Earth and Planetary Science · 25%of post-Noachian geologic history. DavidK.Weiss. Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912,

Earth and Planetary Science Letters 528 (2019) 115847

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Earth and Planetary Science Letters

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Mars in ice ages for ∼25% of post-Noachian geologic history

David K. Weiss

Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912, United States of America

a r t i c l e i n f o a b s t r a c t

Article history:Received 8 December 2018Received in revised form 7 July 2019Accepted 14 September 2019Available online 26 September 2019Editor: W.B. McKinnon

Keywords:Mars climateMars ice ageobliquitylayered ejecta cratersDLE craterscrater statistics

Mars is currently a hyperarid, hypothermal desert planet, whose surface inventory of water is primarily confined to the north and south polar ice caps. Previous studies have shown that Mars has undergone massive shifts in its spin-axis obliquity (present-day is 25.2◦) due to secular spin orbit resonances. During periods of higher obliquity, water-ice from the polar caps is mobilized to the mid-latitudes (∼35◦obliquity) and even the equator (≥ 45◦ obliquity), where it is deposited as snow and accumulates over time to form thick regional surface ice sheets. Abundant evidence exists today for the remnants of these ice ages in the form of debris-covered glaciers and ice deposits, but due to the chaotic nature of orbital simulations beyond ∼20 Ma, it has remained unclear to what temporal extent Mars has experienced such ice ages. Recent developments have suggested that impact events which formed in martian surface ice deposits exhibit a distinctive double-layered ejecta morphology. In tandem with cratering statistics, this observation offers the potential to better our understanding of the history of ice ages on Mars. This work explores the timing of ice age events by evaluating the size-frequency distribution of craters forming in surface ice. Using Hartmann isochron model ages, this work shows that Mars has experienced mid-latitude ice ages for up to a cumulative ∼680 Myr out of the past 3.6 Ga, and experienced equatorial ice ages for up to a cumulative ∼250 Myr within the same time period. The results of this study indicate that Mars has experienced mid-latitude/equatorial ice age states for up to approximately 25% of its post-Noachian geologic history, emphasizing that much of the geologic history of Mars is dominated by the presence of widespread non-polar surface ice sheets.

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1. Introduction

Orbital simulations have demonstrated that Mars has under-gone wide variations in its spin-axis obliquity throughout its his-tory (e.g., Laskar et al., 2004). Evidence for this process is present within the geologic record in the form of buried surface ice de-posits. During periods of relatively higher martian obliquity, polar ice is mobilized to lower latitude regions, where it can accumu-late to form thick surface ice sheets (Fig. 1) (Head et al., 2003, Madeleine et al. 2009, 2014) that may be later buried by sub-limation till (e.g., Bramson et al., 2017), volcanic ash (e.g., Head and Weiss, 2014), or crater ejecta (e.g., Black and Stewart, 2008). Mars is thought to have been characterized by relatively low at-mospheric pressure (∼7 mbar) during the Amazonian period (∼3.2 Ga to present; Michael 2013) (e.g., Carr and Head, 2010). Similarly, low atmospheric pressures (in the few 10’s of mbar range; Bristow et al., 2017) may have been present in the later Hesperian period (∼3.6–3.2 Ga; Michael 2013). Under these atmospheric conditions, general circulation models have shown that for obliquities of ∼35◦ ,

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surface ice is concentrated in the mid-latitudes (poleward of ∼25◦latitude) (Madeleine et al., 2009), and Mars enters a mid-latitude ice age state (Fig. 1; bottom middle panel). For obliquities greater than ∼45◦ , surface ice is concentrated in the equatorial regions (± ∼25◦ latitude) (Forget et al., 2006; Madeleine et al., 2009), and Mars enters an equatorial ice age state (Fig. 1; bottom right panel). These obliquity shifts may occur rapidly, within short-term peri-ods of ∼120 Kyr and longer-term periods of ∼1.2 Myr (Laskar et al., 2004), during which low-latitude surface ice deposits can ac-cumulate (Madeleine et al., 2009). The timing and duration of ice age events throughout Mars geologic history, however, remains un-clear.

The martian geologic history is fundamentally linked to its cli-mate, but how frequently does Mars experience ice ages? What is the timing of these events, and what is the total cumulative dura-tion that Mars has experienced both mid-latitude and equatorial ice ages? This contribution uses a class of martian crater land-form recently suggested to be related to glacial deposits to evaluate these questions. First, the paper reviews previous research that has used glacial-related geologic features to constrain the cumulative duration of martian ice ages (Section 2). Then, Section 3 discusses the formation of double-layered ejecta (DLE) craters and how these

2 D.K. Weiss / Earth and Planetary Science Letters 528 (2019) 115847

Fig. 1. Schematic representation of the martian surface ice distribution as a function of obliquity and CO2 atmospheric pressure. Mars is depicted as varying shades of orange, and ice-cover is depicted as white. At high atmospheric pressures (>100 mbar and <2 bar; see Kite et al., 2014 and summary in Section 5.2 of Weiss and Head (2017b)thought to have characterized the Noachian period (∼ 4 to 3.6 Ga; Michael 2013), surface ice is predicted to be concentrated in the high elevations (Wordsworth et al., 2013). Under these conditions, obliquity plays a secondary role, in which higher obliquity concentrates ice deposits at lower latitudes. At low atmospheric pressures that characterize the Hesperian and Amazonian periods (e.g., Carr and Head, 2010), obliquity determines the distribution of surface ice (Forget et al., 2006; Madeleine et al., 2009): increasing obliquity concentrates ice deposits at lower latitudes. The bottom middle panel (∼30-40◦ obliquity and ≤0.1 bar) illustrates the mid-latitude ice age scenario explored in this study. The bottom right panel (≥45◦ obliquity and ≤0.1 bar) illustrates the equatorial ice age scenario explored in this study. (For interpretation of the colors in the figure(s), the reader is referred to the web version of this article.)

landforms might assist in evaluating the timing of martian ice ages. Next, Section 4 evaluates the population of DLE craters and esti-mates the cumulative duration of ice ages from cratering statistics. Finally, Section 5 discusses the results and broader implications of this study.

2. Previous work on the duration of martian ice ages

Although the obliquity history (and thus the ice age history) is unknown beyond 20 Ma due to the chaotic nature of the obliq-uity statistical analysis (Laskar et al., 2004), the documentation of widespread debris-covered ice deposits in the mid-latitudes (Head et al., 2003; Plaut et al., 2009; Fastook and Head, 2014; Bramson et al., 2015; Viola et al., 2015; Stuurman et al., 2016; Dundas et al., 2018) and equatorial region (Shean et al., 2007; Fastook et al., 2008; Head and Weiss, 2014) provide evidence for the occurrence of martian ice ages. Further evidence for these ice ages comes in the form of impact craters within the ice deposits: when a small impact event occurs into the ice sheet and produces a crater contained entirely within the surface ice deposit, the adjacent sur-rounding terrain becomes armored from rapid sublimation (Wrobel et al., 2006). This armoring may be due to shock blast and thermal effects which melt/vaporize the volatile fraction of the icy surface and leaves the surface indurated with salts or dust (Wrobel et al., 2006). When the climate shifts and the unarmored surface ice is no longer stable, the surrounding icy deposit ostensibly sublimes away, leaving behind a pedestal crater perched atop a steep-sided mesa composed of icy deposits (Kadish et al., 2008). Although the dielectric constants of pedestal craters examined by Nunes et al. (2011) are consistent with either a porous silicate or an ice/silicate mixture, the concentration of pedestal craters in the mid-latitudes and presence of marginal sublimation pits (Kadish et al., 2008) provide strong support for an icy pedestal composition.

Recent work has shown that the ages of the pedestal crater population point to mid-latitude surface ice emplacement periodi-cally for a cumulative duration of at least ∼90 Myr within the past 1 Myr to 3.6 Ga (Kadish and Head, 2014), but the likelihood that numerous pedestal craters have been completely erased through sublimation or other processes prevented this analysis from de-termining the total cumulative ice age duration throughout Mars history.

Fassett et al. (2014) found that the crater size-frequency distri-bution (CSFD) of mid-latitude impact craters that appear to super-pose pre-existing glacial deposits and were then infilled by debris-covered glacial ice (known as concentric crater fill; e.g., Fastook and Head, 2014) points to a cumulative mid-latitude ice age du-ration of at least ∼600 Myr. These authors considered this value a lower bound, however, because continued sublimation of the as-sociated glacial ice would remove evidence for contemporaneous snow/ice emplacement. Much like for the pedestal craters, subli-mation of the features used as criteria for dating would prevent the statistical treatment of the larger (now absent) population of ice-related craters, leading to a lower bound estimate of the cu-mulative ice age duration. Due to the paucity of the entire suite of glacial landforms at the equator, it also remains unclear to what temporal extent Mars has experienced equatorial ice ages. These factors have made evaluating the total duration of martian ice ages difficult.

3. Double-layered ejecta (DLE) craters

Double-layered ejecta (DLE) craters are an additional geomor-phological landform that has been hypothesized to be related to surface ice only recently, and has thus not been included in the previous analyses. Martian DLE craters range from ∼1 km to ∼35 km in rim-crest diameter, are concentrated in the middle to high latitudes, and are characterized by two ejecta facies (e.g., Bar-low, 2005; Weiss and Head, 2017a). The inner facies commonly exhibits a broad rampart, longitudinal ridges and grooves, and an annular depression at the base of the rim (a “moat”) (Carr et al., 1977; Schultz and Gault, 1979; Boyce and Mouginis-Mark, 2006; Weiss and Head, 2013). The outer facies typically exhibits a longer runout distance (relative to other martian layered ejecta craters; Barlow, 2005; Li et al., 2015) and a subdued rampart with a more sinuous terminus (Barlow, 1994; Boyce and Mouginis-Mark, 2006).

DLE craters have been hypothesized to form through a vari-ety of mechanisms that involve impact into a volatile-rich sub-strate (Barlow 1994, 2005; Osinski, 2006; Boyce and Mouginis-Mark, 2006; Jones and Osinski, 2015). These models which in-corporate impact into a volatile-rich substrate differ, however, in the mechanism by which the ejecta is emplaced. These different models include: (1) Ejecta interaction with atmospheric vortices

D.K. Weiss / Earth and Planetary Science Letters 528 (2019) 115847 3

Fig. 2. Schematic representation of the timing of climate change and crater formation on Mars. (A) Double-layered ejecta (DLE) craters form during martian ice ages (Weiss and Head, 2013, 2017a). (B) When the surface is free of surface ice, other more typical crater morphologies form (C), and DLE craters are preserved (Weiss and Head, 2017a). DLE craters may thus record the timing of ice ages on Mars.

(Schultz and Gault, 1979; Schultz, 1992); (2) Collapse and base surge of an explosion column (Boyce and Mouginis-Mark, 2006); (3) Some combination of the above factors (Barlow, 2005; Boyce and Mouginis-Mark, 2006; Komatsu et al., 2007); (4) Impact melt overtopping the crater rim (Osinski, 2006; Osinski et al., 2011); (5) Impact into a buried icy layer (Senft and Stewart, 2008); (6) A landslide of the near-rim crest ejecta (Komatsu et al., 2007; Wulf and Kenkmann, 2015); or (7) Impact into a surface ice layer fol-lowed by a landslide of near-rim crest ejecta (the glacial substrate model; Weiss and Head, 2013, 2017a).

Although the exact formation mechanism by which DLE craters form remains under debate, this paper adopts the glacial substrate model for DLE crater formation on the basis of their association with a wide variety of features that point to formation in sur-face ice (summarized in Weiss and Head, 2017a): (1) ring-mold craters and (2) expanded secondary craters on the ejecta facies of DLE craters; (3) proximity to pedestal craters; (4) sublimation pits at the margins of the outer facies, (5) anomalously high ejecta runout distance of the outer facies (possibly due to ice lubrica-tion); (6) excessively high ejecta volume which is consistent with a 5–100 m thick underlying ice layer; and (7) kinematic, frictional, and morphological similarity (e.g., longitudinal grooves) of inner facies ejecta with terrestrial landslides which overran glaciers. In this model, larger impact events (relative to those which form pedestal craters) which excavate material from beneath surface ice deposits can be identified by their unique double-layered ejecta morphology (Fig. 2) (Weiss and Head, 2013, 2017a). DLE craters are predicted to form on the surface when it is ice-covered (Fig. 2A): in the mid-latitudes during periods of moderate obliquity, and in equatorial regions in periods of high obliquity (Fig. 1). Unlike

pedestal craters and concentric crater fill (discussed in Section 2above), continued sublimation of the ice deposit does not erase the distinctive ejecta morphology that acts as a geomorphic marker of past surface ice (Fig. 2B), and so DLE craters arguably preserve a unique record of the absolute timing of ice ages on Mars (rather than a lower limit, as in Section 2). Consequently, the latitudinal distribution (Fig. 3B) and size-frequency distribution of the DLE crater population offers a means to probe the ancient ice age his-tory of Mars. Next, the size-frequency distribution of these craters is evaluated in order to estimate the cumulative duration of mar-tian ice ages.

4. Observational data and crater statistics

The criteria used here for classifying DLE craters is based pri-marily on the presence of (1) a relatively circular (low sinuosity) inner ejecta facies with a broad rampart which exhibits a “moat” of depressed elevation surrounding the rim; but may also exhibit (2) longitudinal grooves superposing the inner facies; and (3) a more sinuous, longer runout distance outer ejecta facies with a more subdued rampart. This classification criteria is broadly equivalent to the “Type 1” crater classification criteria outlined in Barlow and Boyce (2015) and Barlow (2018).

The observed DLE crater population was extracted from the Robbins and Hynek (2012) database (Fig. 3). This work found that accurate classification of DLE morphology based on the adopted criteria may be attained from this database by sorting the “MOR-PHOLOGY_EJECTA_1” field as containing DLEPC, DLERC, DLEPS, MLEPS, Rd/MLEPC, Rd/MLEPS, Rd/DLEPC, Rd/DLEPS, and the “MOR-PHOLOGY_EJECTA_3” field as containing Pin Cushion; readers are

4 D.K. Weiss / Earth and Planetary Science Letters 528 (2019) 115847

Fig. 3. Latitudinal relationships for the DLE crater population from the Robbins and Hynek (2012) database. (A) DLE craters (black dots) overlain on MOLA gridded topography and MOLA hillshade data. (B) The relative frequency of DLE craters in each latitudinal bin weighted by the surface area in each bin. DLE craters are present globally but are concentrated in the mid-latitudes. (C) Truncated cumulative crater size-frequency distribution of DLE craters poleward of 25◦ (black circles) and equatorward of 25◦ (red squares). The best fit isochrons are shown as the black lines, and predict a model age for the mid-latitude DLE craters of 680 Myr (±20 Myr Poisson error), and a model age for the equatorial DLE craters of 250 Myr (±10 Myr Poisson error). These provide estimates on the cumulative duration of martian ice ages. Note that at bin sizes ≥ 22.6 km, the CSFD for the mid-latitude population poorly matches the isochron. These craters comprise only 3% of the sample population; truncating the CSFD at 22.6 km yields a model age of 690 Myr (±20 Myr Poisson error), while the 32 km truncation or no truncation yields 680 Myr (±20 Myr Poisson error). For the equatorial sample population, craters ≥ 22.6 km represent 5.7% of the sample population; truncating the CSFD at 22.6 km yields a model age of 260 Myr (±10 Myr Poisson error), while the 32 km truncation or no truncation yields 250 Myr (±10 Myr Poisson error). Thus, the discrepancies between the CSFDs and the isochrons at larger diameter bins yield negligible differences in model age results.

referred to Robbins and Hynek (2012) for details on these classi-fication criteria. This classification criteria was independently veri-fied to correctly identify DLE craters. This population contains 3036 craters between 1.5 and 66 km in diameter. To produce a CSFD from this population, root-2 diameter bin spacing and sizes are used, following Hartmann (2005) and Michael (2013). The lower end bin size is restricted to 5.66 km due to rollover at small crater sizes (smaller impact craters forming in surface ice sheets form pedestal craters rather than DLE craters; Kadish et al., 2008, Weiss and Head, 2015), and the upper end bin size is truncated to 32 km due to the lack of confidence in the accurate classification of DLE craters at diameters greater than ∼30 km (due to false pos-itives and because larger impacts into ice likely do not exhibit a DLE morphology; Weiss and Head, 2013, 2015). This truncated cumulative distribution yielded a total of N = 1615 craters used for the observed CSFD of the DLE crater population. The area de-nominator for the CSFD is taken as the entire surface area within

the latitude bands of interest (e.g., Fassett et al., 2014). Latitude bands were divided on the basis of general circulation model re-sults (Forget et al., 2006; Madeleine et al., 2009) and the observed latitudinal distribution of martian DLE craters (Fig. 3B): 25◦ to 80◦N and S (mid-latitude population), and 25◦S to 25◦N (equatorial population). This analysis was also performed using incremental isochrons and without the 32 km diameter truncation; the results remained unchanged.

The observed truncated CSFD of the mid-latitude (poleward of 25◦ latitude) DLE crater population is plotted as the black circles in Fig. 3C (N = 1306). The effective model age for this popula-tion sample is 680 Myr (±20 Myr Poisson error) in the Hartmann (2005) chronology (Michael, 2013). The observed truncated CSFD of the equatorial DLE crater population (equatorward of 25◦ lati-tude) is plotted as the red squares in Fig. 3C (N = 309). The effec-tive model age for this population sample is 250 Myr (±10 Myr Poisson error). These results indicate a cumulative mid-latitude ice

D.K. Weiss / Earth and Planetary Science Letters 528 (2019) 115847 5

Fig. 4. The apparent model CSFD age that a 50 Myr ice age event would exhibit as a function of the time at which the ice age event occurred. The data shown is the first derivative of the martian chronology function (Hartmann, 2005; Michael, 2013) normalized to a 50 Myr timestep. Between 0 and 2.6 Ga, the duration of the 50 Myr ice age is correctly reproduced; before 2.6 Ga, however, the higher cratering rate causes a 50 Myr ice age to result in a CSFD which could indicate a much longer ice age duration.

age duration of 680 Myr and a cumulative equatorial ice age du-ration of 250 Myr in the Hartmann (2005) chronology (Michael, 2013), or 1.2 Gyr (±30 Myr Poisson error) and 410 Myr (±20 Myr Poisson error), respectively, with the Neukum production function (Ivanov, 2001). Next, the results are discussed in the context of the broader implications for martian ice age history.

5. Results and discussion

The truncated crater-size frequency distribution of the DLE crater population corresponds to a cumulative mid-latitude ice age duration of 680 Myr and a cumulative equatorial ice age dura-tion of 250 Myr in the Hartmann (2005) chronology (Michael, 2013). This mid-latitude ice age duration estimate of ∼680 Myr corresponds closely to the ∼600 Myr minimum duration found by Fassett et al. (2014). This work also places a new estimate on the duration of the equatorial ice age as 250 Myr. This estimate is consistent with (but exceeds by a factor of ∼1.7–5.6) the esti-mated ∼45–150 Myr cumulative formation timescale of the Thar-sis Montes glaciers that was based on glacial flow models coupled with parameterized climate model results and estimated orbital model results parameter fluctuations (Fastook et al., 2008).

5.1. Ice age timing

Can these models provide any insight into the timing of the ice ages? Critically, the impact flux in the solar system has not been constant through time, which influences interpretations of the crater statistical analyses. Note that this paper restricts the ice age timing discussion to the geologic record since 3.6 Ga based on the lack of defined ejecta morphologies associated with Noachian-aged craters due to fluvial erosion (Mangold et al., 2012), which would prevent classification of DLE craters, if any. Fig. 4 shows the “apparent” duration that a 50 Myr ice age would exhibit when viewed with CSFD statistical analysis at any given time within the past 3.6 Ga. These results show that the apparent duration of a 50 Myr ice age would be correctly predicted by CSFD statistics to be 50 Myr between 0 and 2.6 Ga due to the constant cratering rate during this period (Fig. 4). Before 2.6 Ga, however, the higher cratering rate would allow the duration of a 50 Myr ice age to ap-pear much longer when viewed in CSFDs, e.g.: 100 Myr at 3.0 Ga, 300 Myr at 3.3 Ga, and 1 Ga for a 50 Myr ice age event at 3.5 Ga (Fig. 4).

On this basis, some ice age history solutions can be ruled out. For the mid-latitude case, lengthy ice age events at or before ∼3.45 Ga are likely not recorded in the DLE crater population because the apparent duration of a 50 Myr ice age event at this time would produce a CSFD with a best-fit age of 700 Myr (Fig. 4),

which exceeds the model age of the population. For the equatorial case, a 50 Myr ice age event before 3.3 Ga would exhibit an ap-parent duration greater than the population model age of 250 Myr, and so lengthy equatorial ice age events before ∼3.3 Ga are likely not recorded in the DLE crater population.

Because ice ages prior to 2.6 Ga would account for a dis-proportionally greater fraction of the total ice age duration, the cumulative duration of ice ages derived from cratering statistics (Section 4) are valid only under the condition that all of the ice age events occurred within the past ∼2.6 Ga. Consequently, the ice age duration estimates introduced in this paper are considered to be absolute upper bounds. If any of the DLE craters which built up the population shown in Fig. 3C were formed before 2.6 Ga, their presence in the CSFD would artificially inflate the estimated dura-tion. Future work dating a large sample of individual DLE craters in conjunction with the present analysis would allow a more firm estimate of the ice age durations.

5.2. Proxy for obliquity

These results may broadly inform on the climate and obliquity history of Mars, but note that these ice age duration estimates likely do not correspond 1:1 with the duration of different obliq-uity excursions (e.g., Fig. 7 in Fastook et al., 2008). This is because surface ice deposits that were emplaced during periods of high obliquity can be armored from sublimation beneath thin lag de-posits for hundreds of Myr, even during periods of lower obliquity (e.g., Head et al., 2003, Black and Stewart, 2008; Fastook and Head, 2014; Bramson et al., 2015, 2017; Viola et al., 2015; Stuurman et al., 2016; Dundas et al., 2018). For example, if the lag deposit were sufficiently thin as to allow DLE craters to form (by frictional melting of the ice sheet and subsequent ejecta sliding lubrication; Weiss and Head, 2017a), then DLE craters could continue to form on the surface even during periods of lower obliquity.

Because this process would only serve to reduce the requi-site duration of high obliquity excursions (relative to the ice age duration), however, the upper bound ice age duration estimates may also place upper bounds on the cumulative duration of high obliquity excursions. If the DLE population has not experienced significant resurfacing since 3.6 Ga, this work defines a maximum cumulative duration of 680 Myr for obliquities between ∼30 −40◦ , and a maximum cumulative duration of 250 Myr for obliquities ≥ 45◦ since 3.6 Ga.

5.3. Summary of results

In summary, this study estimates the cumulative duration of mid-latitude ice age events (Fig. 1; bottom middle panel) to be

6 D.K. Weiss / Earth and Planetary Science Letters 528 (2019) 115847

at most 680 Myr. The DLE crater population examined in this study predicts that the vast majority of recorded mid-latitude ice age events likely occurred more recently than ∼3.45 Ga. The cu-mulative duration of equatorial ice age events (Fig. 1; bottom right panel) is estimated to be at most 250 Myr; the DLE crater population used in this study predicts that the vast majority of recorded equatorial ice age events likely occurred more recently than ∼3.3 Ga. The result that most ice ages are recorded more re-cently than ∼3.3 to ∼3.45 Ga may indicate that the ice age events themselves did not occur until this time period, or alternatively that resurfacing (e.g., by Early Hesperian flood basalts; Head et al., 2002) or erosion (e.g., Mangold et al., 2012) erased the DLE crater population and/or ejecta morphology (and evidence for lengthy ice ages) that formed prior to ∼3.3–3.45 Ga. If widespread resurfac-ing/erosion of the DLE crater population/ejecta did occur it would imply that the “upper bound” cumulative durations (680 Myr and 250 Myr) are actually lower bounds. If the DLE population has not experienced significant resurfacing, the upper limit for the cumu-lative duration in which Mars’ obliquity ranged between ∼30−40◦since 3.6 Ga is 680 Myr, and the upper limit cumulative duration for obliquities ≥ 45◦ since 3.6 Ga is 250 Myr.

6. Conclusions

Assuming that DLE craters do indeed form through impact into surface ice deposits, these results suggest that since the end of the Noachian period, within the past 3.6 Gyr, Mars spent up to 680 Myr in mid-latitude ice ages (Fig. 1; bottom middle panel) and up to 250 Myr in equatorial ice ages (Fig. 1; bottom right panel). Because mid-latitude and equatorial ice ages would not occur si-multaneously, this represents a cumulative duration of ∼0.93 Gyr (±50 Myr Poisson error), comprising approximately 25% of post-Noachian geologic history. Given the prediction that both obliquity shifts (Laskar et al., 2004) and surface ice accumulation may oc-cur on timescales of tens to hundreds of Kyr (Madeleine et al., 2009), ice ages on Mars may have occurred at least throughout the entire Amazonian period, and appear to be recorded in the double-layered ejecta crater population for time periods younger than ∼3.3 to 3.45 Ga. Future work involving the individual dating (e.g., Kadish and Head, 2014) of DLE craters would be valuable in establishing the timing of specific martian ice age events.

Acknowledgements

Many thanks to Ashley Palumbo and James Cassanelli for fruit-ful discussions regarding 3D general circulation model results. The author is grateful to Bill McKinnon, Bob Grimm, Joe Boyce, and two anonymous reviewers and for insightful reviews that improved the quality of the manuscript.

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