Calculation of radar backscatter modulations from internal waves

Calculations of microwave backscatter from the ocean surface using the small-perturbation method (first-order Bragg approximation), a modified Kirchhoff approximation, and a two-scale composite model derived from the modified Kirchhoff expression are described, and predictions of the modulation in the cross section induced by internal wave features are presented. The calculations demonstrate that the modified Kirchhoff approximation and the composite model yield equivalent cross sections if the cutoff wave number separating the long- and short-wavelength regions in the composite model is chosen to be roughly one-third the Bragg wave number. The interaction of internal waves and surface waves, assumed to modulate an equilibrium wind wave spectrum over wavelengths extending from about 0.1 to 10 m, results in significant perturbations to the L band (24 cm) and X band (3 cm) cross sections at incidence angles from 23° to 50°. These calculations indicate that the large modulations observed in X band synthetic aperture radar images of internal waves are due, at least in part, to the tilting of the X band Bragg scatterers by the internal-wave-modulated long-wavelength surface waves.