Refraction Considered Radar Equation for Snow-Covered Sea Ice Surface

Interpretation of the waveform observed from satellite microwave radar altimeters is essential for the estimation of the thickness of snow and sea ice. Previous studies have relied on the radar equation to interpret backscattered signals from the snow-covered ice surface; however, that equation does not account for refraction at the snow surface, which changes the direction of the radar pulse. Therefore, this study derived a modified radar equation for a snow-covered sea ice surface that explicitly considers refraction. Compared to the ordinary equation, the modified equation produces different return powers and waveform shapes. Two primary mechanisms drive these differences: (1) changes in wavefront geometry, which reduce the return power by the square of the snow refractive index, and (2) decreased incidence angles at the ice surface, which amplify the return power with increasing distance from nadir. The combined effect resulted in a dampened and broadened waveform, which can influence the interpretation and retracking of the waveform. Therefore, it is recommended that this modified radar equation be implemented to update the existing waveform simulators.