Simulation of SAR image cross spectra from mixed ocean waves

A 6-parameter frequency spectrum with two peaks and a cos-2s type spreading function is used to simulate the mixed waves. The spaceborne and airborne synthetic aperture radar (SAR) image cross spectra of mixed waves in different significant wave height, wave length, wave direction and wave component are then calculated by using Engen's nonlinear transformation formula. Analysis based on above simulation indicate that (1) the cross spectra of mixed waves dilate in range direction and shrink in azimuth direction (the so-called azimuth cutoff effect); (2) the cutoff effect increases for waves with larger wave height, or for waves with shorter wave length, or for waves propagating closer the azimuth direction, or for waves containing more wind wave component, or for spaceborne SAR; (3) the cross spectra split into two parts for waves propagating along range direction (the so-called double-peak phenomenon); (4) the direction ambiguity of ocean waves can be removed by using the imaginary part of cross spectra; (5) in addition to the contribution of wind wave part and swell part of the mixed waves, the cross spectra of mixed waves consist of an extra term which leads to an inherent error when using ESA's Envisat ASAR level 2 algorithm to retrieve ocean waves (see the companion paper submited to this symposium).