Modelling significant wave height in the North Atlantic

The surface of the ocean, and so such quantities as the significant wave height, can be thought of as a random surface in space which develops over time. In this paper, we explore certain types of random fields (in space and time) as models for the significant wave height and fit these models to data obtained from the TOPEX-Poseidon satellite. The data consist of observations along different one-dimensional tracks over time. It is assumed that, for the region of ocean considered and for a fixed time, the data can be considered stationary. Further-more, the shape of the data suggests that it is reasonable to use a lognormal distribution. As the covariance function may change over time, the model chosen is fitted to the data for each time separately. The data over space exhibit variation at different scales and hence the covariance function needs to reflect this property. Consequently, a mixture of Gaussian functions is assumed for the covariance function. To fit the model to the data, the theoretical variogram is fitted to the empirical variogram using weighted least squares. Stochastic models for the variation of the parameter values were investigated. The results of fitting these models are discussed and interpreted