It is established for the first time that the spatial distribution of breaking waves on the ocean surface is a multifractal process. This result is based on an analysis of airborne visible and near-infrared imagery of the ocean surface under a limited range of wind speed and fetch. A detailed study of the optical spectra of the images and the cumulative probability structure of the prevalent background shows that the lower-intensity reflective areas follow a Rayleigh probability distribution. By contrast, the higher-intensity pixels associated with the scattered light from foam and breaking waves demonstrate scaling characteristics in both the optical spectra and the cumulative probability distributions. It is demonstrated that the degree to which the whitecaps are singularities on a dark background is described by a Lipschitz exponent α, which uniquely tags each breaking wave. This identification process, called ''fractal'' or ''singularity filtering'', leads to a critical condition αc=1 tentatively associated with the crossover from active entraining whitecaps to passively dissipating foam. The multifractal representation associated with the degree of singularity is simply a restatement that the imagery is composed of a continuum of sets, where each set consists of those breaking waves at a particular phase in their existence.

The fractal spectrum of the image above a threshold is shown to be representable by a fractal generator. Physically, the fractal generator models the energy exchange in a breaking wave field as a flux of energy input from the atmosphere to the wave field cascaded over scales of the order of a kilometer to meters. If the energy flux is further parameterized in terms of the receiving area, an assumption similar to closure techniques used in classical turbulence models, the empirical results symmetrically span Phillips's basic arguments for the energy flux terms controlling a wind-driven sea. ¿ American Geophysical Union 1994