Correction of Amplitudes of Bragg Lines in the Sea Echo Doppler Spectrum of an Ocean Radar

Abstract

Amplitudes of Bragg lines in the Doppler spectrum of high frequency or very high frequency (VHF) ocean radar sea echoes are important because they are used in normalizing the second-order scattering when calculating ocean wave spectra. These amplitudes were originally formulated using the first-order perturbation theory and are modified if the perturbation is expanded to the third order. Although the magnitude of the amplitude correction is of the same order as the second-order scattering, the effect has not been considered. This study formulated and investigated the correction. The formulation includes the effects of double scattering, bound waves, and second-order tilt modulation. If triple scattering is considered and the sea surface is assumed to be a perfect conductor, the backscattered field for a grazing incidence diverges. Therefore, the sea surface is treated as a finite conductor and the effective sea surface impedance is considered. Two types of model are constructed here. One includes triple scattering and the other does not. The correction predicted by the model, including triple scattering, is as large as the first-order radar cross section; therefore, this model is inappropriate. The author presents the method for estimating ocean wave spectra based on the third-order theory and describes the method of experiment that would be required to verify the theory. This study is consistent with the previous studies that pointed out radar-estimated wave height was lower than buoy-measured wave height at high sea conditions. Therefore, the third-order amplitude correction is important for the estimation of wave height by ocean radar, especially at high sea states and for VHF radar.