Shadows on a planetary surface and implications for photometric roughness

We advocate the use of fractal surface statistics as a simple, quantitative, and general model for planetary surface roughness. We determine the shadowing behavior of a wide range of fractal surfaces using computer simulations, and present an empirical function that reproduces their observed behavior within statistical uncertainties. We compare the shadowing behavior of fractal surfaces to four analytic shadowing models for random surfaces and find that three of these, including the Hapke (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 verifying and extending previous interpretations of the Hapke (1984) roughness parameter. We hypothesize that the scale which dominates surface shadowing, and by extension photometric roughness, is the smallest surface scale for which shadows exist and that this scale is a function of intrinsic physical parameters such as the single scattering albedo and particle phase function. If correct, a major implication of this hypothesis is that photometric roughness may have different physical meanings on different surfaces. (C) 1998 academic Press.