Meter-Scale Topographic Roughness of the Moon: The Effect of Small Impact Craters

High-resolution digital terrain models (DTMs) generated from the Lunar Reconnaissance Orbiter Camera (LROC) Narrow Angle Cameras (NACs) provide an opportunity to study surface roughness of the Moon at meter scale. In this study, we mapped and investigated meter-scale topographic roughness over 462 regions of the Moon using NAC DTMs. Our results show that, at meter to hectometer scales, there are obvious differences in median bidirectional slope, root-mean-square (RMS) height, and median absolute slope between maria and highlands. In terms of the median value, ratios of the bidirectional slope, RMS height, and median absolute slope within the maria and highlands are 1: 2.4, 1: 3.0, and 1: 2.7, respectively. However, up to a baseline of similar to 0.2 km, no discernible differences in the Hurst exponent and median differential slope exist between the maria and highlands. The Hurst exponent varies from 0.7 to 0.95, with a median value of 0.9 within both the maria and highlands. To identify potential factors affecting meter-scale roughness of the Moon, we compared the maria with volcanic features on Earth and Mars, as well as the lunar highlands with simulated cratered terrains. We found that the Hurst exponents within the lunar maria are much larger than those of the volcanic features on Earth and Mars, mainly because the lunar maria accumulated more impact craters with diameters smaller than 1 km. The Hurst exponents within the highlands are consistent with those of the simulated cratered terrains, whose surface roughness depends primarily on crater shape, number density, and stratigraphic age. All these results indicate that lunar surface roughness at meter to hectometer scales is mainly controlled by small degraded impact craters.