Colin M Dundas
email: cdundas@usgs.gov

Michael T Mellon

Susan J Conway

Ingrid J Daubar

E Kaj

Lujendra Williams

James J Ojha

Ali M Wray

Shane Bramson

Alfred S Byrne

Mcewen

Kaj E Williams

Lujendra Ojha

James J Wray

Ali M Bramson

Shane Byrne

Alfred S Mcewen

Liliya V Posiolova

Gunnar Speth

Donna Viola

Margaret E Landis

Gareth A Morgan

Asmin V Pathare

Widespread Exposures of Extensive Clean Shallow Ice in the Mid-Latitudes of Mars

établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Introduction

One of the key needs identified by the Mars science community is the inventory and characterization of non-polar near-surface ice [START_REF] Smith | 6 th International Conference on Mars Polar Science and Exploration: Conference summary and five top questions[END_REF]MEPAG ICE-SAG Report, 2019). This is a fundamental question for determining the near-surface H2O abundance on Mars and the processes by which it is transported, deposited, and modified.

Theory indicates that ice stability is controlled by temperature and the atmospheric water vapor content (e.g., [START_REF] Leighton | Behavior of carbon dioxide and other volatiles on Mars[END_REF][START_REF] Mellon | Geographic variations in the thermal and diffusive stability of ground ice on Mars[END_REF][START_REF] Mellon | The distribution and behavior of Martian ground ice during past and present epochs[END_REF][START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF][START_REF] Schorghofer | Stability and exchange of subsurface ice on Mars[END_REF][START_REF] Chamberlain | Response of Martian ground ice to orbitinduced climate change[END_REF][START_REF] Steele | Regolith-atmosphere exchange of water in Mars' recent past[END_REF], and thus a stability boundary varies over time depending on the history of those parameters. This climatic change in turn is governed by variations in Mars' orbit and obliquity (e.g., [START_REF] Murray | Periodic insolation variations on Mars[END_REF][START_REF] Ward | Large-scale variations in the obliquity of Mars[END_REF][START_REF] Laskar | Long term evolution and chaotic diffusion of the insolation quantities of Mars[END_REF].

Small adjustments of the ice-table depth in response to climate changes can occur within hundreds of years even in the presence of salt crusts or other plausible diffusion barriers (e.g., [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF][START_REF] Hudson | Diffusion barriers at Mars surface conditions: Salt crusts, particle size mixtures, and dust[END_REF]. However, thick bodies of ice might survive through intervals of instability (e.g., [START_REF] Schorghofer | History and anatomy of subsurface ice on Mars[END_REF][START_REF] Bramson | Preservation of mid-latitude ice sheets on Mars[END_REF]. There is evidence that shallow (<10 m) mid-latitude ice has survived for tens of millions of years [START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF] and debris-covered glaciers have an estimated mean age of 110 Ma since the last major ice accumulation [START_REF] Fassett | An extended period of episodic northern mid-latitude glaciation on Mars during the Middle to Late Amazonian: Implications for long-term obliquity history[END_REF]. Thus the distribution of ice is influenced by its stability in the geologically recent past as well as the present. Additionally, early expectations were that most subsurface ice would simply fill in the pore space of the regolith (e.g., [START_REF] Squyres | Geomorphic evidence for the distribution of ground ice on Mars[END_REF][START_REF] Mellon | Geographic variations in the thermal and diffusive stability of ground ice on Mars[END_REF]. However, many lines of evidence (e.g., [START_REF] Boynton | Distribution of hydrogen in the near surface of Mars: Evidence for subsurface ice deposits[END_REF][START_REF] Mellon | Ground ice at the Phoenix landing site: Stability state and origin[END_REF][START_REF] Smith | H2O at the Phoenix landing site[END_REF][START_REF] Mouginot | The 3-5 MHz global reflectivity map of Mars by MARSIS/Mars Express: Implications for the current inventory of subsurface H2O[END_REF][START_REF] Conway | Decameter thick remnant glacial ice deposits on Mars[END_REF][START_REF] Bramson | Widespread excess ice in Arcadia Planitia, Mars[END_REF][START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF][START_REF] Stuurman | SHARAD detection and characterization of subsurface water ice deposits in Utopia Planitia, Mars[END_REF][START_REF] Pathare | Driven by excess? Climatic implications of new global mapping of near-surface waterequivalent hydrogen on Mars[END_REF] now point to the widespread occurrence of excess or massive ice (terminology per van Everdingen (1998)) rather than pore ice, requiring additional processes such as snowfall (e.g., [START_REF] Madeleine | Amazonian northern mid-latitude glaciation on Mars: A proposed climate scenario[END_REF]2014), thermal cycling to enhance porosity [START_REF] Fisher | A process to make massive ice in the Martian regolith using longterm diffusion and thermal cracking[END_REF], or migration of thin liquid films to generate ice lenses (e.g., [START_REF] Sizemore | Initiation and growth of Martian ice lenses[END_REF].

Hence, assessing the distribution, concentration, and structure of ground ice is vital for understanding recent Martian climate and its variations.

Ground ice in the Martian mid-latitudes is widespread, but almost always underneath a desiccated protective layer of dry permafrost. This structure was first predicted by [START_REF] Leighton | Behavior of carbon dioxide and other volatiles on Mars[END_REF] and subsequently confirmed by refined models (e.g., [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF][START_REF] Schorghofer | Stability and exchange of subsurface ice on Mars[END_REF][START_REF] Chamberlain | Response of Martian ground ice to orbitinduced climate change[END_REF][START_REF] Steele | Regolith-atmosphere exchange of water in Mars' recent past[END_REF]. Observations from gamma-ray and neutron spectroscopy (e.g., [START_REF] Boynton | Distribution of hydrogen in the near surface of Mars: Evidence for subsurface ice deposits[END_REF][START_REF] Mitrofanov | Neutron mapping of Mars with high spatial resolution: First results of the FREND experiment of the ExoMars project[END_REF][START_REF] Pathare | Driven by excess? Climatic implications of new global mapping of near-surface waterequivalent hydrogen on Mars[END_REF], thermal emission (e.g., [START_REF] Bandfield | High-resolution subsurface water-ice distributions on Mars[END_REF][START_REF] Bandfield | Martian high-latitude permafrost depth and surface cover thermal inertia distributions[END_REF][START_REF] Piqueux | Widespread shallow water ice on Mars at high latitudes and mid latitudes[END_REF], and direct excavation by the Phoenix lander [START_REF] Mellon | Ground ice at the Phoenix landing site: Stability state and origin[END_REF][START_REF] Smith | H2O at the Phoenix landing site[END_REF] confirm this structure. Unfortunately, the desiccated layer shields the ice from direct view, and exposed ice is expected to sublimate rapidly at mid-latitudes and create a new covering deposit, so the ice is usually concealed beneath dust and regolith.

Natural exposures provide local information about the current state of subsurface ice, such as the ice content, geographic distribution, and layering at each site. There are two main categories of natural exposure. Small craters (Fig. 1a) pierce the desiccated cover and create temporary exposures or excavate formerly buried ice onto their ejecta blankets [START_REF] Byrne | Distribution of mid-latitude ground ice on Mars from new impact craters[END_REF][START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF]. These constitute high-resolution point samples of the ice table and provide a valuable data set for comparison with less-direct, lower-resolution approaches to understanding the distribution of ice. However, these craters are small and shallow features, and the impact events also modify the ice relative to its baseline state. Direct, high-resolution vertical information on undisturbed midlatitude ice structure was minimal until the discovery of scarp exposures (Fig. 1b) cutting through the ice [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. The scarps are kilometers long, tens of meters high, and expose cross sections through the ice, revealing layering and unconformities. This ice was interpreted as sintered snow with a very low lithic content, and indications of glacial flow exist at one location. Rocks (>50 cm diameter) fell out of one of the scarps over three Mars years, suggesting ongoing sublimation, which was also indicated by weakening of H2O spectral absorption features over the course of the summer [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. In addition to the scarps and craters, exposed ice has been reported in some gully alcoves where it may be exposed by active erosion [START_REF] Dundas | The formation of gullies on Mars today[END_REF][START_REF] Khuller | Evidence of water-rich snow deposits within Martian gullies[END_REF], but this process has not been studied in depth.

The scarps are incised in surface-mantling deposits. Latitude-dependent mantle deposits were first observed by Mariner 9 [START_REF] Soderblom | Latitudinal distribution of a debris mantle on the Martian surface[END_REF]. They were initially thought to be aeolian dust deposits, but higher-resolution imaging provided evidence that they contain ice [START_REF] Mustard | Evidence for recent climate change on Mars from the identification of youthful near-surface ground ice[END_REF], in some cases forming thick units with a high ice content [START_REF] Conway | Decameter thick remnant glacial ice deposits on Mars[END_REF]. Layering indicates deposition in multiple distinct episodes [START_REF] Schon | A recent ice age on Mars: Evidence for climate oscillations from regional layering in mid-latitude mantling deposits[END_REF]. Polygonal cracking visible in some of these units (e.g., [START_REF] Mangold | High latitude patterned grounds on Mars: Classification, distribution and climatic control[END_REF]Levy et al., 2009a) indicates a structural integrity that is best interpreted as thermal contraction cracking of solid ice or ice-cemented regolith. These surfacemantling deposits are now widely thought to have been deposited as mixtures of snow or frost and dust (in unknown and probably variable proportions) within the last few million years during periods when Mars' axial tilt was higher than at present (e.g., [START_REF] Mustard | Evidence for recent climate change on Mars from the identification of youthful near-surface ground ice[END_REF][START_REF] Head | Recent ice ages on Mars[END_REF][START_REF] Schon | A recent ice age on Mars: Evidence for climate oscillations from regional layering in mid-latitude mantling deposits[END_REF][START_REF] Madeleine | Recent Ice Ages on Mars: The role of radiatively active clouds and cloud microphysics[END_REF]. [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF] documented seven scarp exposure sites in the southern hemisphere and one cluster in Milankovič crater in the north; [START_REF] Harish | Water-ice exposing scarps within the northern mid-latitude craters on Mars[END_REF] reported two additional scarps in the northern hemisphere. However, neither conducted a comprehensive survey. Additionally, the number of known ice-exposing craters has more than doubled since publication of [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF]. This work reports an assessment of the locations and properties of ice-exposing scarps in current data in both the northern and southern mid-latitudes and reports on the expanded data set of icy craters.

Methods

Data

The data sets used for this work included Thermal Emission Imaging System (THEMIS; [START_REF] Christensen | The Thermal Emission Imaging System (THEMIS) for the Mars 2001 Odyssey mission[END_REF] Daytime Infrared mosaics, Context Camera (CTX; Malin et al., 2007) images, and High Resolution Imaging Science Experiment (HiRISE;[START_REF] Mcewen | Mars Reconnaissance Orbiter's High Resolution Imaging Science Experiment[END_REF] images. The THEMIS products use daytime infrared observations and provide near-global mosaics at 100 m/pix [START_REF] Fergason | The THEMIS controlled mosaics of Mars and final smithed kernels[END_REF]. CTX images have near-global coverage at 6 m/pix. HiRISE images reprojected to 25 or 50 cm/pix cover only a small fraction of the surface and include a central swath with two additional colors (from blue-green and near-infrared filters) within the wider red-filter image. These images were often targeted to center on the features studied here. We used HiRISE data through Mars Reconnaissance Orbiter orbit 64,199 for study of icy craters and through orbit 66899 for icy scarps. We also inspected data from the Compact Reconnaissance Imaging Spectrometer for Mars (CRISM;Murchie et al., 2007) where available. CRISM is a visible and near-infrared spectrometer, which can provide more definitive evidence for water ice than our other data sets, but observations are spatially limited and often do not include the near-infrared wavelengths that provide the strongest evidence for ice. We followed the same CRISM processing techniques used in [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF].

Most HiRISE images include a near-infrared channel, so they do not detect the same wavelengths as the human eye. Thus when displayed in color, they do not show true colors. In the enhanced-color images shown in the figures herein (which are from standard Reduced Data Records), the near-infrared filter data are displayed as red, the red filter data are displayed as green, and the blue-green filter data are displayed as blue, and the images are stretched to show local contrast and emphasize color variations; this is standard procedure for HiRISE color products [START_REF] Delamere | Color imaging of Mars by the High Resolution Imaging Science Experiment (HiRISE)[END_REF]. The stretch is scene dependent for each observation, so conclusions about the apparent color of features in different images depend on the scene having a similar range of colors and shadows. This is often roughly true on Mars, where surface dust tends to be uniformly reddish. However, differences in topography, atmospheric dust content, illumination, and sublimation of ice can produce apparent differences in color between images as well as color changes in unchanged parts of the surface when comparing images of the same site.

Both raw HiRISE data and calibrated top-of-atmosphere reflectance for each channel are available via the Planetary Data System.

Materials that appear blue in stretched images may have a reddish true color but are brighter than their surroundings in the HiRISE blue-green channel. Material that appears white is brighter in all three channels, but generally not white in true color. We refer to these enhanced colors as "relatively blue" or "relatively white" in the text below.

Relatively blue or relatively white coloration is not diagnostic of exposed ice (notably, mafic materials including basaltic sand also appear relatively blue (Keszthelyi et al., 2008;[START_REF] Delamere | Color imaging of Mars by the High Resolution Imaging Science Experiment (HiRISE)[END_REF]). However, we considered the combination of a relatively blue or relatively white color closely associated with the distinctive morphology of a scarp or new crater sufficient to classify a feature as an ice exposure with a high degree of confidence. Changes over time often support the presence of ice, as described below.

Ice-Exposing Scarps

We conducted a survey of the distribution of ice-exposing scarps with the properties described by [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. We searched the THEMIS Daytime Infrared controlled mosaics [START_REF] Fergason | The THEMIS controlled mosaics of Mars and final smithed kernels[END_REF] In the southern hemisphere, we searched latitudes 45-70 S (planetocentric), and observed scarps only between 50-61 S. Based on the results of this search, we limited the northern-hemisphere survey to 45-65 N. All scarps identified in the northern hemisphere were between 53-59 N, indicating that these bounds were sufficiently wide.

Further support for these bounds is provided by [START_REF] Vincendon | Water ice at low to midlatitudes on Mars[END_REF], who searched CRISM data and found no exposed perennial ground ice between 45 S and 50 N. We looked for irregular pits greater than a few hundred meters across and checked candidates using images from CTX to look for the main identifying characteristic of ice-exposing scarps: an approximately straight, smooth, sharp-edged, pole-facing scarp (Fig. 1b).

Candidates possessing such a scarp were classified as probable if no HiRISE color data were available or considered confirmed if they displayed a distinct relatively blue coloration in HiRISE images. In some of the cases from [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF], spectral evidence provides additional confirmation of water ice, but CRISM data are often not available. An additional requirement was that coloration was present in late spring or summer (no earlier than Ls=70 in the north or Ls=250 in the south, although in most cases color data exist from after the solstice), to rule out lingering seasonal frost. The precise duration of seasonal frost depends on latitude, slope, aspect, and substrate (cf. [START_REF] Vincendon | Water ice at low to midlatitudes on Mars[END_REF][START_REF] Dundas | The formation of gullies on Mars today[END_REF] but these bounds make seasonal frost unlikely. Some sites were classified as confirmed but marginal. In these cases, the morphology matched other scarps, but the coloration was weak or only occurred on a small part of the scarp (Fig. 2a). Most scarps identified as candidates based on morphology were confirmed to have at least some relatively blue coloration (in the cases where HiRISE images exist), but some, particularly in Milankovič crater (Fig. 2b), have coloration matching the surrounding terrain. The latter are likely to be exposures that are partially or completely covered by an opaque coating of dust or debris, which is likely thin since the morphology remains sharp. Alternatively, the ice at such scarps might contain sufficient lithic material to suppress the coloration. Users of this data set may be able to treat the probable scarps as confirmed if future HiRISE or other observations meet the color criteria outlined above or yield spectral evidence of ice.

We considered the possibility that the scarps could be locations of year-round frost stability rather than exposed subsurface ice. Frost on steep (~30) mid-latitude slopes such as crater walls near 45 latitude survives until LS~40 in the north and LS~180 in the south; near 55, it persists until LS~50 and LS~210, respectively [START_REF] Vincendon | Water ice at low to midlatitudes on Mars[END_REF][START_REF] Dundas | The formation of gullies on Mars today[END_REF]. Near the poles H2O frost survives into summer on level ground (e.g., [START_REF] Appéré | Winter and spring evolution of northern seasonal deposits on Mars from OMEGA on Mars Express[END_REF] and the very steep pole-facing scarps have insolation roughly equivalent to the poles, although they receive more re-radiated heat from other slopes. However, the scarps are erosional features, as they incise into and remove surface material and have scarp-parallel ridges indicating past positions [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. Blocks falling from one scarp indicate an ongoing average retreat rate of millimeters per Mars year [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF] and the same processes should act on other scarps, which lack embedded rocks. Despite this, scarps retain relatively blue coloration through the summer. Although some scarps possibly reach an equilibrium state or even aggrade, the evidence that the scarps begin as erosional features, are actively retreating at present, and yet retain the coloration of ice year-round is inconsistent with persistent frost; the existence of morphologically identical scarps without icy coloration also indicates that the scarp topography does not produce long-lived frost. Additionally, CRISM band depth ratios at one scarp suggest coarse-grained ice rather than fine-grained frost. Finally, scarp temperatures rise above the H2O frost point [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. Thus, although there might be occasional cases of persistent frost, exposed ice is the dominant explanation.

The quality and completeness of the THEMIS mosaics are generally good, and the area where scarp pits might have been obscured or lost in data gaps is small. We also spot-checked many patches with deep shading from topography by examining CTX images and did not find any examples of pits or scarps hidden in this way. We used CTX data to more closely examine pits and scarps found in THEMIS mosaics that appeared consistent with the morphological criteria noted above. Those features are best seen when kilometer-scale and larger, but smaller pits that appeared to match the morphology were also inspected. Examination of hundreds of smaller or marginal-quality candidates gives us confidence that the above criteria were effective in identifying scarps. Examining every single pit or slope in the THEMIS-surveyed area at CTX resolution was not practical. In regions of dense pitting such as scalloped terrain, we inspected those severalhundred-meter scale features that appeared particularly sharp and distinct in the THEMIS mosaics, and in the course of this survey we also examined large numbers of other pits and slopes. This examination was sufficient to demonstrate that few scarps are not part of the pits that are distinctive in the THEMIS IR mosaics, although some exist.

Additionally, survey results demonstrate that some scarps display gradations in morphology. In aggregate, this survey likely includes nearly all sharply defined iceexposing scarps in the surveyed latitude zones that are near kilometer scale and larger. This completeness scale is not well defined, but we estimate that it is between 500 meters and 1 kilometer. Some smaller and less well-defined exposures are included here, but more probably remain to be discovered. The two scarps reported by [START_REF] Harish | Water-ice exposing scarps within the northern mid-latitude craters on Mars[END_REF] were independently identified by our survey, supporting its effectiveness in identifying scarps at these scales.

We measured scarp morphometric data in near-nadir HiRISE images.

Orthorectified images are not available for most sites, so precise geometric correction was not possible and all dimensions are approximate, but for typical near-nadir viewing geometry the distortion is small except on steep topography. Morphometric data include the end-to-end straight-line distance, the greatest plan-view width, the estimated retreat distance (between the scarp face and any geomorphic indication of the initiation point), and the orientation of a line connecting the scarp endpoints.

Only one site has a high-resolution digital terrain model (DTM) [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. For some sites where appropriate images exist, we made slope estimates using the shadow method of [START_REF] Dundas | Effects of lava heating on volatile-rich slopes on Io[END_REF]. This method takes advantage of the fact that for a given Sun position and slope azimuth, there is a unique slope angle at which the slope begins to cast shadows. We identified locations on the brink of self-shadowing by selecting sections of slope with patchy coverage by local shadows. This method has two major limitations. First, for any given Sun position it can only indicate particular slope/aspect combinations, which may not be representative of the whole scarp and certainly do not capture local variability. This could also result in biases when comparing between sites, since the available images might favor different slope/aspect combinations at different sites. Second, the method requires manual estimation of the downhill direction. This is challenging, especially on curved slopes, and results in large uncertainties. This method gives good results when applied to the scarp with a corresponding high-resolution DTM, but the inherent limitations must be considered in interpretation. Directional distortion due to map projection is minor for standard HiRISE images, which are reprojected in equirectangular projection with a center latitude near the image center.

We also documented the presence or absence of several possibly related geomorphic features in the vicinity of the scarps. These include scalloped depressions (cf. [START_REF] Morgenstern | Deposition and degradation of a volatile-rich later in Utopia Planitia and implications for climate history on Mars[END_REF][START_REF] Soare | Thermokarst lakes and ponds on Mars in the very recent (Late Amazonian) past[END_REF][START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF]2010;[START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF], expanded craters (cf. [START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF][START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF], and irregular pits, all of which may indicate sublimation and ice loss, as well as surface lineations indicative of flow (cf. [START_REF] Squyres | Martian fretted terrain: Flow of erosional debris[END_REF][START_REF] Milliken | Viscous flow features on the surface of Mars: Observations from high-resolution Mars Orbiter Camera (MOC) images[END_REF]. These features were documented if they appeared on the same material unit as the scarp and were within 10-20 km distance. For confirmed scarps with HiRISE coverage, we also documented smaller-scale features of the scarp-hosting unit within hundreds of meters of the scarp crest. These included polygons (interpreted as created by thermal contraction cracking; [START_REF] Mellon | Small-scale polygonal features on Mars: Seasonal thermal contraction cracks in permafrost[END_REF], surface boulders, which are of interest since their occurrence on top of deposits potentially originating as snowpack is surprising, and indications of layering exposed by the scarp, which could preserve a climate record.

Ice-Exposing Craters

New impact locations are usually identified by manual searches of images from CTX or other medium-resolution images, where they appear as dark markings due to disturbance of surface dust (Malin et al., 2006;Daubar et al., 2013). This leads to a bias towards detecting new impacts in high-albedo, low-thermal inertia (dusty) regions. These detections are also dependent on having before-and-after imaging to constrain their formation dates, and the availability of such imagery varies spatially and temporally.

Follow-up with higher-resolution imaging from HiRISE is usually needed to confirm the presence of a crater and determine its size. In some cases at middle and high latitudes, the new impacts reach deeply enough to excavate ice. The ice gradually sublimates, causing excavated material to change color to match the nearby regolith over a period of months to years [START_REF] Reufer | Models of high velocity impacts into dust-covered ice: Application to Martian northern lowlands[END_REF][START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF]. Hence, only impacts formed within the last few months or years are reliable probes for ice. Unfortunately, sublimation and the associated fading of the ice exposures are fastest at the lowest latitudes, where the presence or absence of ice is least certain, implying that detection of ice is also least efficient at those latitudes. At higher latitudes, the seasonal polar cap is particularly effective at obscuring fresh impacts, as dark blast zones within the bounds of the seasonal cap are erased within the first winter [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF] due to dust deposition or redistribution, although ice sometimes remains distinct. Additionally, the dark markings surrounding new impacts can fade within several Mars years, and more changes to the blast zones are seen at higher absolute latitudes (Daubar et al., 2016), likely due to seasonal processes, implying that the overall detections of new craters are less efficient at high latitudes.

A strong theoretical and observational basis indicates that shallow ground ice is almost ubiquitous poleward of ~45-50 N/S and rare equatorward of ~30-35 N/S (e.g., [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF][START_REF] Bandfield | Martian high-latitude permafrost depth and surface cover thermal inertia distributions[END_REF][START_REF] Pathare | Driven by excess? Climatic implications of new global mapping of near-surface waterequivalent hydrogen on Mars[END_REF][START_REF] Piqueux | Widespread shallow water ice on Mars at high latitudes and mid latitudes[END_REF], but the true boundary within that range is an unknown that can be tested with observations of these craters. Therefore, we examined all new craters poleward of 35 N/S and made an interpretation of the icy status based on the criteria discussed below.

We use HiRISE enhanced color observations as our primary means of determining whether ice is likely exposed. The ice exposed by craters is bright and generally appears relatively blue or relatively white in HiRISE enhanced color. Relatively white coloration is uncommon in non-polar HiRISE images and with appropriate context can be highly indicative of frost or ice. Relatively blue coloration can also be due to mafic materials (Fig. 3a), but we treat it as indicative of ice when other evidence is strongly supportive of this interpretation: i.e., the material is substantially brighter than surroundings rather than simply distinct in color. An additional indicator of ice is that material is distinct from other ejecta and crater floor materials, suggesting that some ejecta is ice and some is icefree even if both are relatively blue. This is expected because the Martian surface is mostly mafic, even when ice is present. For small exposures, the ice is often in discrete patches with a distinct color relative to other excavated material. Other than the initial decision to only examine craters above 35, latitude was not used to interpret the presence of ice, since the distribution of ice is not completely understood. Some material interpreted as ice was slightly relatively yellow, but substantially brighter than the surroundings and in settings where thermal contraction polygons also strongly support the presence of subsurface ice. Possible ice with a relatively yellow coloration has been reported in a gully alcove elsewhere on Mars [START_REF] Khuller | Evidence of water-rich snow deposits within Martian gullies[END_REF], so this coloration is consistent with the presence of ice as well.

CRISM can provide definitive spectral tests for ice in some cases where the exposure is large enough [START_REF] Byrne | Distribution of mid-latitude ground ice on Mars from new impact craters[END_REF]), but we do not use this as part of our diagnostic process because most of the marginal cases are small (2-10 m diameter craters) and unlikely to produce an unambiguous spectral signal in 18 m/pix CRISM data.

In many cases appropriate CRISM observations do not exist. Three factors, however, support a general interpretation of the impact features meeting these color criteria as icy, rather than exposed salts or other bright lithic material: (1) CRISM confirmation of ice at several sites that share the indicators that we use for ice [START_REF] Byrne | Distribution of mid-latitude ground ice on Mars from new impact craters[END_REF]; (2) lack of spectral detections of other materials that might account for the bright deposits; and (3) fading and disappearance over time consistent with sublimation at many of these sites [START_REF] Reufer | Models of high velocity impacts into dust-covered ice: Application to Martian northern lowlands[END_REF][START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF]. Since there is a strong theoretical basis to expect ice at these latitudes and cryogenic landforms are common around the craters, this is the simplest interpretation; as discussed below, our diagnostic criteria are likely underestimating the occurrence of ice.

We also note candidates where we consider the evidence for ice to be less compelling. These are divided into (1) probable ice, where ice is our preferred interpretation but not considered definitive due to very small size, weaker color contrast with other ejecta, or lack of a well-defined crater; and (2) possible ice, where there is a small color feature in the crater with minor contrast, or a bright feature that could be due to topographic effects. Some sites initially classified as possible or probable were later elevated to confirmed if the candidate exposure became less distinctive over time in a manner consistent with sublimation and lag development (i.e., a color feature reverting to match adjacent surfaces more quickly than the general fading of the blast zone). Some low-and mid-latitude impacts (e.g., Fig. 3b) expose relatively bright material that contrasts with a dark surface but is not interpreted as icy. Few of these exist in our study latitudes. The surface geomorphology surrounding these sites generally does not suggest ice (in particular, no polygons are interpreted as thermal contraction cracks).

Most of these craters occur at low latitudes (<35) outside our survey area, where theoretical models suggest that shallow ice is unlikely (e.g., [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF].

Additionally, most or all of the ejected material is bright rather than isolated patches. At low latitudes ice should be covered by a significant thickness (>1 m) of regolith or it would otherwise sublimate rapidly, so if there were ice, it would occur in the ejecta as a mix of ice and non-icy regolith. These bright ejecta deposits may be similar to exposures of bright material by rover wheels in Gusev crater (e.g., [START_REF] Rice | Temporal observations of bright soil exposures at Gusev crater, Mars[END_REF] or other surface/subsurface compositional or grain size differences. While these craters provide information about the Martian subsurface, they are not considered further in this discussion of subsurface ice.

The icy craters that we document are those that expose persistent bright ice that remains distinct for months to years while sublimating, indicating clean ice with a low lithic content. Some apparently non-icy craters may have exposed subsurface pore ice, which would be all but impossible to detect from orbit. As shown by the Phoenix lander excavations, exposed pore-filling ice is dark, and in summer at mid-to-high latitudes it sublimates enough to create a surface coating that is indistinguishable from regolith within days [START_REF] Mellon | Ground ice at the Phoenix landing site: Stability state and origin[END_REF][START_REF] Smith | H2O at the Phoenix landing site[END_REF]. This is much shorter than the typical time between the impact and acquisition of HiRISE images. Candidate impacts at high latitude are usually imaged by HiRISE within weeks of the initial detection in lowerresolution images, but that initial detection can be one to several years after the crater formed. One caveat is that the impact process may generate fractures and fine-grained material, which would be brighter than the pore ice exposed by the Phoenix lander, but a small amount of sublimation would still quickly produce an opaque cover under those conditions. Additionally, the small size of many of these craters means their shallow depths of only tens of centimeters may not be enough to reach the ice table. Finally, at high latitudes the seasonal cap reworks the surface, removing blast zones and obscuring ice, which can preclude detection and confirmation if craters are not imaged or re-imaged before winter. Thus, the set of craters we consider confirmed ice exposures are a minimum, and subsurface ice could exist at other known or unknown impact locations.

Scarp Observations

The full set of scarp exposures is given in Tables S1-S2 and mapped in Fig. 4. Below, we discuss some relevant morphological and geographical observations.

Scarp Distribution

In the southern hemisphere, 21 confirmed exposure sites were identified in the southern hemisphere (some with multiple scarps), along with two candidates lacking ice coloration, and one for which no HiRISE color data were available at the time of writing.

The southern-hemisphere scarps are confined to a narrow range of longitudes near the Hellas basin, not evenly distributed throughout the latitude band. Most of the exposures are between 80-115 E longitude and 50-61 S latitude, similar to those previously known. A few occur in scalloped terrain (cf. [START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF] at 50-61E and a small cluster near 137 E.

Scarps in the northern hemisphere are strongly concentrated in the mantling deposits within Milankovič crater (54.5 N, 213.5 E), which we subdivided into four sites in Table S1 based on the four cardinal directions. Over 70 features have the morphology of ice-exposing scarps at this location, although in HiRISE data some lack the relatively blue coloration indicative of exposed ice. Beyond Milankovič, a handful of scarp sites occur in crater-fill materials farther east, and one occurs in northern Utopia Planitia (96E).

Scarp Morphology and Morphometry

Most scarps have a simple morphology (e.g., Fig. 1b), but a few have several subparallel faces (Fig. 5) or are divided into adjacent segments. Many exhibit faint, crude layering or color banding, but distinctive sub-meter-scale layers are uncommon (Fig. 6).

Scarp lengths range from 200 m-6.5 km, and plan-view scarp widths range from 20-200 m. Length, width, and estimated retreat distance are loosely correlated (Fig. 7a,b).

Latitude appears to weakly influence the upper envelope of scarp retreat distance, with somewhat greater scarp retreat at lower latitude (Fig. 7c). This may indicate active formation of new scarps, coupled with faster retreat at lower latitudes, because retreat distance should be a function of scarp age and sublimation rate. The latter will be influenced by latitude. However, the ratio of scarp length to retreat distance (the planview aspect ratio of the pits) shows no trend with latitude (Fig. 7d). This aspect ratio indicates the extent to which the scarp widens as it retreats. All scarps in both hemispheres approximately face the pole but most are oriented slightly east of due poleward, with a typical offset from N/S of 5-10. This offset could relate to morning/afternoon asymmetries in temperature combined with the thermal inertia of the surface reducing peak temperature. Individual scarps have along-scarp orientation variations on the same order as this offset.

The one scarp for which high-resolution topographic data exist (southern scarp #1) has typical slopes of ~45 with moderate variations both vertically and laterally [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. Shadow-derived estimates at four locations on this scarp are 47-49, demonstrating that the method gives reasonable results for typical scarp geometry. Shadow-derived slope estimates for other scarps with appropriate shadow conditions are given in Table S3. In the southern hemisphere, slopes range from 41-60, with most between 45-50. In the north, a variety of confirmed and candidate exposures have slopes of 40-64. The mean slope in the north (53) is similar to that in the south (49). These estimates suggest that southern scarp #1 is typical. These slopes indicate that the planview widths of the scarps approximate the vertical relief to within a factor of 2. Furthermore, the pits do not necessarily reach all the way to the bottom of the ice, so the ice thicknesses may be even larger.

As reported in [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF], scarp-parallel features indicate that scarps retreat generally equatorward and that retreat is uniform along the length of the scarp.

Triangular or other shapes of the resulting pits indicate that the scarp width can vary over time (Fig. 8). Scarp retreat appears to be close to uniform along the length of the scarp, such that when the retreat direction is oblique rather than normal to the scarp, the orientation of the scarp remains unchanged (Fig. 8). Notches in the plan-view shape of pits (Fig. 8) suggest that scarp retreat occasionally reactivates only over part of its length; the other parts may reactivate later, giving rise to the small parallel outliers seen in some pits. The aspect ratio of the scarp pits shows substantial scatter (Fig. 7d), so the rate at which scarps widen as they retreat is highly variable.

Scarp Setting

The regional properties of the locations are broadly similar in both hemispheres.

All of the identified scarps occur within deposits that appear to mantle the regional surface (Fig. 9); although in a few cases, the uppermost part of the mantling deposit may have been removed (Fig. 9c). In the southern hemisphere, the kilometer-scale regional slopes around the scarps and pits are mostly pole-facing but generally low (typically ~5 in the Mars Orbiter Laser Altimeter digital elevation model), and some are nearly flat.

The scarps there are often associated with the slopes of few kilometer-scale local massifs or crater walls. In the northern hemisphere, the vast majority of scarps and candidate scarps are in Milankovič crater. They are found on all slope orientations therein, but primarily on the west side of the crater (Fig. 10). As in the south, the regional slopes are generally low. The material on the slopes of the crater may have a low density (at least within the upper 5 meters) as it has a low radar surface reflectivity [START_REF] Morgan | Subsurface water ice mapping (SWIM) on Mars: Radar surface reflectivity[END_REF].

The other northern-hemisphere candidates are found within materials that infill few kilometer-scale impact craters. The regional albedos from the Thermal Emission Spectrometer (TES; [START_REF] Christensen | Mars Global Surveyor Thermal Emission Spectrometer experiment: Investigation description and surface science results[END_REF]) are all close to 0.2, and the regional apparent thermal inertias from TES [START_REF] Putzig | Apparent thermal inertia and the surface heterogeneity of Mars[END_REF] are between 128-225 J m -2 K -1 s -0.5 , consistent with a surface layer of unconsolidated dry soil a centimeter or more deep, with the sole exception of the site in Utopia.

Although the scarps are characteristically within mantling deposits, the associated geomorphology is variable. Candidate ice-loss features (scalloped depressions and expanded craters) are found near some of the scarps, but in most cases the landforms are not well-defined examples. However, irregular pits that do not closely match the scalloped or expanded morphologies are almost ubiquitous across the scarp-hosting mantling deposits. Arcuate lineations indicative of ice flow are uncommon. In the plateau material at the top of the scarp, polygons (likely due to thermal contraction of ice) are common but not ubiquitous, and often not well defined, which may indicate that the ice is deep enough to not experience strong thermal cycles or that it anneals effectively without infall of material into the cracks. In some cases the surface material consists of aeolian bedforms and so may currently be too mobile to develop defined polygons. The brink of the scarp is often broken into blocky fragments that might be defined by subtle polygonal fractures that have generated little surface relief. Polygons are also common on the walls and floors of some pits. The upper surface of the scarp-forming material usually has few boulders, particularly in the northern hemisphere.

CRISM data confirm exposed ice at several scarps (Table S1) beyond those described in [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. Detections at two of the scarps were independently confirmed by [START_REF] Harish | Water-ice exposing scarps within the northern mid-latitude craters on Mars[END_REF]. Notably, one observation of the icy scarp at 57 N, 95.7 E (northern scarp site #4) shows a distinct water ice signature, as well as an ambiguous spectral signature in the visible to near-infrared, suggesting impure ice. The simultaneously acquired HiRISE image shows only a weak color signature covering parts of the scarp, leading to a classification of confirmed but marginal. This suggests that all scarps with the classic morphology could be ice exposures, regardless of coloration.

Either the covering lag is too thin to completely suppress the ice spectral signature or the lithic content of the ice is high enough in some cases that the coloration seen in HiRISE is minimal. If the coloration is from a lag coating, it must be very thin, as a dust coating of tens of microns can be opaque at visible wavelengths [START_REF] Wells | Mars: Experimental study of albedo changes caused by dust fallout[END_REF][START_REF] Fischer | The continuum slope of Mars: Bidirectional reflectance investigations and applications to Olympus Mons[END_REF]. If the coloration reflects the bulk ice composition, this is still consistent with a high ice content. [START_REF] Cull | Composition of subsurface ices at the Mars Phoenix landing site[END_REF] show that for as little as 10 weight % lithics (>95 volume % ice) the visible color contrast may be minimal, and [START_REF] Clark | Spectral properties of ice-particulate mixtures and implications for remote sensing. 1. Intimate mixtures[END_REF] showed substantial darkening and weak spectral absorption features for even smaller amounts of non-ice material, depending on its albedo. Further monitoring with HiRISE might distinguish between these possibilities, as lags could be removed episodically. [START_REF] Harish | Water-ice exposing scarps within the northern mid-latitude craters on Mars[END_REF] also noted some scarps at northern scarp site #5 with relatively blue coloration but no spectral signature of ice, likely because the scarps were substantially shadowed.

Numerous pits were examined and determined not to meet the morphological criteria for likely ice exposures. Some of these may be former scarps that have become buried under sublimation lags that are thick enough to obscure the sharp morphology of clean exposures. Examples of pits without distinct scarps are shown in Fig. 11 for comparison, and Fig. 8 shows a pit that mostly lacks exposures apart from a small outlier scarp.

Crater Observations

HiRISE images now cover 48 ice-exposing impact sites (Fig. 12 and Table S4).

The diameter of ice-exposing and non-ice-exposing craters poleward of35 N/S is shown in Fig. 13. Diameter scales linearly with maximum excavation depth for small craters [START_REF] Melosh | Impact Cratering: A Geologic Process[END_REF], and Fig. 13 also shows 0.084 the crater diameter. This value is given since the maximum excavation depth is ~1/10 of the transient crater diameter and the transient crater is ~0.84 the final diameter for simple craters [START_REF] Melosh | Impact Cratering: A Geologic Process[END_REF]; although seemingly precise, this depth should only be treated as an approximation. The data set is more extensive than that in [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF] but is broadly similar and does not change the interpretations made therein. Those include the widespread occurrence of clean ice with local heterogeneity, as well as the latitudinal distribution in the northern hemisphere, which suggests that the long-term atmospheric water vapor content was higher than at present and/or that there is a near-surface concentration of vapor. The morphology of the ice exposures ranges from small fractions of the crater interior to extensive icy ejecta. Several important new observations and their interpretations are discussed below.

Weak material over a strong layer produces characteristic crater morphologies of flat floors and benches or terraces for craters with diameters approximately 4-10 times the weak layer thickness [START_REF] Quaide | Thickness determination of the lunar surface layer from lunar impact craters[END_REF]. The depth to the strong layer can be estimated using the methods of [START_REF] Bart | The quantitative relationship between small impact crater morphology and regolith depth[END_REF]. For sites with exposed ice, there is a high likelihood that such a strong layer is the top of the ice table since the ice is known to exist and should provide a strength contrast. We apply this method at sites with multiple flatfloored craters. Those craters are often not the same as those with visible ice, since the ice exposures tend to be in the largest craters that penetrate more deeply into the ice table.

(For sites without confirmed bright ice, the morphology could be produced by pore ice but also by shallow bedrock or another strength contrast, making the interpretation less certain.) The results (Table 1) show significant variability in depth to the strong layer between different craters in individual clusters. This likely reflects both real local depth variation and measurement uncertainty. In combination with differences in the visibility of ice in similarly sized craters [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF], this indicates that heterogeneities in the ice table depth and ice content are significant at scales of tens to hundreds of meters.

Fewer new craters (icy or not) have been discovered in the southern hemisphere in comparison with the north, mainly because the less extensive dust cover in the south inhibits detection, but also due to different imaging and search techniques that vary by region. The distribution is still sufficiently sparse that the southern latitudinal boundary is not well defined. However, the number and distribution of icy impacts observed in the southern hemisphere has expanded significantly relative to [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF], and the lowest-latitude ice detection in the south is now at 46.2 S. That crater is on a slight polefacing slope with nearby gullies and thus may not be representative of level ground, but there is also a probable candidate on flat ground at 42.6 S.

In the northern hemisphere, the lowest-latitude detection remains at 39.1 N. This location is part of a southward excursion of icy crater detections extending between ~145-205 E where ice detections are common between 40-50 N (Fig. 12). This contrasts with a lack of confirmed icy craters at those latitudes between 205-255 E. The region lacking icy craters corresponds to terrain where stability models predict that ice should be quite shallow and extend particularly far towards the equator due to high albedo and low thermal inertia [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF], so it is possible that pore ice is dominant at the top of the ice table there. Some of the non-ice-exposing craters in this area have flat floors which could indicate such a pore ice table, but this interpretation is nonunique. At other longitudes, new crater detections between 40-50N are sparse, and the only other ice detections equatorward of 47.4 N are on lineated valley fill; these detections may not indicate extant ice under the surface in those areas apart from within the lineated valley fill.

Two craters near Protonilus Mensae excavated lineated valley fill and confirm the presence of ice within a few meters of the surface there between 41-42 N (Fig. 14). This could be the top of glacial ice that has been detected in similar material by the Shallow Radar (SHARAD; [START_REF] Holt | Radar sounding evidence for buried glaciers in the southern mid-latitudes of Mars[END_REF][START_REF] Plaut | Radar evidence for ice in lobate debris aprons in the midnorthern latitudes of Mars[END_REF][START_REF] Petersen | High ice purity of Martian lobate debris aprons at the regional scale: Evidence from an orbital radar sounding survey in Deuteronilus and Protonilus Mensae[END_REF], the top of which is not detectable at SHARAD resolution (approximately 10 m in ice); however, ice-rich lenses or other structures within a thicker debris cover cannot be ruled out. In the eastern part of the crater shown in Fig. 14a, ice exposed in the crater wall appears to make up the core of a surficial topographic ridge (a part of the surface type sometimes referred to as "brain-coral" or "brain" terrain (e.g., Noe [START_REF] Noe Dobrea | Patterned ground as an alternative explanation for the formation of brain coral textures in the mid latitudes of Mars: HiRISE observations of lineated valley fill textures[END_REF][START_REF] Levy | Concentric crater fill in Utopia Planitia: History and interaction between glacial "brain terrain" and periglacial mantle processes[END_REF]) that was cut by the impact, providing information about the subsurface structure of such material. In both of these craters the visible ice exists mostly in discrete blocks, in contrast with most others; this suggests that the shallow subsurface ice is in discrete bodies surrounded or covered by ice-free debris, which may indicate that ice at these locations is unstable and sublimating, since ice would be expected to cement the regolith pore space at these depths if it were stable.

Polygons attributed to thermal contraction cracking (e.g., [START_REF] Mellon | Small-scale polygonal features on Mars: Seasonal thermal contraction cracks in permafrost[END_REF] are nearly ubiquitous at the sites of ice-exposing impacts. They are occasionally found around new impacts where HiRISE images do not show bright ice but much less frequently. At some of those sites impacts probably exposed pore ice or did not excavate to the depth of the ice table. This suggests that thermal-contraction polygons and presentday ice are strongly correlated and that relict ice-free polygons are uncommon. However, the morphology of the polygons is diverse, including high-centered and low-relief features, irregular or incomplete polygon networks, as well as regularly spaced low-relief hummocks without defined fractures. Thus, the relationship between the detailed polygon morphology observable at HiRISE resolution and the presence of excess ice is not simple, but ice-exposing craters are sparse and offer limited information about the vertical structure of the ice.

An 18 m-diameter crater that formed on the south polar layered deposits (SPLD) during southern winter of Mars Year 34 showed minimal bright ice once the seasonal frost had vanished (Fig. 15ab) and was classified as probable. This crater is discussed more extensively in [START_REF] Landis | South Polar Layered Deposits near-surface properties inferred from a dated impact crater[END_REF]. A second crater cluster in the southern midlatitudes has been observed to form with ejecta superposing seasonal frost (Fig. 15c). This site also lacks bright ice once defrosted, but the craters are much smaller and may not have excavated to ice. In both cases the crater morphologies appear minimally affected by the presence of CO2 frost at the time of impact, demonstrating that seasonal frost probably has little effect on the long-term cratering record except for extremely small craters.

The SPLD and Protonilus craters also enable us to assess whether any of the observed bright ice is due to melting/refreezing (cf. [START_REF] Reufer | Models of high velocity impacts into dust-covered ice: Application to Martian northern lowlands[END_REF] or condensation of vapor post-impact, rather than representing the original state of ground ice. If the former were the case those effects would be expected to be strongest in the largest craters, which represent the most energetic impacts. Small bolides should be slowed by the atmosphere and their small craters should have little if any melting, so we can rule out the possibility of impact generation of clean ice if it does not occur in the larger craters.

The 18 m crater on the SPLD (Fig. 15a,15b) is larger than most lower-latitude craters with visible ice exposures but has negligible amounts of bright ice. The SPLD certainly contains significant ice content in bulk (at least 85%; [START_REF] Plaut | Subsurface radar sounding of the south polar layered deposits of Mars[END_REF][START_REF] Zuber | Density of Mars' south polar layered deposits[END_REF] although the near surface could be pore-filling ice, and theory indicates that ice should begin at depths of centimeters there (e.g., [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF]. Likewise, discrete ice blocks occur around the largest ice-exposing crater (Fig. 14a) as well as several others. Long-baseline temporal monitoring of several craters demonstrates shrinking and disappearance of blocks of ejected ice, as reported at other sites by [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF], suggesting that the blocks are massive ice. These blocks are inconsistent with melt pools or condensation. Thus, several of the largest ice-exposing craters have characteristics that show that the bright ice is not produced by the impact process. This implies that the observed clean ice represents the natural state of the pre-impact ice for most or all craters.

High ice contents (well above pore-filling) are widespread in the shallow subsurface at latitudes above ~40 N.

Only five of the confirmed ice-exposing impacts have an H2O ice signature in CRISM data (Table S4), while 23 have CRISM data without an ice detection. All five are among the larger craters or clusters of several craters and have large swaths of ice in their ejecta rather than small exposures in the crater itself. In some locations, we also analyzed repeat CRISM observations, but the absorption bands attributed to water ice were weak and barely detectable above the noise. Either atmospheric haze, accumulated surface dust, or spectral mixing and signal being averaged into multiple pixels precluded detection of ice in the later CRISM images after the initial observation. This demonstrates that extensive areal exposures and contemporaneous observations are required for ice detection by CRISM, as even the largest ice exposures only occupy portions of a handful of pixels.

Discussion

Importance of Subsurface Ice Exposures

These surveys of scarps and craters directly provide information about the nature and distribution of subsurface ice on Mars. They also provide an extensive set of locations that can be used for validation of the presence and properties of ice indicated by other data and models. While they have not been studied in situ, these locations provide more direct and localized information on the state of the ice than other methods currently available. This level of verification and detail is useful for interpreting other data sets (e.g., [START_REF] Pathare | Driven by excess? Climatic implications of new global mapping of near-surface waterequivalent hydrogen on Mars[END_REF][START_REF] Piqueux | Widespread shallow water ice on Mars at high latitudes and mid latitudes[END_REF], for design of possible ice-detection instruments (e.g., [START_REF] Haltigin | Orbital Synthetic Aperture Radar for subsurface ice detection on Mars: Scientific rationale and Canadian technical concept[END_REF], and for the possible use of ice by human explorers (cf. [START_REF] Heldmann | Midlatitude ice-rich ground on Mars as a target in the search for evidence of life and for in situ resource utilization on human missions[END_REF][START_REF] Putzig | Subsurface Water Ice Mapping (SWIM) on Mars to support in situ resource utilization[END_REF].

Both the craters and scarps provide information about the local state of the ice table, but the difference in the nature of the exposure and exposure process poses challenges for analyzing the two together. For instance, impact-exposed ice is often relatively white while the scarps are generally relatively blue. This may indicate some degree of impact modification (e.g., fracturing reducing the grain size or increasing porosity). Additionally, these differences in relative color could in part be related to the surrounding terrain. Quantitative photometry including assessment of topography and atmospheric scattering is needed before such color differences can be confidently interpreted. The craters represent semi-random samples (subject to detection biases), while certain regions or certain ice properties may be conducive to scarp formation, as discussed below. Finally, different properties are measurable for each: for instance, craters primarily provide information on the depth to ice. Scarps place lower bounds on the ice thickness, but the depth to the top of the ice may be obscured by material falling from the scarp crest. Despite this, in some places ice, can be seen within 1 m of the scarp crest [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF] and could be exposed by craters.

The expanded surveys presented here are generally consistent with previous interpretations of the state and distribution of ice based on a more limited sampling of features [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF]2018). The larger data sets presented here do provide several new insights into the origins, properties, and distribution of subsurface ice, discussed in the following sections.

Distribution, Properties, and Origins of Subsurface Ice

The lowest-latitude detection of ice based on craters is unchanged in the north compared with [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF]. Exposure of clean ice by new impacts is common, indicating that such ice is widespread at shallow depths. The poleward-shallowing trend of ice in crater exposures reported by [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF] is confirmed by the additional data reported here, with depth and latitudinal boundary similar to theoretical predictions.

Poleward of ~50 N/S latitude, most dated new impacts either definitely or possibly expose bright ice. In crater clusters the larger craters generally expose bright ice and the smaller ones do not (Table S4), but in several instances this relation is reversed. The latter requires lateral heterogeneities in the distribution or concentration of ice in the upper meter of the subsurface or variable impact properties and distribution of ejecta. The depth to ice also has significant local variability when measured within crater clusters (Table 1), consistent with theoretical predictions [START_REF] Sizemore | Effects of soil heterogeneity on Martian ground-ice stability and orbital estimates of ice table depth[END_REF] and excavations by the Phoenix lander [START_REF] Mellon | Ground ice at the Phoenix landing site: Stability state and origin[END_REF].

The apparent variation in icy crater detections between 40-50 N, from frequent icy craters between 145-205 E to a lack at 205-255 E, corresponds with features in several other data sets. This zone of low-latitude icy craters corresponds to a region where neutron spectroscopy shows high ice content (greater than pore-filling) extending to lower latitudes than in the rest of the northern hemisphere [START_REF] Pathare | Driven by excess? Climatic implications of new global mapping of near-surface waterequivalent hydrogen on Mars[END_REF]. The transition near 205 E approximately matches the transition from abundant expanded craters (to the west) to few (to the east) in the mapping of [START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF], although that map has little coverage west of 190 E. [START_REF] Viola | Geomorphological evidence for shallow ice in the southern hemisphere of Mars[END_REF] show that expanded craters equatorward of 40 N are concentrated between 185-205 E. The zone of icy craters also corresponds to radar detections of a low dielectric constant (interpreted as indicating a high ice content extending to tens of meters depth), which are concentrated between 180-215 E [START_REF] Bramson | Widespread excess ice in Arcadia Planitia, Mars[END_REF] and interpreted as a regional ice sheet. The high bulk ice content of this unit has been challenged based on radar loss tangent estimates [START_REF] Campbell | Fine-scale layering of Mars polar deposits and signatures of ice content in nonpolar material from multiband SHARAD data processing[END_REF], but the agreement of the ice exposures and neutron spectroscopy suggests that at least the upper centimeters of the material are ice-rich, which is further supported by the observation of expanded craters [START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF].

A similar ice sheet has been proposed in the Utopia region [START_REF] Stuurman | SHARAD detection and characterization of subsurface water ice deposits in Utopia Planitia, Mars[END_REF] based on mapping of radar reflectors that indicated a dielectric constant similar to that of ice. No new impact detections are in the region of radar reflectors mapped by [START_REF] Stuurman | SHARAD detection and characterization of subsurface water ice deposits in Utopia Planitia, Mars[END_REF], likely because a lack of surface dust makes such detections rare (Fig. 12). However, one ice-exposing crater is within the broader geomorphic unit of mesas and scalloped depressions [START_REF] Kerrigan | The periglacial landscape of Utopia Planitia: Geologic evidence for recent climate change on Mars[END_REF] that contains the reflectors. Such scalloped depressions have been attributed to partial sublimation of an ice-rich unit (e.g., [START_REF] Morgenstern | Deposition and degradation of a volatile-rich later in Utopia Planitia and implications for climate history on Mars[END_REF][START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF][START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF][START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF], the top of which may be indicated by the crater exposure.

Scarp exposures provide relatively weak constraints on the global distribution and properties of ice on Mars, since they are at higher latitudes than many of the craters and may not reflect the typical state of shallow subsurface ice. However, they provide important constraints on local properties. The scarps generally occur in surface-mantling deposits. Mantling deposits that have been interpreted as ice-rich are common at middle to high latitudes (e.g., [START_REF] Mustard | Evidence for recent climate change on Mars from the identification of youthful near-surface ground ice[END_REF][START_REF] Head | Recent ice ages on Mars[END_REF][START_REF] Milliken | Viscous flow features on the surface of Mars: Observations from high-resolution Mars Orbiter Camera (MOC) images[END_REF][START_REF] Schon | A recent ice age on Mars: Evidence for climate oscillations from regional layering in mid-latitude mantling deposits[END_REF]; the scarp regions appear somewhat more extensively mantled than other areas, but this is difficult to quantify. The fact that scarps occur only in a narrow latitude band in both hemispheres suggests that some process controlled by latitude is important to exposing the ice, meaning that similar ice could exist elsewhere. However, since the scarps are concentrated at certain longitudes while ground ice is expected to be ubiquitous at these latitudes (e.g., [START_REF] Mellon | The presence and stability of ground ice in the southern hemisphere of Mars[END_REF][START_REF] Schorghofer | Stability and exchange of subsurface ice on Mars[END_REF][START_REF] Chamberlain | Response of Martian ground ice to orbitinduced climate change[END_REF], some other factor(s) relating to the state of ice or the physical processes exposing it is also necessary to explain the scarp distribution. These observations can be explained if ice exposures occur within a subset of mantling deposits where ice is particularly thick and/or pure, providing longitudinal or local control, and if particular latitudinal conditions (e.g., insolation and temperature) are required to create and maintain the exposure. Supporting this possibility, the scarps in the southern hemisphere are mostly located in longitudes where neutron spectrometer data show high ice contents (60-90 weight percent) extending to relatively low latitudes [START_REF] Pathare | Driven by excess? Climatic implications of new global mapping of near-surface waterequivalent hydrogen on Mars[END_REF]. The same region also overlaps the location of the largest concentration of scalloped depressions and thermokarst landforms in the southern hemisphere [START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF][START_REF] Viola | Geomorphological evidence for shallow ice in the southern hemisphere of Mars[END_REF], also consistent with high ice contents. Scarps and their host mantling units often appear localized near massifs or crater walls, which might help concentrate snow deposition in incipient glaciers, but these correlations with other data sets suggest that the scarp-hosting ice bodies are associated with high regional ice contents. In this interpretation, the ice at the exposures represents an ice-rich end-member of the diversity of Martian near-surface mantling and ice deposits. Fully testing this hypothesis requires more information on the state of ground ice at locations without scarps; crater exposures are too shallow to provide a full comparison.

The ice exposed in the scarps likely originated as snow or frost, which has now been compacted. This is based on two main lines of evidence. First, the hosting units typically drape the surface in a manner consistent with atmospheric deposition rather than infilling topographic lows, and the scarp properties imply a very low lithic content [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. Second, the fine crosscutting layers observed at some scarps (Fig. 6) are most consistent with snow, since subsurface growth of ice lenses or other structures (e.g., [START_REF] Sizemore | Initiation and growth of Martian ice lenses[END_REF] would likely parallel the surface and not produce crosscutting relationships. (This could arise within an airfall deposit that was partially eroded and then covered, but the high ice content [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF] is better explained by snow or frost.) Moreover, non-snow theories for the development of high subsurface ice contents on Mars, such as ice lens growth or enhanced vapor diffusion (e.g., [START_REF] Fisher | A process to make massive ice in the Martian regolith using longterm diffusion and thermal cracking[END_REF][START_REF] Sizemore | Initiation and growth of Martian ice lenses[END_REF] operate in the near surface rather than building units >100 m thick.

The presence of boulders on the surface of scarp-hosting units was noted as a puzzle by [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. If the massive ice deposits are consolidated snow, they should lack clasts larger than windblown sand or dust. The additional scarps included in this larger sample set mostly exhibit few or no surface boulders at the top of the unit. This observation is more favorable for a snowpack model than are abundant boulders, but the presence of any large rocks remains a puzzle. Rocks can be concentrated by sublimation processes [START_REF] Aylward | Formation of coarse sediment lags in ice-sediment mixtures: A geomorphic signature of sublimation on regolith surfaces[END_REF], but must be present initially. Indications of glacial-style flow are rare at these locations, so rafting to concentrate rocks at the surface may be an insufficient explanation for boulders superposing the ice. An alternative is that boulders are lifted and held at the surface during ice accumulation [START_REF] Schorghofer | History and anatomy of subsurface ice on Mars[END_REF], but boulders are embedded within ice at one scarp [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. A similar process of locking boulders within seasonal CO2 frost and moving them via differential thermal contraction is a possible explanation for horizontal boulder sorting at other locations [START_REF] Orloff | Possible mechanism of boulder clustering on Mars[END_REF]. An additional possibility is that these surface boulders are ejecta from nearby impact craters, although the sparse craters on the surface of the mantling deposits suggest that impacts since those deposits were emplaced were not sufficient. The scarps surveyed here are distinctly different from the steep slopes at the edge of the north polar layered deposits (NPLD), which have slopes up to 70 over 300meter baselines and are approximately vertical over some shorter intervals [START_REF] Russell | Seasonally active frost-dust avalanches on a north polar scarp of Mars captured by HiRISE[END_REF]. These slopes also occur in a body of ice with low dust content, estimated to be <2% [START_REF] Picardi | Radar soundings of the subsurface of Mars[END_REF]. Despite active avalanching and slope retreat [START_REF] Russell | Seasonally active frost-dust avalanches on a north polar scarp of Mars captured by HiRISE[END_REF], the NPLD scarps generally have dusty coloration except on the flat residual cap [START_REF] Byrne | The polar deposits of Mars[END_REF], although because this is inferred from relative color, quantitative inferences about the ice content are difficult.

In comparison with the scarps, the craters provide relatively little constraint on the deposition and modification processes of the ice. They demonstrate the widespread occurrence of processes that create high ice contents in the shallow subsurface, but the small penetration depth and exposure size, and disruption of the ice by impact, make it difficult to distinguish between the various candidate processes. Boulders are common around many of the craters, as at the scarps.

Scarp Formation and Evolution

The scarps pose a significant puzzle: how is the bare ice exposure created and maintained, when a covering lag is expected to develop within years and sublimation is actively occurring? Landscape evolution modeling suggests that a steep exposure of dusty ice would gradually become shallower because the base would be buried under the debris released by its own sublimation and retreat [START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF]. The straight geometry of the scarps may reduce this effect because the debris at the base is not collected from a wide area. The scarps are quite steep and could shed debris rather than accumulating a surface cover, like the steep slopes of parts of the NPLD [START_REF] Russell | Seasonally active frost-dust avalanches on a north polar scarp of Mars captured by HiRISE[END_REF]). This appears to be occurring in some cases, but in at least one example the process is building a debris-covered lower slope and deactivating sublimation on the lower scarp [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF]. Some scarps may be partially or completely debris covered (Figs. 2b,8,11), so in some conditions this process may cease. Additionally, how such a slope is created in the first place or how scarps reactivate after accumulating surface debris is not obvious. The scarps do not resemble impact features, which are typically circular, but runaway growth from small impacts is a possibility. Fault movement can be ruled out at one location by a lack of vertical offset [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF], and at no site is there any indication of fault-like deformation extending beyond the scarp. Additionally, ridges indicating scarp retreat are inconsistent with movement on a fault. The scarps face the pole regardless of the slope orientation and sometimes occur on level surfaces, which rules out any gravity-driven failure.

Two possible factors in creating and maintaining scarps are seasonal frost and aeolian transport. CO2 frost can transport material either via basal sublimation (e.g., [START_REF] Kieffer | Cold jets in the Martian polar caps[END_REF][START_REF] Pilorget | Formation of gullies on Mars by debris flows triggered by CO2 sublimation[END_REF] or by loading a steep slope and avalanching as observed at the NPLD [START_REF] Russell | Seasonally active frost-dust avalanches on a north polar scarp of Mars captured by HiRISE[END_REF], and winds could also strip away a sublimation lag. The gradual fading of color contrast and weakening of ice spectral signatures on one scarp over the course of a summer [START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF] were consistent with frost effects, as a lag might accumulate over the summer before being removed by frost in the following winter and spring, and lineations suggesting frostdriven mass wasting occur on scarps in early spring images (Fig. 16a). The latitudinal dependence of scarp occurrence is consistent with a role for CO2 frost but would require some additional control, since such frost is ubiquitous in the winter at middle and high latitudes, and the abundance on the scarps is not known. Frost and wind effects are not mutually exclusive. Ridge structures at some scarp locations (Fig. 16b) resemble features interpreted as dust bedforms [START_REF] Geissler | The birth and death of transverse aeolian ridges on Mars[END_REF] or indurated dust [START_REF] Bridges | Aeolian bedforms, yardangs, and indurated surfaces in the Tharsis Montes as seen by the HiRISE camera: Evidence for dust aggregates[END_REF] elsewhere on Mars. These are oblique to the scarp and cut by it, suggesting limited mobility relative to the scarp retreat timescale. For comparison, modeling of sublimation conditions at migrating NPLD trough sites suggests that removal of a sublimation lag by surface winds is likely necessary for sublimation to continue over prolonged periods there [START_REF] Bramson | A migration model for the polar spiral troughs of Mars[END_REF].

Cliffs on terrestrial debris-covered glaciers offer both insights and contrasts. Cliff exposures can be created by sliding of the debris layer, or collapse into lakes or meltwater conduits (e.g., [START_REF] Kirkbride | The temporal significance of transitions from melting to calving termini at glaciers in the central Southern Alps of New Zealand[END_REF][START_REF] Sakai | Distribution characteristics and energy balance of ice cliffs on debris-covered glaciers, Nepal Himalaya[END_REF]. Neither of these is likely on Mars, given the low slopes and lack of a significant meltwater system at Martian temperatures.

In the Himalayas on Earth, equator-facing slopes are quickly covered by debris, while pole-facing ice cliffs persist and act as important drivers of ice loss, because they receive less insolation and are steep enough to shed debris [START_REF] Sakai | Distribution characteristics and energy balance of ice cliffs on debris-covered glaciers, Nepal Himalaya[END_REF][START_REF] Buri | Aspect controls the survival of ice cliffs on debriscovered glaciers[END_REF]. Differences in the radiative balance of the upper and lower parts of the slope as a function of aspect are important to the development of the cliffs: at some aspects, melting and retreat of the lower slope is enhanced, helping to maintain a steep exposure, while for others the reverse is true [START_REF] Sakai | Distribution characteristics and energy balance of ice cliffs on debris-covered glaciers, Nepal Himalaya[END_REF]. If such a dependency exists for the relevant conditions on Mars, then for sufficiently clean ice, it could enable steepening and runaway growth of a small exposure. A somewhat similar process is observed in models of scalloped depressions, where small disturbances initially cause the bottom of a depression to drop rapidly [START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF]. Antarctic analogs indicate that calving of blocks via thermal expansion-induced cracking may be an important driver of the retreat of steep scarps (e.g., [START_REF] Levy | Accelerated thermokarst formation in the McMurdo Dry Valleys[END_REF]. This has not yet been observed on Mars but is possible, and the scarp faces often appear fractured.

In a number of cases, scarps occur in the vicinity of other possible ice-loss landforms and sometimes definitively within the same unit (e.g., Fig. 9). The relationship between the scarp pits and scalloped depressions (e.g., [START_REF] Morgenstern | Deposition and degradation of a volatile-rich later in Utopia Planitia and implications for climate history on Mars[END_REF][START_REF] Soare | Thermokarst lakes and ponds on Mars in the very recent (Late Amazonian) past[END_REF][START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF]2010;[START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF] is not fully understood, but they appear to form and evolve differently. The major evidence for this difference is that linear ridges are observed parallel to some scarps (Fig. 8), indicating that the scarps retreat in a straight line. Scalloped depressions, by contrast, have arcuate internal ridges [START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF]Dundas, 2017a). The scarps typically widen as they retreat, resulting in crudely triangular pits that are narrow on the poleward side and widest at the exposed scarp, unlike scalloped depressions (Fig. 9c) and suggesting localized origination.

Additionally, the largest scarp pits are commonly multiple kilometers across and occur in relative isolation, while scalloped depressions are typically smaller until mergers create larger complex landforms. Scalloped depressions are commonly interpreted to be sublimation-thermokarst that form via sublimation of an ice-rich unit much like that revealed in the scarps [START_REF] Morgenstern | Deposition and degradation of a volatile-rich later in Utopia Planitia and implications for climate history on Mars[END_REF][START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF]2010;[START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF][START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF], so one possibility is that they represent different styles of evolution relating to the occurrence of exposed surface ice versus loss through a lag.

Poorly defined expanded craters also occur near some scarps. These are interpreted as sublimation-modified impact craters [START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF][START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF], and the best examples are in Milankovič crater (Fig. 9b). However, while the expanded craters there appear in surface-mantling deposits similar to those hosting the scarps, they are generally not adjacent: the expanded craters are mostly outside the rim of Milankovič, while the scarps are in the crater interior. This could indicate a difference in material properties or surface age, since most of the expanded craters in this region of Mars may be tens of millions of years-old secondary craters [START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF], so the surface-mantling deposits within the crater could be younger. Alternatively, this could indicate a role for the effects of local slope or topography. Near the scarps, irregular pits are more common than either scalloped depressions or expanded craters; given the setting and substrate, these probably also represent ice-loss features.

Rather than treating scarps, scalloped depressions, and expanded craters as entirely distinct features, they may be best viewed as the result of different initial conditions and evolutionary pathways for ice-rich deposits affected by sublimation, frost, and wind. Hence, scallop-like landforms arise when disturbances destabilize the surface and cause sublimation through a lag, and expanded craters are fundamentally similar but result from relatively large initial disturbances (impacts) that are not completely erased by sublimation as the crater expands. In cases of strong sublimation, expansion might eventually make the original crater unrecognizable and transition to a scallop-like feature.

Both of these morphologies have been effectively modeled via lag-controlled sublimation alone [START_REF] Dundas | Modeling the development of Martian sublimation thermokarst landforms[END_REF]Dundas, 2017a) and retreat should concentrate on the warmest, least-stable slopes. Exposed scarps fit within this framework if they represent a different mode where wind, CO2 frost, or other factors maintain a bare ice surface which retreats more quickly than ice that is covered by lithic debris, and thus occurs on the slopes where those effects are strongest. The typically straight scarp morphology represents a notable contrast from the other features. Individual landforms could change modes: for instance, a scarp exposure might emerge within a scalloped depression if erosion on the pole-facing slope removes lithic debris, and scarps could become buried if the debris ceases to be removed effectively. The resulting morphologies could be compound features dependent on the initial conditions and variations of the driving forces over time, due both to climate variations and the changing shape of the landform itself. This model raises two important questions. First, under what circumstances do these processes produce well-defined scalloped depressions or expanded craters versus irregular pits? And second, in regions of unstable or marginally stable ice, how much ice is lost to the atmosphere by this localized landform evolution, in comparison with uniform sublimation?

Implications for Martian Climate and Ice Processes

The present-day distribution and properties of ice on Mars record the history of climate, as they reflect an integrated history of deposition, internal processes (such as densification and ice-lens formation), and sublimation. Ice that exists today is either aggrading, stable, or was originally deposited in such abundance that subsequent periods of instability have not been sufficient to remove it. The observations and interpretations above provide some high-level insights about this history.

Atmospheric water vapor content is a major control on the distribution of stable ice. If the ice-exposing craters are sampling the upper part of a thick massive ice body in the Arcadia region as discussed above, then the elevated atmospheric water content required to stabilize ice at the lowest-latitude craters [START_REF] Dundas | HiRISE observations of new impact craters exposing Martian ground ice[END_REF] might date to the time of deposition or a time-integrated average over subsequent time rather than the most recent climate, since thick ice units can survive over protracted periods while slowly sublimating (e.g., [START_REF] Schorghofer | History and anatomy of subsurface ice on Mars[END_REF][START_REF] Bramson | Preservation of mid-latitude ice sheets on Mars[END_REF]. If the ice was deposited as snow, that water content would be a lower bound, since surface snow deposition requires more water vapor than subsurface stability. However, the lag developed during retreat must be thinner than predicted by [START_REF] Bramson | Preservation of mid-latitude ice sheets on Mars[END_REF] assuming nominal conditions for the present day, or the shallow subsurface ice probed by these craters contains excess ice above the deposit indicated by the radar reflectors.

Alternative histories for atmospheric water vapor might allow survival with a thinner lag, or sublimation lags may restrict sublimation more than observed in laboratory experiments [START_REF] Hudson | Water vapor diffusion in Mars subsurface environments[END_REF]. A generalized latitudinal model by [START_REF] Schorghofer | History and anatomy of subsurface ice on Mars[END_REF] does allow lags <1 meter over ice sheets with ages of a few million years or less. The survival time of such ice sheets depends on both the climate history and the time and amount of deposition, as well as the thermophysical properties of the lag itself.

As discussed above, scarps may indicate locations of particularly thick, clean ice deposits originating as snow. The apparent high ice content at the scarps suggests that the ratio of ice to dust in the atmosphere was high when deposition was occurring at those locations. Scarps might not exist in all such deposits, and the specific ice bodies hosting scarps may be influenced by local topography. Nevertheless, the scarps likely indicate a subset of favored locations for past ice deposition. Several general circulation model (GCM) studies have examined potential locations of past tropical or mid-latitude snow or frost accumulation under different orbital configurations and axial tilt, with significant differences in the details of model physics as well as in assumptions about H2O sources and atmospheric dust abundance (e.g., [START_REF] Levrard | Recent ice-rich deposits formed at high latitudes on Mars by sublimation of unstable equatorial ice during low obliquity[END_REF][START_REF] Forget | Formation of glaciers on Mars by atmospheric precipitation at high obliquity[END_REF][START_REF] Madeleine | Amazonian northern mid-latitude glaciation on Mars: A proposed climate scenario[END_REF]2014). Due to these differences and the limited sweep of parameter space with any individual model, stating a simple hypothesis that could be tested by comparison with the scarp distribution is not possible at present. Several scenarios do produce concentrated ice accumulation south and southeast of the Hellas basin (hereafter SSE Hellas), which has a marked influence on atmospheric circulation. These include scenarios with low obliquity (15-25) and an equatorial ice source, particularly with a high optical depth of dust in the atmosphere [START_REF] Levrard | Recent ice-rich deposits formed at high latitudes on Mars by sublimation of unstable equatorial ice during low obliquity[END_REF][START_REF] Madeleine | Amazonian northern mid-latitude glaciation on Mars: A proposed climate scenario[END_REF], but also scenarios with 35 obliquity and no equatorial ice source [START_REF] Madeleine | Recent Ice Ages on Mars: The role of radiatively active clouds and cloud microphysics[END_REF]. The seasonal timing of perihelion also strongly affects deposition patterns [START_REF] Madeleine | Amazonian northern mid-latitude glaciation on Mars: A proposed climate scenario[END_REF]2014). [START_REF] Forget | Formation of glaciers on Mars by atmospheric precipitation at high obliquity[END_REF] produced strong deposition east of Hellas, equatorward of the scarps, in a model scenario with 45 obliquity and surface ice at the south polar cap. Scenarios with both low and high obliquity can also produce deposition in the region near Milankovič crater [START_REF] Madeleine | Amazonian northern mid-latitude glaciation on Mars: A proposed climate scenario[END_REF]. Other locations of predicted ice deposition in various scenarios do not correspond with scarps, although some match the locations of debris-covered glaciers (e.g., [START_REF] Holt | Radar sounding evidence for buried glaciers in the southern mid-latitudes of Mars[END_REF][START_REF] Plaut | Radar evidence for ice in lobate debris aprons in the midnorthern latitudes of Mars[END_REF][START_REF] Levy | Sequestered ice contribution to the global Martian water budget: Geometric constraints on the volume of remnant, midlatitude debris-covered glaciers[END_REF], scalloped depressions (e.g. [START_REF] Morgenstern | Deposition and degradation of a volatile-rich later in Utopia Planitia and implications for climate history on Mars[END_REF][START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF]2010;[START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF], or expanded craters (e.g. [START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF]. The evidence from the scarps favors the past occurrence of one or more of the climate scenarios that produce strong deposition at the scarp locations, and the low dust content of the scarp ice may favor those that produce accumulation with a low optical depth atmosphere. However, Mars' orbital elements have varied widely (e.g., [START_REF] Laskar | Long term evolution and chaotic diffusion of the insolation quantities of Mars[END_REF] and the range of plausible parameters and assumptions makes it difficult to pick out a specific scenario that is unambiguously recorded by the ice.

Well-defined meter-scale layering is found in only a few ice-exposing scarps, in contrast with the NPLD where meter-to decameter-scale layering is nearly ubiquitous (e.g., [START_REF] Herkenhoff | Meter-scale morphology of the north polar region of Mars[END_REF]. Unresolved layers (<30 cm thick) may exist at the midlatitude scarp sites, preserving a temporal record at small scales, but the more-common crude layering may possibly be the only well-defined time signal in this ice, or the dust content of the ice may be so low or so uniform that layers are mostly not distinguishable in HiRISE images. This could indicate that the ice accumulated only under a narrow range of atmospheric conditions, while polar accumulation occurred in a wider range of climates. However, surface-mantling deposits without ice exposures at latitudes <45 in the mid-latitudes do show evidence of layering [START_REF] Schon | A recent ice age on Mars: Evidence for climate oscillations from regional layering in mid-latitude mantling deposits[END_REF]. The two scarp locations with the clearest fine layering both have unconformities and crosscutting layers; this may indicate that accumulation at those sites occurred at two different times possibly with different climates or that some of the deposition occurred as windblown drifts rather than uniform fall deposits. In both cases the uppermost material is approximately horizontal and conforms to the present surface, so it was not affected significantly by aeolian transport or by ice flow, although deformation could be concentrated out of view at the base of the ice.

The scarp ice likely records different climate episodes than either of the polar layered deposits. The available data are too limited to constrain any hypothesis for what orbital epochs and climate conditions might be recorded in the scarp ice other than to say that it indicates snow or frost accumulation. Part of this accumulation was likely geologically recent, since mid-latitude mantling deposits have few craters and young surface ages of a few million years [START_REF] Schon | Recent high-latitude resurfacing by a climate-related latitude-dependent mantle: Constraining age of emplacement from counts of small craters[END_REF], although the base of the deposits could be older. [START_REF] Harish | Water-ice exposing scarps within the northern mid-latitude craters on Mars[END_REF] estimated the ages of two scarp-hosting craters to be 25 and 95 Ma, and the surface age of one of the host mantling units to be 1 Ma. [START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF] estimated that a mid-latitude icy deposit in the region of Milankovič crater is tens of millions of years old, and this may include the scarp-hosting ice there, although the characteristic expanded craters are less abundant in the crater interior, which could be a younger deposit (Fig. 9b). These ages are less than or comparable to the 30-100 Ma surface age of the SPLD (e.g., Koutnik et al., 2002), while the entire NPLD may date from the last several million years (e.g., [START_REF] Levrard | Recent formation and evolution of northern Martian polar layered deposits as inferred from a global climate model[END_REF][START_REF] Byrne | The polar deposits of Mars[END_REF][START_REF] Smith | An ice age recorded in the polar deposits of Mars[END_REF]. More important than the specific age is that deposition in the poles and midlatitudes likely occurred under different climate regimes: the locations of net deposition or loss depend on Mars' obliquity and orbital parameters and associated climate changes (e.g., [START_REF] Head | Recent ice ages on Mars[END_REF][START_REF] Levrard | Recent ice-rich deposits formed at high latitudes on Mars by sublimation of unstable equatorial ice during low obliquity[END_REF][START_REF] Forget | Formation of glaciers on Mars by atmospheric precipitation at high obliquity[END_REF][START_REF] Byrne | The polar deposits of Mars[END_REF][START_REF] Madeleine | Amazonian northern mid-latitude glaciation on Mars: A proposed climate scenario[END_REF]2014), so polar and mid-latitude ice accumulated at different parts of the cycle.

Overall, various observations indicate several regions of thick mid-latitude ice accumulation in the Late Amazonian. These include (1) SSE Hellas, as shown by scarps and scalloped depressions [START_REF] Lefort | Scalloped terrains in the Peneus and Amphitrites Paterae region of Mars as observed by HiRISE[END_REF][START_REF] Zanetti | Distribution and evolution of scalloped terrain in the southern hemisphere[END_REF]; (2) western Utopia Planitia, as shown by scalloped depressions and radar reflectors [START_REF] Morgenstern | Deposition and degradation of a volatile-rich later in Utopia Planitia and implications for climate history on Mars[END_REF][START_REF] Lefort | Observations of periglacial landforms in Utopia Planitia with the High Resolution Imaging Science Experiment (HiRISE)[END_REF][START_REF] Stuurman | SHARAD detection and characterization of subsurface water ice deposits in Utopia Planitia, Mars[END_REF]; and (3) the greater Arcadia region, as shown by expanded craters and radar reflectors [START_REF] Viola | Expanded secondary craters in the Arcadia Planitia region, Mars: Evidence for tens of Myr-old shallow subsurface ice[END_REF][START_REF] Bramson | Widespread excess ice in Arcadia Planitia, Mars[END_REF] and some localized scarps. Debris-covered glaciers also indicate deposition concentrated east of Hellas, in Tempe Terra, and in the Deuteronilus and Protonilus Mensae regions [START_REF] Holt | Radar sounding evidence for buried glaciers in the southern mid-latitudes of Mars[END_REF][START_REF] Plaut | Radar evidence for ice in lobate debris aprons in the midnorthern latitudes of Mars[END_REF][START_REF] Levy | Sequestered ice contribution to the global Martian water budget: Geometric constraints on the volume of remnant, midlatitude debris-covered glaciers[END_REF]. Note that other major accumulations could have existed and been subsequently removed, as has occurred for some lobate debris aprons [START_REF] Hauber | Geomorphic evidence for former lobate debris aprons at low latitudes on Mars: Indicators of the Martian paleoclimate[END_REF]. Deposition was probably not simultaneous in all of these regions, and the depositional conditions were also probably variable: ice in debris-covered glaciers and exposed in the scarps likely has a very low dust content [START_REF] Campbell | Fine-scale layering of Mars polar deposits and signatures of ice content in nonpolar material from multiband SHARAD data processing[END_REF][START_REF] Dundas | Exposed subsurface ice sheets in the Martian mid-latitudes[END_REF][START_REF] Petersen | High ice purity of Martian lobate debris aprons at the regional scale: Evidence from an orbital radar sounding survey in Deuteronilus and Protonilus Mensae[END_REF], but the regional deposits in Utopia and Arcadia may be less ice-rich [START_REF] Campbell | Fine-scale layering of Mars polar deposits and signatures of ice content in nonpolar material from multiband SHARAD data processing[END_REF]. No site has all of the ice indicators in abundance. Radar reflectors are sparse in SSE Hellas, although rough topography limits the detectability of possible interfaces in that region [START_REF] Cook | Sparse subsurface radar reflectors in Hellas Planitia, Mars[END_REF]. Radar loss tangents support high ice contents for debriscovered glaciers but not for the Utopia and Arcadia deposits. Scarp exposures are sparse and not found at all in some regions. Additionally, one or the other of scalloped depressions and expanded craters dominate the sublimation-thermokarst population rather than a mix occurring. These differences could reflect differences in the lithic content of the ice (including layering), overburden properties, regional topography (influencing radar clutter) or the regional climate history.

Conclusions

We present distributions of ice-exposing craters and large ice-exposing scarps at middle to high latitudes on Mars. Both types of feature indicate high subsurface ice contents well in excess of pore filling. Regional variations in the crater exposures suggest that high ice content is common at shallow depths at mid-latitudes (~40 N) in the Arcadia Planitia region compared with the northern part of the Tharsis rise, where pore ice may be more common. Above ~50 latitude, clean ice exposures are very common at all longitudes. The nature of ice exposures in some of the largest craters indicates that clean ice is not a product of the impact process. Variations in crater clusters demonstrate that both ice content and the depth to ice have substantial local variability. The scarps are characteristically found between 50-61 N/S and are concentrated at particular longitudes. They appear to form in thick surface-mantling deposits produced by past snowfall and create a distinctive category of sublimation-thermokarst landform. The latitudinal and longitudinal controls suggest that the scarps form in locations with particularly thick, clean ice deposits and are exposed by a latitude-dependent process. Values are given to two significant figures for relative comparison but for typical crater sizes, the potential measurement error on an individual crater is ~30% assuming halfpixel errors in opposite directions for the rim and floor diameter. The range is the spread between the largest and smallest measurements and does not include measurement uncertainty. defrosting. Arrow indicates a minor exposure of relatively-blue material interpreted as probable ground ice; however, despite the ice-rich nature of the SPLD and substantial size of this crater, the distinct ice deposit is minimal even though images were acquired rapidly after formation. Note that the color stretch in this cutout is different from that in A, to emphasize relative color variations; the crater and immediate surroundings are unchanged but there is no longer frost providing a strong relative contrast. C) Small craters with ejecta superposing the seasonal CO2 cap (55.9 S, 264.8 E).

Figures and Captions

  at latitudes equatorward of 65 N/S and the uncontrolled global mosaic version 12.0 (e.g., Edwards et al., 2011) poleward of 65 N/S.

Figure 3 .Figure 4 .

 34 Figure 1. A) Example of an ice-exposing crater (69.3 N, 142.2 E). Note patchy, bright,

Figure 5 .Figure 6 .Figure 13 .Figure 14 .Figure 15 .

 56131415 Figure 5. Southern-hemisphere scarp #15 (56.6 S, 50.6 E) has a complex structure. The

Figure 16 .

 16 Figure 16. Possible modification processes maintaining ice exposures. A) Striations on

Table 1 . Depths to Strong Layer at Impact Sites with Icy Color

 1 Planetocentric latitude, east longitude. N is the number of craters with morphologies indicating weak-over-strong layering, which are not necessarily those with visible ice.

	Latitude	Longitude	N	Mean depth to	Range
				ice (m)
	46.35	176.89	6	0.42	0.28 -0.58
	44.22	164.20	5	0.47	0.26 -0.55
	50.51	265.2	3	0.42	0.32 -0.62
	39.11	190.25	2	0.90	0.69 -1.1
	47.43	112.01	2	0.50	0.40 -0.60

Both of these types of exposures provide important constraints on the climate history of Mars as well as reference locations for other remote-sensing data sets. The Supplementary Data is also available as a USGS Data Release at https://doi.org/10.5066/P9Y8FR1R [START_REF] Dundas | Supplementary Data for "Widespread Exposures of Extensive Clean Shallow Ice in the Mid-Latitudes of Mars[END_REF]. All CTX, HiRISE, and CRISM image data used are available via the Planetary Data System Imaging and Geosciences nodes (https://pds-imaging.jpl.nasa.gov/volumes/mro.html and https://pdsgeosciences.wustl.edu/missions/mro/crism.htm). All map-projected HiRISE images in figures are courtesy NASA/JPL/University of Arizona, and map-projected CTX images are courtesy NASA/JPL/MSSS/University of Arizona. Controlled THEMIS mosaics are publicly available (https://astrogeology.usgs.gov/maps/mars-themis-controlled-mosaics-and-final-smithed-kernels) via Astropedia and uncontrolled mosaics are included as layers in JMARS (http://www.mars.asu.edu/data/), which was used for analysis. The original images used in the mosaics are available via the Planetary Data System Imaging Node (https://pds-imaging.jpl.nasa.gov/volumes/ody.html). Thermal Emission Spectrometer (TES) thermal inertia data are available from the PDS Geosciences node (https://pds-geosciences.wustl.edu/missions/mgs/tes-timap.html) and albedo data at the PDS TES data node (http://tes.asu.edu/products/index.html). The use of trade, product, or firm names is for identification purposes only and does not constitute an endorsement by the U.S. Government.

Acknowledgments