A radar equation for snow-covered targets in radar altimetry

Waveform simulators are commonly used to retrack ice surface elevations from radar altimeter observations. Most simulators apply the radar equation to estimate backscattered power, but this formulation often overlooks refraction at the snow surface. Because snow alters the propagation direction of the radar pulse, refraction modifies both the incidence angle and the geometry of the propagating wavefront.

In this study, we derived a modified radar equation for snow-covered ice surfaces that explicitly accounts for refraction. Implementing this formulation within a waveform simulator produces waveforms that are systematically dampened and broadened relative to those generated using the conventional radar equation. Two main mechanisms account for these differences: (1) changes in wavefront geometry that reduce the returned power by a factor proportional to the square of the snow's refractive index, and (2) decreased incidence angles that increase the returned power at increasing off-nadir distances.

Our results suggest that neglecting refraction in waveform-simulator-based retracking can introduce biases in track points, as the retracker may compensate for unmodeled refraction by overestimating surface roughness. These findings underscore the importance of incorporating refraction into radar altimetry forward models to achieve accurate measurements over snow-covered ice.