Radar altimeters were originally designed to study ocean geodynamics, where the scattering processes are governed entirely by the surface features. These same altimeters have recorded data from over the polar ice sheets, where the scattering processes cannot in general be limited to surface properties. Radar pulse penetration, which gives rise to volume scattering, must also be accounted for in these return waveforms. This pulse penetration affects the altimeter range measurements as well as other information that is derived from the altimeter waveform data. To aid in the study of pulse penetration effects, a waveform model for combining surface and volume scattering effects in the estimation of the radar altimeter returns recorded over continental ice and snow is developed and discussed. The surface scattered waveform model is based on the well-known impulse response method which is capable of accounting for arbitrary altitude, beamwidth, pulsewidth and pointing angle. The newly formulated volume scattered waveform model is also an impulse response based method which differs from previous versions in that it can also be applied to a general altimeter configuration. The two models are time registered and then added together in an arbitrary ratio representing the relative contributions of surface and volume scattering to the overall return power waveform. The combined model can be used to study actual altimeter waveforms by varying the important parameters, including surface roughness and effective extinction coefficient. The capabilities and limitations of this new combined model are also discussed and guidelines for its use are detailed. The combined model is tested by comparing it to the Multimode Aircraft Radar Altimeter (MARA) data which were recorded over and around the Greenland ice sheet in September 1991. Evaluation of this averaged waveform data identified problems that were encountered with the MARA design. A number of techniques are developed in an effort to account for and correct these problems, but none of these attempts were completely successful. The 1991 MARA data are considered usable for waveform analysis, but with the understanding that some error may be present in the final results. The MARA data obtained from the Greenland ice sheet are analyzed for estimates of surface roughness, effective extinction coefficient and ratio of surface to volume scattering strengths. A simple optimization method is employed which achieves a least-squares fit of the combined model to the altimeter data. The result is an estimate of these parameters as a function of location on the ice shelf. To the author's knowledge, this is the first time both surface- and volume-related parameters have been estimated simultaneously from Ka-band radar data. / Ph. D.