Sea-wave fractal spectrum for SAR remote sensing

Abstract

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 and JONSWAP and to real data of the Mediterranean sea. New research directions offered by this spectrum model in SAR remote sensing are addressed.