Modelling Space Variability of Hs in the North Atlantic

Anastassia Baxevani, Igor Rychlik and Richard J. Wilson

Centre for Mathematical Sciences
Mathematical Statistics
Lund Institute of Technology,
Lund University,

ISSN 1403-9338
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. Furthermore, 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. A methodology is suggested based on the relation of the first two moments of total variation of the field and its derivative to the second and fourth order spectral moments. The parameters of the model are then identified as the solution to a system of temporal equations.

The proposed model is validated along the satellite tracks. Distributions of different quantities are then computed and compared to the empirical ones. The results of these comparisons are then discussed and interpreted.