Early Mars climate near the Noachian–Hesperian boundary: Independent evidence

advertisement

Icarus 219 (2012) 25–40

Contents lists available at SciVerse ScienceDirect

Icarus

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / i c a r u s

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, 223 Neville Hall, Orono, ME 04469, USA b

Department of Geological Sciences, Brown University, Providence, RI 02912, USA c

Department of Earth Sciences, Boston University, Boston, MA 02215, USA d Laboratoire de Météorologie Dynamique, Institut Pierre Simon Laplace, Université Paris 6, BP 99, 75252 Paris cedex 05, France a r t i c l e i n f o

Article history:

Received 2 June 2011

Revised 29 December 2011

Accepted 13 February 2012

Available online 24 February 2012

Keywords:

Mars

Mars, climate

Mars, polar caps

Mars, polar geology a b s t r a c t

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 ( 100 ° C) simulated in typical Amazonian climate experiments and typical Noachian–Hesperian geothermal heat fluxes (45–65 mW/m

2

), 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 ( 100 ° C) to the range of 50 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 2012 Elsevier Inc. All rights reserved.

1. Introduction

Current polar layered deposits ( Phillips et al., 2008 ), earlier

Amazonian mid-latitude glacial deposits (

Head et al., 2010

) and tropical mountain glaciers (

Head and Marchant, 2003 ) 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.,

2005a,b; Kadish et al., 2008 ). 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, 1992;

Corresponding author.

E-mail addresses: fastook@maine.edu

(J.L. Fastook), james_head@brown.edu

(J.W. Head).

0019-1035/$ - see front matter Ó 2012 Elsevier Inc. All rights reserved.

doi: 10.1016/j.icarus.2012.02.013

Banks et al., 2009 ). Of concern here are the Late Noachian–Early

Hesperian south circumpolar Dorsa Argentea Formation (DAF)

(

Tanaka and Kolb, 2001

) (

Fig. 1

). The DAF contains features interpreted to be indicative of basal melting beneath a regional ice-rich

deposit ( Head and Pratt, 2001; Ghatan and Head, 2002, 2004; Ghatan et al., 2003; Kress et al., 2010 ) at that time ( Plaut et al., 1988 ).

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, 2002

) despite the fact that water ice can exist in the near subsurface poleward of 60 °

latitude at both poles ( Mitrofanov et al., 2002; Boynton et al., 2002

).

26 J.L. Fastook et al. / Icarus 219 (2012) 25–40

Fig. 1.

(a) 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.

(b) Examples of the esker-like ridges located at the thin arrows in (a). Both are from

Head and Pratt (2001)

.

Fig. 2.

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

3.2 of

Spiga, 2011

). Instead, the surface temperature is always close to radiative equilibrium, whatever the altitude. On Earth the

J.L. Fastook et al. / Icarus 219 (2012) 25–40 27

1500

1000

500

0

-500

-1000

-1500

(a)

Mass Balance (mm/a) [SMB X 0.5]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

10

8

6

4

2

0

-4

20

18

16

14

12

-8

-12

-16

-20

-24

-28

-32

-36

-40

(b)

Mass Balance (mm/a) [SMB X 1.0]

TIME 10Ma

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

8

6

12

10

4

2

0

-4

20

18

16

14

-8

-12

-16

-20

-24

-28

-32

-36

-40

(c)

1500

1000

500

0

-500

-1000

-1500

Mass Balance (mm/a) [SMB X 2.0]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

20

18

16

14

12

6

4

10

8

2

0

-4

-8

-12

-16

-20

-24

-28

-32

-36

-40

(d) Mass Balance (mm/a) [SMB X 3.0]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

1500

1000

500

0

-500

-1000

-1500

8

6

4

2

0

-4

-8

-12

-16

-20

-24

-28

-32

-36

-40

20

18

16

14

12

10

-1500 -1000 -500 0 500 1000 1500

(e) Mass Balance (mm/a) [SMB X 4.0]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

8

6

4

2

0

-4

-8

-12

-16

-20

-24

-28

-32

-36

-40

20

18

16

14

12

10

(f) TEMPERATURE (degree C) [base]

BASE

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

-95

-96

-97

-98

-99

-100

-101

-102

-103

-104

-105

-106

-107

-108

-109

-110

Fig. 3.

Synthetic climate modified from

Madeleine et al. (2009) . (f) Shows the temperature field taken directly from the GCM results. To this we apply the offsets for the

warmer climates. (b) Shows the basic SMB, with sublimation rates modified from

Madeleine et al. (2009)

by a reduction factor of 50 and a radially symmetric accumulation component added. Panels (a, c, d, and e) are the basic SMB times 0.5, 2.0, 3.0, and 4.0.

1500

1000

500

0

-500

-1000

-1500

BED (m)

---

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

3000

2500

2000

1500

1000

500

0

-500

-1000

5500

5000

4500

4000

3500

-1500 -1000 -500 0 500 1000 1500

Fig. 4.

The grid for ice sheet reconstruction from the pole at grid (0, 0) to 60 ° S at the edge of the circle. Resolution is non-uniform but is nominally 30 km. To avoid complications associated with the present ice sheet topography, we truncate elevations at 3000 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.) surface temperature tends to follow the atmospheric lapse rate

(4.5

° C/km moist, 9.5

° C/km dry), which results in less ablation by 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. (2008b)

. 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., 2007

). 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., 2004, 2010

). 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

28 J.L. Fastook et al. / Icarus 219 (2012) 25–40

(a)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [a-00-45]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(b)

8000

7000

6000

5000

4000

3000

2000

1000

1000

1000

1500

[a-00-45]

[]

2000

1500 2000

2500

2500

3000

8000

7000

6000

5000

4000

3000

2000

1000

3000

-1500 -1000 -500 0 500 1000 1500

(c)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [a-00-65]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(d)

8000

7000

6000

5000

4000

3000

2000

1000

1000

1000

1500

1500

[a-00-65]

[]

2000

2000

2500

2500

3000

8000

7000

6000

5000

4000

3000

2000

1000

3000

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

0

-5

-10

-15

-20

-25

-30

-1500 -1000 -500 0 500 1000 1500

Fig. 5.

Basal temperatures (a and c) and vertical profiles (b and d) for SMB 0.5 scenario with no warming and geothermal flux of 45 (a and b) and 65 (c and d) mW/m

2

.

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110 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., 2004,

2010

). For example, valley network activity, suggestive of flowing

streams and a ‘‘warmer and wetter’’ early Mars ( Carr, 1996; Craddock and Howard, 2002; Head et al., 2003; Kargel, 2004; Fassett and Head, 2008a,b

), characterized the highlands at the end of the

Noachian and into the Hesperian. The active water cycle ( Head et al., 2003 ) 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, 2001; Ghatan and Head, 2002, 2004; Ghatan et al., 2003;

Kress et al., 2010

). 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, 1972

), 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

J.L. Fastook et al. / Icarus 219 (2012) 25–40 29

(a)

TEMPERATURE (degree C) [b-00-45]

TIME 10Ma

-1500 -1000 -500

1500 1500

1000

500

0

-500

-1000

-1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

-1

-6

-11

-16

-21

-26

-31

-36

(b)

[b-00-45]

[]

-30

-35

-40

-45

-50

-55

-60

-65

-90

-95

-100

-105

-70

-75

-80

-85

0

-5

-10

-15

-20

-25

-110

(c)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [b-00-65]

TIME 10Ma

-1500 -1000 -500

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

-1

-6

-11

-16

-21

-26

-31

(d)

[b-00-65]

[]

-40

-45

-50

-55

-60

-65

-95

-100

-105

-110

-70

-75

-80

-85

-90

0

-5

-10

-15

-20

-25

-30

-35

Fig. 6.

Basal temperatures (a and c) and vertical profiles (b and d) for SMB 1.0 scenario with no warming and geothermal flux of 45 (a and b) and 65 (c and d) mW/m

2

.

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., 2010 ) 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 0 ° 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, (2) 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. 2

, top). We then assess the magnitude of atmospheric surface temperature increase that would be required to en-

sure basal melting from the top down ( Fig. 2 , 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 500 mb CO

2

, both with and without excess H

2

O ( Johnson et al., 2008

) show warming of the poles of as much as +65 ° C and +25 ° C respectively.

Their models indicate a pole-to-equator gradient of approximately

40 ° 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.

2. The University of Maine Ice Sheet Model (UMISM)

The UMISM, adapted for the martian environment (

Fastook et al., 2004, 2005, 2006

), 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

30

(a)

1500

1000

500

0

-500

-1000

-1500

J.L. Fastook et al. / Icarus 219 (2012) 25–40

TEMPERATURE (degree C) [c-00-45]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(b)

8000

7000

6000

5000

4000

3000

2000

1000

1000

1000

-1500 -1000 -500 0 500 1000 1500

1500

[c-00-45]

[]

2000

1500 2000

2500

2500

3000

8000

7000

6000

5000

4000

3000

2000

1000

3000

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

0

-5

-10

-15

-20

-25

-30

-35

-40

(c)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [c-00-65]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(d)

8000

7000

6000

5000

4000

3000

2000

1000

1000

1000

1500

1500

[c-00-65]

[]

2000

2000

2500

2500

3000

8000

7000

6000

4000

3000

2000

1000

3000

-20

-25

-30

-35

-40

-45

-50

-55

-60

-65

0

-5

-10

-15

-70

-75

-80

-85

-90

-95

-100

-105

-110

-1500 -1000 -500 0 500 1000 1500

Fig. 7.

Basal temperatures (a and c) and vertical profiles (b and d) for SMB 2.0 scenario with no warming and geothermal flux of 45 (a and b) and 65 (c and d) mW/m

2

.

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., 2008a,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. (2004)

and

Solomon et al. (2005)

we adopt a geothermal flux of 45–65 mW/m 2 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 accu-

racy ( Montmessin et al., 2004

) and has proven robust in our earlier glacial modeling studies of reconstructed ice sheets in the Tharsis region (e.g.,

Forget et al., 2006; Fastook et al., 2004, 2005, 2008b ).

J.L. Fastook et al. / Icarus 219 (2012) 25–40 31

(a)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [d-00-45]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(b)

8000

7000

6000

5000

4000

3000

2000

1000

1000

1000

1500

[d-00-45]

[]

2000

1500 2000

2500

2500

3000

8000

7000

6000

5000

4000

3000

2000

1000

3000

(c)

1500

1000

500

0

-500

-1000

-1500

-1500 -1000 -500 0 500 1000 1500

TEMPERATURE (degree C) [d-00-65]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(d)

8000

7000

6000

5000

4000

3000

2000

1000

1000

1000

1500

1500

[d-00-65]

[]

2000

2000

2500

2500

3000

8000

7000

6000

5000

4000

3000

2000

1000

3000

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

0

-5

-10

-15

-20

-25

-30

-35

-1500 -1000 -500 0 500 1000 1500

Fig. 8.

Basal temperatures (a and c) and vertical profiles (b and d) for SMB 3.0 scenario with no warming and geothermal flux of 45 (a and b) and 65 (c and d) mW/m

2

.

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

As yet, however, the model has not been applied toward predictions of SMB for the Noachian–Hesperian era (

Johnson et al.,

2008; Wordsworth et al., 2011 ) and this requires additional

assumptions as noted below.

4. Model assumptions and input

4.1. 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

2 atmosphere. This we do by modifying the GCM climate simulated by

Madeleine et al. (2009)

and obtained using an intermediate obliquity (35 ° ) and a high dust optical depth (2.5). 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. (2009)

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 50 (11 mm/a maximum sublimation instead of more than 50 cm/a). To this we add a radially symmetric pattern of accumulation, with a maximum value of 6 mm/a centered on the pole, declining with distance such that the region of accumulation has a radius of 2450 km. This, combined with the modified

Madeleine et al. (2009)

sublimation rates is designed to produce an ice sheet footprint in accordance with the DAF.

This basic SMB pattern is shown in

Fig. 3 b. Also in Fig. 3 a and c–e

are scaled versions of this basic SMB pattern (times 0.5, 2.0, 3.0, and 4.0) 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

32

1000

500

0

-500

-1000

(a)

TEMPERATURE (degree C) [e-00-45]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

-1500

J.L. Fastook et al. / Icarus 219 (2012) 25–40

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(b)

-1500 -1000 -500 0 500 1000 1500

[e-00-45]

[]

(c)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [e-00-65]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

-96

-101

-106

(d)

8000

7000

6000

5000

4000

3000

2000

1000

1000 1500

[e-00-65]

[]

2000 2500 3000

8000

7000

6000

5000

4000

3000

2000

1000

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

0

-5

-10

-15

-20

-25

-30

-1500 -1000 -500 0 500 1000 1500

Fig. 9.

Basal temperatures (a and c) and vertical profiles (b and d) for SMB 4.0 scenario with no warming and geothermal flux of 45 (a and b) and 65 (c and d) mW/m

2

.

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

0

-5

-10

-15

-20

-25

-30

-35

-40

(a)

65

60

55

50

Percent Wet Bed

[SMB*0.5]

15

14

13

12

9

8

11

10

7

6

5

4

3

2

1

(b)

16

14

12

10

8

6

4

2

0

45

Percentage Wet Bed, SMB X 0.5

5 % threshold

warming= 0

warming=10

warming=20

warming=30

warming=40

warming=50

50 55

Geothermal Flux (mW/m^2)

60 65

45

0 5 10 15 20 25 30 35 40 45 50

Temperature Offset (K)

Fig. 10.

(a) Percentage of the bed that is wet for SMB 0.5 scenario as a function of temperature warming and geothermal heat flux. (b) Vertical transects through (a) at temperature warmings of +0, +10, +20, +30, +40, and +50 ° C with the 5% basal melting threshold shown as a horizontal line for reference.

J.L. Fastook et al. / Icarus 219 (2012) 25–40 33

(a) Percent Wet Bed

[SMB*1.0]

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

(b)

16

14

12

10

8

6

4

2

0

45

5 % threshold

warming= 0

warming=10

warming=20

warming=30

warming=40

warming=50

Percentage Wet Bed, SMB X 1.0

50 55

Geothermal Flux (mW/m^2)

60 65

0 5 10 15 20 25 30 35 40 45 50

Temperature Offset (K)

Fig. 11.

(a) Percentage of the bed that is wet for SMB 1.0 scenario as a function of temperature warming and geothermal heat flux. (b) Vertical transects through (a) as in

Fig. 10 .

(a)

65

60

55

50

Percent Wet Bed

[SMB*2.0]

15

14

13

12

11

10

6

5

4

9

8

7

3

2

1

(b)

16

14

12

10

8

6

4

2

0

45

Percentage Wet Bed, SMB X 2.0

5 % threshold

warming= 0

warming=10

warming=20

warming=30

warming=40

warming=50

45

0 5 10 15 20 25 30 35 40 45 50

Temperature Offset (K)

50 55

Geothermal Flux (mW/m^2)

60 65

Fig. 12.

(a) Percentage of the bed that is wet for SMB 2.0 scenario as a function of temperature warming and geothermal heat flux. (b) Vertical transects through (a) as in

Fig. 10 .

(a)

65

60

55

50

Percent Wet Bed

[SMB*3.0]

15

14

13

12

11

10

9

8

7

6

5

4

3

2

1

(b)

16

14

12

10

8

6

4

2

0

45

Percentage Wet Bed, SMB X 3.0

5 % threshold

warming= 0

warming=10

warming=20

warming=30

warming=40

warming=50

50 55

Geothermal Flux (mW/m^2)

60 65

45

0 5 10 15 20 25 30 35 40 45 50

Temperature Offset (K)

Fig. 13.

(a) Percentage of the bed that is wet for SMB 2.0 scenario as a function of temperature warming and geothermal heat flux. (b) Vertical transects through (a) as in

Fig. 10 .

34 J.L. Fastook et al. / Icarus 219 (2012) 25–40

(a)

65

60

55

50

Percent Wet Bed

[SMB*4.0]

15

14

13

12

11

8

7

10

9

6

5

4

3

2

1

(b)

16

14

12

10

8

6

4

2

0

45

Percentage Wet Bed, SMB X 4.0

5 % threshold

warming= 0

warming=10

warming=20

warming=30

warming=40

warming=50

50 55

Geothermal Flux (mW/m^2)

60 65

45

0 5 10 15 20 25 30 35 40 45 50

Temperature Offset (K)

Fig. 14.

(a) Percentage of the bed that is wet for SMB 4.0 scenario as a function of temperature warming and geothermal heat flux. (b) Vertical transects through (a) as in

Fig. 10

.

Table 1

The minimum geothermal fluxes and temperature warmings that achieve 5% basal melting conditions for the 5 SMB scenarios.

At temperature warming (+ ° C) Climate scenario (base SMB )

5% wet bed threshold

0.5

1.0

2.0

3.0

4.0

Lowest geothermal flux (mW/m 2 )

53

49

47

45

45

50

50

50

50

49

Lowest temperature warming at 65 mW/m 2

40

35

20

18

16

(a)

1500

1000

500

0

-500

-1000

-1500

1500

1000

500

0

-500

-1000

-1500

Mass Balance (mm/a) [d-50-45]

TIME 10Ma

-1500 -1000

-1500 -1000

(d)

TEMPERATURE (degree C) [d-50-45]

TIME 10Ma

-1500 -1000

-1500 -1000

1500

1000

500

0

-500

-1000

-1500

1500

1000

500

0

-500

-1000

-1500

-8

-12

-16

2

0

-4

12

10

8

6

4

-20

-24

-28

-32

-36

-40

20

18

16

14

(b)

Surface [d-50-45]

TIME 10Ma

-1500 -1000 -500 0

-1500 -1000 -500 0

500

500

-1

-6

(e)

-11

-16

-21

-26

-31

-36

-41

-46

-51

-56

-61

-66

-71

-76

-81

-86

-91

1500

1000

500

0

-500

-1000

-96

-101

-106

-1500

WATER (amount) [d-50-45]

TIME 10Ma

-1500 -1000

-1500 -1000

1000

1000

1500

1500

1500

1000

500

0

-500

-1000

-1500

0.070

0.065

0.060

0.055

0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0.000

0.100

0.095

0.090

0.085

0.080

0.075

6000

5500

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0

-500

-1000

10000

9500

9000

8500

8000

7500

7000

6500

(c)

1500

1000

500

0

-500

-1000

-1500

VELOCITY (mm/a) [d-50-45]

TIME 10Ma

-1500 -1000

-1500 -1000

(f)

[d-50-45]

[]

1500

1000

500

0

-500

-1000

-1500

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

2000

1900

1800

1700

1600

1500

1400

-20

-25

-30

-35

-40

-45

0

-5

-10

-15

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

Fig. 15.

The ice sheet configuration for SMB 3.0 scenario for +50 ° C warming with the low geothermal heat flux of 45 mW/m 2 , a threshold state for 5% basal melting. (a) The

SMB with peak accumulation of 18 mm/a and sublimation rate of 33 mm/a. (b) 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.

MOLA topography (

52

Smith et al., 2001

5. Ice sheet modeling results

) shown in

J.L. Fastook et al. / Icarus 219 (2012) 25–40

5.1. The bottom-up induced basal melting case 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. 3

f is the mean annual surface temperature field taken directly from

Madeleine et al. (2009) . Temperatures

range from 95 ° C at 60 ° S to as low at 110 ° C at the pole. It is to this temperature field that we will apply uniform ‘‘offsets’’ to simulate warmer climates.

4.2. Noachian–Hesperian topography

The modeled ice sheet is reconstructed on the bed taken from

Fig. 4

A total of 275 model runs were produced (five climate scenarios, SMB 0.5, 1.0, 2.0, 3.0 and 4.0; five geothermal heat fluxes,

45, 50, 55, 60, and 65 mW/m 2 ; and eleven temperature offsets, 0 to +50 ° C in 5 ° C intervals, each added to the temperature field of

Fig. 3 f). Each scenario was run for 10 Ma, a time sufficient for the

ice sheets to achieve basic equilibrium configurations.

. We use a

52 checkerboard of Finite Element quadrilaterals distorted into a circular grid extending from the pole to 60 ° S that completely

encompasses the DAF ( Fig. 1 ). Resolution in the distorted checker-

board is non-uniform but is nominally 30 km. To avoid complications associated with the present ice sheet topography, we truncate elevations at 3000 m, shown in

Fig. 4

by a solid white line.

35

Using mean annual south polar temperatures typical of Amazonian climate simulations (a 0 remain cold-based.

Figs. 5–9

° C offset or warming) from

Fig. 3 f

(ranging from 95 to 110 ° C,) and the range of Noachian–Hesperian heat fluxes (45–65 mW/m 2 ) described above, south polar ice sheets 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 0.5,

1.0, 2.0, 3.0, and 4.0 from

Fig. 3 a–e) for both 45 (a and b) and 65

(c and d) mW/m 2 . Surface elevation contours are shown at 500 m intervals. Even with the higher geothermal flux, all but a few deep holes (for instance, Schmidt Crater at grid-coordinates 1000,

+200 km in

Fig. 6

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

(a)

1500

1000

500

0

-500

-1000

-1500

1500

1000

500

0

-500

-1000

-1500

Mass Balance (mm/a) [d-20-65]

TIME 10Ma

-1500 -1000

(d)

-1500 -1000 -500 0 500 1000 1500

TEMPERATURE (degree C) [d-20-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

1500

1000

500

0

-500

-1000

-1500

-4

-8

-12

-16

-20

4

2

0

-24

-28

-32

-36

-40

20

18

16

14

12

10

8

6

(b) Surface [d-20-65]

TIME 10Ma

-1500 -1000

-1500 -1000

-31

-36

-41

-46

-51

-56

-61

-66

-71

-11

-1

-6

(e)

-16

-21

-26

1500

1000

500

0

-76

-81

-500

-86

-91

-1000

-96

-101 -1500

-106

WATER (amount) [d-20-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

0.100

0.095

0.090

0.085

0.080

0.075

0.070

0.065

0.060

0.055

0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0.000

(f)

10000

9500

9000

8500

8000

7500

7000

6500

6000

5500

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0

-500

-1000

(c)

1500

1000

500

0

-500

-1000

-1500

VELOCITY (mm/a) [d-20-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

[d-20-65]

[]

1500

1000

500

0

-500

-1000

-1500

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

2000

1900

1800

1700

1600

1500

1400

1300

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110 0

Fig. 16.

The ice sheet configuration for SMB 3.0 scenario for +20 ° C warming with the high geothermal heat flux of 65 mW/m

2

, a threshold state for 5% basal melting. (a–f)

As in

Fig. 15

.

36 J.L. Fastook et al. / Icarus 219 (2012) 25–40

-500

-1000

-1500

1500

1000

500

0

(a)

Mass Balance (mm/a) [d-25-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

-500

-1000

-1500

1500

1000

500

0

10

8

6

4

2

0

-4

-8

-12

-16

-20

-24

-28

-32

-36

-40

20

18

16

14

12

(b)

Surface [d-25-65]

TIME 10Ma

-1500 -1000

-1500 -1000

10000

9500

9000

8500

8000

7500

7000

6500

6000

5500

5000

1500

1000

500

0

-500

-1000

4500

4000

3500

3000

2500

2000

(c)

1500

1000

500

0

-500

-1000

-1500

VELOCITY (mm/a) [d-25-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

2000

1900

1800

1700

1600

1500

1400

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

(d)

TEMPERATURE (degree C) [d-25-65]

TIME 10Ma

1500

1000

500

0

-500

-1000

-1500

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-11

-1

-6

(e)

-16

-21

-26

-31

-36

1500

-41

-46

-51

-56

1000

500

-61

-66 0

-71

-76

-500

-81

-86

-91

-1000

-96

-101 -1500

-106

WATER (amount) [d-25-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

0.065

0.060

0.055

0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0.000

0.100

0.095

0.090

0.085

0.080

0.075

0.070

(f)

[d-25-65]

[]

Fig. 17.

The ice sheet configuration for SMB 3.0 scenario for +25 ° C warming with the high geothermal heat flux of 65 mW/m

2

, 7% basal melting. (a–f) As in

Fig. 15 .

accumulation rate raised only to the 1/8th power. Hence a doubling of the accumulation rate should only yield approximately a

10% thicker ice sheet. This can be seen as one moves from the low-SMB case in

5.2. The top-down induced basal melting case cases

(

Fig. 8 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 1000 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.

Fig. 5

(0.5 times the base) to the high-SMB cases in

Figs. 7–9

(2.0, 3.0, and 4.0 times the base).

Also worth noting is the contrast between the 45 mW/m 2

(

Fig. 8 a and b) and the higher geothermal flux 65 mW/m

2 cases

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. 10–14 . In each figure, panel (a)

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. 3 f) along the horizontal axis, and geothermal heat

flux along the vertical. Also shown in panel (b) of each figure are vertical transects through the companion panel (a) 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. 10 , corresponding to the lowest SMB

0.5 scenario (peak accumulations of 3 mm/a and maximum sublimation of 5 mm/a) shows no significant melting unless the climate is warmed by

50 ° C and the geothermal heat flux increased to 53 mW/m 2 . Alternatively, one achieves melting with 40 ° C warming by raising the geothermal flux to 65 mW/m 2 . As one progresses through the climate scenarios from lower mass throughput (SMB 0.5) to higher

(SMB 4.0), the onset of significant melting (5%) moves to lower temperatures and smaller geothermal fluxes. For the SMB 1.0 scenario (

Fig. 11

), the smallest geothermal heat flux that reaches the

5% threshold within our modeled temperature range is 49 mW/ m 2 at 50 ° C warming, and the lowest warming at the upper range of geothermal heats is 35 ° C.

Figs. 12–14

for SMB 2.0, 3.0, and 4.0

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 4.0 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 16 ° 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

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

J.L. Fastook et al. / Icarus 219 (2012) 25–40

(a) Mass Balance (mm/a) [d-50-50]

TIME 10Ma

-1500 -1000

-500

-1000

-1500

1500

1000

500

0

-1500 -1000 -500 0 500 1000 1500

-500

-1000

-1500

1500

1000

500

0

10

8

6

4

2

0

-4

-8

-12

-16

-20

-24

-28

-32

-36

-40

20

18

16

14

12

(b) Surface [d-50-50]

TIME 10Ma

-1500 -1000

-1500 -1000

10000

9500

9000

8500

8000

7500

7000

6500

6000

5500

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0

-500

-1000

(c)

1500

1000

500

0

-500

-1000

-1500

VELOCITY (mm/a) [d-50-50]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

2000

1900

1800

1700

1600

1500

1400

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

37

(d)

TEMPERATURE (degree C) [d-50-50]

TIME 10Ma

-1500 -1000 -500 0 500 1000 1500

-36

-41

-46

-51

-56

-61

-66

-71

-11

-1

-6

(e)

-16

-21

-26

-31 1500

1000

500

0

-76

-81

-500

-86

-91

-1000

-96

-101 -1500

-106

WATER (amount) [d-50-50]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

0.065

0.060

0.055

0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0.000

0.100

0.095

0.090

0.085

0.080

0.075

0.070

(f)

[d-50-50]

[]

1500

1000

500

0

-500

-1000

-1500

-1500 -1000

1500

1000

500

0

-500

-1000

-1500

0

-5

-10

-15

-20

-25

-30

-35

-40

-45

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

Fig. 18.

The ice sheet configuration for SMB 3.0 scenario for +50 ° C warming with the medium geothermal heat flux of 50 mW/m

2

, 9% basal melting. (a–f) As in

Fig. 15

.

the same level of basal melting, a consequence of reduced shear heating.

Figs. 15 and 16

show two of these ice sheet configurations that just exceeded our 5% threshold, both for the SMB 3.0 scenario

(18 mm/a peak accumulation, 33 mm/a maximum sublimation).

Fig. 15

shows a low geothermal heat flux case (45 mW/m

2

) that requires a full 50 ° C atmospheric surface temperature warming in order to achieve our 5% threshold for significant melting. Shown in this figure are (a) the SMB pattern, (b) 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. 16

shows the same (a–f) for the high geothermal heat flux case

(65 mW/m 2 ), but here only +20 ° 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

700 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 16

are of threshold melting cases that just exceeded an arbitrary 5% melted bed criteria (5% and 6% 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 3.0 scenario with a warming of +25 ° C and a high geothermal heat flux of 65 mW/m 2 . This is a relatively cold ice sheet and so is thicker. Melted basal conditions occur at the same positions as in

Figs. 15 and 16

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. 18

is also for the SMB 3.0 scenario, now for +50 ° 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 2000 mm/a in the regions of fastest flow. Finally,

Fig. 19

, again for the SMB 3.0 scenario, shows the ice sheet configuration for a slightly smaller warming of +40 ° C with a high geothermal heat flux of 65 mW/m 2 . This is the thinnest of the ice sheet configurations presented here. A summary of the ice sheet configurations shown in

Figs. 15–19

is presented in

Table 2

. Of these,

Fig. 18

showing SMB 3.0 with +50 ° C and 50 mW/m 2 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, 2001

).

Fig. 20 , the basal temperatures from

the case shown in

Fig. 18

, 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

38 J.L. Fastook et al. / Icarus 219 (2012) 25–40

-500

-1000

-1500

1500

1000

500

0

(a) Mass Balance (mm/a) [d-40-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

-500

-1000

-1500

1500

1000

500

0

10

8

6

4

2

0

-4

-8

-12

-16

-20

-24

-28

-32

-36

-40

20

18

16

14

12

(b) Surface [d-40-65]

TIME 10Ma

-1500 -1000

-1500 -1000

10000

9500

9000

8500

8000

7500

7000

6500

6000

5500

5000

4500

4000

3500

3000

2500

2000

1500

1000

500

0

-500

-1000

(c)

1500

1000

500

0

-500

-1000

-1500

VELOCITY (mm/a) [d-40-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

2000

1900

1800

1700

1600

1500

1400

1300

1200

1100

1000

900

800

700

600

500

400

300

200

100

0

(d)

1500

1000

500

0

-500

-1000

-1500

TEMPERATURE (degree C) [d-40-65]

TIME 10Ma

-1500 -1000

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1 (e)

-46

-51

-56

-61

-66

-71

-76

-81

-6

-11

-16

-21

-26

-31

-36

-41

1500

1000

500

0

-500

WATER (amount) [d-40-65]

TIME 10Ma

-1500 -1000

-86

-91

-1000

-96

-101 -1500

-106

-1500 -1000 -500 0 500 1000 1500

1500

1000

500

0

-500

-1000

-1500

0.100

0.095

0.090

0.085

0.080

0.075

0.070

0.065

0.060

0.055

0.050

0.045

0.040

0.035

0.030

0.025

0.020

0.015

0.010

0.005

0.000

(f)

[d-40-65]

[]

-20

-25

-30

-35

-40

-45

0

-5

-10

-15

-50

-55

-60

-65

-70

-75

-80

-85

-90

-95

-100

-105

-110

Fig. 19.

The ice sheet configuration for SMB 3.0 scenario for +40 ° C warming with the high geothermal heat flux of 65 mW/m 2 , 11% basal melting. (a–f) As in

Fig. 15

.

Table 2

Summary of ice sheet configurations shown in

Figs. 15–19 .

Figure SMB

15

16

17

18

19

3.0

3.0

3.0

3.0

3.0

Temperature warming (+ ° C)

50

20

25

50

40

Geothermal

(mW/m

2

)

45

65

65

50

65

Melted %

7

9

5

6

11

Average thickness (m)

2215

2961

2669

2135

1936

Volume

(M km

3

)

5.76

7.52

6.79

5.51

5.41

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, 65 mW/ m 2 , the warming required to produce significant basal melting is

+40 ° C for the low throughput case (SMB 0.5) and +20 ° C for the high throughput case (SMB 4.0). Note that this degree of warming would increase maximum temperature for the region to between

70 to 55 ° C, still sufficiently cold that no surface melting would occur. At low heat fluxes, 45 mW/m 2 , more than +50 ° C warming (a maximum temperature for the region of 45 ° C) is necessary to bring the bed to the melting point, even in the highest SMB case

( 4.0), 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, 2001; Kress et al., 2010 ). In

all cases the surface temperatures in the circumpolar regions are still considerably below 0 ° C, and thus independent melting of surface ice is not likely to occur, consistent with geologic observations

( Head and Pratt, 2001 ). GCM results for a suite of obliquities show

similar polar temperature warming (+25 to +50 ° C) as one moves from the current 23 ° obliquity to the extreme of 55 ° predicted by

Laskar et al. (2004)

(see for example

Fig. 6

of

Haberle et al.,

2003 ). Excursions to such extreme obliquities are relatively brief

( 100 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.

J.L. Fastook et al. / Icarus 219 (2012) 25–40 39

1500

1000

-1000

-1500

TEMPERATURE (degree C) [d-50-50]

TIME 10Ma

-1500 -1000 1000 1500

1500

1000

500

0

-500

-1000

-1500

-1

-6

-11

-16

-21

-26

-31

-36

-41

-46

-76

-81

-86

-91

-96

-101

-106

-51

-56

-61

-66

-71

-1500 -1000 1000 1500

Fig. 20.

Basal temperatures for SMB 3.0, +50 ° C, 50 mW/m

2 case of

Fig. 18

, with overlay showing agreement with the identified eskers shown in

Fig. 1

, adjacent to Joly Crater in the center of the DAF.

6. Discussion and conclusions

We show that under mean annual south polar atmospheric temperatures ( 100 ° C) simulated in typical Amazonian climate experiments and estimated Noachian–Hesperian heat fluxes

(45–65 mW/m 2 ), 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 ( 100 ° C) to the range of 50 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 50 to 75 ° C still imply lower latitude mean annual temperatures generally below the melting point of water (

Forget et al., 2004, 2010 ). 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 melt-

ing point of water ( Forget et al., 2004, 2010

). 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, 2007 ), 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, 2008a,b; Marchant and Head, 2007

). 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., 2009. An analysis of sinuous ridges in the southern Argyre

Planitia, Mars using HiRISE and CTX images and MOLA data. J. Geophys. Res.

114, E09003. doi: 10.1029/2008JE003244.

Boynton, W.V. et al., 2002. Distribution of hydrogen in the near surface of Mars:

Evidence for subsurface ice deposits. Science 297 (5578), 81–85.

Carr, M.H., 1996. Water on Mars. Oxford University Press, New York, NY.

Craddock, R.A., Howard, A.D., 2002. The case for rainfall on a warm, wet early Mars.

J. Geophys. Res. 107 (5111). doi: 10.1029/2001JE001505.

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., 1993. The finite-element method for solving conservation equations in glaciology. Comput. Sci. Eng. 1 (1), 55–67.

Fastook, J.L., Head, J.W., Marchant, D.R., Shean, D.E., 2004. Ice sheet modeling:

Terrestrial background and application to Arsia Mons lobate deposit, Mars.

Lunar Planet. Sci. XXXV. Abstract #1352.

40 J.L. Fastook et al. / Icarus 219 (2012) 25–40

Fastook, J.L., Head, J.W., Marchant, D.R., Shean, D.E., 2005. Ice sheet modeling: Mass balance relationships for map-plane ice sheet reconstruction: Applications to

Tharsis Montes glaciation. Lunar Planet. Sci. XXXVI. Abstract #1212.

Fastook, J.L., Shean, D.E., Head, J.W., Marchant, D.R., 2006. Ice sheet modeling during high-obliquity climates on Mars: Application to Tharsis Montes tropical mountain glaciation. Lunar Planet. Sci. XXXVII. Abstract #1794.

Fastook, J.L., Head, J.W., Marchant, D.R., 2008a. Dichotomy boundary glaciation models: Implications for timing and glacial processes. Lunar Planet. Sci. XXXIX.

Abstract #1109.

Fastook, J.L., Head, J.W., Marchant, D.R., Forget, F., 2008b. Tropical mountain glaciers on Mars: Altitude-dependence of ice accumulation, accumulation conditions, formation times, glacier dynamics, and implications for planetary spin-axis/ orbital history. Icarus 198, 305–317.

Forget, F. et al., 1999. Improved general circulation models of the martian atmosphere from the surface to above 80 km. J. Geophys. Res. 104 (E10),

24155–24176.

Forget, F., Haberle, R.M., Montmessin, F., Cha, S., Marcq, E., Schaeffer, J., 2004. 3D

Simulations of the Early Mars Climate with a General Circulation Model. 1st

General Assembly of the European Geophysical Union (Nice, France).

Forget, F., Haberle, R.M., Montmessin, F., Levrard, B., Head, J.W., 2006. Formation of glaciers on Mars by atmospheric precipitation at high obliquity. Science 311

(5759), 368–371.

Forget, F. et al., 2010. 3D modeling of the early martian climate and water cycle.

Bull. Am. Astron. Soc. 42 (4).

Ghatan, G.J., Head, J.W., 2002. Candidate subglacial volcanoes in the south polar region of Mars: Morphology, morphometry, and eruption conditions. J.

Geophys. Res. 107 (E7). doi: 10.1029/2001JE001519.

Ghatan, G.J., Head, J.W., 2004. Regional drainage of meltwater beneath a Hesperianaged south circumpolar ice sheet on Mars. J. Geophys. Res. 109 (E07006).

doi: 10.1029/2003JE002196.

Ghatan, G.J., Head, J.W., Pratt, S., 2003. Cavi Angusti, Mars: Characterization and assessment of possible formation mechanisms. J. Geophys. Res. 108 (E5).

doi: 10.1029/2002JE001972.

Haberle, R.M., Murphy, J.R., Schaeffer, J., 2003. Orbital change experiments with a

Mars general circulation model. Icarus 161, 66–89.

Head, J.W., Marchant, D.R., 2003. Cold-based mountain glaciers on Mars: Western

Arsia Mons. Geology 31 (7), 641–644.

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., Carr, M.H., Russell, P.S., Fassett, C.I., 2003. Martian Hydrology: The Late

Noachian Hydrologic Cycle 7. Vernadsky-Brown Microsymposium 38, MS032.

Head, J.W., Marchant, D.R., Dickson, J.L., Kress, A.M., Baker, D.M., 2010. Northern mid-latitude glaciation in the Late Amazonian period of Mars: Criteria for the recognition of debris-covered glacier and valley glacier landsystem deposits.

Earth Planet. Sci. Lett. 294 (3–4), 306–320.

Johnson, S.S., Mischna, M.A., Grove, T.L., Zuber, M.T., 2008. Sulfur-induced greenhouse warming on early Mars. J. Geophys. Res. 113 (E08005).

doi: 10.1029/2007JE002962.

Kadish, S.J., Head, J.W., Parsons, R.L., Marchant, D.R., 2008. The Ascraeus Mons fanshaped deposit: Volcano ice interactions and the climatic implications of coldbased tropical mountain glaciation. Icarus 197, 84–109.

Kargel, J.S., 2004. Mars: A Warmer Wetter Planet. Springer (Praxis), Berlin,

Heidelberg, New York.

Kargel, J.S., Strom, R.G., 1992. Ancient glaciation on Mars. Geology 20, 3–7.

Kress, A., Head, J.W., Fassett, C.I., 2010. Ridges in the Dorsa Argentea Formation:

Geomorphology and age assessment from buffered crater counting. Lunar

Planet. Sci. XXXXI. Abstract #2355.

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, 343–364.

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 (2), 390–405.

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, 187–222. doi: 10.1016/j.icarus.2007.06.018.

Marion, G.M., Catling, D.C., Claire, M., Zahnle, K.J., 2010. Modeling aqueous perchlorate chemistries with application to Mars. Icarus 207 (2), 675–685.

McGovern, P.J., Smith, J.R., Morgan, J.K., Bulmer, M.H., 2004. Olympus Mons aureole deposits: New evidence for a flank failure origin. J. Geophys. Res. 109 (E08008).

doi: 10.1029/2004JE002258.

Mitrofanov, I. et al., 2002. Maps of subsurface hydrogen from the high energy neutron detector, Mars Odyssey. Science 297 (5578), 78–81.

Montmessin, F., Forget, F., Rannou, P., Cabane, M., Haberle, R.M., 2004. Origin and role of water ice clouds in the martian water cycle as inferred from a general circulation model. J. Geophys. Res. (Planets) 109, E10004.

Montmessin, F., Haberle, R.M., Forget, F., Langevin, Y., Clancy, R.T., Bibring, J.-P.,

2007. On the origin of perennial water ice at the South Pole of Mars: A precession-controlled mechanism? J. Geophys. Res. (Planets) 112, 8.

Phillips, R.J. et al., 2008. Mars north polar deposits: Stratigraphy, age, and geodynamical response. Science 320, 1182–1185.

Plaut, J.J., Kahn, R., Guinness, E.A., Arvidson, R.E., 1988. Accumulation of sedimentary debris in the south polar region of Mars and implications for climate history. Icarus 76 (2), 357–377.

Richardson, M.I., Wilson, R.J., 2002. Investigation of the nature and stability of the martian seasonal water cycle with a general circulation model. J. Geophys. Res.

107 (E55031). doi: 10.1029/2001JE001536.

Rothlisberger, H., 1972. Water pressure in intra- and subglacial channels. J. Glaciol.

11 (62), 177–203.

Shean, D.E., Head, J.W., Marchant, D.R., 2005a. Origin and evolution of a cold-based tropical mountain glacier on Mars: The Pavonis Mons fan-shaped deposit. J.

Geophys. Res. 110 (E05001). doi: 10.1029/2004JE002360.

Shean, D.E., Head, J.W., Marchant, D.R., 2005b. Debris-covered glaciers within the

Arsia Mons fan-shaped deposit: Implications for glaciation, deglaciation and the origin of lineated valley fill. Lunar Planet. Sci. XXXVI. Abstract #1339.

Smith, D.E. et al., 2001. Mars Orbiter Laser Altimeter: Experiment summary after the first year of global mapping of Mars. J. Geophys. Res. 106 (E10), 23689–23722.

Solomon, S.C. et al., 2005. New perspectives on ancient Mars. Science 307, 1214–

1220.

Spiga, A., 2011. Elements of comparison between martian and terrestrial mesoscale meteorological phenomena: Katabatic winds and boundary layer convection.

Planet. Space Sci. 59, 915–922.

Tanaka, K.L., Kolb, E.J., 2001. Geologic history of the polar regions of Mars based on

Mars Global Surveyor data: I. Noachian and Hesperian periods. Icarus 154 (1),

3–21.

Wordsworth, R.D., Forget, F., Millour, E., Madeleine, J.-B., Charnay, B., Haberle, R.,

2011. Modelling the Past Mars Climate and Water Cycle with a Thicker CO

2

Atmosphere. Fourth International Workshop on the Mars Atmosphere:

Modelling and Observations, Paris, France.

Download