Continuous Peak Period Estimates from Discrete Surface-Wave Spectra

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.