Statistical geometry of a small surface patch in a developed sea

The fractal and marginal fractal regimes in surface geometry are studied. The basic notions of fractal geometry are applied to a small surface patch in a developed sea, corresponding to the equilibrium wave number spectrum. Topothesy, outer and inner boundaries of the fractal range, and a cascade pattern in surface geometry are discussed. Theoretical predictions of whitecap and foam coverage are presented. A fractal decomposition for a surface patch is developed based on the Karhunen-Loeve expansion. The resulting series formalizes the cascade process of constructing realization of a Gaussian random patch. The implications of the research for microwave remote sensing signatures are considered.