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



fig 1. Parts of a waveform 

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 providing the best fitting:

  • 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.
  • Po: 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).
eg_waveform_envisat_low_waves_sm eg_waveform_ocean_sm
fig 2. Example of real Envisat (left) and Topex (right) waveforms over the ocean.



  • 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.