Second-Order Bragg Scattering Theory for Time-Evolving Nonlinear Sea Surfaces

A facet-based second-order Bragg scattering theory for nonlinear sea surface scattering is proposed in this letter. The discretized sea surface is a composition of facets with appropriate size, which is large enough in comparison with the radar wavelength and sufficiently small as it can still be regarded as a plane. These small facets are described as a superposition of a group of cosine waves modulated by capillary waves with Bragg and second-order Bragg resonance wavelengths. The contribution of Bragg scattering, second-order Bragg scattering, and their interactions are considered using integral term transformation. The backscattering coefficients from the 2-D Creamer II sea surface in the C- and X-bands are comprehensively analyzed and compared between radar measurements and numerical predictions, demonstrating the capabilities of the theory. The Doppler spectrum results indicate that both the nonlinear nature of the sea surface and the second-order Bragg scattering effects could significantly broaden the Doppler spectrum and shift the Doppler centroid.