Earth's terrestrial surfaces commonly exhibit topographic roughness at the scale of meters to tens of meters. In soil- and sediment-mantled settings topographic roughness may be framed as a competition between roughening and smoothing processes. In many cases, roughening processes may be specific eco-hydro-geomorphic events like shrub deaths, tree uprooting, river avulsions, or impact craters. The smoothing processes are all geomorphic processes that operate at smaller scales and tend to drive a diffusive evolution of the surface. In this article, we present a generalized theory that explains topographic roughness as an emergent property of geomorphic systems (semi-arid plains, forests, alluvial fans, heavily bombarded surfaces) that are periodically shocked by an addition of roughness which subsequently decays due to the action of all small scale, creep-like processes. We demonstrate theory for the examples listed above, but also illustrate that there is a continuum of topographic forms that the roughening process may take on so that the theory is broadly applicable. Furthermore, we demonstrate how our theory applies to any geomorphic feature that can be described as a pit or mound, pit-mound couplet, or mound-pit-mound complex. Earth's surface is constantly roughened by processes that operate quasi-randomly in space and time. For example, in forest settings, trees that topple will uproot soil and deposit a mound and excavate a pit, leaving a pit-mound couplet on the surface. With time, this topographic signature decays due to geomorphic processes rearranging sediment and soil on the surface. In this paper, we develop theory that explains topographic roughness as a balance between processes that create roughness and those that destroy it. We consider several different mechanisms (desert shrub mounds, tree uprooting, river channel avulsions, and impact cratering) and develop a general theory for topographic roughness that applies to many settings. We further Tdevelop theory that allows for a very wide range of natural features that may not be well-described by simple geometric functions. Topographic roughness at scales of meters to tens of meters reflects a balance between roughening and smoothing processes Analytical expressions for topographic roughness exist for many settings Increasingly high-resolution topographic data is a valuable resource for extracting process-specific information from topographic roughness

Water ice has been found in the permanently shadowed regions of impact craters around the lunar South Pole, which makes them ideal areas for in situ exploration missions. However, near the rim of impact craters, construction and exploration activities may cause slope instability. As a result, a better understanding of the shear strength of lunar soil under higher stress conditions is required. This paper mainly uses the finite element method to analyze slope stability to determine the position and shape of the slip surface and assess the safety factor. The height and gradient of the slope, the shear strength of lunar soil, and the lunar surface mission all influence the stability of the slope. We also analyze the soil mechanical properties of a soil slope adjacent to the traverse path of the Chang'E-4 Yutu-2 rover. Determining the stability of the slope at the lunar South Pole impact crater under various loading conditions will enhance the implementation of the lunar surface construction program. In this respect, this paper simulates a lunar mission landing at the Shackleton and Shoemaker craters and indicates that areas with higher cohesion lunar soil may be more stable for exploration in the more complex terrain of the South Pole.