The average impulse response of a rough surface and its applications

TLDR

Short‑pulse scattering from statistically random planar surfaces underpins modern radar altimetry, yet the convolutional model’s assumptions remain largely unexamined. This study develops a theoretical model for short‑pulse scattering from such surfaces with the aim of improving radar altimetry performance. The authors derive simplified expressions for the impulse response and average backscattered power at near‑normal incidence, yielding a closed‑form solution that enables radar antenna pointing‑angle determination and altitude‑bias correction for surface‑roughness effects. The closed‑form solution eliminates the need for two‑dimensional surface integration, and its application to a two‑frequency system suggests a combined long‑pulse altimeter and dual‑frequency approach.

Abstract

This paper is concerned with the theoretical model for short pulse scattering from a statistically random planar surface with particular application to current state of the art radar altimetry, A short review of the assumptions inherent in the convolational model is presented. Simplified expressions are obtained for both the impulse response and the average backscattered power for near normal incidence under the assumptions common to satellite radar altimetry systems. In particular, it is shown that the conventional two-dimensional surface integration can be reduced to a closed form solution. Two applications of these results are presented relative to radar altimetry, namely, radar antenna pointing angle determination and altitude bias correction for pointing angle and surface roughness effects. It is also shown that these results have direct application to the analysis of the two frequency system proposed by Weissman, and a possible combined long pulse altimeter and two frequency system is suggested.