High-Frequency Radar Cross Section of the Ocean Surface With Arbitrary Roughness Scales: A Generalized Functions Approach

A correction term for electromagnetic scattering from the ocean surface with large roughness scales in the HF band is proposed. A generalized functions' method has been employed to obtain the operator equation of the electric field over the ocean surface. Using a dipole antenna with a pulsed sinusoidal signal at the transmitter and employing Fourier series and perturbation theory expansions of the ocean surface, three expressions were derived for the electric field up to the second order, with one of them being a correction term for the first order for large roughness scales. Through a cross section analysis, it is observed that the additional term would represent waves with both large heights and wavelengths but small slopes. This allows for the analysis of extreme wave events using HF radar, which was limited by previously derived small heights and small slope methods.