3.1.2.2. Altimetric measurements over the ocean

The basic schematic outlines of a return echo over the ocean are as follows::

Over an ocean surface, the echo waveform has a characteristic shape that can be described analytically (the Brown model). From this shape, six parameters can be deduced, by comparing the real (averaged) waveform with the theoretical curve:

epoch at mid-height: this gives the time delay of the expected return of the radar pulse (estimated by the tracker algorithm) and thus the time the radar pulse took to travel the satellite-surface distance (or 'range') and back again.
P: the amplitude of the useful signal. This amplitude with respect to the emission amplitude gives the backscatter coefficient, sigma0.
P_o: thermal noise
leading edge slope: this can be related to the significant wave height (SWH)
skewness: the leading edge curvature
trailing edge slope: this is linked to any mispointing of the radar antenna (i.e. any deviation from nadir of the radar pointing).

The radar altimeter receives the reflected wave (or echo), which varies in intensity over time. Where the sea surface is flat (a), the reflected wave's amplitude increases sharply from the moment the leading edge of the radar signal strikes the surface. However, in sea swell or rough seas (b), the wave strikes the crest of one wave and then a series of other crests which cause the reflected wave's amplitude to increase more gradually. We can derive ocean wave height from the information in this reflected wave, since the slope of the curve representing its amplitude over time is proportional to wave height.

Example of real Envisat (left) and Topex (right) waveforms over the ocean

References
- Brown, G. S., The Average Impulse Response of a rough surface and its applications, IEEE Trans. Antennas Propag., 25, 1977.
- Hayne, G. S., Radar Altimeter Mean Return Waveforms from Near-Normal-Incidence Ocean surface scattering, IEEE Trans. Antennas Propag. AP-28, 687-692, 1980.