Submillimeter-Scale Topography of the Lunar Regolith

We have applied computer stereophotogrammetry to Apollo Lunar Surface Closeup Camera (ALSCC) pictures of the lunar surface to construct the first-ever digital topographic relief maps of undisturbed lunar soil over spatial scales from 85 μm to 8.5 cm. Using elevation histograms, fractal analysis, and Hapke's photometric roughness model we show that Apollo 14 (Fra Mauro) Imbrium ejecta is rougher than average Apollo 11 (Mare Tranquilitatis) and Apollo 12 (Oceanus Procellarum) mare surfaces at submillimeter to decimeter size-scales. We confirm the early result of K. Lumme et al. (1985, Earth Moon Planets33, 19–29) that the cumulative distribution of elevations for lunar soil is typically well described by Gaussian statistics. However, cumulative distributions are insensitive to asymmetries in the shapes of elevation histograms: Of 11 discrete elevation histograms we measured, about half exhibit significant deviations from Gaussian behavior. We also confirm Lumme et al.'s finding that the roughnesses of all lunar surfaces increase with decreasing size-scale. We further show that the scale dependence of roughness is well represented by fractal statistics. The rates of change of roughness with size scale, represented by fractal dimension D, are remarkably similar among terrians. After correcting for the contribution of large-scale roughness, our average value of D=2.31±0.06 falls within the range 2.0≤D≤2.4 reported from lunar radar studies. The amplitude of roughness, which we characterize with the rms slope angle at 1-mm scale, varies significantly among terrains. For lunar mare, the average rms slope angle is 16°±4°3 and that for Fra Mauro regolith is 25°±1°. By comparison to radar data, we suggest that the roughness of Fra Mauro (Imbrium ejecta) regolith is similar to that of lunar highland terrains. We find that the Gaussian slope distribution assumed in B. W. Hapke's model (1984, Icarus59, 41–59) adequately describes typical lunar regolith surfaces. A revised form of Hapke's equation that models realistic particle phase functions and the coherent backscatter opposition effect was fitted to disk-resolved lunar photometric observations and yields estimates of θ=27±1° for highland and θ=24±1° for mare regolith. These values of θ as well as the implied relative highland:mare photometric roughness ratio are best matched in our elevation data by the cummulative contributions of surface topography covering all scales greater than 0.1 mm. Less than 5% of the photometrically detected roughness of lunar regolith is contributed by surface relief at scales larger than 8 cm. This conclusion implies that values of θ derived from whole-disk and disk-resolved photometry, respectively, may be taken to represent the same physical quantity. In addition, particulate samples used in goniophotometric measurements should not be assumed to be photometrically smooth (i.e., θ=0°), as is often done in laboratory applications of Hapke's photometric model. The predicted photometric roughness at size scales of 0.1 mm and less significantly exceed photometric estimates and suggests that there exists a measurable size scale below which topographic relief either is not photometrically detectable or is not represented in the Hapke model as macroscopic roughness.