A nonstationary stochastic model for long‐term time series of significant wave height

Abstract

In this paper an attempt is initiated to analyze long‐term time series of wave data and to model them as a nonstationary stochastic process with yearly periodic mean value and standard deviation (periodically correlated or cyclostationary stochastic process). First, an analysis of annual mean values is performed in order to identify overyear trends. It turns out that it is very likely that an increasing trend is present in the examined hindcast data. The detrended time series Y(τ) is then decomposed, using an appropriate seasonal standardization procedure, to a periodic mean value μ(τ) and a residual time series W(τ) multiplied by a periodic standard deviation σ(τ) of Y(τ)=μ(τ)+σ(τ)W(τ). The periodic components μ(τ) and σ(τ) are estimated and represented by means of low‐order Fourier series, and the residual time series W(τ) is examined for stationarity. For this purpose, spectral densities of W(τ), obtained from different‐season segments, are calculated and compared with each other. It is shown that W(τ) can indeed be considered stationary, and thus Y(τ) can be considered periodically correlated. This analysis has been applied to hindcast wave data from five locations in the North Atlantic Ocean. It turns out that the spectrum of W(τ) is very weakly dependent on the site, a fact that might be useful for the geographic parameterization of wave climate. Finally, applications of this modeling to simulation and extreme‐value prediction are discussed.