Modelling Esker Formation on Mars


 <p><strong>Introduction:</strong>&#160; Eskers are sinuous sedimentary ridges that are widespread across formerly glaciated landscapes on Earth. They form when sediment in subglacial tunnels is deposited by meltwater. Some sinuous ridges on Mars have been identified as eskers; whilst some are thought to have formed early in Mars&#8217; history beneath extensive ice sheets, smaller, younger systems associated with extant glaciers in Mars&#8217; mid latitudes have also been identified. Elevated geothermal heating and formation during periods with more extensive glaciation have been suggested as possible prerequisites for recent Martian esker deposition.</p><p>Here, we adapt a model of esker formation with g and other constants altered to Martian values, using it initially to investigate the impact of Martian conditions on subglacial tunnel systems, before investigating the effect of varying water discharge on esker deposition.</p><p><strong>Methods:</strong> To investigate the effect of these values on the operation of subglacial tunnel systems we first conduct a series of model experiments with steady water discharge, varying the assumed liquid density (r<sub>w</sub>) from 1000 kgm<sup>-3</sup> to 1980 kgm<sup>-3</sup> (the density of saturated perchlorate brine) and ice hardness (A) from 2.4x10<sup>-24</sup> Pa<sup>-3</sup>s<sup>-1</sup> to 5x10<sup>-27</sup> Pa<sup>-3</sup>s<sup>-1</sup> (a temperature range of 0&#176;C to -50&#176;C). We then investigate the impact of variable water discharge on esker formation to simulate very simply a possible release of meltwater from an assumed geothermal event beneath a Martian glacier or ice cap.</p><p><strong>Results and Discussion:</strong>&#160; A key aspect of model behaviour is the decrease in sediment carrying capacity towards the ice margin due to increased tunnel size as ice thins. Our results suggest that Martian parameters emphasise this effect, making deposition more likely over a greater length of the conduit. Lower gravity has the largest impact; it reduces the modeled closure rate of subglacial tunnels markedly as this varies with overburden stress (and hence g) cubed. Frictional heating from flowing water also drops, but much less sensitively. Thus, for a given discharge, the tunnels tend to be larger, leading to lower water pressure and a reduction in flow power. This effect is amplified for harder ice. Higher inferred fluid density raises the flow power, but by a smaller amount.</p><p>These effects are clearly seen in the variable discharge experiments. Sediment is deposited on the falling limb of the hydrograph, when the tunnels are larger than the equivalent steady-state water discharge would produce. Sediment deposition occurs much further upglacier from the glacier snout, and occurs earlier on the falling limb leading to longer periods in which deposition occurs.</p><p><strong>Conclusions:</strong> Our results suggest that esker formation within a subglacial meltwater tunnel would be&#160;more likely on Mars than Earth, primarily because subglacial tunnels tend to be larger for equivalent water discharges, with consequent lower water flow velocities. This allows sediment deposition over longer lengths of tunnel, and to greater depths, than for terrestrial systems. Future work will use measured bed topography of a mid-latitude esker to assess the impact of topography on deposition patterns and esker morphology, and we will expand the range of discharges and sediment supply regimes investigated.</p>



Introduction
Eskers are sinuous sedimentary ridges that are widespread across formerly glaciated landscapes on Earth (Figure 1), [e.g. 1]. They form when sediment in subglacial tunnels is deposited by meltwater, and are exposed when ice retreats.
Some sinuous ridges on Mars have been identified as eskers; some are thought to have formed early in MarsÕ history beneath more extensive ice sheets [e.g. 2], but smaller, younger systems ( Figure 2) associated with extant glaciers in MarsÕ mid latitudes have also been identified [3,4]. Elevated geothermal heating and formation during periods with more extensive glaciation have been suggested as possible prerequisites for esker deposition [3,4]. Numerical modeling [5, 6] also supports geothermal heating as a possible cause of the area of assumed liquid water beneath MarsÕ south polar ice cap [7].

Subglacial Hydrology and Esker Formation
The physics of water flow beneath glaciers is well understood and has been extensively modelled. Subglacial water can flow in several types of system: ! thin films of water ! poorly-linked subglacial cavities ! efficient subglacial tunnels Eskers form in tunnels, making them of most concern here. Subglacial tunnels exist in a dynamic balance between: ! ice deformation which tends to close them ! heat released by the flowing water melting tunnel walls tending to open them Tunnels are generally larger, and have lower water pressure where: ! water discharge is high ! ice is thin These conditions are typical near the ice margin. Two recent models [8,9] of esker formation on Earth find that sediment deposition in subglacial tunnels is most likely near the margin as lower water pressure and larger tunnel cross section lowers the sediment carrying capacity of water flow. Deposition also tends to occur during periods of decreasing water discharge as tunnels tend to close more slowly than discharge falls, leading to effectively Ôunder-fitÕ streams.

Results
A key aspect of model behaviour is the decrease in sediment carrying capacity towards the ice margin due to increased conduit size as ice thins [8,9]. Martian parameters emphasise this effect, with lower gravity having the largest impact ( Figure 3). Tunnel diameter increases, leading to a reduction in water pressure, velocity, and flow shear stress. Higher water density reduces these effects somewhat, and harder ice increases them. These effects should make deposition more likely over a greater length of the conduit.

Methods
Here, we adapt [9] with g and other constants adapted to Martian values. We use the model to investigate: a) the impact of Martian conditions on subglacial tunnel systems using a series of model experiments with constant water discharge (50 m 3 s -1 ) varying: i. assumed liquid density (ρ w ) from 1000 kgm -3 to 1980 kgm -3 (the density of saturated perchlorate brine) ii. ice hardness (A) from 2.4x10 -24 Pa -3 s -1 to 5x10 -27 Pa -3 s -1 (a temperature range of 0¡C to -50¡C) b) the impact of variable water discharge on esker formation by simulating very simply a possible release of meltwater from an assumed geothermal event beneath a Martian glacier or ice cap.
Our overall aim is to begin to estimate the water discharge which could have led to recent Martian esker formation. This could help constrain Martian geothermal heat flux and recent mid-latitude ice extent and thickness.

Results (continued)
This effect is borne out by the the variable discharge experiments. Figure 4 A,B (Earth g) show relatively rapid tunnel closure after peak discharge, with conduit enlargement confined to the distal ~ 8-10 km of the tunnel (as in Figure 3). Sedimentation is confined to the last ~ 2 km of the tunnel as water flow power stays high due to conduit closure even as discharge falls. By contrast, Figure 4 C,D (Mars g) shows much slower conduit closure after peak discharge, the conduit is enlarged over most of the model domain (and especially in the last ~ 10 km, as in Figure 3). Sedimentation occurs ~ 10 km upstream of the tunnel mouth as flow power is lower, and begins earlier due to the larger tunnel size.

Conclusions and Future Work
Our results suggest that esker formation within a subglacial meltwater tunnel would be more likely on Mars than Earth, primarily because subglacial tunnels tend to be larger for equivalent water discharges, with consequent lower water flow velocities. This allows sediment deposition over longer lengths of tunnel, and to greater mean depths, than for terrestrial systems.
Future work will use measured bed topography of a mid-latitude esker to assess the impact of topography on deposition patterns and esker morphology. We will also expand the range of discharge regimes investigated by adapting a model of Antarctic subglacial lake drainage [10] to simulate possible Martian subglacial lake drainage events driven by subglacial geothermal events of the type postulated as a possible cause of the inferred liquid beneath MarsÕ South Polar Ice Cap [7].