Joint Time-Frequency Analysis of Small Scale Ocean Storms via the Harmonic Wavelet Transform

Abstract

The paper focuses on utilizing the Harmonic Wavelet Transform (HWT) for estimating the evolutionary power spectrum (EPS) of sea storms. A sea storm is considered herein as a non-stationary stochastic process with a time duration of the order of days. The storm evolution can be represented in three stages: the growth, the peak and the decay. Specifically, during growth the intensity of the wave increases with time until reaching the apex, and then decreases. The analysis is carried out by processing the time series of the free surface elevation recorded at the Natural Ocean Engineering Laboratory of Reggio Calabria, Italy. A peculiarity of the NOEL lab is that a local wind from NNW often generates sea states consisting of pure wind waves that represent a small scale model, in Froude similarity, of ocean storms (www.noel.unirc.it). The main focus of the paper is, first, to acquire a joint time-frequency representation of the storm via estimating the associated EPS, and second, to explore the variability in time of the spectrum and of the dominant frequencies of the storm. The EPS is estimated by utilizing a non-stationary record of the sea surface elevation during a storm recorded at NOEL lab. Further, in this paper, the standard representation of sea storms is also considered. That is, the non-stationary process is represented as a sequence of stationary processes (sea states or buoy records), each of them characterized by an intensity defined by a significant wave height Hs and by a duration Δt. During the time interval Δt the sea surface elevation is considered stationary and the frequency spectrum may be computed via the Fast Fourier Transform (FFT). Results obtained following this procedure, which can be considered essentially as a brute-force application of the short-time FT, are compared with those obtained via a HWT based joint time-frequency analysis.