SHADOWS ON A PLANETARY SURFACE AND IMPLICATIONS FOR PHOTOMETRIC ROUGHNESS

We advocate the use of fractal surface statistics as a simple, quantit ative, and general model for planetary surface roughness. We determine the shadowing behavior of a wide range of fractal surfaces using comp uter simulations, and present an empirical function that reproduces th eir observed behavior within statistical uncertainties. We compare the shadowing behavior of fractal surfaces to four analytic shadowing mod els for random surfaces and find that three of these, including the Ha pke (1984, Icarus 59, 41-59) model, are well approximated by specific cases of a general fractal surface model. In addition, we demonstrate that a fractal surface model provides a way of quantitatively verifyin g and extending previous interpretations of the Hapke (1984) roughness parameter. We hypothesize that the scale which dominates surface shad owing, and by extension photometric roughness, is the smallest surface scale for which shadows exist and that this scale is a function of in trinsic physical parameters such as the single scattering albedo and p article phase function. If correct, a major implication of this hypoth esis is that photometric roughness may have different physical meaning s on different surfaces. (C) 1998 academic Press.