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.

The NASA Artemis program will send humans to the lunar south polar region, in part to investigate the availability of water ice and other in situ resources. While trace amounts of ice have been detected at the surface of polar permanently shadowed regions (PSRs), recent studies suggest that large ice deposits could be stable below cold traps in the PSRs over geologic time. A recent study modeling the rate of ice delivery, ejecta deposition and ice loss from cold traps predicted that gigatons of ice could be buried below 100s of meters of crater ejecta and regolith. However, crater ejecta vigorously mix the target on impact through ballistic sedimentation, which may disrupt buried ice deposits. Here, we developed a thermal model to predict ice stability during ballistic sedimentation events. We then modeled cold trap ice and ejecta stratigraphy over geologic time using Monte Carlo methods. We found that ballistic sedimentation disrupted large ice deposits in most cases, dispersing them into smaller layers. Ice retention decreased in most cases, but varied significantly with the sequence of ejecta delivery, particularly from basin-forming events. Over many model runs, we found that south polar craters Amundsen, Cabeus, and Cabeus B were most likely to retain large deposits of ice at depths up to 100 m, shallow enough to be detectable with ground-penetrating radar. We discuss these findings in the context of the imminent human exploration activities at the lunar south pole.Plain Language Summary Some craters near the south pole of the Moon contain permanently shadowed regions (PSRs) which stay cold enough to trap water vapor as ice. Recent studies have predicted that large amounts of ice could be buried under thick protective layers of lunar soil in the PSRs. Lunar soil is mainly transported by large impacts which launch soil and boulders to distances up to hundreds of kilometers. However, when these projectiles land they have destructive effects and may melt or redistribute buried ice. We simulated this process, called ballistic sedimentation, and predicted the amount of ice it removes. We also simulated ice and soil deposition over billions of years to test how much ice is lost to ballistic sedimentation over time. We predicted which PSRs are most likely to have ice near enough to the surface to detect in future missions. The upcoming Artemis program will send crewed and robotic missions to the lunar south pole region, and our work will help with planning where to land, what instruments to bring, and how much ice we might find.

Crater degradation and erosion control the lifetime of craters in the meter-to-kilometer diameter range on the lunar surface. A consequence of this crater degradation process is that meter-scale craters survive for a comparatively short time on the lunar surface in geologic terms. Here, we derive crater lifetimes for craters of

The roughness properties of impact craters are valuable indicators of crater degradation and can provide insight into crater ages. We evaluate the roughness of lunar craters from different geologic eras, confirming that young, Copernican craters are distinctly rougher than older craters. We evaluate the potential age of small (less than similar to 15 km) craters that are thought to host surface ice by quantifying the roughness inside these craters, as well as outside. Interior roughness may be subdued by slope processes or the presence of volatiles. The distribution of ice-bearing craters is skewed toward roughness values higher than those of pre-Imbrian craters, although no ice-bearing craters are within the Copernican-only domain in roughness space. All of the 15 rough, permanently shadowed craters that are found within the Copernican-only domain lack water-ice detections, suggesting that either ice has not been delivered to these young craters or that it has since been destroyed.

Self-secondaries are secondary craters that are formed on both the continuous ejecta deposits and interior of the parent crater. The possible existence of self-secondaries was proposed in the late 1960s, but their identity, formation mechanism, and importance were not revisited until the new generation of high-resolution images for the Moon have recently became available. Possible self-secondary crater populations have now been recognized not only on the Moon, but also on Mercury, Mars, 1Ceres, 4Vesta, and satellites of the ice giants. On the Moon and terrestrial planets, fragments that form self-secondaries are launched with high ejection angles via spallation during the early cratering process, so that self-secondaries can be formed both within the crater and on the continuous ejecta deposits at the end of the cratering process. Self-secondaries potentially possess profound effects on the widely used age-determination technique using crater statistics in planetary geology, because (1) self-secondaries cause nonuniform crater density across the continuous ejecta deposits, which cannot be solely explained by the effect of different target properties on crater size-frequency distributions; (2) crater chronologies for both the Moon and the other terrestrial bodies are largely based on crater counts on the continuous ejecta deposits of several young lunar craters. The effect of self-secondaries on crater chronology can be well addressed after the spatial distribution, size-frequency distribution, and density evolution of self-secondaries are resolved.

[1] Initial studies of neutron spectrometer data returned by Lunar Prospector concentrated on the discovery of enhanced hydrogen abundances near both lunar poles. However, the nonpolar data exhibit intriguing patterns that appear spatially correlated with surface features such as young impact craters (e. g., Tycho). Such immature crater materials may have low hydrogen contents because of their relative lack of exposure to solar wind-implanted volatiles. We tested this hypothesis by comparing epithermal* neutron counts (i.e., epithermal -0.057 x thermal neutrons) for Copernican-age craters classified as relatively young, intermediate, and old (as determined by previous studies of Clementine optical maturity variations). The epithermal* counts of the crater and continuous ejecta regions suggest that the youngest impact materials are relatively devoid of hydrogen in the upper 1 m of regolith. We also show that the mean hydrogen contents measured in Apollo and Luna landing site samples are only moderately well correlated to the epithermal* neutron counts at the landing sites, likely owing to the effects of rare earth elements. These results suggest that further work is required to define better how hydrogen distribution can be revealed by epithermal neutrons in order to understand more fully the nature and sources (e. g., solar wind, meteorite impacts) of volatiles in the lunar regolith.