Icarus 219 (2012) Contents lists available at SciVerse ScienceDirect. Icarus. journal homepage:

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1 Icarus 19 (1) 5 Contents lists available at SciVerse ScienceDirect Icarus journal homepage: Early Mars climate near the Noachian Hesperian boundary: Independent evidence for cold conditions from basal melting of the south polar ice sheet (Dorsa Argentea Formation) and implications for valley network formation James L. Fastook a, James W. Head b,, David R. Marchant c, Francois Forget d, Jean-Baptiste Madeleine b a Computer Science, University of Maine, 3 Neville Hall, Orono, ME 9, USA b Department of Geological Sciences, Brown University, Providence, RI 91, USA c Department of Earth Sciences, Boston University, Boston, MA 15, USA d Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, Université Paris, BP 99, 755 Paris cedex 5, France article info abstract Article history: Received June 11 Revised 9 December 11 Accepted 13 February 1 Available online February 1 Keywords: Mars Mars, climate Mars, polar caps Mars, polar geology Currently, and throughout much of the Amazonian, the mean annual surface temperatures of Mars are so cold that basal melting does not occur in ice sheets and glaciers and they are cold-based. The documented evidence for extensive and well-developed eskers (sediment-filled former sub-glacial meltwater channels) in the south circumpolar Dorsa Argentea Formation is an indication that basal melting and wetbased glaciation occurred at the South Pole near the Noachian Hesperian boundary. We employ glacial accumulation and ice-flow models to distinguish between basal melting from bottom-up heat sources (elevated geothermal fluxes) and top-down induced basal melting (elevated atmospheric temperatures warming the ice). We show that under mean annual south polar atmospheric temperatures ( 1 C) simulated in typical Amazonian climate experiments and typical Noachian Hesperian geothermal heat fluxes (5 5 mw/m ), south polar ice accumulations remain cold-based. In order to produce significant basal melting with these typical geothermal heat fluxes, the mean annual south polar atmospheric temperatures must be raised from today s temperature at the surface ( 1 C) to the range of 5 to 75 C. This mean annual polar surface atmospheric temperature range implies lower latitude mean annual temperatures that are likely to be below the melting point of water, and thus does not favor a warm and wet early Mars. Seasonal temperatures at lower latitudes, however, could range above the melting point of water, perhaps explaining the concurrent development of valley networks and open basin lakes in these areas. This treatment provides an independent estimate of the polar (and non-polar) surface temperatures near the Noachian Hesperian boundary of Mars history and implies a cold and relatively dry Mars climate, similar to the Antarctic Dry Valleys, where seasonal melting forms transient streams and permanent ice-covered lakes in an otherwise hyperarid, hypothermal climate. Ó 1 Elsevier Inc. All rights reserved. 1. Introduction Current polar layered deposits (Phillips et al., ), earlier Amazonian mid-latitude glacial deposits (Head et al., 1) and tropical mountain glaciers (Head and Marchant, 3) all were deposited from (or contain) cold-based ice; none are associated with basal melting except for some tropical mountain glaciers that were modified by sub-glacial volcanic eruptions (Shean et al., 5a,b; Kadish et al., ). Some features in southern Argyre have been interpreted to be eskers indicative of wet-based glaciation as late as the Middle Amazonian (Kargel and Strom, 199; Corresponding author. addresses: fastook@maine.edu (J.L. Fastook), james_head@brown.edu (J.W. Head). Banks et al., 9). Of concern here are the Late Noachian Early Hesperian south circumpolar Dorsa Argentea Formation (DAF) (Tanaka and Kolb, 1) (Fig. 1). The DAF contains features interpreted to be indicative of basal melting beneath a regional ice-rich deposit (Head and Pratt, 1; Ghatan and Head,, ; Ghatan et al., 3; Kress et al., 1) atthattime(plautetal.,19). What conditions could have led to the formation and evolution of an ice-rich circumpolar deposit such as the Dorsa Argentea Formation in early Mars history? On Mars, as we know it today, water ice at the surface is expected to be less stable on average in the south polar region than in the north polar region because the global topographic asymmetry tends to favor the transport of water to the northern hemisphere (Richardson and Wilson, ) despite the fact that water ice can exist in the near subsurface poleward of latitude at both poles (Mitrofanov et al., ; Boynton et al., ). 1935/$ - see front matter Ó 1 Elsevier Inc. All rights reserved. doi:1.11/j.icarus.1..13

2 J.L. Fastook et al. / Icarus 19 (1) 5 Fig. 1. A sketch map with thin arrows within Hd unit showing the location of features interpreted to be eskers formed by water flowing at the base of an ice sheet. Shown are distributions of Api (polar ice deposits), Apl (polar layered deposits), Hd (Hesperian Dorsa Argentea Formation), and HNu (Hesperian Noachian undivided unit). CA is Cavi Angusti and CS is Cavi Sisyphi. Heavy arrows outside Hd are channels (1 5: Schmidt, Surius, Dzigai, Doanus, and Palcopas Valles respectively) interpreted to be draining Hd. Examples of the esker-like ridges located at the thin arrows in. Both are from Head and Pratt (1). Fig.. Distinguishing between top-down induced basal melting and bottom-up induced basal melting. An ice sheet at typical Amazonian temperatures is cold-based even with enhanced geothermal heat flux. Climate warming can lead to basal melting without producing melting at the surface of the ice sheet. Because the current atmosphere is very thin, the dependence of surface temperature and mass balance to altitude is different than on Earth. Indeed, the surface pressure being only of a few hpa on Mars, contribution of the sensible heat flux to the surface energy budget is almost negligible, and the surface does not follow the adiabatic temperature gradient of the atmosphere (see Section 3. of Spiga, 11). Instead, the surface temperature is always close to radiative equilibrium, whatever the altitude. On Earth the

3 J.L. Fastook et al. / Icarus 19 (1) (d) Mass Balance (mm/a) [SMB X.5] TIME 1Ma Mass Balance (mm/a) [SMB X 3.] TIME 1Ma Mass Balance (mm/a) [SMB X 1.] TIME 1Ma (c) Mass Balance (mm/a) [SMB X.] TIME 1Ma (e) Mass Balance (mm/a) [SMB X.] TIME 1Ma (f) TEMPERATURE (degree C) [base] BASE Fig. 3. Synthetic climate modified from Madeleine et al. (9). (f) Shows the temperature field taken directly from the GCM results. To this we apply the offsets for the warmer climates. Shows the basic SMB, with sublimation rates modified from Madeleine et al. (9) by a reduction factor of 5 and a radially symmetric accumulation component added. Panels (a, c, d, and e) are the basic SMB times.5,., 3., and BED (m) surface temperature tends to follow the atmospheric lapse rate (.5 C/km moist, 9.5 C/km dry), which results in less ablation by Fig.. The grid for ice sheet reconstruction from the pole at grid (,) to S at the edge of the circle. Resolution is non-uniform but is nominally 3 km. To avoid complications associated with the present ice sheet topography, we truncate elevations at 3 m, shown by the white line. Horizontal units are km, while vertical elevations shown by color contours are m. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) melting as well as less accumulation with increasing elevation. But while ablation reduces to zero, accumulation never does, so a typical mass balance profile has negative values at low elevations, an equilibrium line at some elevation where accumulation and ablation are equal, a peak mass balance at some elevation above the equilibrium line, and then a declining positive mass balance beyond that. On Mars, ablation by melting is replaced by sublimation, whose rate varies with altitude mainly as a function of surface pressure (lower pressure, more sublimation) and not surface temperature which, as we just said, is close to radiative equilibrium. Thus on present-day Mars sublimation never goes to zero, but actually increases with elevation. It is thus possible, depending on the vertical structure of the accumulation pattern, to have two equilibrium lines, a lower one and an upper one. It is this sort of mass balance pattern that we suspect produced the flank glaciation on the Tharsis volcanos, a situation we treated in detail in Fastook et al.. Current climate models suggest that ice would only accumulate at the South Pole when the season of the perihelion favors a southern summer significantly colder than in the north (Montmessin et al., 7). This may explain why the Amazonian south polar-layered deposits are older than the north polar-layered deposits. If the atmosphere was thicker during the Noachian and Hesperian eras than today, then conditions at the South Pole may have been very different. For example, with a denser atmosphere, surface temperature distribution would behave much more like that on Earth and follow the adiabatic cooling of the atmosphere, with high altitude regions significantly colder than lower plains (Forget et al.,, 1). Within this context, it is likely that the high southern latitudes would have become a cold-trap where ice would tend to accumulate and form a large

4 J.L. Fastook et al. / Icarus 19 (1) TEMPERATURE (degree C) [a-] TIME 1Ma [a-] (c) TEMPERATURE (degree C) [a-] TIME 1Ma (d) [a-] Fig. 5. Basal temperatures (a and c) and vertical profiles (b and d) for SMB.5 scenario with no warming and geothermal flux of 5 (a and b) and 5 (c and d) mw/m. ice sheet, both because of their latitude and their altitude. It is also possible that the amount of water involved in the atmospheric water cycle was larger than today, and that consequently more water was available to form an ice sheet (Forget et al.,, 1). For example, valley network activity, suggestive of flowing streams and a warmer and wetter early Mars (Carr, 199; Craddock and Howard, ; Head et al., 3; Kargel, ; Fassett and Head, a,b), characterized the highlands at the end of the Noachian and into the Hesperian. The active water cycle (Head et al., 3) implied by these interpretations may have been able to transport large amounts of water into the southern polar region in the Late Noachian and Hesperian. Observed in the DAF are features interpreted to be eskers (Head and Pratt, 1; Ghatan and Head,, ; Ghatan et al., 3; Kress et al., 1). Examples of eskers and their locations are shown in Fig. 1 by thin, sinuous arrows within the Hesperian DAF, labeled as the Hd unit. Api depicts polar ice deposits, Apl polar layered deposits, and HNu the Hesperian Noachian undivided unit. The bolder sinuous arrows in Fig. 1 outside the Hd unit are large channels leading away from the margins of the DAF, interpreted to be drainage channels linked to the basal meltwater esker system beneath the paleo ice sheet. Smaller meltwater drainage channels or systems elsewhere around the margins of the DAF have not been observed or documented, suggesting that regional melting of the top of the DAF did not occur. Eskers form beneath ice sheets when water gathers in basal flow channels kept open by the continuous melting of the ice-cavity wall. Ice melt associated with frictional heat from flowing water tends to balance the overburden-driven creep closure of the cavity (Rothlisberger, 197), permitting continuous water flow. The channels at the bed fill with sediments, and as the ice sheet wanes, the accumulated sediment is left as internally stratified, sinuous ridges. As such, eskers are evidence that basal melting, and possibly regional wet-based glaciation, occurred in the past. There are three possible sources for the water necessary to create eskers. First, the water could come from meltwater generated at the surface of the glacier by significantly increased atmospheric temperatures at the poles to above the melting point; such surface meltwater would drain off the ice sheet into surrounding areas, forming radial channels in the surroundings, and could also be carried to the glacial bed by moulins (narrow holes that connect the surface to the glacial base). The lack of radial channels surrounding

5 J.L. Fastook et al. / Icarus 19 (1) TEMPERATURE (degree C) [b-] TIME 1Ma [b-] (c) TEMPERATURE (degree C) [b-] TIME 1Ma (d) [b-] Fig.. Basal temperatures (a and c) and vertical profiles (b and d) for SMB 1. scenario with no warming and geothermal flux of 5 (a and b) and 5 (c and d) mw/m. the DAF suggests that this extreme case is not likely to be applicable. Two less extreme possible heat sources are available to help generate eskers. First, warming (not melting) of ice due to atmospheric heating and second, warming due to elevated geothermal heat flux. We call the first type top-down induced basal melting and the second type bottom-up induced basal melting. Both of these latter types of melting can occur even if the surface of the ice sheet is well below the melting point. The insulating capability of the ice sheet, coupled with internal shear heating and a geothermal heat flux, can raise the basal temperature to the melting point and water can thus be produced at the bed. We must note here that we are not including the melting point depression associated with perchlorate salts (Marion et al., 1) as this would produce only a very transient melted bed, as the meltwater produced would very quickly dilute the available perchlorate to the point where the melting point would again be close to C. We ask the following two questions: (1) are the observed eskers related to melting from top-down heating (but not surface melting) associated with elevated atmospheric temperatures? Or, alternatively, () are the eskers related to bottom-up heat sources linked to local and regional elevated geothermal fluxes relative to today? We first test the hypothesis that they could be related to bottom up melting due to enhanced geothermal fluxes linked to early stages of planetary thermal evolution, and that sufficient ice accumulated to raise the global melting isotherm to the base of the ice sheet (Fig., top). We then assess the magnitude of atmospheric surface temperature increase that would be required to ensure basal melting from the top down (Fig., bottom). The latter question has important consequences for the equatorial regions, since warming of the poles necessarily warms the equator as well. For example, models for martian atmospheres with 5 mb CO, both with and without excess H O(Johnson et al., ) show warming of the poles of as much as +5 C and +5 C respectively. Their models indicate a pole-to-equator gradient of approximately C. We begin by describing the basic approaches to these questions using the University of Maine Ice Sheet Model (UMISM) and the Mars General Circulation Model of the Laboratoire de Météorologie Dynamique.. The University of Maine Ice Sheet Model (UMISM) The UMISM, adapted for the martian environment (Fastook et al.,, 5, ), is a terrestrial ice sheet model that has been used successfully for time-dependent reconstructions of Antarctic, Greenland, and paleo-icesheet evolution in response to changing

6 3 J.L. Fastook et al. / Icarus 19 (1) TEMPERATURE (degree C) [c-] TIME 1Ma [c-] (c) TEMPERATURE (degree C) [c-] TIME 1Ma (d) [c-] Fig. 7. Basal temperatures (a and c) and vertical profiles (b and d) for SMB. scenario with no warming and geothermal flux of 5 (a and b) and 5 (c and d) mw/m. climate on Earth (Fastook, 1993). UMISM uses a thermo-mechanically coupled Shallow-Ice Approximation (vertically-integrated momentum combined with continuity) where the dominant stress is internal shear and longitudinal stresses are neglected. Primary input to the model is the bed on which the ice sheet is to be reconstructed and the net annual surface mass balance (SMB), or accumulation rate. Secondary input includes the mean-annual surface temperature and the geothermal heat flux, used to calculate internal temperatures from which the mechanical properties of the ice are obtained. In addition, internal temperatures allow for the possibility that the base of the ice reaches the pressure melting point, at which point some sliding criteria can be invoked, a phenomena we have not observed in any modeled martian glaciers of Amazonian time (Fastook et al., a,b). This feature will be key to the investigation of conditions that would produce a melted bed for ice associated with the DAF. The fact that with the exception of bed topography, these inputs are poorly constrained for Mars introduces some uncertainty into the results that will be presented. However, choice of reasonable values for mean annual temperature, geothermal flux, and SMB allow production of results comparable to inferred ice conditions based on geologic observations. Given these uncertainties the choice of a Shallow-Ice Approximation model is also appropriate, since the considerable computational load of a higher-order model would not produce more accurate results. Using data from McGovern et al. () and Solomon et al. (5) we adopt a geothermal flux of 5 5 mw/m as a range appropriate for this time period near the Noachian Hesperian boundary. 3. The Mars GCM of the Laboratoire de Météorologie Dynamique In order to specify the spatial distribution of the SMB of accumulated ice for a glacial flow model, one can arbitrarily choose values and explore consequences and predictions, or use the results from a Global Circulation Model (GCM) as input. Here we choose the latter and employ results from the Laboratoire de Météorologie Dynamique GCM (LMD/GCM) (Forget et al., 1999). This GCM is able to reproduce the present-day water cycle on Mars with good accuracy (Montmessin et al., ) and has proven robust in our earlier glacial modeling studies of reconstructed ice sheets in the Tharsis region (e.g., Forget et al., ; Fastook et al.,, 5, b).

7 J.L. Fastook et al. / Icarus 19 (1) TEMPERATURE (degree C) [d-] TIME 1Ma [d-] (c) TEMPERATURE (degree C) [d-] TIME 1Ma (d) [d-] Fig.. Basal temperatures (a and c) and vertical profiles (b and d) for SMB 3. scenario with no warming and geothermal flux of 5 (a and b) and 5 (c and d) mw/m. As yet, however, the model has not been applied toward predictions of SMB for the Noachian Hesperian era (Johnson et al., ; Wordsworth et al., 11) and this requires additional assumptions as noted below.. Model assumptions and input.1. Noachian Hesperian ice accumulation The goal is to produce an ice sheet whose footprint will approximate the DAF so that we can assess the conditions that will generate melting at the bed under what we assume was a thicker CO atmosphere. This we do by modifying the GCM climate simulated by Madeleine et al. (9) and obtained using an intermediate obliquity (35 ) and a high dust optical depth (.5). In doing so we understand that this synthetic climate is not that which would result from a true GCM for the Noachian Hesperian era; however, we consider it as a typical paleoclimate simulation that will capture salient features such as the spatial distribution of the temperature field as well as the amount and distribution of potential sublimation that might occur in the DAF region. SMB from Madeleine et al. (9) predicted extremely large sublimation rates in the DAF region, and to build an ice sheet in such a climate would require extremely large accumulation rates. We choose to retain the spatial pattern of their sublimation rates, but reduce them by a factor of 5 (11 mm/a maximum sublimation instead of more than 5 cm/a). To this we add a radially symmetric pattern of accumulation, with a maximum value of mm/a centered on the pole, declining with distance such that the region of accumulation has a radius of 5 km. This, combined with the modified Madeleine et al. (9) sublimation rates is designed to produce an ice sheet footprint in accordance with the DAF. This basic SMB pattern is shown in Fig. 3b. Also in Fig. 3aandc e are scaled versions of this basic SMB pattern (times.5,., 3., and.) that we use to test the sensitivity of the ice sheet to our assumed climate. By scaling the basic SMB pattern we obtain the same ice sheet footprint for each, since the equilibrium-line position remains the same and both accumulation and sublimation rates are scaled by the same amount. What is different in these various SMB cases is the flux of ice as it moves from the accumulation zone to the ablation zone. Since internal heat within the body of the ice sheet comes directly from shear heating (stress times strain

8 3 J.L. Fastook et al. / Icarus 19 (1) TEMPERATURE (degree C) [e-] TIME 1Ma [e-] (c) TEMPERATURE (degree C) [e-] TIME 1Ma (d) [e-] Fig. 9. Basal temperatures (a and c) and vertical profiles (b and d) for SMB. scenario with no warming and geothermal flux of 5 (a and b) and 5 (c and d) mw/m. Geothermal Flux (nw/m^) Percent Wet Bed [SMB*.5] Temperature Offset (K) Percentage % threshold warming= warming=1 warming= warming=3 warming= warming=5 Percentage Wet Bed, SMB X Geothermal Flux (mw/m^) Fig. 1. Percentage of the bed that is wet for SMB.5 scenario as a function of temperature warming and geothermal heat flux. Vertical transects through at temperature warmings of +, +1, +, +3, +, and +5 C with the 5% basal melting threshold shown as a horizontal line for reference.

9 J.L. Fastook et al. / Icarus 19 (1) 5 33 Geothermal Flux (nw/m^) Percent Wet Bed [SMB*1.] Temperature Offset (K) Percentage % threshold warming= warming=1 warming= warming=3 warming= warming=5 Percentage Wet Bed, SMB X Geothermal Flux (mw/m^) Fig. 11. Percentage of the bed that is wet for SMB 1. scenario as a function of temperature warming and geothermal heat flux. Vertical transects through as in Fig. 1. Geothermal Flux (nw/m^) Percent Wet Bed [SMB*.] Temperature Offset (K) Percentage % threshold warming= warming=1 warming= warming=3 warming= warming=5 Percentage Wet Bed, SMB X Geothermal Flux (mw/m^) Fig. 1. Percentage of the bed that is wet for SMB. scenario as a function of temperature warming and geothermal heat flux. Vertical transects through as in Fig. 1. Geothermal Flux (nw/m^) Percent Wet Bed [SMB*3.] Temperature Offset (K) Percentage % threshold warming= warming=1 warming= warming=3 warming= warming=5 Percentage Wet Bed, SMB X Geothermal Flux (mw/m^) Fig. 13. Percentage of the bed that is wet for SMB. scenario as a function of temperature warming and geothermal heat flux. Vertical transects through as in Fig. 1.

10 3 J.L. Fastook et al. / Icarus 19 (1) 5 Geothermal Flux (nw/m^) Percent Wet Bed [SMB*.] Temperature Offset (K) Percentage % threshold warming= warming=1 warming= warming=3 warming= warming=5 Percentage Wet Bed, SMB X Geothermal Flux (mw/m^) Fig.. Percentage of the bed that is wet for SMB. scenario as a function of temperature warming and geothermal heat flux. Vertical transects through as in Fig. 1. Table 1 The minimum geothermal fluxes and temperature warmings that achieve 5% basal melting conditions for the 5 SMB scenarios. Climate scenario (base SMB) 5% wet bed threshold Lowest geothermal flux (mw/m ) At temperature warming (+ C) Lowest temperature warming at 5 mw/m Mass Balance (mm/a) [d] TIME 1Ma Surface [d] TIME 1Ma TEMPERATURE (degree C) [d].1 (d) (e) WATER (amount) [d] (f) TIME 1Ma - TIME 1Ma (c) VELOCITY (mm/a) [d] TIME 1Ma [d] Fig. 15. The ice sheet configuration for SMB 3. scenario for +5 C warming with the low geothermal heat flux of 5 mw/m, a threshold state for 5% basal melting. The SMB with peak accumulation of 1 mm/a and sublimation rate of 33 mm/a. Surface elevation (m). (c) Velocity magnitude (mm/a). (d) Basal temperatures ( C), white indicates temperatures at the pressure melting point and would be producing melt water. (e) Water amount. (f) Profile along the x-axis though the dome.

11 J.L. Fastook et al. / Icarus 19 (1) 5 35 rate, and strain rates are velocity gradients), the velocities required to pass the different fluxes of the scaled SMB patterns will have the potential to create significantly more or less internal heat, critical in our assessment of the amount of warming necessary to produce the basal melting capable of producing eskers. Also shown in Fig. 3f is the mean annual surface temperature field taken directly from Madeleine et al. (9). Temperatures range from 95 C at S to as low at 11 C at the pole. It is to this temperature field that we will apply uniform offsets to simulate warmer climates... Noachian Hesperian topography The modeled ice sheet is reconstructed on the bed taken from MOLA topography (Smith et al., 1) shown in Fig.. We use a 5 5 checkerboard of Finite Element quadrilaterals distorted into a circular grid extending from the pole to S that completely encompasses the DAF (Fig. 1). Resolution in the distorted checkerboard is non-uniform but is nominally 3 km. To avoid complications associated with the present ice sheet topography, we truncate elevations at 3 m, shown in Fig. by a solid white line. 5. Ice sheet modeling results A total of 75 model runs were produced (five climate scenarios, SMB.5, 1.,., 3. and.; five geothermal heat fluxes, 5, 5, 55,, and 5 mw/m ; and eleven temperature offsets, to +5 C in 5 C intervals, each added to the temperature field of Fig. 3f). Each scenario was run for 1 Ma, a time sufficient for the ice sheets to achieve basic equilibrium configurations The bottom-up induced basal melting case Using mean annual south polar temperatures typical of Amazonian climate simulations (a C offset or warming) from Fig. 3f (ranging from 95 to 11 C,) and the range of Noachian Hesperian heat fluxes (5 5 mw/m ) described above, south polar ice sheets remain cold-based. Figs. 5 9 show calculated basal temperatures (a and c) and temperature profiles (b and d) for the ice sheets grown in our five different synthetic climates (SMB scaling of.5, 1.,., 3., and. from Fig. 3a e) for both 5 (a and b) and 5 (c and d) mw/m. Surface elevation contours are shown at 5 m intervals. Even with the higher geothermal flux, all but a few deep holes (for instance, Schmidt Crater at grid-coordinates 1, + km in Fig. c where a melted patch emerges) are 15 C or more below the melting point. The profiles cross the ice sheet through the dome, roughly along the x-axis of the grid coordinate system. In the temperature profiles, one can see from the evenly spaced isotherms that the effect of advection of heat by moving material is negligible, to be expected with the low accumulation rates and velocities in the ice sheet. Shear heating is also not contributing significantly. The slope of the linear temperature variation with depth is basically defined by the specified geothermal heat flux (convertible to a temperature gradient by dividing by the conductivity). The higher accumulation cases on the right produce a warmer bed simply by increasing the insulating capability of the ice sheet through its increased thickness. It is worth noting that equilibrium ice sheet elevations do not depend strongly on the magnitude of the accumulation. An analytic solution for a uniform-accumulation ice sheet on a flat bed yields an elevation that depends on the Mass Balance (mm/a) [d-] Surface [d-] 1 TIME 1Ma 1 TIME 1Ma 95 (c) TEMPERATURE (degree C) [d-] WATER (amount) [d-].1 (d) TIME 1Ma -(e) TIME 1Ma.95 (f) VELOCITY (mm/a) [d-] TIME 1Ma [d-] Fig. 1. The ice sheet configuration for SMB 3. scenario for + C warming with the high geothermal heat flux of 5 mw/m, a threshold state for 5% basal melting. (a f) As in Fig. 15.

12 3 J.L. Fastook et al. / Icarus 19 (1) 5 Mass Balance (mm/a) [d] Surface [d] 1 TIME 1Ma 1 TIME 1Ma 95 (c) VELOCITY (mm/a) [d] TIME 1Ma TEMPERATURE (degree C) [d] WATER (amount) [d].1 (d) TIME 1Ma -(e) TIME 1Ma.95 (f) [d] Fig. 17. The ice sheet configuration for SMB 3. scenario for +5 C warming with the high geothermal heat flux of 5 mw/m, 7% basal melting. (a f) As in Fig. 15. accumulation rate raised only to the 1/th power. Hence a doubling of the accumulation rate should only yield approximately a 1% thicker ice sheet. This can be seen as one moves from the low-smb case in Fig. 5 (.5 times the base) to the high-smb cases in Figs. 7 9 (., 3., and. times the base). Also worth noting is the contrast between the 5 mw/m cases (Fig. a and b) and the higher geothermal flux 5 mw/m cases (Fig. c and d). Because the mechanical properties of ice are an exponential function of temperature, the higher geothermal flux case yields a much thinner ice sheet (as much as 1 m thinner) because the warmer, softer ice deforms more easily, allowing for larger velocity gradients, and hence overall faster flow requiring less thickness to pass the same mass flux. This thinner ice provides less insulating thickness counteracting warming due to the higher geothermal flux. In addition, the fact that the thinner ice sheet must pass the same flux of ice through the reduced thickness results in larger velocities and also larger velocity gradients, which then produce more shear heating. Assessment of the magnitude of the competing effects of thinner and less insulating versus faster flowing and greater shear heating can only be effectively assessed with a thermo-mechanically coupled ice sheet model such as UMISM, the model used in this study. Having determined that simply raising the geothermal flux is insufficient to produce significant basal melting, we can now turn to the question of elevated surface temperatures. 5.. The top-down induced basal melting case Under what conditions can basal melting induced by increased atmospheric surface temperatures create meltwater to produce eskers? The threshold for significant water production for each of the climate scenarios is shown in Figs. 1. In each figure, panel shows the percent of the ice sheet bed that reaches the pressure melting point and begins to produce water as a function of the temperature warming (the offset added to the temperature field shown in Fig. 3f) along the horizontal axis, and geothermal heat flux along the vertical. Also shown in panel of each figure are vertical transects through the companion panel at six different temperature offsets. For reference, the 5% melted-bed level is shown. This is the minimum level at which significant quantities of water are produced. Fig. 1, corresponding to the lowest SMB.5 scenario (peak accumulations of 3 mm/a and maximum sublimation of 5 mm/a) shows no significant melting unless the climate is warmed by 5 C and the geothermal heat flux increased to 53 mw/m. Alternatively, one achieves melting with C warming by raising the geothermal flux to 5 mw/m. As one progresses through the climate scenarios from lower mass throughput (SMB.5) to higher (SMB.), the onset of significant melting (5%) moves to lower temperatures and smaller geothermal fluxes. For the SMB 1. scenario (Fig. 11), the smallest geothermal heat flux that reaches the 5% threshold within our modeled temperature range is 9 mw/ m at 5 C warming, and the lowest warming at the upper range of geothermal heats is 35 C. Figs. 1 for SMB., 3., and. show similar trends with higher SMB reaching our 5% threshold for progressively lower temperature and smaller geothermal fluxes, with a summary shown in Table 1. Only the SMB. scenario achieves 5% melting with the lowest geothermal flux modeled, and then only with the highest temperature modeled, and none produce 5% without at least 1 C warming. The main conclusion to draw from these figures is that lower throughput requires either more temperature warming or a higher geothermal flux to achieve

13 J.L. Fastook et al. / Icarus 19 (1) 5 37 Mass Balance (mm/a) [d] Surface [d] 1 TIME 1Ma 1 TIME 1Ma 95 (c) VELOCITY (mm/a) [d] TIME 1Ma (d) TEMPERATURE (degree C) [d] WATER (amount) [d].1 TIME 1Ma -(e) TIME 1Ma.95 (f) [d] Fig. 1. The ice sheet configuration for SMB 3. scenario for +5 C warming with the medium geothermal heat flux of 5 mw/m, 9% basal melting. (a f) As in Fig. 15. the same level of basal melting, a consequence of reduced shear heating. Figs. 15 and 1 show two of these ice sheet configurations that just exceeded our 5% threshold, both for the SMB 3. scenario (1 mm/a peak accumulation, 33 mm/a maximum sublimation). Fig. 15 shows a low geothermal heat flux case (5 mw/m ) that requires a full 5 C atmospheric surface temperature warming in order to achieve our 5% threshold for significant melting. Shown in this figure are the SMB pattern, the surface elevation, (c) the velocity magnitude in mm/a, (d) basal temperatures ( C) with white indicating areas where the bed is at the pressure melting point and melting would be occurring, (e) the water amount (a nominal thickness that should not be construed as a water layer), and (f) a profile showing internal temperatures and surface on a transect approximately along the x-axis through the dome. Fig. 1 shows the same (a f) for the high geothermal heat flux case (5 mw/m ), but here only + C atmospheric surface temperature warming is required to achieve our 5% melted-bed threshold. This ice sheet, even with the higher geothermal heat flux, behaves as a much colder ice sheet, with much steeper margins, as much as 7 m thicker at the dome, and with much more subdued flow velocities. The pattern of melted bed is, however, very similar, with virtually the same pattern of bed at the pressure melting point and basal melting. We would be unable to distinguish between these two cases from the geologic record alone. Both Figs. 15 and 1 are of threshold melting cases that just exceeded an arbitrary 5% melted bed criteria (5% and % respectively). We will now turn to some cases with higher percentages of melted beds that may be more representative of ice sheets that would produce larger quantities of basal water. Fig. 17 shows the SMB 3. scenario with a warming of +5 C and a high geothermal heat flux of 5 mw/m. This is a relatively cold ice sheet and so is thicker. Melted basal conditions occur at the same positions as in Figs. 15 and 1 but are slightly larger, and the amount and areal extent of the water at the bed is increased (7%). Note that velocity magnitudes are also higher. Fig. 1 is also for the SMB 3. scenario, now for +5 C warming and a medium geothermal flux. Melted basal percentage is 9%. The warmer ice sheet is thinner, velocities are still higher, and definite focused areas of flow are occurring over the melted-bed regions. Velocities approach mm/a in the regions of fastest flow. Finally, Fig. 19, again for the SMB 3. scenario, shows the ice sheet configuration for a slightly smaller warming of + C with a high geothermal heat flux of 5 mw/m. This is the thinnest of the ice sheet configurations presented here. A summary of the ice sheet configurations shown in Figs is presented in Table. Of these, Fig. 1 showing SMB 3. with +5 C and 5 mw/m is our favored configuration since it requires the most conservative modifications while producing a melted bed pattern coincident with the observed eskers. Of note is the fact that one of the major patches of calculated melting occurs close to the esker region shown by arrows in Fig. 1 (Head and Pratt, 1). Fig., the basal temperatures from the case shown in Fig. 1, includes an overlay map of site names. The major patch of melted bed lays directly over the DAF region just south of Joly Crater, a feature visible in the example of eskers shown in Fig. 1. In this exercise we have been guided by the geological observations of the extent of the deposit and the presence and distribution of eskers, indicative of basal melting. An ice sheet approximating

14 3 J.L. Fastook et al. / Icarus 19 (1) 5 Mass Balance (mm/a) [d-] Surface [d-] 1 VELOCITY (mm/a) [d-] TIME 1Ma 1 TIME 1Ma 95 (c) TIME 1Ma (d) TEMPERATURE (degree C) [d-] WATER (amount) [d-].1 TIME 1Ma - (e) TIME 1Ma.95 (f) [d-] Fig. 19. The ice sheet configuration for SMB 3. scenario for + C warming with the high geothermal heat flux of 5 mw/m, 11% basal melting. (a f) As in Fig. 15. Table Summary of ice sheet configurations shown in Figs Figure SMB Temperature warming (+ C) Geothermal (mw/m ) Melted % Average thickness (m) Volume (M km 3 ) the estimated footprint of the DAF is created with a reasonable synthetic climate linked to our work with GCM results. Systematic exploration of the parameter space spanning the magnitude of the SMB, the surface temperature, and the geothermal heat flux provide a robust estimate of the conditions under which such an ice sheet could have existed. Thermodynamic calculations of internal temperatures within and at the bed of the ice sheet allow us to identify the conditions under which a melted bed might have occurred, and to assess what the configuration of the ice sheet might have been. At the high end of the geothermal heat fluxes modeled, 5 mw/ m, the warming required to produce significant basal melting is + C for the low throughput case (SMB.5) and + C for the high throughput case (SMB.). Note that this degree of warming would increase maximum temperature for the region to between 7 to 55 C, still sufficiently cold that no surface melting would occur. At low heat fluxes, 5 mw/m, more than +5 C warming (a maximum temperature for the region of 5 C) is necessary to bring the bed to the melting point, even in the highest SMB case (.), although the trend is for the higher SMB to require less warming. At this point, basal melting will start to take place beneath the ice sheet, and this will produce sufficient melting to account for the extensive esker systems observed in the Dorsa Argentea Formation (Head and Pratt, 1; Kress et al., 1). In all cases the surface temperatures in the circumpolar regions are still considerably below C, and thus independent melting of surface ice is not likely to occur, consistent with geologic observations (Head and Pratt, 1). GCM results for a suite of obliquities show similar polar temperature warming (+5 to +5 C) as one moves from the current 3 obliquity to the extreme of 55 predicted by Laskar et al. () (see for example Fig. of Haberle et al., 3). Excursions to such extreme obliquities are relatively brief (1 Ka) and further would not in themselves build an equilibrium ice sheet with sufficient insulating thickness and shear-heating velocity to produce widespread melting at the bed.

15 J.L. Fastook et al. / Icarus 19 (1) TEMPERATURE (degree C) [d] TIME 1Ma Fig.. Basal temperatures for SMB 3., +5 C, 5 mw/m case of Fig. 1, with overlay showing agreement with the identified eskers shown in Fig. 1, adjacent to Joly Crater in the center of the DAF.. Discussion and conclusions We show that under mean annual south polar atmospheric temperatures ( 1 C) simulated in typical Amazonian climate experiments and estimated Noachian Hesperian heat fluxes (5 5 mw/m ), south polar ice accumulations remain cold-based. In order to produce significant basal melting at these typical geothermal heat fluxes, the mean annual south polar atmospheric temperatures must be raised from today s temperature ( 1 C) to the range of 5 to 75 C. This polar surface temperature increase is insufficient to cause melting at the ice sheet surface, but sufficient to induce basal melting of the ice sheet. This increase in surface temperatures required to explain the basal melting of a thick, south circumpolar, ancient ice sheet translates into higher temperatures at lower latitudes, but does not appear consistent with a generally warm and wet early Mars. Mean annual south polar temperatures in the range of 5 to 75 C still imply lower latitude mean annual temperatures generally below the melting point of water (Forget et al.,, 1). On the other hand, these mean annual lower latitude temperatures, while likely to be below the melting point of water, imply equatorial and midlatitude seasonal temperatures that could be in excess of the melting point of water (Forget et al.,, 1). Thus, the late Noachian climate of Mars may have been similar to the current hypothermal, hyperarid climate of the Antarctic Dry Valleys on Earth (Marchant and Head, 7), where seasonal melting occurs in microenvironment/microclimate zones similar to latitudedependent zones on Mars. Such seasonal melting in Antarctica leads to the formation of transient streams and ice-covered lakes that have similarities to the valley networks and open basin lakes on Mars (Fassett and Head, a,b; Marchant and Head, 7). In conclusion, this analysis of the Dorsa Argentea Formation provides an independent estimate of elevated surface temperatures in the mid-latitudes and equatorial regions of Mars near the Noachian Hesperian boundary of Mars history, but favors a cold climate with seasonal melting, rather than a warm, wet climate. Acknowledgments We gratefully acknowledge the scientists and engineers contributing to the success of the NASA Mars Observer, Mars Odyssey, and Mars Reconnaissance Orbiter, and the ESA Mars Express missions. J.W.H. gratefully acknowledges support from NASA through the Mars Data Analysis Program and the Mars Express HRSC Team. J.L.F. gratefully acknowledges support from the NSF for development of the terrestrial version of UMISM through many grants. Thanks are extended to Anne Côté for assistance in manuscript preparation. References Banks, M.E. et al., 9. An analysis of sinuous ridges in the southern Argyre Planitia, Mars using HiRISE and CTX images and MOLA data. J. Geophys. Res. 1, E93. doi:1.19/je3. Boynton, W.V. et al.,. Distribution of hydrogen in the near surface of Mars: Evidence for subsurface ice deposits. Science 97 (557), 1 5. Carr, M.H., 199. Water on Mars. Oxford University Press, New York, NY. Craddock, R.A., Howard, A.D.,. The case for rainfall on a warm, wet early Mars. J. Geophys. Res. 17 (5111). doi:1.19/1je155. Fassett, C.I., Head, J.W., a. The timing of martian valley network activity: Constraints from buffered crater counting. Icarus 195, 1 9. Fassett, C.I., Head, J.W., b. Valley network-fed, open-basin lakes on Mars: Distribution and implications for Noachian surface and subsurface hydrology. Icarus 19, Fastook, J.L., The finite-element method for solving conservation equations in glaciology. Comput. Sci. Eng. 1 (1), Fastook, J.L., Head, J.W., Marchant, D.R., Shean, D.E.,. Ice sheet modeling: Terrestrial background and application to Arsia Mons lobate deposit, Mars. Lunar Planet. Sci. XXXV. Abstract #135.

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