Analytical Techniques for the Doppler Signature of Sea Surfaces in the Microwave Regime—II: Nonlinear Surfaces

This paper extends the results of a previous work by combining hydrodynamic and electromagnetic analytical models for the simulation of the ocean Doppler spectrum at microwave frequencies. We consider weakly nonlinear sea surfaces after the choppy wave model and incorporate them in classical and unified scattering models, namely, the Kirchhoff and weighted curvature approximations. We show that statistical expressions can be obtained for the Doppler spectrum in a way similar to the case of linear surfaces. As expected, the nonlinear nature of the sea surface dramatically impacts the Doppler spectrum at moderate to large incidence angles, with a shift of the central frequency and a broadening of the spectrum. Monte Carlo comparisons are performed with the Creamer model, which is frequently used to describe weakly nonlinear sea surfaces but does not enjoy a statistical formulation for the Doppler characteristics. The same qualitative behavior is found but some quantitative differences are found and discussed.