High-frequency radar cross-sections of swell-contaminated seas for a pulsed waveform

The first- and second-order monostatic cross-sections of swell-contaminated seas for high-frequency ground wave pulsed radar operation are derived from the fundamental electric field equations. In this case, the ocean surface, a mixture of both swell and wind wave components, is first represented with a Fourier series. In one of the two approaches used, the total Fourier coefficient is expanded as a linear sum of the contribution from swell and wind waves without considering the possible interaction between the two regimes; whereas in a second, more general situation, the analysis includes coupling effects between the wind waves and swell. Then, the corresponding electric fields received from the swell-contaminated sea surface are obtained. A Fourier transform of the autocorrelation of the electric fields gives the Doppler power spectral density (PSD), and a comparison between this PSD and monostatic radar range equation yields the radar cross-sections. Simulation shows that the assumption incorporating the coupling effects leads to results that better agree with historical field observations. Overall, the model proposed here not only lays a solid foundation for the development of future swell inversion algorithms, but also reveals the existence of non-linear energy transfer between swell and wind waves from a new perspective.