A nonstationary stochastic model for long-term time series of significant wave height
A nonstationary stochastic model for long-term time series of significant wave height
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DOI：
10.1029/94jc01022
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发表时间：
1995-08
影响因子：
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通讯作者：
G. Athanassoulis;Christos Stefanakos
中科院分区：
文献类型：
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作者：
G. Athanassoulis;Christos Stefanakos
本文尝试对波动数据的长期时间序列进行分析，并将其建模为具有年周期均值和标准差的非平稳随机过程(周期相关或循环平稳随机过程)。首先，对年度平均值进行分析，以确定年度趋势。事实证明，在经过审查的后播数据中，很可能出现了增加的趋势。然后，使用适当的季节标准化过程将去趋势时间序列Y(τ)分解为周期平均值μ(τ)和剩余时间序列W(τ)乘以Y(σ(τ)W(τ)=μ(τ)+σ(τ)W(τ)的周期标准偏差。用低阶傅立叶级数估计和表示周期分量μ(τ)和σ(τ)，并检验剩余时间序列W(τ)的平稳性。为此，计算了不同季节段的W(τ)的谱密度，并进行了比较。结果表明，W(τ)确实可以被认为是平稳的，因此Y(τ)可以被认为是周期相关的。这一分析已应用于北大西洋五个地点的后向投射波数据。结果表明，W(τ)的谱对场地的依赖性很弱，这一事实可能有助于波浪气候的地理参数化。最后，讨论了该模型在仿真和极值预测中的应用。
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.