Remote sensing of the roughness of a fractal sea surface

One use of radar altimeters is to measure surface wind speeds through their effect on the roughness of the sea surface. The specular point reflection model is only appropriate for surfaces with roughness on scales which are large in relation to the radar wavelength. This may not be the case for ocean surfaces. Here we model the sea surface as a fractal on the relevant scales. This is based on Hasselmann's model for nonlinear wave action transfer. The radar cross section for nadir backscatter is derived and its dependence on the radar frequency is determined. The results are compared with the cross section obtained by the specular point model for a smoothed surface, yielding the appropriate cutoff wavenumber. Some existing measurements of the sea surface by altimeter and stereophotogrammetry are discussed, suggesting a smaller fractal dimension for short gravity waves. Dual-frequency altimeters may help determine the synoptic spectral shape.