The work presented here aims at interpreting the pattern observed at low frequencies in wavenumber-frequency (k, ) representations (dispersion diagrams) of radar returns from sea surface. This pattern is sometimes referred to as the "group line" in the literature and is supposed to result from the nonlinear behavior of the signal with respect to surface profile. To confirm this assumption, we have calculated the patterns generated by various nonlinear terms of second order in sea surface height. It is shown that the resolution in frequency of most data is not sufficient to allow for an accurate representation of the group line through an FFT. A methodology is proposed to define an average slope of the group line, which can be interpreted in terms of velocity.
Wavenumber-frequency spectra are obtained by performing a two-dimensional Fourier transform of range-time normalized radar cross-section (NRCS) or Doppler velocity maps. In such diagrams, some energy is present at low space-time frequencies, resulting from the nonlinear behavior of the measured quantity related to the sea surface geometry. This feature is called the group line, since for a narrow-band wave packet the energy is concentrated along a straight line with group velocity as slope. Which physical nonlinear process generates the group line remains an open question. Breaking waves have been proposed as the most probable contributor. However, numerical simulations from weakly nonlinear surfaces without breaking events and experiments performed at low winds also provide such feature. In a companion paper, a theoretical and numerical analysis has permitted to predict the energy distribution of the group line depending on the kind of nonlinearity. It provides some means to characterize a group line in a rigorous way. In this paper, it is used to analyze the group lines derived from the experimental MARLENE data. The group lines computed from the backscattering amplitude behave as the one of the square of sea surface slopes. The analysis of the Doppler velocities provides similar results, which significantly differ from what is expected if breaking waves are the main contributors and do break at velocities reported in the literature. Our results suggest that the group line mainly reflects the asymptotic behavior of the scattering amplitude at grazing incidence, of which the leading nonlinear term is proportional to the square of surface slope.
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