Modeling non-stationary extreme waves using a point process approach and wavelets
Modeling non-stationary extreme waves using a point process approach and wavelets
复制标题
使用点过程方法和小波对非平稳极端波浪进行建模
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
P. Prinos
中科院分区：
文献类型：
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作者：
P. Galiatsatou;P. Prinos
本文建立了一个考虑季节性的极值分析统计模型。将该模型应用于N.爱琴海为了建立该模型，使用非平稳点过程，该过程除了包含时变阈值和周期为一年的谐波函数之外，还包含通过小波变换估计的分量μw（t）。小波变换在本研究中具有双重作用。它通过小波全局和尺度平均功率谱检测信号的显著“周期性”，然后用于重构由这些显著特征表示的时间序列的部分μw（t）。尝试了一些候选模型，其中将μw（t）纳入其位置和尺度参数。为了避免过度参数化，自动模型选择过程的基础上赤池信息准则进行。通过诊断图以图形方式评估获得的最佳模型。最后，“聚合”回报水平与回报期为20年，50年和100年，以及随时间变化的分位数估计，结合小波分析和泊松过程模型的结果，确定一个显着减少回报水平估计的不确定性，相比更简单的非平稳模型。
In the present paper a statistical model for extreme value analysis is developed, considering seasonality. The model is applied to significant wave height data from the N. Aegean Sea. To build this model, a non-stationary point process is used, which incorporates apart from a time varying threshold and harmonic functions with a period of one year, a component μw(t) estimated through the wavelet transform. The wavelet transform has a dual role in the present study. It detects the significant “periodicities” of the signal by means of the wavelet global and scale-averaged power spectra and then is used to reconstruct the part of the time series, μw(t), represented by these significant features. A number of candidate models, which incorporate μw(t) in their location and scale parameters are tried. To avoid overparameterisation, an automatic model selection procedure based on the Akaike information criterion is carried out. The best obtained model is graphically evaluated by means of diagnostic plots. Finally, “aggregated” return levels with return periods of 20, 50 and 100 years, as well as time-dependent quantiles are estimated, combining the results of the wavelet analysis and the Poisson process model, identifying a significant reduction in return level estimation uncertainty, compared to more simple non-stationary models.