A combined surface-and volume-scattering model for ice-sheet radar altimetry

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Abstract
Over the last 15 years, satellite-altimeter data have been used to produce surface-elevation maps of the Greenland and Antarctic ice sheets with a 2 m accuracy. Analysis of Seasat and Geosat cross-over points showed that satellite altimeters can measure changes in the mass balance of the ice sheets. The retracking algorithm used to extract surface elevations from Seasat and Geosat return wave forms is based upon a modified form of the Brown surface-scattering model. Recent work has shown that altimeter wave forms over higher-altitude regions of the ice sheets are affected by sub-surface volume-scattering. Here, we develop a theoretical model for altimeter return wave forms over the ice sheets that is based on a combination of surface-and volume-scattering. By approximating the altimeter’s antenna pattern and transmitted pulse shape with Gaussian functions, we derive a closed-form analytical solution for the return-power volume-scattered from beneath the ice-sheet surface. We then combine the volume-scattering model with the Brown model and apply it to average wave forms from the Greenland and Antarctic ice sheets. The results show that the combined model accurately describes variations in altimeter wave-form shapes that are produced by differing contributions of surface-and volume-scattering to the received power. The combined model is then used to simulate return wave forms from a dual-frequency altimeter. The simulation shows that a two-frequency system can provide quantitative estimates of the absorption and scattering coefficients for near-surface snow.