Susanne Støle-Hentschel

An improved understanding of wave breaking is still a hot topic owing to its relevance in the coupling of ocean and atmosphere. Multiple communities are focusing on numerical simulations of the fully coupled two-phase flow, the validation of such models remains challenging. Herein, we demonstrate how coherent marine radars can help to shed light on how different wave and wind parameters influence the evolution of waves towards breaking in the nearshore. The interpretation of the results is undermined by SWASH simulations of shoaling waves for different wave spectra and two beaches and simulations of radvarimages of these waves. Data of three independent measurement campaigns shows that the shoaling characteristics are strongly influenced by the wave steepness, relative depth the Ursell number and the wind. The influence of individual parameters cannot be isolated, but must be understood in its entirety.

The study analyzes the microwave imaging of shoaling nearshore surface gravity waves during the process of steepening and breaking over two beaches for a wide range of environmental conditions. Data are sourced from two coherent X–band radars, operating under low grazing angle conditions. Using automatic wave tracking on the radar images, the evolution of individual waves is followed over hundreds of meters. The extracted backscatter intensity and Doppler speed form distinct patterns that reveal a non-negligible dependence on environmental conditions. Statistical representations of the backscattered signal are presented by conditional Doppler speed–Intensity histograms. These are composed of ensembles extracted at the radar-facing fronts. This technique helps to focus on the steepening of the wave and minimizes the impact of extremely low-grazing angle imaging mechanisms which are still not well understood. The combination of wind speed and direction as well as initial wave steepness, local depth, and degree of non-linearity contribute to the shapes and centroid positions of the histograms. The backscatter signature exhibited by breaking waves remained consistent and similar throughout all datasets. The results are consistent across radars. Before consolidating the findings, it is imperative to conduct a further investigation of radar imaging of non-linear wave dynamics in shallow water to eliminate any possible influence of imaging mechanisms.

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The work introduces the directional modulation transfer function (MTF) to improve the estimate of direction wave spectra from radar images of ocean waves. In contrast to the established MTF, the presented MTF better captures the directional distribution of wave energy when the spreading is high.

Observations of nearshore waves and wave breaking with two different coherent radars at X-band and two different beaches are presented and compared. These were mostly under low grazing angle conditions, with a wide span of wave and wind conditions, including varying steepness, dispersion and degree of non-linearity, as well as breaking and non-breaking waves. While some of these data has been presented before, the present work offers a unique perspective in comparing observations, which could allow an improved understanding of the effect of environmental conditions and system parameters, with the long term goal of assessing the performance of backscattering models. The analysis includes statistical methods to wave ensembles, as well as individual wave evolution as they shoal and progress towards the shoreline. Observations among systems compare reasonably well, and most of the results can be interpreted with existing backscattering models. However, some discrepancies are found, which require a more in depth analysis.

We propose a methodology for despiking ocean surface wave time series based on a Bayesian approach to data-driven learning known as Gaussian process (GP) regression. We show that GP regression can be used for both robust detection of erroneous measurements and interpolation over missing values, while also obtaining a measure of the uncertainty associated with these operations. In comparison with a recent dynamical phase space–based despiking method, our data-driven approach is here shown to lead to improved wave signal correlation and spectral tail consistency, although at a significant increase in computational cost. Our results suggest that GP regression is thus especially suited for offline quality control requiring robust noise detection and replacement, where the subsequent analysis of the despiked data is sensitive to the accidental removal of extreme or rare events such as abnormal or rogue waves. We assess our methodology on measurements from an array of four collocated 5-Hz laser altimeters during a much-studied storm event in the North Sea covering a wide range of sea states.

We investigate how the extreme wave statistics of a combined windsea and swell appears to be different from the extreme wave statistics of the corresponding windsea and swell partitions. We consider the situation of following long-crested windsea and swell in laboratory experiments and in simulations using a high-order spectral method (HOSM). We also consider the situation of short-crested windsea and swell crossing at nearly right angle, corresponding to the sea state when the Prestige accident happened, in hindcast simulations combined with HOSM. For cases when the two wave systems do not interact much, the combined wave system appears to be more Gaussian than the corresponding partitioned wave systems, consistent with the central limit theorem. This result is found for kurtosis and exceedance probability of envelope and crest height.

Extreme wave statistics of unidirectional and counter-propagating seas are investigated, for the special case of long-crested irregular waves, with laboratory experiments and with numerical simulations using the higher order spectral method. Both the kurtosis of the surface elevation and the exceedance probability of the crest height are larger in unidirectional seas than in counter-propagating seas. Numerical simulations show that even a small amount of wave energy travelling against an essentially unidirectional wave system can significantly reduce the kurtosis of the surface elevation.