Abstract
A combination of stochastic and deterministic models is applied for the study of ocean wind waves. Timeseries of significant wave height and mean zero up-crossing period, obtained from globally scattered floating buoys, are analyzed in order to construct a double periodic model, and select an optimal marginal distribution and dependence function for the description of the stochastic structure of wind waves. It is concluded that wind waves, in contrast to the atmospheric wind speed process, are mostly governed by the seasonal periodicity rather than the diurnal periodicity, which is often weak and can be neglected. Also, the Pareto-Burr-Feller distribution is found to be a fair selection among other common three-parameter marginal distributions. The dependence function is simulated through the Hurst-Kolmogorov (HK) dynamics using the climacogram (i.e., variance of the averaged process in the scale domain), a stochastic tool that can robustly estimate both the short-term fractal and long-range dependence behaviors both apparent at the wind wave process. To test the validity of the model, a stochastic synthesis of the wind wave process is performed through the Symmetric Moving Average scheme, focused on the explicit preservation of the probabilistic and the dependence structures. Finally, the stochastic model is applied for simulation to an offshore station southeast of Australia having one of the largest record lengths. The energy potential is also estimated through the significant wave height and the mean zero up-crossing period of both the synthetic and observed timeseries, and the effectiveness of the model is further discussed.