An analytical approach to the statistical moments associated with large ocean waves.

The non-Gaussian statistical behavior of ocean surface gravity waves is usually studied via computationally expensive direct Monte Carlo simulations of the ocean surface. We, however, directly solve the Zakharov ocean surface equations, analytically arriving at ocean surface statistical moments via Wiener Chaos Expansions (WCE). We thus apply our ocean surface kurtosis time evolution result to deduce the time evolution of ocean surface rogue wave probability. Additionally, we also demonstrate a probabilistic approach to the time evolution of ocean wave energy deterministically via the Wiener Chaos Expansion method, demonstrating the possibility of the use of the Wiener Chaos Expansion method in understanding the probabilistic behavior of the time-evolution of ocean wave energy for wave power applications.