Scattering From Nonlinear Gravity Waves: The “Choppy Wave” Model

Abstract

To progress in the understanding of the impact of non-linear wave profiles in scattering from sea surfaces, a non-linear model for infinite depth gravity waves is considered. This model, termed the "Choppy Wave Model" (CWM), is based on horizontal deformation of a linear, reference random surface. It is numerically efficient and enjoys explicit second-order statistics for height and slope, which makes it well adapted to a large family of scattering models. We incorporate the CWM into a Kirchhoff or Small-Slope Approximation and derive statistical expressions for the corresponding incoherent cross section. We insist on the importance of "undressing" the wavenumber spectrum to generate a non-linear surface with a prescribed spectrum. Interestingly, the inclusion of non-linearities is found to be practically compensated by the spectral undressing process, an effect which might be specific to the CWM and needs to be investigated in the framework of fully non-linear models. Accordingly, the difference between the respective NRCS is rather small. The most noticeable changes are faster azimuthal variations and a slight increase of the radar returns at nadir. A statistical analysis of sea clutter in the framework of a Two-Scale Model is also performed at large but nongrazing incidence. It shows a pronounced polarization dependence of the distribution of large backscattered amplitudes, the tail being much larger in horizontal polarization and for small resolution cell. Surface non-linearities are shown to increase the tail of the amplitude distribution, as expected. Less obviously, their relative impact is found lesser in horizontal polarization. This raises the question of the actual contribution of non-linearities in radar sea spikes at nongrazing angles.

An analytical model for the description of the full‐polarimetric sea surface Doppler signature

“…Nouguier et al . [] used the iterative procedure proposed by Elfouhaily et al . [] to perform the undressing.…”

“…Recently, the use of the Choppy Wave Model (CWM) in combination with the weighted curvature approximation [ Nouguier et al ., ] in the context of sea Doppler spectrum calculation has shown significant advantages in terms of analytical simplicity and numerical efficiency. However, the Weighted Curvature Approximation (WCA) does not provide a full‐polarimetric description of the sea surface Doppler signature.…”

Sea Surface Microwave Scattering at Extreme Grazing Angle: Numerical Investigation of the Doppler Shift

“…The geometrical transformation operated by the CWM induces a modification of the original prescribed spectrum, a process which is referred to as "dressing." An appropriate generation of CWM would require a preliminary step of "undressing" the reference spectrum, a procedure which is discussed in [29] and [35]. The dressing of the spectrum results in a small increase of the high-frequency components of the wavenumber spectrum but is not expected to impact significantly the shape of the normalized Doppler spectrum.…”

Scattering Analysis for Ship Kelvin Wakes on Two-Dimensional Linear and Nonlinear Sea Surfaces

“…In this paper, we give two kinds of nonlinear sea surfaces, i.e., CWM model and Creamer (2) model. For the CWM model, it is analytically tractable, numerically efficient, and robust to the inclusion of high frequencies and is based on horizontal rather than vertical local displacement of a linear surface [11]. For the Creamer (2) model, it is based on the Hamiltonian formalism under the weak wave-turbulence theory and is performed through the nonlinear transformation of the Hilbert transform of the linear surface [12,13].…”