SSC San Diego San Diego, CA 92152--5001

This report presents an approximate formula for the grazing reflection of a circular source by the rough sea. The formula can be applied, for example, to the reflectivity along the center of a sun glint pattern or to the reflectivity of a missile plume (considered as a circle) as seen from the deck of a ship. In the optical region, the reflectivity of an ocean without gravity waves can be calculated using geometrical optics. The reason is that the wavelength of the radiation being reflected is much less than the radius of curvature of a typical capillary wave facet. The ocean can therefore be modeled as a collection of flat, mirror-like facets whose tilts fluctuate at random under the wind's influence. If the slope of a facet is correct, a ray from a source such as the Sun will be reflected into an optical receiver such as the eye. The problem then reduces to finding the Fresnel reflectivity of a small seawater mirror and counting the relative number of mirrors which, on average, can reflect a ray from the source into the receiver. Of course, Cox and Munk (1954, 1955, and 1956) have already addressed this problem in a famous series of papers. They measured the statistical occurrence of various capillary wave slopes by taking photographs of sun glitter from an airplane. However, their equation for reflected radiance applies to the case where the ocean is observed from above, not to the grazing case. When calculating reflectivity, Cox and Munk assumed that a patch of ocean of area A appears to have an area of A sinY when viewed from the side at a grazing angle, Y. In other words, for that part of their calculation, they assumed that the patch was flat. Because radiance involves the power received per unit solid angle per unit projected area, and because the projected area..