Shallow-Water Observations of Rogue Waves, Height Distributions, and Spectral Moments

Abstract Wave height distributions in the shallow nearshore region are mainly inferred from idealized laboratory experiments or numerical studies. Here, we show that these findings do not represent real-world conditions of swell-dominated shallow nearshore regions. Long-term, high-resolution pressure records are converted to surface elevation time series based on a shallow-water nonlinear transfer function. The fixed-point observations cover a wide range of wave nonlinearities, quantified by the Ursell number, 2 < Ur < 245. Wave height distributions, crest height distributions, and spectral moments are inconsistent with published results from laboratory experiments. The crest height distribution of the linear portion of the observed waves is well represented by the Rayleigh distribution. This changes to a Weibull distribution for higher nonlinearities, and crests are taller than in a Gaussian sea. For fully nonlinear waves, the distribution curve becomes slightly convex, indicating that rogue crests, η / H s > 1.25, are more frequent than a Weibull fit through the bulk of the data would predict. Wave height distributions for nonlinear waves follow a composite Weibull distribution, and large waves occur less frequently in shallow water compared to deep water. Skewness increases with wavefield nonlinearity. Kurtosis remains nearly unaffected by shoaling. Kurtosis is a weak function of skewness with n ≤ 1 being smaller than second-order wave dynamics predict ( n = 2). On average, maximum crest height increases with kurtosis. This applies, to a lesser degree, for maximum wave heights. Rogue crests, η / H s > 1.25, occur about 4 times more frequently in nonlinear wave conditions than in linear waves. Rogue waves, H / H s > 2.2, are extremely rare with return periods of several weeks to months. Significance Statement The nearshore region provides the link between the land and the ocean. Surface waves in the shallow coastal ocean are significantly different to waves in the open ocean. Nevertheless, many coastal wave applications rely on results based on open ocean data, or idealized laboratory experiments and limited numerical simulations. Here, we present real-world results of distributions of wave heights, wave shape, and occurrence rates of rogue waves and rogue crests, based on long-term observations within 1 km of the beach. These results can be used to better parameterize wave-related exchange processes as well as warnings of extreme events.