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Impact cratering produces characteristic variations in the topographic power spectral density (PSD) of cratered terrains, which are controlled by the size-frequency distribution of craters and the spectral content (shape) of individual features. These variations are investigated here in two parallel approaches. First, a cratered terrain model, based on Monte Carlo emplacement of craters and benchmarked by an analytical formulation of the one-dimensional PSD, is employed to generate topographic surfaces at a range of size-frequency power law exponents and shape dependencies. For self-similar craters, the slope of the PSD, β, varies inversely with that of the production function, α, leveling off to 0 at high α (surface topography dominated by the smallest craters) and maintaining a roughly constant value (β ∼ 2) at low α (surface topography dominated by the largest craters). The effects of size-dependent shape parameters and various crater emplacement rules are also considered. Second, we compare the model-derived predictions for the behavior of the PSD with values of β calculated along transects from the Lunar Orbiter Laser Altimeter (LOLA). At small scales (∼115 m to 1 km) model predictions agree well with the PSD slope over the observed range of lunar size-frequency distributions. Differences between global PSD slopes at subkilometer and kilometer scales reflect a scale separation in roughness consistent with prior observations using a variety of surface roughness parameters. Understanding the statistical markers left by the impact cratering process on the lunar surface is useful for distinguishing between competing geological processes on planetary surfaces throughout the solar system.

We present maps of the topographic roughness of the Moon at hectometer and kilometer scales. The maps are derived from range profiles obtained by the Lunar Orbiter Laser Altimeter (LOLA) instrument onboard the Lunar Reconnaissance Orbiter (LRO) spacecraft. As roughness measures, we used the interquartile range of profile curvature at several baselines, from 115 m to 1.8 km, and plotted these in a global map format. The maps provide a synoptic overview of variations of typical topographic textures and utilize the exceptional ranging precision of the LOLA instrument. We found that hectometer-scale roughness poorly correlates with kilometer-scale roughness, because they reflect different sets of processes and time scales. Hectometer-scale roughness is controlled by regolith accumulation and modification processes and affected by the most recent events, primarily, geologically recent (1–2 Ga) meteoritic impacts. Kilometer-scale roughness reflects major geological (impact, volcanic and tectonic) events in earlier geological history. Young large impact craters are rough, and their roughness decreases with age. The global roughness maps revealed a few unusually dense clusters of hectometer- and decameter-size impact craters that differ in their morphology and settings from typical secondary crater clusters and chains; the origin of these features is enigmatic. The maps can assist in the geological mapping of the lunar maria by revealing contacts between volcanic plain units. The global roughness maps also clearly reveal cryptomaria, old volcanic plains superposed by younger materials, primarily crater and basin ejecta.

In June 2009 the Lunar Reconnaissance Orbiter (LRO) spacecraft was launched to the Moon. The payload consists of 7 science instruments selected to characterize sites for future robotic and human missions. Among them, the Lunar Orbiter Laser Altimeter (LOLA) was designed to obtain altimetry, surface roughness, and reflectance measurements. The primary phase of lunar exploration lasted one year, following a 3-month commissioning phase. On completion of its exploration objectives, the LRO mission transitioned to a science mission. After 7 years in lunar orbit, the LOLA instrument continues to map the lunar surface. The LOLA dataset is one of the foundational datasets acquired by the various LRO instruments. LOLA provided a high-accuracy global geodetic reference frame to which past, present and future lunar observations can be referenced. It also obtained high-resolution and accurate global topography that were used to determine regions in permanent shadow at the lunar poles. LOLA further contributed to the study of polar volatiles through its unique measurement of surface brightness at zero phase, which revealed anomalies in several polar craters that may indicate the presence of water ice. In this paper, we describe the many LOLA accomplishments to date and its contribution to lunar and planetary science.

Shackleton crater is nearly coincident with the Moon's south pole. Its interior receives almost no direct sunlight and is a perennial cold trap, making Shackleton a promising candidate location in which to seek sequestered volatiles. However, previous orbital and Earth-based radar mapping and orbital optical imaging have yielded conflicting interpretations about the existence of volatiles. Here we present observations from the Lunar Orbiter Laser Altimeter on board the Lunar Reconnaissance Orbiter, revealing Shackleton to be an ancient, unusually well-preserved simple crater whose interior walls are fresher than its floor and rim. Shackleton floor deposits are nearly the same age as the rim, suggesting that little floor deposition has occurred since the crater formed more than three billion years ago. At a wavelength of 1,064 nanometres, the floor of Shackleton is brighter than the surrounding terrain and the interiors of nearby craters, but not as bright as the interior walls. The combined observations are explicable primarily by downslope movement of regolith on the walls exposing fresher underlying material. The relatively brighter crater floor is most simply explained by decreased space weathering due to shadowing, but a one-micrometre-thick layer containing about 20 per cent surficial ice is an alternative possibility.

Mercury’s coupled 3:2 spin‐orbit resonance in conjunction with its relatively high eccentricity of ∼0.2 and near‐zero obliquity results in both a latitudinal and longitudinal variation in annual average solar insolation and thus equatorial hot and cold regions. This results in an asymmetric temperature distribution in the lithosphere and a long wavelength lateral variation in lithosphere structure and strength that mirrors the insolation pattern. We employ a thermal evolution model for Mercury generating strength envelopes of the lithosphere to demonstrate and quantify the possible effects the insolation pattern has on Mercury’s lithosphere. We find the heterogeneity in lithosphere strength is substantial and increases with time. We also find that a crust thicker than that of the Moon or Mars and dry rheologies for the crust and mantle are favorable when compared with estimates of brittle‐ductile transition depths derived from lobate scarps. Regions of stronger and weaker compressive strength imply that the accommodation of radial contraction of Mercury as its interior cooled, manifest as lobate scarps, may not be isotropic, imparting a preferential orientation and distribution to the lobate scarps.

The valley floor of a 33.9 km2 watershed in western Colorado experienced gradual sedimentation from before ∼ 6765 to ∼ 500 cal yr BP followed by deep incision, renewed aggradation, and secondary incision. In contrast, at least four terraces and widespread cut-and-fill architecture in the valley floor downstream indicate multiple episodes of incision and deposition occurred during the same time interval. The upper valley fill history is atypical compared to other drainages in the Colorado Plateau.One possible reason for these differences is that a bedrock canyon between the upper and lower valley prevented headward erosion from reaching the upper valley fill. Another possibility is that widespread, sand-rich, clay-poor lithologies in the upper drainage limited surface runoff and generally favored alluviation, whereas more clay-rich lithologies in the lower drainage resulted in increased surface runoff and more frequent incision. Twenty-two dates from valley fill charcoal indicate an approximate forest fire recurrence interval of several hundred years, similar to that from other studies in juniper–piñon woodlands. Results show that closely spaced vertical sampling of alluvium in headwater valleys where linkages between hillslope processes and fluvial activity are relatively direct can provide insight about the role of fires in alluvial chronologies of semi-arid watersheds.

Physicians have been restricting sodium chloride in the diets of patients with hypertension with varying degrees of enthusiasm since 1904. 1 Apparently as early as the turn of the century this dietary restriction was under active consideration in Europe, but it was not until 1922 when Allen and Sherrill 2 reported satisfactory results in a series of 180 patients that we hear of this treatment in the United States. The method was not generally accepted by members of the medical profession, however, and contemporary reports of smaller series of cases 3 did not confirm Allen's original results. In 1928 Addison4 pointed out that it was the sodium ion in the restriction of sodium chloride which was the effective agent. In 1944 with Kempner's report 5 of satisfactory results with a rice and fruit juice diet there was a rebirth of interest in the dietary treatment of hypertension. It was evident