where c = the speed of light
The altimeter product of primary interest to scientists is the Altimeter range measurement, which, when subtracted from a precise satellite orbit referenced to a mathematical ellipsoid gives a measure of the surface height above that reference ellipsoid. Subtracting the geoid height which is a good approximation of sea level from the surface height yields a surface height with respect to sea level.
The altimeter measures the range using an onboard tracker, This instrument receives and filters the return signal into time bins of varying resolution. The output from the filter, referred to as the waveform, gives information on the surface characteristics within the range window. The altimeter maintains acquisition by keeping the signal within the range window. The tracker predicts the range by centering the waveform at the pre-designated tracking gate. The onboard system can predict precise ranges for the normally-distributed ocean surfaces. Typical ocean waveforms have a sharp ramp and slowly declining trailing edge, where the mid-point of the ramp is centered at the tracking gate.
Over ice surfaces, the performance of the radar altimeters differs significantly from the performance over oceans due to the higher slopes of the ice surface, variations in the surface reflection and penetration of the radar signal in the snow surface, and generally irregular surface geometry. Waveforms over sea ice and ice sheet are very different than the typical ocean waveforms. Information about the ice sheet surface properies can be obtained by examination of the waveforms. The range correction (typically a few meters) to account for variations of the waveform shape and positioning of the waveform in the window of range gates is obtained by a procedure known as Retracking