Time and space scales of significant wave heights

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Abstract
This paper presents a study of the temporal and spatial variability of the significant wave height (Hs) based on stationarity and correlation (spectral) analyses. A sea state is defined as a stationary state of a piecewise stationary stochastic random wave process. Rupture detection, i.e., detection of abrupt changes in Hs, is used to identify the stationary components of the wave process. A sea state is characterized by its energy (i.e., Hs) and by its duration of stationarity (spatial analysis) and length of stationarity (temporal analysis). Intensive in situ measurements of Hs and Geosat radar altimeter data are used to study the temporal and spatial Hs scales at two locations, in the North Sea and in the equatorial Atlantic.The stationarity analysis leads to the following results; (1) duration and length show a great variability and are distributed according to exponential probability laws, (2) Hs is distributed according to a Gumbel probability law in both time and space, (3) energy and duration and energy and length can be considered as statistically independent, and (4) the duration and length distributions present very similar nondimensional statistical characteristics. Stationary state detection can also be used to filter the high‐frequency geophysical and/or instrumental noise from the Hs variations. A spectral analysis is performed on the raw Hs, the stationary states, and the residual. The salient features of the results are summarized as follows: (1) for both locations, the spectra of the filtered data are consistent with a power law dependence on the wavenumber or frequency, (2) the spectral dependence is nearly the same for time and space, which suggests a mean linear dispersion relation for Hs, (3) the slope of the spectra are close to the −5/3 turbulence cascade (−1.74 for the North Sea, −1.69 for the equatorial Atlantic), and (4) the residual spectrum is nearly a white noise spectrum indicating the quality of the stationary state detection filtering.