It is reported here that the ocean surface under a sufficiently high wind is a multi-fractal process, consisting of breaking wave singularities. It has been argued elsewhere that the singularity strength associated with individual breaking wave implies a distinct energy state within a continuum of such states whose entropy is associated with a fractal dimension. When the multi-fractal process is modelled in the simplest, non-trival multiplicative energy flux cascade -as a Besicovitch-Cantor process - 3 independent variable are required for a full description. It is shown that when a closure assumption is invoked which relates the 2 sub-process energy fluxes as a power-law in their respective receiving areas (the process' support), the 2 exponents involved are remarkably constant within the experimental variation arising from different aircraft imaging sorties over different sea states. The results is a reduction of complexity from 3 to just 1 independent variable to describe any realization; this parameter is referred to as the multi-fractal equivalent of the Beaufort scale. ¿American Geophysical Union 1993