Glaciation in the Late Noachian Icy Highlands: Ice accumulation, distribution, flow rates, basal melting, and top-down melting rates and patterns

Planetary and Space Science 106 (2015) 82–98

Contents lists available at ScienceDirect

Planetary and Space Science journal homepage: www.elsevier.com/locate/pss

Glaciation in the Late Noachian Icy Highlands: Ice accumulation, distribution, flow rates, basal melting, and top-down melting rates and patterns James L. Fastook a,n, James W. Head b a b

School of Computing and Information Science, University of Maine, Orono, ME 04469 USA Department of Earth, Environmental and Planetary Sciences, Brown University, Providence, RI 02912 USA

ar t ic l e i nf o

a b s t r a c t

Article history: Received 26 June 2014 Received in revised form 6 November 2014 Accepted 22 November 2014 Available online 10 December 2014

Geological evidence for extensive non-polar ice deposits of Amazonian age indicates that the current cold and dry climate of Mars has persisted for several billion years. The geological record and climate history of the Noachian, the earliest period of Mars history, is less certain, but abundant evidence for fluvial channels (valley networks) and lacustrine environments (open-basin lakes) has been interpreted to represent warm and wet conditions, including rainfall and runoff. Alternatively, recent atmospheric modeling results predict a “cold and icy” Late Noachian Mars in which moderate atmospheric pressure accompanied by a full water cycle produce an atmosphere where temperature declines with elevation following an adiabatic lapse rate, in contrast to the current situation on Mars, where temperature is almost completely determined by latitude. These results are formulated in the Late Noachian Icy Highlands (LNIH) model, in which these cold and icy conditions lead to the preferential deposition of snow and ice at high elevations, such as the southern uplands. What is the fate of this snow and ice and the nature of glaciation in such an environment? What are the prospects of melting of these deposits contributing to the observed fluvial and lacustrine deposits? To address these questions, we report on a glacial flow-modeling analysis using a Mars-adapted ice sheet model with LNIH climate conditions. The total surface/near-surface water inventory is poorly known for the Late Noachian, so we explore the LNIH model in a “supply-limited” scenario for a range of available water abundances and a range of Late Noachian geothermal fluxes. Our results predict that the Late Noachian icy highlands (above an equilibrium line altitude of approximately þ 1 km) were characterized by extensive ice sheets of the order of hundreds of meters thick. Due to extremely cold conditions, the ice-flow velocities in general were very low, less than a few mm/yr, and the regional iceflow pattern was disorganized and followed topography, with no radial flow pattern typical of an equilibrium ice sheet. Virtually the entire ice sheet is predicted to be cold-based, and thus the range of wet-based features typically associated with temperate glaciers (e.g., drumlins, eskers, etc.) is not predicted to occur. Wet-based conditions are predicted only locally in the thickest ice (on the floors of the deepest craters), where limited subglacial lakes may have formed. These LNIH regional ice-sheets provide a huge reservoir of potential meltwater as a source for forming the observed fluvial and lacustrine features and deposits. Top-down melting scenarios applied to our LNIH ice sheet model predict that periods of punctuated warming could lead to elevated temperatures sufficient to melt enough snow and ice to readily account for the observed fluvial and lacustrine features and deposits. Our model indicates that such melting should take place preferentially at the margins of the ice sheets, a prediction that can be tested with further analyses. & 2014 Elsevier Ltd. All rights reserved.

Keywords: Mars Noachian highlands Climate Glaciation Ice sheet model Meltwater

1. Introduction The record of non-polar ice deposits throughout the Amazonian suggest a cold and dry climate not significantly different from the

n

Corresponding author. E-mail address: [email protected] (J.L. Fastook).

http://dx.doi.org/10.1016/j.pss.2014.11.028 0032-0633/& 2014 Elsevier Ltd. All rights reserved.

present climate observed on Mars (Head and Marchant, 2008), where latitudinal movement of ice is largely in response to the varying obliquity component of the spin-axis/orbital parameters (Laskar et al., 2004). When one looks further into the past to the Noachian, the record is less clear and the characterization of the early martian climate is less certain. The existence of liquid water that flowed across the surface (Carr, 1995); Irwin et al., 2005; Fassett and Head, 2008a; Hynek et al.,

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

2010) as well as open- and closed-basin lakes (Fassett and Head, 2008b) has led many to suggest that early Mars was “warm and wet” with rainfall (pluvial) activity (Masursky et al., 1977; Craddock and Maxwell, 1990; Craddock and Maxwell, 1993; Craddock et al., 1997; Clifford and Parker, 2001; Hynek and Phillips, 2001; Craddock and Howard, 2002; Pondrelli et al., 2008; Achille and Hynek, 2010). Furthermore, many studies suggest prolonged periods of rainfall in amounts at least comparable to that occurring in Earth’s arid or semiarid regions (Barnhart et al., 2009; Hoke et al., 2011; Howard, 2007; Irwin et al., 2011; Matsubara et al., 2013). Associated lakes, deltas, and alluvial fans show complex histories of fluctuating water and sediment discharges (Malin and Edgett, 2003; Moore and Howard, 2005; Di Achille et al., 2006; Fassett and Head, 2005, 2008; Di Achille and Hynek, 2010; Ponderelli et al., 2010; Grant et al., 2011; Buhler et al., 2011, 2014; Hoke et al., 2014), and these have often been interpreted to imply extended periods of precipitation and runoff (Moore et al., 2003; Jerolmack et al., 2004; Matsubara et al., 2011). Lacustrine and fluvial strata in Gale Crater, some of it examined in detail in situ, could represent millions of years of warmer and wetter condition in early Hesperian time (Grotzinger et al., 2014). Debated are 1) the total duration of the fluvial periods, 2) whether the fluvial erosion was continuous or episodic, and 3) the nature of the specific climate conditions that prevailed before and after (or during and between) the fluvial activity. Others argue that the early martian climate was more likely to have been much colder and considerably drier (Gaidos and Marion, 2003; Fairen, 2010; Head et al., 2014) based on a number of lines of evidence that include proposed phyllosilicate formation mechanisms (Ehlmann et al., 2011), low erosion rates (Golombek et al., 2006), poorly integrated valley networks with the open-basin lakes that suggest short-term episodic fluvial formation rather than long-term pluvial activity (Stepinski and Coradetti, 2004), as well as the possibility that the form of most precipitation might have been snowfall (nivial) (Scanlon et al., 2013). However, little geomorphic evidence for typical wet-based glacial landforms (e.g., drumlins, eskers, etc.) dating from the Noachian has been cited in the southern uplands and elsewhere. Late Noachian eskers have been mapped locally in the south polar Dorsa Argentea Formation (Kress and Head, 2014), an extensive unit interpreted to represent the existence of a Late-Noachian/Early Hesperian south circumpolar ice sheet (Head and Pratt, 2001; Kress and Head, 2014). Even with evidence for Late Noachian eskers beneath an extensive south circumpolar ice sheet, and the ice thicknesses required to produce them, glacial flow modeling studies suggest a mean-annual temperature during the Late Noachian well below freezing (Fastook et al., 2012), also arguing for a “cold and icy” early martian climate. Terrestrial analogs from the Antarctic Dry Valleys demonstrate that fluvial activity can take place at mean annual temperatures well below freezing (Marchant and Head, 2007; Head, 2014; Head and Marchant, 2014). Recent estimates of the rate of water lost to space (Chassefiere and Leblanc, 2011) indicate reduced amounts of water available for a “wet” Mars. Modeling results based on data from a martian meteorite (Cassata et al., 2012) are used to interpret the meteorite measurements as requiring lower atmospheric pressures. These data and interpretations, when coupled with the faint young Sun, make it very difficult for atmospheric modelers to produce a “warm and wet” early Mars (Haberle, 1998). “Extreme” events such as meteorite impacts have been proposed whereby an ephemeral “steam” atmosphere lasting a few thousand years might exist and produce the observed landforms (Segura et al., 2002; Segura et al., 2008; Toon et al., 2010); however, landform evolution modeling seems to contradict these findings (Moore et al., 2003; Jerolmack et al., 2004; Barnhart et al., 2009 Matsubara et al., 2011). Punctuated volcanic outgassing (Halevy and Head, 2014) has also been proposed as an ice-melting scenario. Recent atmospheric modeling results (Forget et al., 2013; Wordsworth et al., 2013) demonstrate that moderate atmospheric

83

pressures accompanied by a full water cycle produce a Late Noachian atmosphere where temperature declines with elevation following an adiabatic lapse rate, in contrast to the current situation on Mars, where temperature is almost completely determined by latitude. Lower temperatures at higher elevations encourage the movement of water from the “warmer” lowlands to the colder southern highlands, where it is sequestered in the form of regional ice sheets above an ice stability line (ISL) that occurs close to 1000 m elevation. The hydrological system is thus globally horizontally stratified (Head et al., 2003), with a global permafrost layer separating the surface from vertical integration and communication with any deeper groundwater. Furthermore, the horizontally stratified hydrologic system in the Late Noachian Icy Highlands model means that water migrates from the lowlands to the highlands, precipitates, and accumulates as snow and ice in a “one-way” direction. Once water in the lowlands is exhausted, the hydrological cycle becomes “dormant” until the system is activated by some source of melting (top-down or bottom-up), and meltwater drains to the lowlands to temporarily renew the cycle. Thus, this ice, effectively “stored” at higher elevations, might then be released by “extreme” events, such as meteorite impacts or volcanism, without the need to invoke a “steam” atmosphere. Further geological implications of this “cold and icy” scenario are explored in Head (2014) and Head and Marchant (2014) who suggest that meltwater produced seasonally during these episodes might flow naturally toward the lowlands in the areas where the geologic record requires liquid water to be present and flowing across the landscape. In this scenario, as the climate cooled again, water frozen below the ISL would sublime and return to the highlands as snowfall (Wordsworth et al., 2013; Scanlon et al., 2013). On Earth, water sources for large ice-sheet growth come primarily from oceanic evaporation, but oceans are not predicted on Mars in the LNIH model. Rather, any water or ice at low elevations is rapidly transported to the highlands and remains frozen there until a significant warming event occurs. In this analysis, we explore the implications of glaciation predicted by the Wordsworth et al. (2013) Late Noachian Icy Highlands (LNIH) model. We analyze the nature and development of the “icy highlands” using glacial flow models and address the following questions: What is the available reservoir of surface and near-surface water? What is the areal distribution of snow and ice? What is the average ice thickness and thickness distribution? Is the ice wet-based or cold-based, and if wet based, in what locations? What are the flow rates of the ice? What are the regional patterns of ice flow (equilibrium ice sheet or local topography dominated)? What are the predictions for resulting glacial and periglacial landforms that might be recognized in the geological record? Could the glacial deposits be a source of meltwater for the observed fluvial and lacustrine features? Under what scenarios might melting of these deposits provide sufficient meltwater to account for the observed fluvial and lacustrine features?

2. Methodology In order to address these questions, a modeling exercise is run using a Mars-adapted University of Maine Ice Sheet Model (Fastook et al., 2012). Note that all time units are reported in Earth years) with a climate defined by Wordsworth et al. (2013), (i.e., with both a latitudinal and an elevation lapse rate, warmer toward the equator and colder at higher elevations). How much water is available during the LNIH scenario? The nature and distribution of Late Noachian equilibrium Icy Highlands ice deposits are related to the total available supply of water in the Noachian, a poorly known

84

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Fig. 1. The bed for the model area encompassing a circular area centered on Hellas basin (topography, in km). Fig. 1a is a global picture of the gridded area. Fig. 1b is the same region shown in grid coordinates. The grid is composed of a deformed 200  200 checkerboard grid of finite-element quadrilaterals with a nominal resolution of 25 km. Note that in Fig. 1b the South Pole is located at grid (0,0) and the x- and y-axes are in km.

Fig. 2. Mass balance as a function of elevation, separated into accumulation (positive – red dashed curve) and ablation (negative – blue dot-dashed curve) components, and the resulting net mass balance (solid black) defined such that the ice stability/equilibrium line elevation occurs at 1000 m. By separating the components we are able to reduce the positive component as the volume approaches the supply limit.

quantity (Carr, 1996). The quantity of interest, however, is not the total inventory of water, but instead the amount of water that is available in the surface and near-surface environment (Carr and Head, 2014). For example, the thickness of ice underlying Amazonian-aged pedestal craters (Kadish et al., 2010) suggests that Late Amazonian mid-latitude ice accumulation was “supply-

Fig. 3. Mass balance parameterization of Fig. 2 applied to the model domain in mm/yr. The solid black line marks the ice stability/equilibrium line, defined to occur at an elevation of 1000 m, where accumulation exactly balances ablation and the net mass balance is zero. As the volume of the ice sheet approaches the supply limit the positive component of the mass balance is reduced modifying this initial mass balance configuration and raising the ice stability/equilibrium line.

limited”: this means that the amount of ice available for mobilization and deposition in the mid-latitudes was limited by the supply of water available as ice in the polar layered terrains, near-surface shallow ice deposits and the regolith (Fastook and Head, 2013). In a similar manner, the LNIH glacial supply is determined not by the total Late Noachian water budget, but by the amount of ice available

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

85

Fig. 4. Global temperatures generated from a base temperature, a cosine function of latitude with a pole-to-equator amplitude, and a vertical lapse rate (a, c, and e) compared with results from the LMD Generic Climate Model (Wordsworth et al., 2013) for various atmospheric pressures (b, d, and f).

in the Late Noachian global surface/near-surface water reservoir, excluding the deeper cryosphere, groundwater and water sequestered in aqueous minerals. Carr and Head (2014) describe the current near-surface water budget as consisting of the current polar caps (Smith et al., 1998; Zuber et al., 1998), and non-polar ice sequestered in the near surface or available by vapor diffusion from the shallow regolith. Carr and Head (2014) adopted a volume representing an  34 m Global Equivalent Layer (GEL) or 5  106 km3. In our current analysis, we employ Late Noachian surface/near-surface water budgets in multiples (1X to 20X) of this estimate of the current value. We do this in a series of “supplylimited” scenarios (Fastook and Head, 2014) for this 1X to 20X range of available water. Although we acknowledge that the upper end of this range may be implausible, the actual Early Noachian water budget and its fate are not at all constrained (see Carr, 1996, Figs. 7–11). Thus, we include these potentially extreme scenarios to demonstrate what is and what is not possible for a

reasonable range of supply limits. The model is run with a range of Late Noachian geothermal fluxes (45–65 mW/m2) recently utilized by key workers in the field (Solomon et al., 2005; Clifford et al., 2010). Much higher geothermal fluxes might have been generated very locally at volcanic sources in parts of the Late Noachian highlands (Cassanelli et al., 2014) and possibly by the hypothesized inception of the Tharsis plume at low southern latitudes and its progressive migration to its present equatorial position (Zhong, 2009; Hynek et al., 2011; Cheung and King, 2014). The bed for the model area is shown in Fig. 1 encompassing a circular area centered on Hellas basin. On the left (Fig. 1a) is a global representation of the gridded area, and on the right (Fig. 1b) the same region shown in grid coordinates. The grid is composed of a deformed 200  200 checkerboard of finite-element quadrilaterals with a nominal resolution of 25 km. Note that in Fig. 1b the South Pole is located at grid (0,0) and the x- and y-axes are in km.

86

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Fig. 5. Temperature as a function of elevation and latitude. Temperature decreases at higher latitudes and elevations, with latitude through a cosine function with a 20 K amplitude from equator to pole, and with elevation through a  2.4 K/km lapse rate appropriate for an atmospheric pressure of 1 bar (see Fig. 4e,f).

A supply-limited model is required because if unlimited growth is allowed, the ice sheet volume quickly exceeds the known inventory of water available on Mars. By maintaining separate positive (accumulation) and negative (ablation) mass balance components we can limit growth to a specific volume by reducing the positive component as the computed volume of the ice sheet approaches a defined supply-limited volume. Fig. 2 shows these three components of the mass balance: the accumulation (dashed red), the ablation (dot-dashed blue), and the net sum of these two (solid black). We employ a simple linear scheme designed to yield an ice stability, or equilibrium line (accumulation and ablation equal in magnitude producing a net of zero) at 1000 m elevation, as in Wordsworth et al. (2013). Above this elevation the net will be positive, capped to not exceed 10 mm/yr above an elevation of 2000 m. In a similar fashion, the accumulation component decreases with elevation going to zero below  3000 m. The ablation term is a uniformly negative 5 mm/yr typical of the summer sublimation rates produced for a moderate-obliquity climate in Madeleine et al. (2009). Fig. 3 shows this parameterization applied to the model domain. The solid black line marks the ISL, or equilibrium line, defined to occur at an elevation of 1000 m, where accumulation exactly balances ablation and the net mass balance is zero. Although this is the ISL location for the present topography, as the volume of the ice sheet grows and approaches the supply limit, the positive component of the mass balance is reduced, modifying this initial mass balance configuration and raising the ISL. Temperature is slightly more complex in an adiabatic world, with both a latitudinal lapse rate cooling from equator to the pole, and an elevation lapse rate cooling with height. Since surface elevation is changing in the presence of a growing ice sheet, a fixed temperature field such as is available from GCM model results is insufficient. Instead we choose a simple parameterization, tuned to initially match GCM results, shown in Fig. 4. The right-hand column (b, d, and f) shows mean annual temperature results from the LDM Generic Climate Model (Wordsworth et al., 2013) for three representative atmospheric pressures, 0.008, 0.2, and 1.0 bar. Shown in the left-hand column (a, c, e) for each of these are the results of a simple parameterization derived from a

base temperature, a cosine function of latitude with a pole-toequator amplitude, and an elevation lapse rate. Fig. 4a,b for the low-pressure case shows the coldest base temperature (158 K), the largest pole-to-equator amplitude (53 K), and the smallest elevation lapse rate (  0.5 K/km). As pressure increases (Fig. 4c-f), the required base temperature warms (173 and 223 K for 0.2 and 1.0 bar respectively), the pole-to-equator amplitude is reduced (50 and 20 K), and the elevation lapse rate increases ( 2.0 and  2.4 K/km). The 1.0 bar parameterization shown in Fig. 4e was used in all model runs. Applying this parameterization to the 40000 modeled points from Fig. 1b, we obtain the temperature versus elevation trend shown in Fig. 5 with individual stars for each point color coded to indicate latitude. Results for the six supply limits (1X, 2X, 5X, 10X, 15X, and 20X) and three geothermal flux cases (45, 55, and 65 mW/m2), obtained after 106 model years (a sufficiently long time interval for the ice sheets to have reached a steady-state configuration), are shown in Fig. 6 and summarized in Table 1. Fig. 6a shows the areal extent in millions of km2 of the resulting ice sheet as a function of supply for each of the three geothermal fluxes, Fig. 6b the average thickness (m), Fig. 6c the percentage of the ice sheet area that reaches the melting point at the bed, and Fig. 6d the maximum velocity observed in the modeled ice sheet (mm/yr). In addition to these four, Table 1 also shows the total volume in millions of km3, which is of course dictated by the limiting supply volume. Also included in Table 1 is the maximum thickness, which generally occurs in a deep crater away from the margin of the ice sheet. Such craters are usually the first location to experience basal melting during growth of the ice sheet. Figs. 7–12 show configurations for the various supply-limited volumes (1X, 2X, 5X, 10X, 15X, and 20X). In each of these the first column shows the surface elevation (m) of the resulting ice sheet for each of the three geothermal heat fluxes (a, e, and i for 45, 55, and 65 mW/m2 respectively), the second column (b, f, and j) the companion ice thicknesses (m), the third column (c, g, and k) the basal temperatures (K), and the fourth column (d, h, and l) the maximum observed column-averaged velocities (mm/yr).

3. Results: discussion Utilizing the results of these model runs under different ice budget and geothermal gradient conditions, we can now begin to address the questions raised initially about 1) the areal distribution of snow and ice, 2) the average ice thickness and thickness distribution, 3) whether the ice is wet-based or cold-based, and if wet-based, in what locations, 4) flow rates of the ice and the regional patterns of ice flow, and 5) predictions for resulting glacial and periglacial landforms that might be recognized in the geological record. Average ice sheet thicknesses range from a few hundred meters for the 1X case (Fig. 7b, f, j) to well over a km for the 10X to 20X cases (Figs. 10 to 12b, f, j). With the thin ice required by the 1X and 2X cases, no bottom melting is observed (Figs. 7 and 8c, g, k), even in the infilled craters where the ice thickness approaches 1 km. Very limited bottom melting in craters,  1% by area, is first observed with a supply limit of 5X (Fig. 9c, g, k with melted regions outlined in red). As would be expected, higher geothermal flux results in greater melted area, with the 45 mW/m2 case (Fig. 9c) showing only six individual isolated points (0.025 Mkm3) with the bed at the melting point. As the geothermal flux is increased to 55 mW/m2 (Fig. 9g), more than 60 points (0.243 Mkm3), many of them contiguous, now reach the melting point. At 65 mW/m2 (Fig. 9k), close to 200 points (0.654 Mkm3) have melted beds. In all cases basal melting is confined to deep craters where the ice is

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

87

Fig. 6. Shown as functions of the six supply cases (1X, 2X, 5X, 10X, 15X, and 20X) are a) the area of the ice sheets (106 km3), b) the average thickness (m), c) the percentage of the ice sheet area that reaches the melting point, and d) the maximum velocity observed (mm/yr). The solid black corresponds to a geothermal flux of 45 mW/m2, the dashed red to 55 mW/m2, and the dot-dashed blue to 65 mW/m2.

thickest. Increasing supply to 10X increases the number of craters with basal melting (Fig. 10c, g, k), but still does not produce any widespread areas of melted bed except in the highest geothermal flux case (Fig. 10k), where melted percentage exceeds 10% and much of the bed is close to the melting point. The 15X case (Fig. 11c, g, k) demonstrates the most marked transition from localized crater melting ( 5% for 45 mW/m2, Fig. 11c) to broader widespread melting as the geothermal flux is increased (18% at 55 mW/m2, Fig. 11g and 30% at 65 mW/m2, Fig. 11k). Only at the unreasonably high supply (Carr and Head, 2014) of 20X (Fig. 12c, g, k) does any widespread melting occur for the lowest geothermal flux (14%, Fig. 12c), with most in the thick interior of the now much larger ice sheet. At the highest geothermal flux for a 20X supply (Fig. 12k), basal melting is widespread and approaches the margins of the ice sheet, allowing for the possibility of regions of fast flow

analogous to terrestrial ice streams. These can be seen in the velocity figures (Fig. 12l). As would be expected, higher geothermal heat flux results in a warmer ice sheet that is softer and flows more readily, resulting in thinner ice sheets covering a larger area since the total volume is constrained by the supply limit. This effect is insignificant for the 1X to 5X cases, but for 10X the warmer ice results in a 3% reduction in average thickness going from a geothermal heat flux of 45 to 65 mW/m2. For a 15X supply, the reduction is almost 9%, while for 20X average thickness is reduced by over 13%. In these cases water lubrication of the bed (i.e., sliding) also contributes to the thinner, areally larger ice sheet. Since supplies greater than 10X are unlikely (Carr and Head, 2014), we conclude that any melting beneath a Noachian ice sheet would be confined to deep craters filled with thick ice. These

88

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Table 1 Showing the 18 cases for six supplies (1, 2, 5, 10, 15, and 20 times the surface and near surface ice,  5 million km3; Carr and Head, 2014) and three geothermal fluxes (45, 55, and 65 mW/m2). Supply Geothermal flux (mW/m2) Average Thickness (m) Maximum Thickness (m) Melted area % Maximum Velocity (mm/yr) Volume (Mkm3) Area (Mkm2) 1X

45 55 65

278 278 278

676 698 718

0 0 0

11 12 13

5.29 5.29 5.29

19.02 19.02 19.02

2X

45 55 65

424 424 424

1376 1412 1445

0 0 0

35 37 37

10.53 10.53 10.53

24.81 24.82 24.83

5X

45 55 65

726 724 722

2711 2758 2778

0.07 0.67 1.80

84 117 170

26.23 26.23 26.24

36.11 36.20 36.34

10X

45 55 65

1091 1079 1058

3272 3401 3544

2.0 5.3 13

218 431 899

52.49 52.49 52.51

48.12 48.65 49.65

15X

45 55 65

1398 1355 1278

3987 4187 4297

5.5 18 30

490 1126 2929

78.61 78.57 78.51

56.23 57.98 61.44

20X

45 55 65

1642 1545 1426

4625 5250 5472

14 31 46

1387 4074 7229

104.4 104.3 103.8

63.61 67.49 72.79

For each case average thickness, maximum thickness, percentage of the ice sheet bed that has reached the melting point, maximum velocity, total volume, and area are shown.

Fig. 7. Ice sheet configuration for the 1X supply-limited volume. The first column shows the surface elevation (m) of the resulting ice sheet for each of the three geothermal heat fluxes (a. 45 mW/m2, e. 55 mW/m2, and i. 65 mW/m2), the second column (b, f, and j) the companion ice thicknesses (m, with values less than 8 m shown as black), the third column (c, g, and k) the basal temperatures (K), and the fourth column (d, h, and l) the column-averaged velocities (mm/yr, with values less than 0.1 mm/yr shown as black).

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

89

Fig. 8. Ice sheet configuration for the 2X supply-limited volume, following the same layout as Fig. 7.

might form subglacial lakes, analogous to terrestrial lakes such as Vostok in Antarctica (Siegert and Rigley, 1998; Siegert et al., 2001; Kwok et al., 2000; Bell et al., 2002; Studinger et al., 2004; Richter et al., 2013), that would infill with sediment, perhaps contributing to the explanation for the shallow, degraded character of Noachian highland craters (Craddock and Maxwell, 1993; Craddock et al., 1997; Craddock and Howard, 2002; Weiss and Head, 2014). We conclude that the Late Noachian icy highlands are unlikely to have ever had widespread wet bed conditions, although the presence of limited “lakes” in deep craters is a possibility given a supply limit of 4 5X. This means that Late Noachian glacial activity is unlikely to produce and preserve an array of distinctive wet-based glacial and periglacial landforms (e.g., drumlins, eskers, etc.) (Benn and Evans, 2010, p. 259–332). Cold-based ice sheets such as we expect for the Noachian icy highlands are known from terrestrial analogs to leave few traces on the landscape (Kleman, 1994; Kleman and Hattestrand, 1999; Marchant and Head, 2007). The thin ice sheets, with typical velocities ranging from 0.1 to 1 mm/year for the 1X case (Fig. 7d, h, l) and up to 4-5 mm/yr for the 2X case (Fig. 8d, h, l) do not show the organized flow of an equilibrium ice sheet (radial flow from a dome center toward the lower-elevation ice sheet margins). Instead, with an almost uniform ice layer draping the terrain, most flow follows topographic slopes down mountainsides and scarps, and into crater interiors. This pattern of flow with thin ice

cover could enhance the shedding of any exposed crater rim crest debris onto the ice surface; as in the case of Amazonian-aged concentric crater fill (CCF) (Levy et al., 2009; 2010), this debris could be carried into the crater interior, potentially producing CCF-like deposits on the crater floors (Fastook and Head, 2013). Even the 5X case (Fig. 9d, h, l), with typical velocities in the 10 to 50 mm/yr range, displays a very disorganized flow pattern typical of flow down topographic slopes. The 10X case (Fig. 10d, h, l), with velocities of 30–90 mm/yr away from the margins, does display the flow pattern of an equilibrium ice sheet (Paterson, 1994; Hooke, 2005; Greve and Blatter, 2009), with radial flow from interior domes toward the margin. In this case, narrow regions of “fast” flow, with velocities exceeding 100 mm/yr, are observed near the margin and concentrated in low topographic areas. These “ice streams” (Hughes, 1977; Raymond, 2000; Schoof, 2002; Hughes et al., 2011) are even more pronounced in the 15X and 20X cases (Figs. 11 and 12d, h, l), with velocities of 500 to well over 1000 mm/yr. It is worth noting that for the thin ice sheets of the 1X and 2X cases, there is little increase in velocity as the geothermal heat is increased. For the 5X case we see a doubling of velocity as the geothermal heat flux is increased from 45 to 65 mW/m2 since the thicker ice provides greater insulation of the bed, allowing for warmer, softer ice at depth where the bulk of the internal deformation occurs. The effect is even more pronounced for the 10X–20X cases, with a four to five times increase in

90

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Fig. 9. Ice sheet configuration for the 5X supply-limited volume, following the same layout as Fig. 7.

maximum observed velocity as the geothermal heat flux is increased from 45 to 65 mW/m2. For the Late Noachian Icy Highlands we conclude that the velocities in general are very low, less than a few mm/yr, and that the flow pattern should be disorganized and follow topography, with no radial flow pattern typical of an equilibrium ice sheet (Paterson, 1994; Hooke, 2005; Greve and Blatter, 2009).

4. Scenarios for top-down melting and volumes of meltwater Having established that for reasonable supply limits, the ice sheet is cold-based, we now investigate the response of the ice sheet to short-lived top-down climatic warmings such as might be produced by large meteor impacts (e.g., Toon et al., 2010) or periods of intense volcanism (e.g., Halevy and Head, 2014). These LNIH regional ice-sheets provide a ready source of meltwater for the formation of the fluvial (valley networks) and lacustrine (openbasin lakes) features and deposits known to have existed in this region. Open-basin lakes (OBL) are those that have both an inlet and outlet fluvial channel; in an analysis of the altitude of these channels for each member of the population of 4210 open-basin lakes, Fassett and Head (2008b) estimated the volume of water required in the lake to cause drainage at the outlet channel. This

value is a minimum, of course, because the presence of the outlet channels indicates that water was actively draining from the OBL for some currently unspecified period of time. As a baseline minimum estimate of the magnitude of meltwater required, we assume that all of the open-basin lakes were filled simultaneously, and we adopt for this minimum estimate a value of  0.42 Mkm3, the total volume of all of the filled open-basin lakes measured by Fassett and Head (2008b). For perspective, this value,  0.42 Mkm3, represents less than 10% of the current (1X) surface/near-surface ice volume (Carr and Head, 2014), less than 5% of the 2X value, and less than 2% of the 5X value. Applying a specified warming to the ice sheet is relatively simple for the temperature field, since we are using a parameterization that begins with a base temperature and then applies both a latitudinal and elevation lapse rate to obtain a temperature at a specific point (Fig. 4e). Changing the base temperature produces a uniform shift of the global temperature field. Modification of the mass balance field (Figs. 2 and 3) is not as simple, since the ablation component that defines the equilibrium, or ice stability line is dominated by sublimation rather than melting. Since we know the lapse rate, 2.4 K/km, from our parameterization of Fig. 4e,f we can simply shift the straight lines of Fig. 2 up by 416 m per degree of warming. However, since sublimation does not produce meltwater, a complimentary approach must be taken that involves the calculation of positive degree-days (PDD), an approach

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

91

Fig. 10. Ice sheet configuration for the 10X supply-limited volume, following the same layout as Fig. 7.

common in terrestrial ice sheet models (Huybrechts et al., 1991). The use of PDDs involves imposing a seasonal amplitude onto the mean annual temperature, and summing for each day of the year the total number of degrees that the daily mean temperature is above freezing. PDDs have been shown to correlate well with melting on terrestrial glaciers, and a common value used is 8 mm iceequivalent melting per PDD for an ice surface (Huybrechts et al., 1991). Braithwaite (1995) expands on this with an energy-balance model that correlates well with available data, obtaining values for the PDD factor ranging from 8.07 to 8.32 mm/PDD for an ice surface and 2.89 to 3.67 mm/PDD for a snow-covered surface. In the energy-balance model, melting is determined by four fluxes: 1) the turbulent-sensible flux, dependent on wind velocity and temperature difference between the glacier surface and the air; 2) the latent-heat flux, dependent on wind velocity and the difference between the vapor pressure of the air and the saturation vapor pressure at the glacier surface; 3) the short-wave flux, dependent on the albedo and the solar insolation; and 4) the longwave flux, dependent on the effective emissivity of the cloudy sky and the Stephan-Boltzmann relationship. Of these the dominant flux is the short-wave flux, demonstrated by the fact that the albedo difference between ice (0.3) and snow (0.7) almost exactly accounts for the 8 to 3 mm/PDD difference in the PDD factors for the two different surfaces. Given the greater distance of Mars from

the Sun, and the fact that the early Sun was as much as 25% less bright (Gough, 1981), we would expect a 0.33 reduction for a martian PDD factor, based primarily on the reduced short-wave flux. Also, since we are modeling a transient climate warming from a generally very cold climatic state, we expect the surface to have a relatively high snow-like albedo. As such, we adopt 1.08 mm/PDD as representative of a possible martian value. Our transient event is represented by a sinusoidally-varied base temperature in our temperature parameterization (Fig. 4e) with a duration from start to finish of 2000 years, begun after one million years of steady growth for the 5X, 55 mW/m2 case (Fig. 9e,f,h), with warmings of þ 10 to þ19 K. The temporal variation of the base temperature is shown in Fig. 13a and volume losses are summarized in Table 2. Since we are including both a shift of the ice stability line in the sublimation-dominated parameterization of Fig. 4e as well as a melting-dominated PDD calculation, we need to separate the response of the ice sheet to these two mechanisms. Response to the shift of the ISL is immediate for any warming, since we raise the ISL by  400 m for every degree of warming, but, because sublimation is capped at 5 mm/yr, once the ISL is above the highest terrain, the rate of loss reaches a plateau. This is apparent in Fig. 13b showing the volume response for warmings of 10 to 19 K. During the 2000 year warming event the loss due to raising the ISL ranges from 0.17 Mkm3 for þ10 K warming to 0.23 Mkm3 for

92

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Fig. 11. Ice sheet configuration for the 15X supply-limited volume, following the same layout as Fig. 7.

þ19 K warming, presumably due to sublimation in the now larger ablation region. On the other hand, the PDD calculation will not produce any melting until the warmest point on the ice sheet is within half the seasonal amplitude of the melting point (the total swing from winter to summer, 40 K, is taken from the 451 obliquity Fig. 13 of Wordsworth et al. (2013), for point B on the highlands west of Hellas), so the volume change for the PDD calculation only, shown in Fig. 13c, displays no loss for warmings of þ10 and þ12, and only 5.4  10  3 Mkm3 for þ14 K. A warming of þ16 K begins to show an effect (0.06 Mkm3), but only at a value of þ17 K warmer is the effect comparable to the effect of shifting the ISL by a similar amount (0.17 Mkm3). However, once the threshold has been crossed whereby the mean annual temperature of a significant number of ice sheet points are within half the seasonal amplitude of the melting point, mass loss by melting accelerates rapidly, with þ18 and þ 19 yielding melt amounts of 0.45 and 0.99 Mkm3. Fig. 13d shows volumes with both effects active, with values that are simply the sum of the individual effects, suggesting that there is no synergy in their combination (a plausible possibility, since both effects lower the surface into a warmer atmosphere). Our assumption is that the shifting ISL increases the area of mass loss by sublimation, whereas the PDD calculation of melting reflects the amount of liquid water released onto the landscape. With our minimum target volume of  0.42 Mkm3 (Fassett and

Head, 2008b), we conclude that a 2000 year transient warming of approximately þ18 K would release sufficient meltwater to fill all of the open-basin lakes. For reference, Halevy and Head (2014) have recently shown that episodic warming of a Late Noachian Icy Highlands climate by punctuated volcanism could raise the global mean annual temperature by 26 K, clearly bringing the lower latitudes to temperatures comfortably exceeding the 273 K for several months of the year. Given the uncertainty in the duration of climate warming due to meteor impacts or volcanic eruptions, climatic events with a 2000-year duration may not be the exact duration expected. We thus investigate a minimal duration end-member, the amount of melting one might obtain from a single-year melting event. This value can then be used as a baseline for application to assessing the plausibility of durations of warming derived from other perspectives to account for the observed fluvial and lacustrine features. Results are shown in Fig. 14. Extracting and calculating temperature from our Fig. 4e parameterization for all points above the 1000 m ISL, we can impose various degrees of warming by offsetting the base temperature in the parameterization. We apply a seasonal swing of 40 K, similar to the magnitude seen in the McMurdo Dry Valleys, where the mean annual temperature is 253 K and where seasonal melting is known to occur; for example, Marchant and Head, 2007; Head and Marchant, 2014). Applying this seasonal cycle with a seasonal swing of 40 K we can count

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

93

Fig. 12. Ice sheet configuration for the 20X supply-limited volume, following the same layout as Fig. 7.

PDDs and compute a melting for each point for various PDD factors ranging from high albedo snow (1.1 mm/PDD) to low albedo ice (3.4 mm/PDD). Averaging these and multiplying by the area of our 5X, 55 mW/m2 ice sheet (Fig. 9e,f,g) we obtain a potential mass loss for a single year with warmer temperatures. In Fig. 14, the top x-axis shows the amount of warming applied, and the bottom x-axis, the average temperature of the points above the ISL that defines the boundaries of the cold-climate ice sheet. Also shown is the target volume of 0.42 Mkm3 from Fassett and Head (2008b), representing the total volume of all open-basin lakes. With a snow surface (PDD factor of 1.4 mm/PDD) it is difficult to obtain our target volume in a single year, requiring a warming of þ40 K that brings the average temperature to an unreasonable 285 K. For a lower albedo PDD factor, such as one for an ice surface (2.6 mm/PDD), our target volume is reached in a single year with a warming just under þ30 K, resulting in an average temperature very close to the melting point. It is worth noting that the presence of dark impurities in the ice could reduce the albedo further, resulting in larger PDD factors (Alley, 2007; McConnell et al., 2007; Ramanathan and Carmichael, 2008), resulting in larger melt amounts for lower warmings (although too much accumulated on the surface can have the opposite effect of armoring the surface and lowering melt rates; Wilson and Head, 2009). Important for more detailed assessment of this problem is the state of the ice surface and the nature and transformation of snow to firn

and ice (e.g., Cassanelli and Head, 2014) and its influence on topdown melting. In summary, scenarios for a single year of warming of the Late Noachian Icy Highlands glacial scenario are sufficient in some cases (e.g., the dusty ice scenario) to produce a volume of meltwater comparable to our minimum estimate of the total volume of all open-basin lakes (Fig. 15). More extended periods of top-down melting associated with punctuated warmings could produce even greater volumes, and specific spin-axis/orbital parameter conditions could produce even longer periods characterized by seasonal melting, despite mean annual temperatures well below freezing, as in the case of the McMurdo Dry Valleys on Earth (e.g., Head and Marchant, 2014). We conclude that the Late Noachian Icy Highlands glacial scenario provides a huge reservoir of potential meltwater, and a ready source for abundant and volumetrically significant meltwater that may be sufficient to account for the observed valley networks and open-basin lakes, under several plausible top-down melting scenarios (e.g., peak seasonal temperatures above 273 K, Head and Marchant, 2014; spin-axis/orbital parameter perturbations under specific conditions, Laskar et al., 2004; large impact events, Toon et al., 2010; punctuated volcanic eruptions, Halevy and Head, 2014). Estimates of the volume of material eroded to form the valley networks, permitting estimation of the volume of water necessary to carve them, have been made (e.g., Carr, 1995; Carr and Malin, 2000;

94

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Fig. 13. (a) The 2000 year warming event for warmings from þ10 to þ 19 degrees, following a 106 year spinup. (b) The volume change of the ice sheet resulting from only shifting the ice stability line by 416 m per degree of warming in accordance with the 2.4 K/km lapse rate. (c) The volume change resulting from only the positive degree-day calculation of melting due to the warming event. (d) The volume change with both effects active simultaneously showing that there is no synergy. In all of these the black solid line indicates the þ10 K warming. Patterned red, green, blue, magenta, orange, and gray lines show þ 12, þ 14, þ 16, þ17, þ 18, and þ19 K warming respectively.

Table 2 Summarizing the results of a 2000 year climate warming for various amplitudes showing separately the effect of raising the ice stability line by 416 m/K in accordance with a lapse rate of 2.4 K/km, which results in mass loss primarily by increasing the sublimation area. Warming (K)

Shifted Ice Stability Line Volume Loss Only Sublimation (Mkm3)

Positive Degree-Day Volume Loss Only Melting (Mkm3)

Both Mechanisms Active Simultaneously (Mkm3)

10 12 14 16 17 18 19

0.1701 0.1902 0.2071 0.2202 0.2252 0.2296 0.2335

0 0 5.400  10  3 6.070  10  2 0.1671 0.4469 0.9942

0.1703 0.1909 0.2124 0.2796 0.3951 0.6775 1.2303

Also shown separately is the mass loss by melting from a positive degree-day calculation with a PDD factor of 1.08 mm/PDD. Also shown is the mass loss with both effects active simultaneously to rule out the possibility of synergy. The positive degree-day only case represents the release of liquid water onto the landscape.

Williams and Phillips, 2001; Hoke et al., 2011); recent estimates (Rosenberg and Head, 2014) suggest that values approximately 10 x the current (  34 m GEL) surface/near surface water inventory on Mars could account for their erosion and formation. In general, episodes of punctuated heating and melting of the LNIH ice sheet, cycled through the valley network system over extended periods, could readily account for their formation. Not yet determined is the detailed mechanism of top-down heating and melting, the

Fig. 14. Volume loss for a single year of warmer temperatures for PPD factors ranging from high-albedo snow (1.08 mm/PDD shown by the solid black line) to low-albedo ice (2.55 mm/PDD shown by the patterned orange line). Intermediate values 1.35, 1.65, 1.95, and 2.25 mm/PDD are shown by patterned red, green, blue, and magenta lines respectively. The top horizontal axis shows warming and the bottom horizontal axis shows equivalent average temperature of model points above the ice stability line at 1000 m. The gray patterned horizontal line indicates target volume from Fassett and Head (2008b) (the total volume of all 210 open basin lakes in their catalog, 0.42 Mkm3).

predicted regional valley network patterns and associated landforms, and their comparison to the observed VN distribution and patterns. Preliminary comparisons of the global distribution of

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

95

Fig. 15. Conceptual block diagram of glaciation in the Late Noachian Icy Highlands Model (Wordsworth et al., 2013). a) Steady state LNIH environment. b) Effects during episodic warming above 273 K by punctuated volcanism (e.g., Halevy and Head, 2014), large impacts (e.g., Segura et al., 2002, 2008), or other factors. The top of the cryosphere is the dry active layer, in diffusive equilibrium with the atmosphere. Highest crater in a) is above the ELA so has snow and ice deposited on the rim, which melts to contribute to the valley network system in b).

valley networks and open basin lakes with the LNIH ( þ1 km ELA) distribution of snow and ice shows a close correlation (Head and Marchant, 2014), but more detailed studies are required to compare the nature of valley networks with the predictions of “warm and wet” and “cold and icy” climate models.”

5. Conclusions Recent climate-modeling results (Forget et al., 2013; Wordsworth et al., 2013 suggest that the Late Noachian climate supported adiabatic conditions, with preferential highland growth of glaciers and ice sheets (Fig. 15). We investigated the character of an ice sheet that is predicted to have formed in the Late Noachian Icy Highlands (LNIH) climate scenario in the circum-Hellas highlands, using a range of available moisture supply and different geothermal fluxes. In particular we examined three features of ice sheets that leave a lasting impact on the landscape after the ice sheets are removed: 1) where and how extensively is the bed melted, 2) where and how rapidly is the ice flowing, and 3) are the ice sheets candidates for meltwater production of sufficient volume under known top-down melting scenarios to account for

the observed fluvial and lacustrine features? All of these features of ice sheets leave characteristic deposits and features detectable from orbit (e.g., Benn and Evans, 2010). We now return to the set of questions first raised about LNIH glaciation and summarize our findings: 1. What is the available reservoir of surface and near-surface water?: On the basis of the uncertainty in this value for Late Noachian Mars, we adopted a LN surface/near-surface water budget of from  1X to 20X the current value estimated by Carr and Head (2014) (1X¼  34 m GEL,  5  106 km3). 2. What is the areal distribution of snow and ice?: We found that the ice was very widespread and relatively evenly distributed above the Wordsworth et al. (2013) ice stability line altitude estimated at þ1 km. 3. What is its average ice thickness and thickness distribution?: On the basis of the most plausible Late Noachian water budgets (o5X current) and under nominal LN climate conditions, the icy highlands surface ice cover is predicted to be predominantly less than a few hundred meters thick. 4. Is the ice wet-based or cold-based, and if wet-based, in what locations?: Availability of a water supply comparable to the present surface/near-surface volume (1X; Carr and Head,

96

5.

6.

7.

8.

9.

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

2014) produces no melted bed, even in deep craters. At higher values of available ice (2X to 5X), the glacial ice sheets are uniformly cold-based. Only in the most extreme cases of unreasonably large supply volumes and high geothermal heat flux are widespread wet bed conditions observed within the model results. In summary, under supply-limited ( o5X) mean LN geothermal gradient conditions, ice accumulation is insufficient to produce basal melting except very locally. In these cases, where ice thickness exceeds 2 km (commonly at the bottom of the deepest impact craters), some basal melting may occur, and potentially produce subglacial lakes. This extensive ice cover also provides an opportunity for the interaction of ascending and erupting magma with the overlying ice, potentially leading to phreatomagmatic eruptions, localized melting and temporary local wet-based glacial conditions (e.g., Head and Wilson, 2002, 2007; Shean et al., 2005; Scanlon et al., 2014). What are the flow rates of the ice?: Velocities in the low-tomoderate supply cases are generally minimal (o a few cm to mm/a), much lower than ice flow velocities on Earth, except in extreme cold-based glacial conditions such as the upland stable zone of the McMurdo Dry Valleys (see Marchant and Head, 2007). Only for the unreasonably large supply volumes are greater flow velocities observed. What are the regional patterns of ice flow (equilibrium ice sheet or local topography dominated)?: The thin ice (the order of hundreds of meters) and low flow velocities ( oa few cm to mm/a) produce a disorganized flow pattern that basically follows topographic slopes, unlike the pattern of radial flow typical of an equilibrium ice sheet. What are the predictions for resulting glacial and periglacial landforms that might be recognized in the geological record?: Since wet-based conditions are only observed in the smaller supply-limited cases, Late Noachian glacial activity is unlikely to produce and preserve an array of distinctive wet-based glacial and periglacial landforms (e.g., drumlins, eskers, etc.) (Benn and Evans, 2010, p. 259–332). Flow rates are so low that cold-based drop moraines (e.g., Marchant and Head, 2007) might also be inhibited from forming. What is the most likely volume of the available Late Noachian reservoir of surface and near-surface water?: On the basis of our analyses and the lack of evidence for widespread wet-based glaciation in the Noachain, we infer that the Late Noachian surface/near-surface ice budget is very likely to be less than 5X the current value (see Carr and Head, 2014, for further discussion). Could the glacial deposits be a source of meltwater for the observed Late Noachian fluvial and lacustrine features?: If one applies top-down melting to the Late Noachian Icy Highlands, significant volumes of meltwater can be generated over short time scales (Fig. 15). Two scenarios are explored here, one involving a 2000 year period of moderately higher temperatures, and the other a single year of much higher temperatures. For the 2000-year climate excursion, temperature warming of þ18 K (recent models have shown that episodic warming by punctuated volcanism could raise the LNIH global mean annual temperature by 26 K; Halevy and Head, 2014) produces 0.45 Mkm3, an amount close to our minimum target volume of 0.42 Mkm3 (the total volume of water in the population of open-basin lakes measured by Fassett and Head, 2008b). In the second scenario, raising surface temperatures to 273 K for a single Mars summer is predicted to produce between 0.15 and 0.4 Mkm3, depending on whether the PDD factor used was for snow or for ice. This single summer phase of heating melts between 4 and 11 m of the upper ice deposits, close to our minimum target volume. Thus, this top-down single-summer melting of the ice deposit

produces between 3 and 10 km3 of meltwater per km of icesheet margin length, comparable to 0.6% to 1.5% of the total ice deposit. 10. In summary, the Late Noachian Icy Highlands model provides a huge reservoir of glacial ice, and under several plausible topdown melting scenarios serves as a ready source for abundant and volumetrically significant meltwater that could form the observed valley networks and open-basin lakes.

Acknowledgments We gratefully acknowledge the Mars Data Analysis Program (MDAP) (Grant NNX11AI81G) and the European Space Agency Mars Express Mission membership on the High-Resolution Stereo Camera (HRSC) Team (JPL 1488322). Also thanks to the National Science Foundation who funded the development of the terrestrial version of the ice sheet model (NSF 0337165, 9873556, 9526348). Thanks are extended to David Weiss and James Cassanelli for helpful discussions and reviews of earlier versions of the manuscript.

References Achille, G.D., Hynek, B.M., 2010. Ancient ocean on Mars supported by global distribution of deltas and valleys. Nat. Geosci 3, 459–463. Achille, G. Di, Marinangeli, L., Ori, G.G., Hauber, E., Gwinner, K., Reiss, D., Neukum, G., 2006. Geological evolution of the Tyras Vallis paleolacustrine system, Mars. J. Geophys. Res. 111, E04003, http://dx.doi.org/10.1029/2005JE002561. Alley., R.B., 2007. “C“ing Arctic climate. Science 317 (5843), 1333–1334. Barnhart, C.J., Howard, A.D., Moore, J.M., 2009. Long-term precipitation and latestage valley network formation: Landform simulations of Parana Basin, Mars. J. Geophys. Res. 114, E01003, http://dx.doi.org/10.1029/2008JE003122. Bell, R.E., Studinger, M., Tikku, A.A., Clarke, G.K.C., Gutner, M.M., Meertens, C., 2002. Origin and fate of Lake Vostok water frozen to the base of the East Antarctic ice sheet. Nature 416 (6678), 307–310. Benn, D.I., Evans, D.J.A., 2010. Glaciers and Glaciation, second ed Hodder Education, London and New York p. 802. Braithwaite, R.J., 1995. Positive degree-day factors for ablation on the Greenland ice sheet studied by energy-balance modelling. J. Glaciol 41 (137), 153–160. Buhler, P.B., Fassett, C.I., Head, J.W., Lamb, M.P., 2011. Evidence for paleolakes in Erythraea Fossa, Mars: Implications for an ancient hydrological cycle. Icarus 213, 104–115. http://dx.doi.org/10.1016/j.icarus.2011.03.004. Buhler, P.B., Fassett, C.I., Head, J.W., Lamb, M.P., 2014. Timescales of fluvial activity and intermittency in Milna Crater, Mars. Icarus 241, 130–147. http://dx.doi.org/ 10.1016/j.icarus.2014.06.028. Carr, M.H., 1995. The Martian drainage system and the origin of networks and fretted channels. J. Geophys. Res 100, 7479–7507. Carr, M.H., 1996. Water on Mars. Oxford University Press, Oxford p. 229. Carr, M.H., Malin, M.C., 2000. Meter-scale characteristics of martian channels and valleys. Icarus 146 (2), 366–386. Carr, M..H., Head, J.W., 2014. Martian unbound water inventories: Changes with time. Lunar Planet. Sci. XXXXV #1427. Cassanelli, J.P., Head, J.W., 2014. Firn densification in a Late Noachian “Icy Highlands” Mars: Implications for ice sheet evolution and thermal response. Planet. Space Sci. In Review. Cassanelli, J.P., Head, J.W., Fastook, J.L., 2014. Late Noachian “Icy Highlands” Mars: Implications for melting and groundwater recharge across the Tharsis rise. Lunar Planet. Sci. 45, 1501. Cassata, W.S., Shuster, D.L., Renne, P.R., Weiss, B.P., 2012. Trapped Ar isotopes in meteorite ALH 84001 indicate Mars did not have a thick ancient atmosphere. Icarus 221, 461–465. http://dx.doi.org/10.1016/j.icarus.2012.05.005. Chassefière, E., Leblanc, F., 2011. Constraining methane release due to serpentinization by the observed D/H ratio on Mars. Earth Planet. Sci. Lett 310, 262–271. http://dx.doi.org/10.1016/j.epsl.2011.08.013. Clifford, S.M., Lasue, J., Heggy, E., Boisson, J., McGovern, P., Max, M.D., 2010. Depth of the Martian cryosphere: revised estimates and implications for the existence and detection of subpermafrost groundwater. J. Geophys. Res.: Planet 115, E07001. http://dx.doi.org/10.1029/2009JE003462. Clifford, S.M., Parker., T.J., 2001. The evolution of the Martian hydrosphere: Implications for the fate of a primordial ocean and the current state of the northern plains. Icarus 154, 40–79. Craddock, R A, Howard., A D, 2002. The case for rainfall on a warm, wet early Mars. J. Geophys. Res 107 (E11), 21–36. http://dx.doi.org/10.1029/2001JE001505. Craddock, R.A., Maxwell, T.A., 1990. Resurfacing of the Martian highlands in the Amenthes and Tyrrhena region. J. Geophys. Res.: Solid Earth 95 (B9), 14265–14278. http://dx.doi.org/10.1029/JB095iB09p14265.

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

Craddock, R.A., Maxwell, T.A., 1993. Geomorphic evolution of the Martian highlands through ancient fluvial processes. J. Geophys. Res.: Planet 98 (E2), 3453–3468. http://dx.doi.org/10.1029/92JE02508. Craddock, R.A., Maxwell, T.A., Howard, A.D., 1997. Crater morphometry and modification in the Sinus Sabaeus and Margaritifer Sinus regions of Mars. J. Geophys. Res.: Planet 102 (E6), 13321–13340. http://dx.doi.org/10.1029/ 97JE01084. Ehlmann, B.L., Mustard, J.F., Murchie, S.L., Bibring, J.-P., Meunier, A., Fraeman, A.A., Langevin, Y., 2011. Subsurface water and clay mineral formation during the early history of Mars. Nature 479, 53–60. http://dx.doi.org/10.1038/nature10582. Fairén, A.G., 2010. A cold and wet Mars. Icarus 208, 165–175. http://dx.doi.org/ 10.1016/j.icarus.2010.01.006. Fassett, C.I., Head, J.W., 2008a. The timing of Martian valley network activity: Constraints from buffered crater counting. Icarus 195, 61–89. Fassett, C.I., Head, J.W., 2008b. Valley network-fed, open-basin lakes on Mars: Distribution and implications for Noachian surface and subsurface hydrology. Icarus 198, 37–56. Fastook, J.L., Head, J.W., 2013. Amazonian non-polar glaciation: Supply‐limited glacial history and the role of ice sequestration (XXXXIV). Lunar Planet. Sci. #1256. Fastook, J.L., Head, J.W., 2014. Amazonian mid- to high-latitude glaciation on Mars: Supply‐limited ice sources, ice accumulation patterns, and concentric crater fill glacial flow and ice sequestration. Planet. Space Sci 91, 60–76. http://dx.doi.org/ 10.1016/j.pss.2013.12.002. Fastook, J.L., Head, J.W., Marchant, D.R., Forget, F., Madeleine, J.-B., 2012. 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. Icarus 219, 25–40. Forget, F., Wordsworth, R., Millour, E., Madeleine, J.-B., Kerber, L., Leconte, J., Marcq, E., Haberle, R.M., 2013. 3D modelling of the early Martian climate under a denser CO2 atmosphere: Temperatures and CO2 ice clouds. Icarus 222, 81–99. http://dx.doi.org/10.1016/j.icarus.2012.10.019. Gaidos, E., Marion, G., 2003. Geological and geochemical legacy of a cold early Mars. J. Geophys. Res 108 (E6), 5055. http://dx.doi.org/10.1029/2002JE002000. Golombek, M.P., Grant, J.A., Crumpler, L.S., Greeley, R., Arvidson, R.E., Bell III, J.F., Weitz, C.M., Sullivan, R., Christensen, P.R., Soderblom, L.A., Squyres, S.W., 2006. Erosion rates at the Mars Exploration Rover landing sites and long-term climate change on Mars. J. Geophys. Res 111, E12S10. http://dx.doi.org/10.1029/ 2006JE002754. Gough, D.O., 1981. Solar interior structure and luminosity variations. Sol. Phys 74 (1), 21–34. Grant, J.A., Irwin, R.P., Wilson, S.A., Buczkowski, D., Siebach., K., 2011. A lake in Uzboi Vallis and implications for Late Noachian–Early Hesperian climate on Mars. Icarus 212, 110–122. http://dx.doi.org/10.1016/j.icarus.2010.11.024. Greve, R., Blatter., H., 2009. Dynamics of Ice Sheets and Glaciers. Advances in Geophysical and Environmental Mechanics and Mathematics. Springer, Dordrecht Heidelberg London New York. Grotzinger, J.P., Sumner, D.Y., Kah, L.C., Stack, K., Gupta, S., Edgar, L., Rubin, D., Lewis, K., Schieber, J., Mangold, N., Milliken, R., Conrad, P.G., DesMarais, D., Farmer, J., Siebach, K., Calef, F., Hurowitz, J., McLennan, S.M., Ming, D., Vaniman, D., Crisp, J., Vasavada, A., Edgett, K.S., Malin, M., Blake, D., Gellert, R., Mahaffy, P., Wiens, R.C., Maurice, S., Grant, J.A., Wilson, S., Anderson, R.C., Beegle, L., Arvidson, R., Hallet, B., Sletten, R.S., Rice, M., Bell, J., Griffes, B. Ehlmann J., Anderson, R.B., Bristow, T.F., Dietrich, W.E., Dromart, G., Eigenbrode, J., Fraeman, A., Hardgrove, C., Herkenhoff, K., Jandura, L., Kocurek, G., Lee, S., Leshin, L.A., Leveille, R., Limonadi, D., Maki, J., McCloskey, S., Meyer, M., Minitti, M., Newsom, H., Oehler, D., Okon, A., Palucis, M., Parker, T., Rowland, S., Schmidt, M., Squyres, S., Steele, A., Stolper, E., Summons, R., Treiman, A., Williams, R., Yingst, A., MSL Science Team, 2014. A habitable fluvio-lacustrine environment at Yellowknife Bay, Gale Crater, Mars. Science 343, 1242777. http://dx.doi.org/10.1126/science.1242777. Haberle, R.M., 1998. Early Mars climate models. J. Geophys. Res 103 (E12), 28,467–28,479. Halevy, I., Head, J.W., 2014. Episodic warming of early Mars by punctuated volcanism. Nature Geoscience, 1–4. http://dx.doi.org/10.1038/NGEO2293. J.W. Head. Cold and icy Noachian Mars: insights into the hydrological system and cycle from the Antarctic McMurdo dry valleys. Fifth International Workshop on the Mars Atmosphere: Modelling and Observation, Oxford, January 13–16 2014. J.W. Head, M.H. Carr, P.S. Russell, C.I. Fassett. Martian hydrology: the Late Noachian hydrologic cycle 7. Vernadsky-Brown Microsymposium 38, #MS032, 27–29 October 2003. Head, J.W., Marchant, D.R., 2008. Evidence for non-polar ice deposits in the past history of Mars (XXXIX). Lunar Planet. Sci. #1295. Head, J.W., Marchant., D.R., 2014. The climate history of early Mars: Insights from the Antarctic McMurdo Dry Valleys hydrologic system. Antarctic Sci 26, 774–800. http://dx.doi.org/10.1017/S0954102014000686. Head, J.W., Pratt, S., 2001. Extensive Hesperian-aged south polar ice sheet on Mars: Evidence for massive melting and retreat, and lateral flow and ponding of meltwater. J. Geophys. Res 106 (E6), 12275–12299. Head, J.W., Wilson., L., 2002. Mars: a review and synthesis of general environments and geological settings of magma—H2O interactions. In: Smellie, J.L., Chapman, M.G. (Eds.), Volcano–Ice Interaction on Earth and Mars, 202. The Geological Society, London, pp. 27–57. Head, J.W., Wilson, L., 2007. Heat transfer in volcano–ice interactions on mars: Synthesis of environments and implications for processes and landforms. Annal. Glaciol 45 (1), 1–13.

97

Head, J.W., Wordsworth, R., Forget, F., Madeleine, J.-B., Halevy, I., 2014. Late Noachian “Cold and Icy Highlands” model: Geological predictions for equilibrium environments and equilibrium/non-equilibrium melting scenarios (XXXXV). Lunar Planet. Sci. Conf. #1412. Hoke, M.R.T., Hynek, B.M., Di Achille, G., Hutton., E.W.H., 2014. The effects of sediment supply and concentrations on the formation timescale of Martian deltas. Icarus 228, 1–12. http://dx.doi.org/10.1016/j.icarus.2013.09.017. Hoke, M.R.T., Hynek, B.M., Tucker, G.E., 2011. Formation timescales of large Martian valley networks. Earth Planet. Sci. Lett 312, 1–12. http://dx.doi.org/10.1016/j. epsl.2011.09.053. Hooke, R. LeB., 2005. Principles of Glacier Mechanics, second ed. Cambridge University Press, Cambridge. Hughes, T., Sargent, A., Fastook, J.L., 2011. Ice-bed coupling beneath and beyond ice streams: Byrd Glacier, Antarctica. J. Geophys. Res 116 (F03005). Hughes., T.J., 1977. West Antarctic ice streams. Rev. Geophys. Space Phys 15, 1–46. Huybrechts, P., Letreguilly, A., Reeh., N., 1991. The Greenland ice sheet and greenhouse warming. Paleogeogr. Paleoclimatol. Paleoecol 89 (4), 399–412. Hynek, B.M., Beach, M., Hoke, M.R.T., 2010. Updated global map of Martian valley networks and implications for climate and hydrologic processes. J. Geophys. Res 115, E09008. http://dx.doi.org/10.1029/2009JE003548. Hynek, B.M., Phillips, R.J., 2001. Evidence for extensive denudation of the Martian highlands. Geology 29 (407–410), E07007. Hynek, B.M., Robbins, S.J., Š rámek, O., Zhong, S.J., 2011. Geological evidence for a migrating Tharsis plume on early Mars. Earth Planet. Sci. Lett 310, 327–333. Irwin III, R.P., Howard, A.D., Craddock, R.A., Moore., J.M., 2005. An intense terminal epoch of widespread fluvial activity on early Mars: 2. Increased runoff and paleolake development. J. Geophys. Res 110, E12S15. http://dx.doi.org/10.1029/ 2005JE002460. Irwin, R.P., Craddock, R.A., Howard, A.D., Flemming., H.L., 2011. Topographic influences on development of Martian valley networks. J. Geophys. Res 116, E02005. http://dx.doi.org/10.1029/2010JE003620. Kadish, S.J., Head, J.W., Barlow, N.G., 2010. Pedestal crater heights on Mars: A proxy for the thicknesses of past, ice-rich, Amazonian deposits. Icarus 210 (1), 92–101. http://dx.doi.org/10.1016/j.icarus.2010.06.021. Kleman, J., 1994. Preservation of landforms under ice sheets and ice caps. Geomorphology 9, 19–32. Kleman, J., Hattestrand, C., 1999. Frozen-bed Fennoscandian and Laurentide ice sheets during the Last Glacial Maximum. Nature 402, 63–66. Kress, A.M., Head, J.W., 2014. Late Noachian and Early Hesperian ridge systems in the South Circumpolar Dorsa Argentea Formation, Mars: Evidence for two stages of melting of an extensive Late Noachian ice sheet. Planet. Space Sci , http://dx.doi.org/10.1016/j.pss.2014.11.025. Kwok, R., Siegert, M J, Carsey, F D, 2000. Ice motion over Lake Vostok, Antarctica: Constraints on inferences regarding the accreted ice. J. Glaciol 46 (155), 689–694. Laskar, J., Correia, A.C.M., Gastineau, M., Joutel, F., Levrard, B., Robutel, P., 2004. Long term evolution and chaotic diffusion of the insolation quantities of Mars. Icarus 170 (2), 343–364. http://dx.doi.org/10.1016/j.icarus.2004.04.005. Levy, J.S., Head, J.W., Marchant, D.R., 2009. Concentric crater fill in Utopia Planitia: History and interaction between glacial “brain- terrain” and periglacial mantle processes. Icarus 202 (2), 462–476. http://dx.doi.org/10.1016/j.icarus.2009.02.018. Levy, J.S., Head, J.W., Marchant, D.R., 2010. Concentric crater fill in the northern mid-latitudes of Mars: Formation processes and relationships to similar landforms of glacial origin. Icarus 209 (2), 390–404. http://dx.doi.org/10.1016/j. icarus.2010.03.036. Madeleine, J.-B., Forget, F., Head, J.W., Levrard, B., Montmessin, F., Millour, E., 2009. Amazonian northern mid-latitude glaciation on Mars: a proposed climate scenario. Icarus 203, 390–405. http://dx.doi.org/10.1016/j.icarus.2009.04.037. Malin, M.C., Edgett, K.S., 2003. Evidence for persistent flow and aqueous sedimentation on early Mars. Science 302, 1931–1934. http://dx.doi.org/10.1126/ science.1090544. Marchant, D.R., Head, J.W., 2007. Antarctic dry valleys: Microclimate zonation, variable geomorphic processes, and implications for assessing climate change on Mars. Icarus 192 (1), 187–222. http://dx.doi.org/10.1016/j.icarus.2007.06.018. Masursky, H., Boyce, J.M., Dial, A.L., Schaber, G.G., Strobell., M.E., 1977. Classificatin and time of formation of Martian channels based on Viking data. J. Geophys. Res 82, 4016–4038. Matsubara, Y., Howard, A.D., Gochenour, J.P., 2013. Hydrology of early Mars: Valley network incision. J. Geophys. Res.: Planet 118, 1365–1387. http://dx.doi.org/ 10.1002/jgre.20081. McConnell, J.R., Edwards, R., Kok, G. L, Flanner, M.G., Zender, C.S., Saltzman, E.S., Banta, R., Pasteris, D.R., Carter, M.M., Kahl, J.D.W., 2007. 20th-Century industrial black carbon emissions altered Arctic climate forcing. Science 317 (5843), 1381–1384. Moore, J.M., Howard, A.D., Dietrich, W.E., Schenk, P.M., 2003. Martian layered fluvial deposits: Implications for Noachian climate scenarios. Geophys. Res. Lett 30 (24), 2292. http://dx.doi.org/10.1029/2003GL019002. Paterson, W.S.B, 1994. The Physics of Glaciers, third ed Pergamon, Oxford. Pondrelli, M., Rossi, A.P., Marinangeli, L., Hauber, E., Gwinner, K., Baliva, A., Di Lorenzo, S., 2008. Evolution and depositional environments of the Eberswalde fan delta. Mars Icarus 197, 429–451. http://dx.doi.org/10.1016/j.icarus.2008.05.018. Ramanathan, V., Carmichael, G., 2008. Global and regional cli- mate changes due to black carbon. Nat. Geosci 1, 221–227. http://dx.doi.org/10.1038/ngeo156. Raymond, C.F., 2000. Energy balance of ice streams. J. Glaciol 46 (155), 665–674. Richter, A., Fedorov, D.V., Fritsche, M., Popov, S.V., Lipenkov, V. Ya., Ekaykin, A.A., Lukin, V.V., Matveev, A. Yu., Grebnev, V.P., Rosenau, R., Dietrich, R., 2013. Ice

98

J.L. Fastook, J.W. Head / Planetary and Space Science 106 (2015) 82–98

flow velocities over Vostok Subglacial Lake, East Antarctica, determined by 10 years of GNSS observations. J. Glaciol 59 (214), 315–326. http://dx.doi.org/ 10.3189/2013JoG12J056. Rosenberg E.N. and Head J.W. The water volume required to erode the valley networks on Mars: Implications for Late Noachian climate. 5th Moscow Solar System Symposium, Moscow, PS-07, 2014. Scanlon, K.E., Head, J.W., Madeleine, J-B, Forget, F., 2013. Orographic precipitation in valley network headwaters: Constraints on the ancient Martian atmosphere. Geophys. Res. Lett. 40, 4182–4187. http://dx.doi.org/10.1002/grl.50687. Scanlon, K.E., Head, J.W., Wilson, L., Marchant, D.R., 2014. Volcano–ice interactions in the Arsia Mons tropical mountain glacier deposits. Icarus 237, 315–339. Schoof, C., 2002. Basal perturbations under ice streams: Form drag and surface expression. J. Glaciol 48 (162), 407–416. Segura, T.L., Toon, O.B., Colaprete, A., 2008. Modeling the environmental effects of moderate-sized impacts on Mars. J. Geophys. Res 113, E11007. http://dx.doi.org/ 10.1029/2008JE003147. Segura, T.L., Toon, O.B., Colaprete, A., Zahnle, K., 2002. Environmental effects of large impacts on Mars. Science 298, 1977–1980. Shean, D.E., Head, J.W., Marchant, D.R., 2005. Origin and evolution of a cold-based tropical mountain glacier on Mars: The Pavonis Mons fan-shaped deposit. J. Geophys. Res 110, E05001. http://dx.doi.org/10.1029/2004JE002360. Siegert, M.J., Ellis-Evans, J.C., Tranter, M., Mayer, C., Petit, J.-R., Salamation, A., Priscu, J.C., 2001. Physical, chemical and biological processes in Lake Vostok and other Antarctic subglacial lakes. Nature 414, 603–609. Siegert, M.J., Ridley., J.K., 1998. An analysis of the ice-sheet surface and subsurface topography above the Vostok Station subglacial lake, central East Antarctica. J. Geophys. Res 103 (B5), 10195–10208. Smith, D.E., Zuber, M.T., Frey, H.V., Garvin, J.B., Head, J.W., Muhleman, D.O., Pettengill, G.H., Phillips, R.J., Solomon, S.C., Zwally, H.J., Banerdt, W.B., Duxbury, T.C., 1998. Topography of the northern hemisphere of Mars from the Mars Orbiter Laser Altimeter. Science 279, 1686–1692. http://dx.doi.org/10.1126/ science.279.5357.1686. Solomon, S.C., Aharonson, O., Aurnou, J.M., Banerdt, W.B., Carr, M.H., Dombard, A.J., Frey, H.V., Golombek, M.P., Hauck, S.A., Head, J.W., Jakosky, B.M., Johnson, C.L.,

McGovern, M.T., Neumann, G.A., Phillips, R.J., Smith, D.E., Zuber, M.T., 2005. New perspectives on ancient Mars. Science 307, 1214–1220. Stepinski, T.F., Coradetti, S., 2004. Comparing morphologies of drainage basins on Mars and Earth using integral-geometry and neural maps. Geophys. Res. Lett 31, L15604. http://dx.doi.org/10.1029/2004GL020359. Studinger, M., Bell, R.E., Tikku, A.A., 2004. Estimating the depth and shape of subglacial Lake Vostok’s water cavity from aerogravity data. Geophys. Res. Lett 31 (12), L12401. http://dx.doi.org/10.1029/2004gl019801. Toon, O.B., Segura, T., Zahnle., K., 2010. The formation of Martian river valleys by impacts. Annu. Rev. Earth Planet. Sci 38, 303–322. http://dx.doi.org/10.1146/ annurev–earth–040809–152354. Weiss, D.K., Head, J.W., 2014. Crater degradation in the Noachian Highlands of Mars: Assessing the role of regional snow and ice deposits on a cold and icy early Mars (In Review). Planet. Space Sci. Williams, R.M.E., Phillips, R.J., 2001. Morphometric measurements of Martian valley networks from Mars Orbiter Laser Altimeter (MOLA) data. J. Geophys. Res 106 (E10), 23,737–23,751. Wilson, L., Head, J.W., 2009. Tephra deposition on glaciers and ice sheets on Mars: Influence on ice survival, debris content and flow behavior. J. Volcanol. Geothermal Res 185, 290–297. http://dx.doi.org/10.1016/j.jvolgeores.2008.10.003. Wordsworth, R., Forget, F., Millour, E., Head, J.W., Madeleine, J.-B., Chanay, B., 2013. Global modelling of the early Martian climate under a denser CO2 atmosphere: Water cycle and ice evolution. Icarus 222, 1–19. http://dx.doi.org/10.1016/j. icarus.2012.09.036. Zhong, S., 2009. Migration of Tharsis volcanism on Mars caused by differential rotation of the lithosphere. Nat. Geosci 2, 19–23. http://dx.doi.org/10.1038/ NGEO392. Zuber, M.T., Smith, D.E., Solomon, S.C., Abshire, J.B., Afzal, R.S., Aharonson, O., Fishbaugh, K., Ford, P.G., Frey, H.V., Garvin, J.B., Head, J.W., Ivanov, A.B., Johnson, C.L., Muhleman, D.O., Neumann, G.A., Pettengill, G.H., Phillips, R.J., Sun, X., Zwally, H.J., Banerdt, W.B., Duxbury, T.C., 1998. Observations of the north polar region of Mars from the Mars Orbiter Laser Altimeter. Science 282, 2053–2060.