The NASA Dawn mission revealed that the floor of Occator crater on the dwarf planet Ceres (in the main asteroid belt between Mars and Jupiter) is populated with small quasi-conical hills. Many of these features exhibit morphometric properties that are like those of ice-cored periglacial hills called pingos. Alternatively, some of these Cerean hills have also been hypothesized to be cryovolcanic in origin. If these hills are analogous to pingos, they represent ice-rich environments that are attractive targets for future exploration. We report new constraints on the morphologies of the Occator hills that aid in determining their origin. We also directly test how morphologically similar the hills in Occator are to pingos and volcanic cones on Earth using comparative statistical analyses. Using a novel application of kernel density estimation and Markov chain Monte Carlo methods we show that the morphologies of terrestrial pingos and volcanic cones are quantifiably distinct, and that the Cerean hills share significant morphometric similarities with pingos on Earth. Our findings indicate that a statistical treatment of morphometry alone can be a powerful tool for classifying and comparing planetary surface features, and that the majority of the resolved Cerean hills are morphometrically more similar to pingos than to small terrestrial volcanic cones.
From 2015 to 2018 CE, the NASA Dawn mission explored the solar system's innermost dwarf planet, Ceres (https://www.nasa.gov/mission_pages/dawn/main/index.html; Russell et al., 2016). Dawn determined that Ceres is a differentiated object with an ~40-km-thick ice-rich crust of density ~1300 kg/m3 (Ermakov et al., 2017). This low crustal density is supported by observed geomorphological features suggestive of abundant near-surface ground ice, such as lobate landslides, pitted terrain, and floor-fractured craters (e.g., Schmidt et al., 2017; Hughson et al., 2018, 2019; Buczkowski et al., 2019; Raponi et al., 2019; Sizemore et al., 2019).
Occator crater on Ceres was chosen as the target for Dawn's second extended mission (Ceres Extended 2 Elliptical orbit [C2E]), during which Dawn collected image data with resolution as fine as ~3 m/pixel. These data revealed an abundance of conical, domical, and flat-topped hills not previously discernable (Fig. 1). Nearly 75% of these hills occur in geologic material interpreted to have been emplaced as water-rich impact melt, exhibit morphologies similar to those of ice-cored periglacial hills called pingos (Schmidt et al., 2020; Scully et al., 2020), and are distinct from features common to impact basins (Schenk et al., 2020). While similar landforms have been observed on Mars (e.g., Dundas and McEwen, 2010), these features are the first documented instance of possible pingo analogs on a dwarf planet. Alternatively, many of the Occator hills have also been hypothesized to be cryovolcanic in origin (e.g., Nathues at al., 2020).
On Earth, pingos form via seasonal injection and subsequent freezing of pressurized groundwater at their base (e.g., Müller, 1959; Holmes et al., 1968). Pingo growth typically occurs hydrostatically via pore-water expulsion from permafrost aggradation (e.g., Mackay, 1998) or hydraulically via topographically driven groundwater injection (e.g., Müller, 1959). Both styles of pingo formation can produce cryohydrologic features of similar morphology (e.g., Soare et al., 2011, 2020).
Ultimately, in situ sampling and methods like ground-penetrating radar and resistivity tomography will be needed to definitively test the pingo or cryovolcanic origin hypotheses for Occator's small hills. Currently, however, imaging and topography are the best available tools for investigating these features. In this study, we used morphometric and statistical techniques to identify, physically characterize, and analyze the population-wide properties of topographically resolved hills in Occator. We also analyzed pingos from the Tuktoyaktuk Peninsula in the Northwest Territories (Canada) and volcanic cones from both Snæfellsnes Peninsula in Iceland and the San Francisco volcanic field in Arizona (USA) to quantify unique morphometric aspects of these terrestrial features and to develop a framework that would place the Cerean hills in context between these contrasting morphologic populations.
While it is unlikely that the Occator hills originated from silicate volcanism or seasonal ground-ice growth, and with the understanding that all terrestrial surface features are modified by biological and erosive processes that are not believed to be active on Ceres, we used terrestrial volcanic cones and pingos as imperfect morphologic analogs for potential cryovolcanic and cryohydrologic features in Occator. This is justifiable because Cerean cryovolcanoes are hypothesized to form in an analogous fashion to terrestrial cinder cones via cryolava extrusion and ballistic sedimentation (Quick et al., 2019; Nathues et al., 2020), and refreezing impact melt is hypothesized to create subsurface pressure gradients conducive to pingo-analog formation (Schmidt et al., 2020). Results from these characterizations were used to determine whether significant differences exist between these sets of genetically distinct terrestrial hills and whether there were any systematic similarities between the potential analog populations and the Occator hills.
We topographically examined the pingo candidates identified by Schmidt et al. (2020) using Dawn Framing Camera (FC) C2E image data (~3–5 m/pixel) and a primary mission–derived digital terrain model (DTM) of Occator (NASA Planetary Data System, https://sbnarchive.psi.edu/pds3/dawn/fc/DWNCLSPG_2/, accessed 2018). To supplement the primary DTM, we created C2E-based DTMs where image coverage was sufficient using the Ames Stereo Pipeline (Beyer et al., 2018). The lateral resolution of the primary DTM is ≤32 m/pixel, while the C2E DTMs have a corresponding resolution of ≤5 m/pixel. Vertically resolved mounds were characterized by taking topographic profiles along each of their mutually orthogonal major and minor planform axes. We used these profiles to measure each hill's planform eccentricity, mean height-to-diameter ratio (H:D), root-mean-square (RMS) maximum flank slope, mean symmetry, RMS skewness (how much a hill “leans” to one side), and mean excess kurtosis (a measure of how elongated the flanks of a hill are). The three latter metrics were measured using statistical techniques by treating the elevation profiles of investigated hills as analogous to probability density functions (PDFs). A detailed description of these metrics is provided in the Supplemental Material1.
Following the characterization of the Cerean hills, we repeated this exercise for terrestrial pingos and volcanic cones. The Tuktoyaktuk and Snæfellsnes Peninsulas were examined using the ArcticDEM digital surface model (Porter et al., 2018), which has a lateral resolution of ~2 m/pixel. We used Shuttle Radar Topography Mission data (lateral resolution ~30 m/pixel) to investigate the San Francisco volcanic field (https://doi.org/10.5066/F7PR7TFT). Terrestrial base images and mosaics were provided by Google Earth™ and Planet Labs, Inc. (https://www.planet.com/) with resolution ≤20 m/pixel.
We used kernel density estimation (KDE) (Rosenblatt, 1956; Parzen, 1962; Pedregosa et al., 2011) to resolve the distributions of the physical metrics among the analyzed hill populations on Ceres and Earth (Fig. 2). KDE is a non-parametric method for estimating the PDF of a random variable. After the PDFs of the metrics were estimated, we conducted a probabilistic analysis of the Occator hills using a Metropolis-Hastings-style Markov chain Monte Carlo (MCMC) model (Metropolis et al., 1953; Robert and Casella, 1999) to infer their morphometric character. This model estimated the likelihood that a specific Cerean hill's shape is similar or dissimilar to that of a pingo or small terrestrial volcanic cone by simultaneously comparing its metrics to the respective PDFs of the Tuktoyaktuk pingos, Icelandic cones, and San Francisco volcanic field cones. If a hill is poorly described by its topographic details as either pingo-like or volcanic cone-like in shape, the model assigns it an “alternative morphology” label. Prior to applying this method on Ceres data, we verified the method's ability to discriminate between a variety of pingos and volcanic cones on Earth. By repeating our MCMC analysis for each Cerean hill, we holistically constrained how similar the morphologies of these hills are to those of the terrestrial analogs (see the Supplemental Material for method details and validation).
We characterized 74 topographically resolved hills in Occator crater, 448 pingos on the Tuktoyaktuk Peninsula, 37 cones on the Snæfellsnes Peninsula, and 87 cones within the San Francisco volcanic field. The KDE-derived PDFs of the metrics for the Cerean and terrestrial hills are shown in Figure 3. We examined the flat-topped, conical, and domical Cerean hills separately using KDE and found their morphometrics to be broadly similar. Thus, for the remainder of this analysis, we treated the Cerean hills as belonging to a single population.
The Cerean hills are tightly distributed with respect to their symmetry, skewness, and excess kurtosis. They are highly symmetric with a pan-morphology mean symmetry coefficient of 0.89 (Fig. 3A), a low skewness of 0.09 (Fig. 3B), and the excess kurtosis of these features is tightly distributed around a mean of −0.81 (Fig. 3C). In contrast to the aforementioned parameters, the maximum flank slope values for the Cerean hills are broadly distributed from 2.8° to 63.4° with a mean of 22.3° (Fig. 3D). The planform eccentricity and H:D of the Occator hills are also broadly distributed from 0.02 to 0.93 and from 0.02 to 0.26, with means of 0.60 and 0.10, respectively (Figs. 3E and 3F).
The RMS maximum-slope PDF for the Tuktoyaktuk pingos is largely similar in form to that of the Occator hills, and both are peaked near 10°. In contrast, the slope PDF for the San Francisco volcanic field cones is tightly peaked around 28.5°. The Icelandic cones display a broad quasi-symmetrical distribution around 39.0°. A similar pattern is observed for the coefficient of skewness, where the morphologies of the Cerean hill and Earth pingo PDFs are largely homologous and tightly peaked but differ significantly from those of the PDFs of the more loosely distributed volcanic cones. The Cerean hills have the most negative mean excess kurtosis, which implies their margins are well defined and terminate discretely rather than diffusely, similarly to terrestrial pingos. The Tuktoyaktuk pingos are the most symmetric terrestrial population with an expected index of 0.87, while the San Francisco volcanic field and Icelandic cones have means of 0.84 and 0.79, respectively. The eccentricity PDFs of all populations are similar in form and overlap significantly; the same is true for the H:D PDFs. Table S1 in the Supplemental Material summarizes the mode, median, expected value, and standard deviation for each metric of the studied populations.
Results of the MCMC model are shown in Figure 4. The model ingests the morphometric data derived from the KDE analyses and outputs confidence estimates that a given Cerean hill resembles a specific terrestrial feature class. Given the non-exhaustive nature of the utilized metrics and comparison data, we have reported these values as “affinities” to underscore the fact that they are not true genetic probabilities.
Mathematical and visual examination of the derived PDFs indicates that the morphologies of the Tuktoyaktuk pingos are quantifiably distinct from those of terrestrial volcanic cones in all metrics except for excess kurtosis and planform eccentricity. They are also more similar to the morphologies of the Cerean hills than to those of either class of volcanic cones, particularly in their symmetry, skewness, and flank slope. The Occator hills are defined by their high symmetry, low skewness, large negative excess kurtosis, and broadly low maximum flank slopes. The difference in the symmetry and skewness PDFs of the Cerean hills and Tuktoyaktuk pingos relative to the volcanic cones is largely attributable to their summit morphologies. The volcanic cones typically display asymmetric summit craters on the order of tens of meters deep, whereas pingos and the Cerean hills tend to lack these features. The maximum flank slope for the Cerean hills is also similar to that of the terrestrial pingos with a mean well below the anticipated angle of repose (Ermakov et al., 2019).
The H:D PDFs of the volcanic cones, though differing in their widths, are largely co-located, implying a characteristic volcanic behavior within our investigated regions, which is consistent with previous investigations (e.g., Wood, 1980). The modes and expected values for these curves are both significantly larger than what is displayed by the pingos. The shape of the Cerean hills’ H:D PDF is intermediate to those of the Tuktoyaktuk pingos and volcanic groups. This indicates that the Occator hills are more “oblate” than the terrestrial volcanic cones but more “prolate” than pingos.
These characteristic aspect ratios, negative excess kurtosis, low maximum slope values, and high symmetries cause the Cerean hills to predominantly manifest as broad, axisymmetric, blister-like domes with distinctive margins that are more pingo-like in character than terrestrial volcanic–like. However, studies of H:D for Martian scoria cones have shown that this ratio is systematically smaller compared to that of similar cones on Earth, likely due to an increased radius of ballistic sedimentation (Brož et al., 2015). This may be further exaggerated on Ceres.
The assertion that the Occator hills are pingo-like in their morphology is further supported by the MCMC analysis (Fig. 4). The model-produced affinities of the Cerean hills—regardless of whether only pingo and volcanic morphologies (Fig. 4A) or pingo, volcanic, and the alternative morphologies (Fig. 4B) were considered—indicate that a majority of the Occator hills are morphometrically more like pingos than like small terrestrial volcanic cones. However, the number of Occator hills identified as having an alternative morphology is likely an undercount due to the incomplete morphometric description of the investigated hills. In the case where the output affinities were constrained to pingos and volcanic cones, 48 of the 74 Occator hills were found to be dominantly pingo-like in character. This number increased to 52 when the alternative morphology was considered, though the magnitude of each hill's pingo-like affinity decreased, indicating that the Occator hills have a unique morphometric signature.
While this analysis indicates that the Occator hills are morphologically more similar to pingos than terrestrial volcanic cones, it does not in itself prove a genetic connection. Nor does this analysis speak quantitatively to the morphologic similarities that may exist between the Occator hills and other hill forms such as lava domes, solid-state diapirs, or other impact debris that may be relevant to Ceres and should be considered in future studies (Bland et al., 2019).
Our results demonstrate that statistical treatments of morphological metrics can be powerful tools for classifying and contextualizing planetary landforms. Approaches like the methods presented here open new quantitative dimensions for landform analysis and classification in the Earth and planetary sciences, work that has been predominantly qualitative in the past. On Earth, pingos are easily differentiated from volcanic cones using our KDE-derived metrics. The observed morphologies and strong pingo-like traits of the Cerean hills suggest their formation is more closely tied to hydrologic processes than to terrestrial-style explosive volcanism, but further investigation is necessary to fully place these features in context with other hill forms throughout the solar system. Nevertheless, the Cerean hills likely represent important exploration targets for understanding the nature of hydrogeologic processes in the solar system.
We thank the NASA Dawn flight, instrument, and science teams. All data used in this study are available in NASA's Planetary Data System: Small Bodies Node (https://pds-smallbodies.astro.umd.edu), the U.S. Geological Survey's Earth Explorer database (https://earthexplorer.usgs.gov), and the Polar Geospatial Center (https://www.pgc.umn.edu). This research was supported by the Dawn mission. We thank Eileen McGowan and an anonymous reviewer for their constructive comments.