The Long-Term Wind and Wave Spectra of the Mediterranean Sea

It is a well-known fact that long-term time series of wind and wave data are modelled as nonstationary stochastic processes with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic processes). Using this model, the initial nonstationary series are decomposed to a seasonal (periodic) mean value m(t) and a residual time series W(t) multiplied by a seasonal (periodic) standard deviation s(t), of the form Y(t) = m(t) + s(t)W(t). The periodic components m(t) and s(t) are estimated using mean monthly values, and the residual time series W(t) is examined for stationarity. For this purpose, spectral densities of W(t) are obtained from different seasonal segments, calculated and compared with each other. It is shown that W(t) can indeed be considered stationary, and thus Y(t) can be considered periodically correlated. This analysis has been applied to model wind and wave data from several locations in the Mediterranean Sea. It turns out that the spectrum of W(t) is very weakly dependent on the site, a fact that might be useful for the geographic parameterization of wind and wave climate.