6.1 Atmospheric Water Content
We found that atmospheric water contents as high as 25 pr µm (column abundance at 0 km elevation) are needed for ice stability at the lowest-latitude (least stable) sites. Given various sources of uncertainty, we caution against overemphasizing specific values. The primary result of the modeling is that the distribution of ice in the northern hemisphere is broadly consistent with an atmospheric water content of at least twice the present value, assuming that H2O is well mixed with CO2. The relevant value of near-surface water vapor density represents the long-term average, where “long term” is the time scale for ice to adjust to new climate conditions. (This definition is inherently loose since sublimation and deposition rates vary with temperature, burial depth, and atmospheric water content, but substantially filling the pore space of initially dry regolith may require tens of thousands of years [Mellon and Jakosky, 1993], while centimeter-scale adjustments of the ice depth take ~100–1000 years [Mellon et al., 2004].) A higher average water content is consistent with the results of Chamberlain and Boynton , who suggested that it could vary by a factor of ~3 in the recent past due to variation in the longitude of perihelion (with ~50,000 year period) and is presently near a minimum.
Alternatively (or additionally), the near-surface humidity could be higher than expected based on column abundances if the water vapor is concentrated near the surface rather than well mixed. This is consistent with the interpretations of humidity measurements made by the Phoenix Lander [Zent et al., 2010] and with some low-resolution atmospheric profiles [Smith et al., 2011]. This possibility could affect the stability of apparent near-surface liquid flows attributed to brines [McEwen et al., 2011]. A third possible effect is that stable ice could be more extensive than expected if the vapor pressure above the ice table is controlled by brines formed by deliquescent salts in the regolith. Salty solutions have a reduced vapor pressure, and deliquescence might maintain a lower vapor pressure, thereby reducing the rate of diffusion to the atmosphere. Mellon et al.  considered this unlikely since at that time salts at the Phoenix landing site were thought to be uniformly distributed in the soil [Hecht et al., 2009], while liquid would concentrate salts as it evaporated. However, subsequent work has suggested concentrations of deliquescent perchlorate salts, consistent with occasional small-scale melting [Cull et al., 2010a]. Either of these effects would make ice more stable and widespread under all climate conditions.
6.2 Nature of Visible Ice
The nature of Martian ground ice is an important question. A common assumption is that ground ice fills the pore spaces of regolith (pore ice), which is a natural consequence of atmospheric vapor deposition [Mellon and Jakosky, 1993; Hudson et al., 2009]. However, recent observations have demonstrated the occurrence of ice contents greater than the natural soil pore space (excess ice). The frequency, distribution, and thickness of excess ice are important in understanding the full range of permafrost processes on Mars because such ice probably did not form via simple vapor deposition.
Observations of excess ice on Mars include direct excavation of ice with less than 1% soil content by the Phoenix Lander [Smith et al., 2009b; Mellon et al., 2009; Cull et al., 2010b]. On a regional scale, near-surface volumetric ice contents up to 85% have been suggested to extend over broad areas at high latitude based on GRS data, which probe depths of a meter or less [e.g., Boynton et al., 2002; Prettyman et al., 2004; Feldman et al., 2008, 2011]. Volume fractions of 50–100% ice have been suggested to extend to a few tens of meters depth in the northern hemisphere based on radar observations [Mouginot et al., 2010]. The high end of this range would indicate large amounts of very clean excess ice. Levy et al. [2008; 2009] suggested that some thermal contraction polygon morphologies indicate excess ice, although Mellon et al. [2008b, 2009] argued that such ice is not volumetrically dominant in the upper 3–5 m and has little effect on polygon morphology, based on modeling of polygon dimensions.
A number of processes have been proposed as the source of excess ice on Mars, including vapor diffusion coupled with thermal expansion and contraction to create extra pore space [Fisher, 2005] or burial of snow deposited under past climate conditions driven by orbital variations [e.g., Head et al., 2003; Mischna et al., 2003; Levrard et al., 2004; Schorghofer, 2007; Schorghofer and Forget, 2012]. Mellon et al.  favored ice lens formation through migration of thin films of liquid present at subfreezing temperatures at the Phoenix landing site; work of Sizemore et al.  using the model of Rempel  suggests that this is plausible. Frozen floodwaters, pingos, or buried glaciers have been considered but are unlikely to be the sources of regionally extensive excess ice [Mellon et al., 2008a]. Debris-covered glaciers have been observed in some locations in radar data [Holt et al., 2008; Plaut et al., 2009]. The lobate aprons where some craters expose ice may be such features, but they are not ubiquitous across the northern plains.
Byrne et al.  and Dundas and Byrne  suggested that the impact-exposed ice also represents excess ice, at lower latitudes than indicated by GRS data, and thus, that excess ice is widespread. Here we further discuss this issue. The ice visible at the crater sites described here is clean ice with low regolith content, based on sublimation modeling [Dundas and Byrne, 2010]. The observed persistence time scales indicate that the ice remains visible through a period in which one or more millimeters of exposed ice should sublimate. This conclusion is reinforced by the continued visibility of ice well beyond the intervals considered by Dundas and Byrne , and the observed brightening at several sites suggests that lags are occasionally stripped away, most likely by wind. Direct deposition of new frost on level surfaces (as seen in Figure 9) is unlikely since the high thermal inertia of ice means that near-surface ice is warmer than the surroundings during the coldest part of the night, but it is possible that condensed particles could settle out. Modeling by Kossacki et al.  also indicates millimeters of sublimation during the period in which ice remained visible. Kossacki et al.  proposed that darkening was due to changes in optical properties rather than lag development, but even in this scenario, the persistence of visible ice requires that it be clean, or an opaque lag would be produced before other changes became relevant. The observed brightening is also more consistent with lag development and removal since vapor-deposited frost would be very clean.
Excavated excess ice in the craters is also consistent with the observations by the Phoenix Lander. Exposed pore ice there was darker than ice-free soil [Mellon et al., 2009] and receded beneath an opaque lag within a few days, whereas excess ice remained visibly bright for months while sublimating several millimeters [Smith et al., 2009b]. Icy crater ejecta should sublimate particularly quickly, since an insulating layer of regolith below will raise peak temperatures in the thin icy ejecta layer. This is consistent with the general tendency for the crater cavities to remain icy longest.
However, it is possible that the impact process has affected the observed ice. Modeling of the impacts at sites 1–5 by Reufer et al.  indicates that some amount of melting is likely in the larger craters, although none is expected in the smaller craters with relatively deep ice. (Note that this is likely even if ice has a higher effective strength than that used by Reufer et al.  in estimating crater sizes, because the smaller craters mostly excavate regolith, making this parameter less important.) We have not observed any flow-like morphologies that might suggest that ejecta was fluid mud but cannot rule out smaller amounts of melting. The most important question is whether clean surface ice forms from pore ice, since this could make it difficult to distinguish preexisting excess ice. Melting by an impact into pore ice would initially produce mud. This could produce clean ice if water seeped from wet mud, pooled, and froze before reinfiltrating. This process depends on a number of factors, including the local regolith permeability and grain size (smaller grains will have a larger contact area for heat exchange with infiltrating water), the regolith salt content leading to brine formation, the temperature of regolith material in the ejecta and crater cavity, the size and shape of depressions in which water could pool, the temperature reached by the meltwater, and even the season and time of day of the impact. This system is difficult to model, as it is complex and poorly constrained. An additional complication is that recondensation of water vapor frost might occur at the rapidly cooling surface, but the very heterogeneous covering of many crater cavities and ejecta (Figure 1) suggests that this is not the dominant process.
It is also possible that the high temperature of ejecta and crater bowl material could drive the desiccation of the topmost layer of mud. The Lunar Crater Observation and Sensing Satellite impact experiment used a projectile with kinetic energy comparable to some cases modeled by Reufer et al.  and produced a crater that Schultz et al.  estimated was 25–30 m in diameter. Hayne et al.  estimated that parts of the crater were heated to over 950 K, which would drive extremely rapid loss of water or ice.
Regardless of the events in the complex Martian environment immediately after impact, several observations indicate that much of the observed ice was originally clean—that is, excess ice. Some blocks of ejecta at site 7 were visibly icy in early HiRISE images (Figure 8 and Animation S1 of the supporting information), and it is unlikely that significant pooling or condensation would be concentrated on ejecta blocks. Icy, blocky material has also been observed elsewhere (Figure 7). The disappearance of half-meter-scale blocks at site 7 (Figure 8) also strongly suggests that they were mostly composed of excess ice. Alternatively, it is possible that the blocks of ice-cemented regolith could disappear if high winds occurred after sublimation caused the blocks to disaggregate. After a dust storm at the Viking Lander 1 site, centimeter-scale changes were observed in materials that had previously been disturbed by the lander, and peak winds need only have lasted for seconds [Moore, 1985]. However, the dark blast zone remained prominent at site 7 after block disappearance, suggesting that aeolian effects have not been great over the same time period.
Visible ice occurs in small craters where the regolith cover was likely decimeters thick; based on the modeling of Reufer et al. , it is unlikely that significant melting occurred there. There are also a number of small craters with no visible ice even though nearby craters of comparable size do have such ice (Figure 4), and in several cases, they have flat or terraced floors (Figure 8) indicating interaction with a strong layer, probably the ice table. Burial by the ejecta of other craters could occur in some cases. However, at site 1, the largest crater has no visible ice and sits in a part of the cluster with few nearby craters, while the icy craters were downrange and in a more dense part of the cluster, suggesting that burial is not the reason that ice is not seen in the largest crater. These observations indicate that such craters do not produce much clean ice in the impact process, and thus, where it is observed in similarly sized craters, it is likely to predate the impact.
Therefore, while some of the observed clean ice may have been produced by impact, in other cases, it is likely to be original excess ice with low regolith content. Spectral modeling of the craters by Cull et al.  suggested regolith contents on the order of 1%, similar to that observed by the Phoenix Lander. Although the origin of the clean ice is uncertain in some cases, these craters suggest that excess ice is common where ground ice is found, at least in the relatively high-albedo regions where we can detect new impacts. However, the differences between comparably sized craters within individual clusters also indicate that there are heterogeneities in ice content on short-length scales. Variable distributions of ice around craters may also be due to heterogeneities in the ground ice, if they are not caused by oblique impacts.
Models for the origin of excess ice must account for this heterogeneity, as well as the common presence of boulders on the surface. Both of these observations are problematic if the ice is the result of a snowpack from a very recent “ice age,” since there has been little time for impacts to garden boulders to the surface or for local heterogeneities to develop. However, the presence of boulders on the SPLD outlier at site 19 demonstrates that such gardening can occur at some level. (The estimated surface age of the SPLD is 30–100 Ma [Koutnik et al., 2002], but gardening may be faster on thinner ice.) An older snowpack could avoid these issues but must survive in midlatitude regions with episodic instability. One model by Schorghofer and Forget  suggests that an ice sheet formed 863 ka ago could persist to the present at the latitude of the icy craters, while one from 4.45 Ma would not. However, the younger ice sheet would allow less time for impact gardening. Complete gardening to a depth of even 1 m requires hundreds of millions of years [Hartmann et al., 2001] but the time scale to distribute boulders over the surface could be less. It remains to be seen whether the other parts of parameter space can make this model entirely consistent. The enhanced vapor diffusion model of Fisher  is consistent with surface boulders but required several Ma to produce high ice contents below depths of a few decimeters and did not consider the variations in temperature, water vapor abundance, and ice stability that have occurred over that time frame. Ice lenses could form within soil containing boulders and be heterogeneous if the regolith is nonuniform. However, Sizemore et al.  suggest that ice lensing should produce lenses between 5 and 20 cm depth. Most of the craters excavate to these depths, yet we observe that larger craters appear icier and do not see clear evidence for confinement of ice to such a layer—ice is observed throughout the walls of the large craters at sites 7 (Figure 1g) and 9 (Figure 1i), which excavated to >2 m depth. This interpretation is complicated by potential slumping of ice on the walls and the possibility that some of the clean ice was produced during the impact event. In some cases, the ice may be the core of lobate aprons like those observed by radar [Holt et al., 2008; Plaut et al., 2009]. This suggests that the covering lag is thin (Holt et al.  could only constrain it to be less than 10 m). At site 19, it is likely that the exposure is SPLD ice, presumably deposited from the atmosphere. Visible ice at site 19 is consistent with a very low dust content for the near-surface SPLD and a very thin dust lag. However, both on the SPLD and on ice-rich lobate aprons, other ice formation processes within lag deposits cannot be ruled out.
The lack of bright, clean ice in the two previously known new craters in the southern mid-latitudes was consistent with the hemispheric asymmetry in volumetric ice content suggested by Mouginot et al. . However, the quality of the HiRISE data for one of these sites is poor. At the other site, the initial image had a high incidence angle, which can make ice hard to distinguish, and the seasonal cap could have modified the surface before the second image was acquired. Three southern hemisphere craters have since been discovered at mid-latitudes to high latitudes. One of the newly found craters impacted the SPLD and another impacted a possible thin SPLD outlier based on MOLA topography. It is surprising that one of these showed no visible ice, since studies of the SPLD suggest bulk dust contents of 0–10% [Plaut et al., 2007] or 15% [Zuber et al., 2007]. The ice-free crater may not have been large enough to penetrate a dust lag. Alternatively, a bulk ice content of ~10% is consistent with small-scale variations between very clean and dust-rich layers, and the crater could have formed in the latter. The third new southern impact site is off the SPLD and does show bright material. This suggests that clean ice exists in the south as well, but the present data set is not large enough to draw strong conclusions. We note that GRS data do suggest high volumetric ice contents in the south [e.g., Boynton et al., 2002; Prettyman et al., 2004; Feldman et al., 2008].
6.3 Periglacial Geomorphology
Thermal contraction polygons are expected to be a good indicator of ground ice on Mars [e.g., Mellon, 1997]. We find hints of patterning at most ice-exposing impact sites, although it is often not well developed. Several different polygon morphologies are observed. High-centered polygons at several sites could be consistent with the sublimation-polygon model of Levy et al. . More puzzling is the absence of well-developed thermal contraction polygons immediately around craters at sites 10 and 11 (Figures 1j and 1k), although both have regular rolling hummocks, and polygon troughs occur nearby. One possible explanation for this is that the ice is buried too deeply to experience the strong temperature oscillations required to cause cracking. Mellon et al. [2008b] found that for the Phoenix landing site, an ice table depth >20 cm would inhibit polygon formation. This effect should be generally applicable, although the particular limiting depth may vary with latitude and thermophysical properties. However, both impact sites are located in regions where models indicate that ice should occur at very shallow depths, suggesting that small polygons should also occur. It is possible that polygons have not had sufficient time to develop, or they are obscured by a competition with other processes such as eolian resurfacing. Alternatively, they may be too small or have too little relief to be readily distinguished in HiRISE images. Either explanation indicates that the absence of visible, well-defined polygons does not always imply the absence of shallow ground ice. Moreover, if excess ice is common at these sites as discussed above, then there is not a simple relationship between polygon morphology and the occurrence of excess ice.
Scalloped textures and elongate depressions observed at several crater sites resemble features seen in Utopia and south of Hellas. Pole-oriented scalloped depressions in various regions of Mars have been interpreted as thermokarst [e.g., Morgenstern et al., 2007; Lefort et al., 2009], which forms when excess ice becomes unstable and ice loss drives surface subsidence. Formation of pole-oriented scallops by sublimation of excess ice has been successfully modeled [Dundas et al., 2011]. However, the depressions seen in the vicinity of impact sites are often not oriented toward the pole. It is not clear whether this requires a different formation mechanism or simply implies that some regional factor such as wind or long-baseline slopes can influence the orientation. The apparently expanded craters at several sites (Figure 6) may be thermokarst-modified craters. Since thermokarst collapse requires significant quantities of excess ice, visible ice is expected around new craters near thermokarst features. This is indeed observed, supporting thermokarst interpretations of these landforms.