First-order theory and analysis of MF/HF/VHF scatter from the sea

Scatter from the sea near grazing from MF through VHF is analyzed in this paper. Results based on the compensation theorem show that the dependence upon the grazing angles, as well as upon frequency, range, and the effective surface impedance, can be removed for vertical polarization as the familiar "Norton attenuation factors." Time variation of the surface is included, and results are derived for both the average received power and its spectral density. The first-order dispersion relationship for gravity waves is used to show that the received spectrum from a patch of sea consists of two discrete Doppler shifts above and below the carrier, predictable from simple Bragg diffraction considerations. Using the Phillips wind-wave model as an upper limit for wave heights, estimates for
\sigma^{0}
(radar cross section per unit area) of - 17 dB are obtained near grazing. Both the magnitude of
\sigma_{\upsilon\nu}^{0}
predicted from theory and the nature of the received spectrum are compared with measurements, and the agreement supports the theory on both counts. Finally, the use of MF/HF radars for measuring sea state is suggested and discussed.