and reports from people working offshore (e.g. on fixed platforms or routing ships) are raising questions on the adequacy of conventional wave statistics for the prediction of extremes during short-crested storm conditions. Indeed, wave statistics has been traditionally derived from time measurements, i.e. at a fixed point. Recently, experimental evidence has proved that the maximum sea surface elevation occurring at a fixed point of the sea is smaller than the maximum occurring over a surrounding area. Hence, unless the space dynamics of wave groups is fully included inside the area, the measured maximum at a point or over a smaller area underestimates the actual maximum. To overcome this fact, during the last decade stochastic models to calculate maxima of Gaussian multidimensional random fields, i.e. Piterbarg's theorem and Adler and Taylor's Euler Characteristic approach, have been applied to wave statistics. According to these theories, we should be able to estimate the expected maxima that can occur over an area (space) during a short-crested sea state of given duration (time), giving an explanation to the experimental evidence.
The aim of this doctoral thesis is to investigate and discuss these recently applied stochastic models, in order to contribute changing the paradigm of wave analysis: from time to space-time domain. Thus, we worked on multiple fronts with multiple approaches. Field campaigns allowed us to validate stochastic models and to propose a data analysis procedure to characterize sea states at a given location with respect to space-time wave extremes. Analytical and numerical approaches served us to give possible solutions to the well-recognized lack of directional wave spectra, i.e. the input of the multidimensional stochastic models. Indeed, we propose closed formulae to calculate the input spectral parameters in a context of idealized sea states and we develop an ad hoc version of the SWAN (Simulating WAves Nearshore) model, called SWAN-ST (SWAN Space-Time), to allow space-time extreme analysis to be performed on realistic domains. Moreover, analytical and numerical model outputs were used to investigate the dependence of wave extremes upon specific physical parameters governing wind wave mechanics (i.e. wind speed, fetch length, ambient current speed and bottom slope). Finally, we tested the numerical modeling of space-time extremes on realistic domains by running a 3 years hindcast of on the Mediterranean Sea
