Deterministic and Stochastic Modelling of Ocean Surface Waves

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Predicting the mean wave statistics in the nearshore, for instance the significant wave height, has predominantly been the domain of operational stochastic wave models based on the radiative transport (or energy balance) equation. Although reasonably successful in the nearshore, these models were originally developed for oceanic scales, and necessarily neglect or parametrise processes that are only significant in shallow water, such as the linear processes of interference and diffraction, or the nonlinear triad wave-wave interactions and dissipation due to wave breaking. In this dissertation we investigate the possibility of predicting the wave statistics on small scales in strongly non-linear conditions, such as found in the surfzone, using the recently developed Surface WAves till SHore (SWASH) model, whereas on larger scales we pursue a generalisation of existing stochastic models by incorporating coherent effects, hereby extending these models to include interference and diffractive effects.