Sea-wave fractal spectrum for SAR remote sensing

A new model of the sea-wave directional spectrum based on fractals is proposed. An innovative aspect of the work is the theoretical approach used to get the `fractal sea spectrum'. The common spectrum models are described by empirical expressions derived from fitting experimental data. Starting from a definition of a fractal model of the sea surface, the spatial autocorrelation function is calculated and the directional sea spectrum derived by taking its two-dimensional Fourier transform. The fractal spectrum explicitly accounts for the fractality of the sea. The spectrum theoretically explains why its slope in the equilibrium range depends on the fractal dimension D of the sea surface and can be expressed by the relationship 2D-7, as usually claimed from experimental data. The spectrum is validated by comparing it to the common spectra of Pierson-Moskowitz (1964) and JONSWAP and to real data of the Mediterranean Sea. New research directions offered by this spectrum model in SAR remote sensing are addressed