The geological interpretation of photometric surface roughness

B. Hapke's (1984, Icarus 59, 41–59) photometric equation includes a roughness parameter (θ) which models the effects of spatially unresolved topographic relief on the bidirectional reflectance of planetary surfaces. In this study, the relationship between photometrically determined values of θ and topographic scale is investigated with the use of a computer-generated kilometer-scale relief map whose topographic facets on scales less than a few meters are assumed to be covered with smooth particulate materials. The introduction of meter- to kilometer-scale topographic relief to an otherwise smooth surface alters its integral photometric behavior in a way which is generally consistent with the predictions of Hapke's equation. Comparison of values of θ estimated from topography at many scales to that obtained from photometric behavior confirms that the roughness characterized by θ is an integral property over all scales up to the resolution limit of the photometric data used in its determination. Results from this study show that reliable determination of photometric roughness from disk-integrated data or from disk-resolved photometric observations of individual geological features requires observations which extend from small phase angles out to phase angles above 90°. Given adequate phase angle coverage, θ can successfully distinguish terrains whose integral roughnesses are fundamentally different.