Continuous peak period estimates from discrete surface-wave spectra

Pieter B. Smit, Galen Egan, Isabel Houghton
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Abstract

Peak periods estimated from finite resolution frequency spectra are necessarily discrete. For wind generated surface gravity waves, conflicting considerations of robust (quasi)-stationary statistics, and high spectral resolution, combined with the inverse relation between frequency and period, this typically implies that swell periods (above 10 s) are resolved at best at 𝒪(1) s intervals. Here we consider a method to improve peak period estimates for finite resolution spectra. Specifically, we propose to define the peak period based on continuous spectra derived from a spline-based interpolation of the discretely sampled monotone cumulative distribution function. The method may directly be applied to existing discrete spectra—the original time-domain data (which may not be available) are not required. We compare reconstructed spectra and derived peak periods to parametric shapes and field data. Peak estimates are markedly improved, allowing for better tracking of e.g., swells. The proposed method also marginally improves spectral levels and shape for a given discretely sampled estimate.
从离散面波频谱估算连续峰值周期
根据有限分辨率频谱估算的峰值周期必然是离散的。对于风力产生的海面重力波来说,稳健(准)稳态统计和高频谱分辨率这两个相互矛盾的考虑因素,再加上频率和周期之间的反比关系,通常意味着涌浪周期(10 秒以上)最多只能以𝒪(1) 秒的间隔来分辨。在此,我们考虑采用一种方法来改进有限分辨率频谱的峰值周期估算。具体来说,我们建议根据离散采样单调累积分布函数的基于样条插值的连续光谱来定义峰值周期。该方法可直接应用于现有的离散光谱--不需要原始时域数据(可能无法获得)。我们将重建的光谱和推导的峰值周期与参数形状和现场数据进行了比较。峰值估计有了明显改善,从而可以更好地跟踪涌浪等。对于给定的离散采样估计值,所提出的方法还能略微改善频谱水平和形状。
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