Millimeter- to Decimeter-Scale Surface Roughness of the Moon at the Chang'e-4 Exploration Region

The surface slope and roughness of the Moon have been investigated extensively over a wide baseline range except millimeter to decimeter scales. In this study, we present for the first time millimeter-to decimeter-scale surface slope and roughness of the Moon at China's Chang'e-4 landing regions (∼20 m across) using the Digital Terrain Model (DTM) with a resolution of 5 mm/pixel. The bidirectional slope at the 7 mm scale can be larger than 40° with a median value of ∼10°. The root-mean-square (RMS) height within a window size of 125 mm varies from ∼1 mm to ∼18 mm with a median value of ∼4 mm. Both the bidirectional slope and RMS height show scale-dependent behaviors and the parameter of scale dependence, the Hurst exponent, is ∼0.6–0.85. We also synthesized the bidirectional slope at baseline from micrometer to kilometer, showing that bidirectional slope decreases from ∼60° at micrometer to ∼1° at a kilometer. At millimeter-scale, surface roughness is mainly controlled by small impact craters, rocks, and regolith properties. Our roughness results not only bridge the gap in understanding surface roughness from traditional topographic data sets to radar and thermal observations, but also provide valuable information about lunar regolith characteristics, and small-scale geological processes.