Two‐Dimensional Spectra of Radar Returns from Sea: 1. Theoretical and Numerical Study of the Group Line

Abstract

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.

Two‐Dimensional Spectra of Radar Returns From Sea: 2. Analysis of the Group Line From Experimental Data

“…For azimuth angles below 30 • , the slope remains almost unchanged. This completes the justification of the use of a one-dimensional model in Platzer et al (2019) to predict the characteristics of the group lines in up-wave conditions. For large azimuth angles, the group line is still observable, even though the energy in first-order dispersion relation is drastically reduced, as already pointed out in Figure 4 of Plant and Farquharson (2012).…”

“…Some results about dispersion diagrams obtained by applying a two-dimensional Fourier transform to radar returns acquired by high-resolution radar systems have been presented in this paper and in the companion paper Platzer et al (2019). In the latter, a way to estimate the slope of the group line has been proposed and applied here to the experimental data acquired during the MARLENE campaign Fabbro et al (2017).…”

“…It has also been pointed out in Platzer et al (2019) that the duration of recorded time series, typically 1 min here, does not provide a high enough resolution in frequency to accurately describe the group line. Therefore, an empirical formula has been established to take this inaccuracy into account, which predicts the average value that would be computed from a 2-D Fast Fourier Transform (FFT), namely,…”

“…Since the backscattered field is recorded at less than 1,000 radar cells in range, a zero-padding method is used to improve the wavenumber resolution of the 2-D FFT. In accordance with the theoretical results presented in Platzer et al (2019), a mask is applied to filter out values of outside the interval [ u , p ]. The weighted average frequency of the group line is then derived from where (k, ) is the cut of the dispersion diagram along the axis for a given wavenumber k. The results of the data processing of the two images presented in (2) almost coincide and have the same decreasing behavior.…”

“…surfaces are described by a Pierson-Moskowitz spectrum combined with Creamer's approach Creamer et al (1989), and an analysis of Doppler spectra has been performed . The dispersion diagram obtained from such numerical simulations (L-band, horizontal polarization), without breaking, also provides a group line Platzer et al (2019), the slope of which differs from the average Doppler velocity. In the same way, numerical simulations based on nonlinear Schrödinger equation do exhibit such features for weakly nonlinear one-dimensional surfaces Krogstad and Trulsen (2010).…”