|Title||Detection of extreme events from a SAR image spectrum|
|Publication Type||Technical memorandum|
|Secondary Title||ECMWF Technical Memorandum|
It is shown that the nonlinear mapping relation between a surface gravity wave spectrum and its SAR image spectrum, as derived by Hasselmann and Hasselmann (1991), is not complete. The reason for this is that the velocity bunching effect is so nonlinear that effects of skewness are as important as the nonlinear terms already retained in the Hasselmann and Hasselmann approach. Furthermore, certain effects of kurtosis need to be retained as well, but these will mainly affect the shape of the azimuthal correlation function. For a Gaussian sea the azimuthal correlation function, which reflects the statistical properties of the sea surface, can be approximated by a Gaussian function, This is expected to be an adequate model in most cases. However, for extreme waves there are departures from the Normal distribution. This then will result in departures from the Normal shape of the azimuthal correlation function as well. In other words, an analysis of the azimuthal cutoff may reveal information on the non-gaussian statistics of the sea surface, and may indicate the enhanced occurrence of freak waves.