In the present paper, a compound stochastic model is formulated and validated, resolving the state-by-state, seasonal and interannual variabilities of S H. The model is a combination of two cyclostationary random processes modelling the variability of mean monthly values and mean monthly standard deviations, respectively, and of a stationary random process modelling the residual, state-by-state, variability. In this way, the time series of significant wave height is given the structure of a multiple-scale compound stochastic process.
It is well known that long-term time series of significant wave height exhibit a number of features, namely random variability, serial correlation, seasonal periodicity and, possibly, a long-term climatic trend, evolving in different time scales. Athanassoulis and Stefanakos, in a series of works (Athanassoulis and Stefanakos, 1995; 1998; Stefanakos, 1999; Stefanakos and Athanassoulis, 2001), have established a nonstationary modelling, according to which a many-year long time series of significant wave height is modelled as a cyclostationary stochastic process with yearly periodically varying mean value and standard deviation. A multi-year long-term trend can also be included in the model, if the data shows that such a trend is present; see, e.g., Athanassoulis and Stefanakos (1995), WASA Group (1998), Carter (1999) and references cited there. In the present work, we shall disregard this question, since the data we have at our disposal are not long enough to resolve this feature. Last decades, measurements from satellite altimeters have made available a large amount of wave data with a worldwide coverage. These datasets have been used for various sea wave applications, such as extreme value calculations (Charriez et al., 1992; Barstow and Krogstad, 1993; Cooper and Forristall, 1997; Panchang et al., 1999) wave climate studies (Tournadre and Ezraty, 1990; Tournadre, 1993; Carter et al., 1995), etc..
