Frank Pattyn @ ULB

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Dynamics of subglacial lakes in Antarctica

Ice flow over subglacial lakes

Radio-echo-sounding in East Antarctica has revealed the existence of numerous subglacial lakes. The largest one is Lake Vostok (14 000 km²), near the homonymous Russian Station and drilling site. Lake Vostok is associated with a prominent morphological surface feature within the Antarctic ice sheet, as the ice-sheet surface is relatively flat and featureless, consistent with the surface of an ice shelf. Other distinct features of the ice flow over Lake Vostok are revealed by the surface velocity field determined from radar interferometry: (i) an increase in ice velocity over the lake (extension flow) followed by a decrease in ice speed passed the lake (compression flow), and (ii) a slight turning of the ice flow over the lake, most visible over the central part of Lake Vostok where surface slopes are small. Here, we present for the first time a set of comprehensive experiments of ice flow over a subglacial lake using a numerical higher-order ice sheet model.

The experiment below consists of simulating the ice flow over a subglacial lake with the 3D higher-order model by considering a stress-free basal surface (lubricated spot) stretching over two grid points and situated approximately 100 km from the ice divide. The orientation of the so-called subglacial lake with respect to the major ice flow is similar to the situation of Lake Vostok. Results indicate that the surface velocity over the subglacial lake increases to reach a maximum near the center of the lake, and decreases again at the downstream edge of the lake (Figure 1a). Moreover, the ice-sheet flow field seems only locally influenced by the presence of the lake, as the velocities downstream from the lake are similar to those if no lake were present (Figure 2). Also the turning of the ice flow is visible in this experiment, as the surface slope of the lake depends on the orientation of the lake towards the surrounding ice flow. The maximum slope is therefore found in the longitudinal direction of the lake.

A flattening of the surface topography above the lake is observed in Figures 1b and 2, conform observations in Antarctica, which is associated with a low basal shear stress (Figure1f). The zone of influence of other stress components (longitudinal and transverse stresses, Figures 1c, d, e) is much larger than the effective area occupied by the lake. These stress components show a distinct `butterfly' pattern that extents for more than 100 km in either horizontal direction.

High-resolution experiment

The above experiment is rather coarse in model resolution. Therefore a similar experiment was carried out on a much more detailed scale, and by considering a continuous change in basal friction. A uniform slab of ice of 80 by 80 km in size and H = 1600m thick, lying on gently sloping bed (a = 0.115º) is considered. The basal boundary condition is written as t_b v_b = b², where t_b is the basal drag, v_b is the basal velocity vector and b² is a friction coefficient. For large b², v_b is small or zero (ice is frozen to the bedrock); for b² = 0, ice experiences no friction at the base (slippery spot) as is the case for an ice shelf. In the experiment below, the basal friction coefficient b² is defined by a sine function ranging between 0 and 20 kPa a/m (Figure 3d). Periodic lateral boundary conditions were applied and the model was run to steady state. The effect of a slippery spot on the ice slab is shown by a local increase in ice velocity where friction is low (Figure 3c) as well as a flattening of the ice surface above this spot (Figure 3a). This flattening is due to a thinning of the ice upstream from the slippery spot and thickening of the ice downstream (Figure 3b) and is a direct result of the lack of basal shear across the slippery spot.

Ice flow over subglacial Lake Vostok, Antarctica

Lake Vostok is associated with a prominent morphological surface feature within the Antarctic ice sheet. The ice-sheet surface above the lake is rather flat and featureless, consistent with the surface of an ice shelf. Ice flows over the lake in a general west-east direction (Figure 4). Once over the lake the ice flow in the south is diverted towards the southeast (Kapitsa and others, 1996), a feature that is confirmed from an analysis of internal radar reflection layers (Bell and others, 2002). Moreover, this along-lake flow component seems persistent since the Last Glacial Maximum (Bell and others, 2002). On the contrary, velocity vectors derived from interferometry show a different direction, i.e. more towards the east (Kwok and others, 2000). The northern part of the lake is largely unexplored and velocity measurements are lacking (Figure 4).

Although the ice surface above the lake is relatively flat, an along-lake north-south slope is prominent, tilting 60m over a horizontal distance of more than 250 km. Over the lake, the ice is thicker in the north (up to 4300m) and thins to 3700m in the south (Studinger and others, 2003). Lake Vostok has an ice-water interface sloping at eleven times the ice surface gradient (but in the opposite direction), which indicates that the overlying ice is in hydrostatic equilibrium (Siegert and others, 2001). According to (Souchez and others, 2004), the inclined ice-lake interface should be considered as the result of a dynamic equilibrium: melting in the north of the lake and freezing in the south are conducive in the long run to a horizontal interface but, in the mean time accreted ice is exported out of the lake by glacier movement, maintaining the inclination of the surface. This refreezing is due to a well developed water circulation in the lake (Souchez and others, 2000; Wuest and Carmack, 2000; Williams, 2001; Siegert and others, 2001; Mayer and others, 2003). Lake Vostok is thus quite unique in an ice-dynamical way, encompassing a variety of ice-deformational features in a nutshell.

A comprehensive understanding of the ice flow across Lake Vostok demands the use of a so-called higher-order ice-sheet model, i.e. a model that besides deformation due to vertical shearing, takes into account normal stress components as well. Mayer and Siegert (2000) investigated the ice flow along a longitudinal transect with a 2D higher-order flow line model, but these experiments were carried out in a diagnostic fashion (ice-sheet geometry was kept fixed). Here, we investigated the ice flow across Lake Vostok using a dynamical 3D thermomechanical higher-order ice-sheet model, which shows - for the first time - the major ice-dynamical features of this area in a prognostic fashion. The purpose of the experiments is to determine the ice flow field across the whole lake and to identify the processes responsible for the flat surface topography, the along-lake slope component, the ice flow turning across the lake, and Lake Vostok's influence on the regional dynamics of the East-Antarctic ice sheet.

Model description

Brief overview of results

A first series of experiments are diagnostic, i.e. the velocity field is calculated based on the present observed ice-sheet geometry that was kept fixed. This involves a `no lake' (DNL) and a `lake' (DLE) experiment, where for the latter a stress-free basal surface was considered within the lake boundaries (b²_lake = 0). These experiments are also isothermal. For large ice sheets, however, A(T) shows a clear temperature dependence and might vary over several orders of magnitude. Coupling the temperature to the ice flow field in the diagnostic mode resulted in numerical instabilities since the ice sheet geometry is not relaxed and steep surface gradients lead to large horizontal and vertical temperature gradients, especially near the coast and the Transantarctic Mountains. Although such a coupling influences the magnitude variations of the velocity field, it has less impact on the direction of the ice flow, which is the main issue of the diagnostic experiments. Temperature coupling is included in the next series of experiments.

The prognostic experiments are defined as follows: starting from the present-observed ice geometry, the model ran forward in time in a diagnostic fashion, i.e. by keeping the ice geometry fixed, until the temperature field attained a steady state (without coupling the temperature to ice dynamics). Subsequently, temperature was coupled to the ice dynamics and the surface topography was allowed to react (prognostic run). The model was thus run forward for another 10,000 years to reach a situation close to steady state. There is no explicit treatment of the lake/bed or the lake/ice interface, nor is there any treatment of water circulation. Our sensitivity analysis consists of three prognostic experiments, a `lake' experiment (LE), where the lake is determined as a stress-free spot or b<sup>2</sup><sub>lake</sub> = 0, a `no lake' experiment (NL) where b²_lake is determined by a basal sliding relationship, and a `lake' experiment with buoyancy (LBE). For the LE experiment, the ice/water interface was kept fixed in time and only the ice/air surface changed in time. In the LBE experiment, both ice/water and ice/air interfaces were altered to fulfill buoyancy. The prognostic experiments take between two and three days of calculation on a PC with a Pentium 4 -- 2.2 GHz processor (which is 50--200 times slower than a calculation according to the shallow-ice approximation).

Conclusions

For the first time, a dynamical 3D thermomechanical simulation of the ice flow across Lake Vostok is presented. The model results show that by treating the ice/lake interface as a stress-free surface (similar to an ice shelf), major ice-dynamical features such as the surface flattening and turning of the ice flow across the lake, are accurately reproduced, even though subglacial lake dynamics are not treated explicitly.

A relatively stable velocity pattern - with a local ice divide that crosses Lake Vostok - is obtained when taking into account buoyancy effects. This also assures an along-lake southward slope, maintaining the tilted ice/water interface. However, the tilted ice/water interface shows the tendency to level when the model is allowed to run on a longer time scale, which indicates that the lake water circulation plays a decisive role in balancing melting in the north and accretion in the south. Only when coupling a model of lake water circulation to the ice sheet model, a more comprehensive insight in these processes might be obtained.

According to the experiments, ice velocities are the highest in the northern sector of the lake. Lake Vostok can therefore be considered as the onset of an enhanced ice-flow feature, more precisely the onset of the Totten Glacier catchment.

On the origin of subglacial Lake Vostok, Antarctica

There is some debate on the origin of subglacial Lake Vostok and whether the water within the present subglacial lake system contains biota that survived the buildup of the Antarctic ice sheet. One theory suggests that Lake Vostok existed as a preglacial lake before glaciation of the continent at around 15 Ma ago, survived the subsequent period of ice sheet growth, and remained stable beneath the thick ice cover to the present day (Duxbury and others, 2001). Another hypothesis challenges this view by stating that the early phase of build-up would have resulted in ice grounding throughout the trough which the lake now occupies (Siegert, 2004).

According to Duxbury and others (2001) the lake could have survived the growth of the ice sheet as long as the preglacial lake was more than 53m deep. In their model, subglacial Lake Vostok is considered as an approximate closed system. However, if Lake Vostok existed as a preglacial lake, the closure of the Lake Vostok system must have happened between the initiation of the ice sheet and the establishment of a stable ice cover in East Antarctica (Siegert, 2004). Therefore, the dynamic evolution of the ice sheet and its interaction with the preglacial lake should be accounted for in determining whether subglacial Lake Vostok is a direct remnant of a preglacial surficial lake.

Siegert (2004) demonstrates that the preglacial lake could not have survived the buildup of the Antarctic ice sheet: water flow beneath an ice mass is controlled by the hydraulic potential gradient. If the magnitude of surface slope is larger than one tenth the basal slope, water can be driven out of a topographic depression and flow `up hill'. Two ice-sheet model studies (Huybrechts, 1993; DeConto and Pollard, 2003) show that during the inception and growth of the Antarctic ice sheet, the ice sheet margin was situated close to Lake Vostok. The steep margin of the ice sheet across Lake Vostok implies high subglacial hydraulic potential gradients, which led Siegert (2004) to conclude that basal water is evacuated as the steep ice sheet margin progresses over the lake. However, none of the above models take into account the interaction of the ice sheet with the underlying lake, whether it be a preglacial or a subglacial lake, and only consider an ice sheet more or less frozen to the underlying bedrock.

Below I present a physical mechanism that allows for subglacial Lake Vostok to survive the buildup of the ice sheet, by taking into account the interaction of the ice sheet with the preglacial / subglacial lake. This hypothesis is supported by the fact that the surface of a preglacial lake as well as the interface between a subglacial lake and the overriding ice sheet can be regarded as a slippery spot. Ice flow over a slippery spot results in a surface flattening, hence implies lower subglacial hydraulic potential gradients, due to their dependence on surface slope. This would prevent water to be driven out the subglacial trench. To verify this hypothesis the following dynamic experiment was carried out. On a rectangular domain of 1500 by 1500 km, a small steady-state ice cap was established by defining the surface mass balance distribution in such a way that the margin of the ice cap lies near the preglacial lake (Fig. 10).

Running the model for t = 0 to 10000a, gradually increases the size of the accumulation area in time so that the model ice cap overrides the preglacial lake (defined as a slippery spot with b²_lake = 0). Once overridden, it becomes a subglacial lake (Fig. 10). The same experiment was repeated without the presence of a lake.

The `dynamic lake' experiment shows that when the ice sheet margin crosses the lake, the air/ice surface interface remains relatively flat as compared to the situation in which a lake is not considered (Fig. 11). The surface of the ice sheet across the lake never exceeds slopes higher than 0.4 deg, while without ice/lake interaction, surface slopes exceed 1.5 deg (Fig. 12). It is therefore likely that subglacial water is not driven out of the system, as hydraulic potential gradients remain too low. Surface slopes across the lake would even become lower if a subglacial depression (trough) was considered in the model. Furthermore, increasing the lake size (at present the model lake size is 25 by 25 km) would have a similar effect.

If Lake Vostok existed as a preglacial lake prior to 15 Ma ago, it could have survived subsequent mid-Miocene glaciation, and remained stable beneath the thick ice cover to the present day, as stipulated by Duxbury and others (2001). Model simulations demonstrate that due to the interaction of the ice sheet with the lake surface (treated as a slippery spot), ice-sheet surface slopes near the edge of the ice sheet remain low, so that subglacial water is not driven out of the subglacial trough due to enhanced hydraulic potential gradients. Survival of the lake after initiation of the Antarctic ice sheet implies that possible microorganisms and their remnants within the water can be older than 5-30 Ma.

References

Pattyn, F. (2003) A new three-dimensional higher-order thermomechanical ice sheet model: basic sensitivity, ice stream development and ice flow across subglacial lakes. Journal of Geophysical Research (Solid Earth), 108 (B8), 2382, doi:10.1029/2002JB002329. (PDF)

Pattyn, F., B. De Smedt and R. Souchez (2004) Influence of subglacial Lake Vostok on the regional ice dynamics of the Antarctic ice sheet: a model study. Journal of Glaciology 50 (171): 583-589. (PDF).

Pattyn F. (2004) Comment on the comment by M. J. Siegert on “A numerical model for an alternative origin of Lake Vostok and its exobiological implications for Mars” by N. S. Duxbury et al. Journal of Geophysical Research, 109 (E11004), doi:10.1029/2004JE002329. (PDF).

Pattyn, F. (2008) Investigating the stability of subglacial lakes with a full Stokes model. Journal of Glaciology. 54(185): 353-361. (doi:10.3189/002214308784886171) (PDF).