Probabilistic Water Bidirectional Reflectance Distribution Function, Version 2

Reflections of a laser beam from a water surface are inherently probabilistic, depending on the surface state at the particular location and time. Measured statistics on wave states allow probabilistic calculations of wave height and slope at the location and time of reflections. These, in turn, are used to calculate the bidirectional reflectance distribution function (BRDF) in a probabilistic sense based on multiple deterministic BRDF values. A complete model of probabilistic water BRDF is detailed, with accompanying illustrations of BRDF for selected conditions. In general, the BRDF decreases rapidly with increasing wind speed, and the probabilistic BRDF is significantly less than the deterministic BRDF under identical conditions. An empirical model of water BRDF for more rapid calculations is based on results from the probabilistic model.