A theory on the distribution function of backscatter radar cross section from ocean waves of individual wavelength

A new and simple method of interpreting the “distribution” of the backscatter radar cross section (RCS) from ocean waves of individual wavelength is presented. Using the Kirchhoff scattering (Physical Optics) theory, the “cumulative” RCS from the ambient waveheight spectrum is first computed as a function of the wavenumber. Differentiating this cumulative RCS yields the distribution function of the RCS from ocean waves of different wavenumbers. The present study shows, as a general feature, that the maximum RCS contribution tends to come from the ocean waves of wavenumbers closer to the Bragg wavenumber as the radar incidence angle increases. Under low wind speeds (~2 m/s) and at incidence angles between 200 and 45°, the dominant RCS contribution at both C-band and L-band comes from ocean waves of wavenumbers close to the Bragg wavenumber. Under intermediate to high wind speeds (~10-15 m/s) and at the small incidence angle of 200, the radar backscatter is dominated by long ocean waves with little contribution from the Bragg waves at both bands. At the intermediate incidence angles (~35° to 45°), the RCS distribution is centered at wavenumbers near the Bragg wavenumber at all wind speeds from 2 m/s to 15 m/s. These features are more pronounced at C-band than at L-band. The present theory is based on the Kirchhoff scattering model, and as such, its validity may also be limited to a range of small to intermediate incidence angles where the polarization effect is not very significant. The RCS distribution is evaluated for the ambient sea surface and the surface perturbed by varying currents induced by the interaction between the current and bottom topography