Monte Carlo simulations for studying the relationship between ocean wave and synthetic aperture radar image spectra

A theoretical model previously developed for describing the imaging of monochromatic ocean waves by synthetic aperture radar (SAR) is extended to relate ocean wave spectra to SAR image spectra. Since the SAR response to the moving ocean surface is nonlinear for a large range of ocean wave parameters, this relationship can, in general, not be described by a linear mapping transfer function. SAR image spectra are calculated from given ocean wave spectra by applying Monte Carlo simulation techniques. The computer simulations are performed with varying SAR parameters and for a unidirectional wave field propagating in azimuth direction. Though the model calculations are only one dimensional, they reveal the following basic features of the SAR imaging mechanism: (1) If the nonlinearity of the imaging is sufficiently strong, then the peak of the SAR image spectrum is shifted towards lower azimuthal wave numbers. (2) One parameter suitable for characterizing the degree of nonlinearity is the average velocity bunching parameter , which for SEASAT-SAR is given by , where λm is the dominant wavelength and Hs the significant waveheight in meters, and ϕ the azimuth angle (ϕ = O for azimuthally traveling waves). (3) The amount of the azimuthal shift of the spectral peak depends on c, SAR integration time, and on the width of the ocean wave spectrum. It increases with integration time and spectral width. (4) In case of a fully developed wind sea, shifts of spectral peaks toward lower azimuthal wave numbers become significant for SEASAT-SAR if . For , the relative azimuthal wavenumber shift is of the order of 1/2. If , the peak of the image spectrum is located near zero wave number and no wave information can be extracted from the SEASAT-SAR image spectrum.