Over the past decade satellite observations have revealed that active subglacial lake systems are widespread under the Antarctic ice sheet, including the ice streams, yet we have insufficient understanding of the lake-drainage process to incorporate it into ice sheet models. Process models for drainage of ice-dammed lakes based on conventional “R-channels” incised into the base of the ice through melting are unable to reproduce the timing and magnitude of drainage from Antarctic subglacial lakes estimated from satellite altimetry given the low hydraulic gradients along which such lakes drain. We developed a process model in which channels are mechanically eroded into deformable subglacial sediment (till) instead (“T-channel”). When applied to the known lakes of the Whillans/Mercer system, the model successfully reproduced the key characteristics of estimated lake volume changes for the period 2003–2009. If our model is realistic, it implies that most active lakes are shallow and only exist in the presence of saturated sediment, explaining why they are difficult to detect with classical radar methods. It also implies that the lake-drainage process is sensitive to the composition and strength of the underlying till, suggesting that models could be improved with a realistic treatment of sediment – interfacial water exchange.
Since the initial observation of “large flat circular basins” on the ice surface of the ice by Russian pilots during
International Geophysical year (Robinson, 1964) and the inference of those basins as lakes beneath the ice sheet, there have been
over 300 subglacial lakes discovered throughout the continent using a variety of geophysical methods (Wright and Siegert,
2012). Until the mid 2000's radio echo sounding (RES) was the primary technique for identifying subglacial lakes (Carter et al.,
2007; Siegert et al., 2007), and this method confirmed that many of the anomalously flat features previously identified on the ice
surface resulted from the long term storage of free water at the ice sheet base, including Lake Vostok (Ridley et al., 1993),
which measures over 12 500
Since 2005, a variety of repeat satellite observations of the ice surface have revealed patterns of surface uplift and subsidence consistent with the filling and draining of subglacial water bodies (e.g. Gray et al., 2005; Wingham et al., 2006; Fricker et al., 2007). In contrast to “RES lakes”, most “active lakes” have been found beneath fast flowing ice streams and outlet glaciers (Fig. 1a and b). Many of the active lakes that have been surveyed with RES (e.g. Christianson et al., 2012; Siegert et al., 2013; Wright et al., 2014) lacked the characteristic basal reflections (hydraulic flatness, specularity, and brightness relative to surroundings; see Carter et al., 2007) traditionally used to distinguish subglacial lakes. These discrepancies appear to result from qualitative differences between active lakes and RES lakes. It is believed that active lakes might have a greater impact on ice dynamics, by their location under the fast-flowing ice streams and their ability to episodically hold back and then release large volumes of water into the subglacial environment. So far only two episodes of temporary ice acceleration correlating with subglacial lake drainage events have been reported, on Byrd Glacier (Stearns et al., 2008) and Crane Glacier (Scambos et al., 2011).
Critical to resolving the link between ice dynamics and lake activity is determination of the mechanism by which lake drainage occurs. While some ice sheet models (Johnson and Fastook, 2002; Goeller et al., 2013; Livingstone et al., 2013) have begun to incorporate primitive elements of subglacial lake dynamics, they still do not have a realistic treatment of observed lake drainage processes. R-channels have been hypothesized as a lake-drainage mechanism in Antarctica (e.g Wingham et al., 2006; Evatt et al., 2006; Carter et al., 2009), as they are known the drain ice-dammed lakes in temperate glacial environments. More recently however several complimentary lines of evidence have called into question the ability of an R-channel to form (Hooke and Fastook, 2007) and close (Fowler, 2009) in subglacial conditions typical of Antarctica, the latter suggesting that channels incised into the till may be the preferred mechanism.
In this work we test an existing R-channel model (Kingslake and Ng, 2013) on a domain based upon several well-studied lakes in the Whillans/Mercer system and develop a new model for the filling and drainage of Antarctic subglacial lakes where lake drainage occurs through channels in the underlying sediment (a till-channel, or “T-channel”) and compare the lake volumes output by both models. We aim to: (i) provide better context for ongoing observations of lake volume change with respect to the subglacial hydrology, (ii) understand how lake filling and draining affects ice flow, (iii) gain insight into the discrepancies between the locations of active and RES lakes; and (iv) move towards a consistent parameterization of subglacial lake activity in ice sheet modeling.
Models for subglacial water transport and distribution include at least one of three categories: distributed sheet flow; groundwater; and channelized flow. The simplest and most common models for ice sheet basal water flow (e.g. Le Brocq et al., 2009) tend to invoke some form of distributed system that spreads water laterally. In such systems, water pressure increases with water flux and while basal traction decreases. More sophisticated models, however, prefer to accommodate sliding by deformation of the subglacial till, making basal traction decrease through increasing till porosity (e.g. Tulaczyk, 2000). Given that subglacial till is widely understood to lack the transmissivity necessary to accommodate the water fluxes at the base of the Antarctic ice sheet (Alley, 1989), changes in till water storage have been accommodated by exchange with a distributed system (e.g. Christoffersen et al., 2014; Bougamont et al., 2014). These more sophisticated distributed/groundwater exchange modes show the most consistency with borehole (Engelhardt and Kamb, 1997; Christner et al., 2014) and seismic observations (Blankenship et al., 1987) of the basal environment.
Channelized systems are those in which water flux is concentrated in one or more low-pressure conduits. These conduits, often referred to as “R-channels,” are thermally-eroded into the ice by turbulent heat generated by water moving down a hydraulic gradient (Rothlisberger, 1972; Nye, 1976). As the relative area of the ice bed interface occupied by these systems is small, they can support lower water pressures. The relative efficiency of these systems for evacuating water can also draw water away from surrounding distributed systems leading to a net slowdown of the ice as these systems evolve. This slowdown is especially pronounced in areas where the supply of water varies temporally and where surface slopes are steep enough that channels erode quickly when melt water supply is high and then lose pressure when supply subsequently dwindles (e.g. Sundal et al., 2011). The drop of water pressure in the channelized system then pulls water away from adjacent distributed systems (Andrews et al., 2014). Due to the requirement of turbulent heat for initiating “R-channels” and time varying input for the more significant pressure variations, this process has received far more consideration for the steeply-sloped margins of Greenland where the subglacial system receives a substantial portion of the meltwater from surface ablation (e.g., Pimentel and Flowers, 2011; Schoof, 2010; Werder et al., 2013). In contrast, the basal water system for most of Antarctica does not receive surface meltwater and is often at low hydraulic slopes, such that the heat generated by water moving down gradient is likely not sufficient to erode an R-channel (Alley, 1989), and channelization has therefore typically not been considered in basal water models for Antarctica (e.g. Bougamont et al., 2011; Le Brocq et al., 2009). In the last few years, however, increased consideration has been given to the possibility of channels incised in the sediments instead of the overlying ice (e.g. Van der Wel et al., 2013; Kryke-Smith and Fowler, 2014), and to the role of channelization in the drainage of subglacial lakes (e.g. Evatt et al., 2006; Carter et al., 2009).
Most of our understanding of the drainage of subglacial lakes comes from studies of glacial-dammed lakes on temperate glaciers in
alpine environments (e.g. Clarke, 2003; Werder et al., 2013) where floods descend 100
Antarctic subglacial floods occur on larger spatial and longer temporal scales than alpine subglacial floods: water typically
descends 10
In this paper we develop, test, and compare models for lake drainage via an R-channel (Kingslake and Ng, 2013) alongside a model with in which channels are formed via mechanical erosion of underlying till (“T-channels”) on a domain with geometry similar to that found for flowpaths draining Antarctic subglacial lakes. We tested the output from these models with observations to see which one was able to reproduce estimates of the inferred timing and magnitude for subglacial lake drainage events most closely.
We developed two models for this work, each based on the same parameters but with a different module for channelization. Our first model (henceforth the “R-channel model”) is adapted directly from a formulation presented by Kingslake and Ng (2013) for a lake drained by a combined distributed system and R-channel as the patterns of ice flow predicted in that work appear qualitatively similar to observed ice flow associated with lake drainages in Antarctica (e.g. Stearns et al., 2008). Our second model replaces R-channels with channels mechanically incised into the underlying deformable till (henceforth “T-channel”). We derive formulations for erosion, deposition, and creep closure from theoretical work presented in Walder and Fowler (1994) and Ng (1998, 2000).
By comparing the lake volume time series output by the combined R-channel model and the T-channel model, we can (i) perform a diagnostic test for Fowler (2009)'s statement that drainage could occur for sediments that behave like erodible-deformable ice, (ii) develop tools to predict future lake drainage, and a potential prototype for incorporating lake drainage in ice sheet basal hydrology models; and (iii) form a conceptual basis for coupling more complex models of sediment and water dynamics.
Subglacial water flows from areas of high hydraulic potential to areas of lower hydraulic potential. Hydraulic potential,
Given that
In the classic R-channel model transmissivity is controlled by aperture, which is controlled by a balance of erosion
Our model for channelization by mechanical erosion into the sediments is composed of many elements of models for R-channels
thermally incised into the ice (e.g. Fowler, 1999; Evatt et al., 2006; Kingslake and Ng, 2013), but borrows formulas for net
erosion and viscous closure from Walder and Fowler (1994) and Ng (2000). Although more complex and presumably more precise
mathematical language for conduits incised at least partially into the sediment has been introduced by Hewitt et al. (2011),
van der Wel et al. (2013) and Kryke-Smith and Fowler (2014), this simplified model can act as a basis for these higher order
process models. As with the R-channel, transmissivity for a till channel is governed by aperture (
By this system of equations, channel growth via erosion is a function of water velocity and is sensitive to the sediment size
and the channel geometry. Moreover, a channel can only be eroded once water exceeds a threshold velocity. At lower water fluxes
channels in the will not form and sheet flow will dominate. Channel closure via deformation is a function of the effective
pressure of the water (
Conservation of mass is accomplished with:
The distributed or sheet flow system, common to both the combined R-channel and T-channel model is governed by three primary
equations: two concern the conservation of mass; a third governs the evolution of
For a lake, we assume that the hydraulic potential is the sum of the bed elevation and overburden pressure (from the height of
the ice column) at the centre of the lake and that it changes uniformly. With the subscript
These systems of Eqs. (2)–(16) are solved on a 1-dimensional finite difference domain, consisting of a source lake, intermediate
points, and a destination lake. The point at which
Given our initial uncertainties about the onset of channelization it is simpler to run our model when the source lake is
filling, such that outflow in minimized, and the lake level is well below high stand. We initialize the model assuming that
water pressure equals overburden pressure and that there is a constant supply of meltwater MC along the flowpath downstream of
the lake. With these initial values, we calculate the initial water layer thickness, assuming
Initially water will flow from the seal, towards the lake; as the lake level and lake hydraulic potential increase, however,
water will begin flow out of the lake over the seal. Due to the inverse relationship between
Cessation of channelization occurs once
Once the channel is initiated we calculate the geometry of a proto-channel (Eqs. 7, 11), assuming
We tested both the combined R-channel and T-channel models, on an idealized domain in which the section between the source lake
and the seal, and the seal and the destination lake are approximated with straight-line segments (Fig. 3a). This domain was
based on a simplified version of the flowpath connecting the well-studied (e.g. Christianson et al., 2012) Subglacial Lake
Whillans (SLW) to the Ross Sea from (Carter and Fricker, 2012; see Fig. 1b for location, 3b for comparison).
To demonstrate the ability of the T-channel model to reproduce the timing and magnitude of actual observed lake drainage
events, we also applied it to several “real” domains for flowpaths draining lakes in lower Whillans and Mercer ice
streams, including SLW (Fig. 3b), Lake Conway (SLC) and Lake Mercer (SLM) (Fig. 3c) and Lake Engelhardt (SLE)
(Fig. 3d). For these domains values for elevation
Our R-channel model was unable to reproduce the observed timing and magnitude of floods in the domain. Although there was some
thermal erosion of an opening it took nearly 10
The timing (
In all model runs lake drainage began when
In many of the model runs the amplitude of the filling and draining cycle decreased over time in contrast to experiments in Fowler (1999) and Evatt et al. (2006) in which the oscillations in volume increased. In our model this dampening of the filling/drainage cycle appears to result from the fact that outflow through the channelized system continued long after the lake reached low stand, such that the net filling rate was lower, as was the subsequent high stand. We explored this dampening in more detail in our sensitivity studies (Sect. 4.2).
A comparison between the model output from an idealized domain and one that uses more realistic flow path geometry shows almost
no qualitative difference, with recurrence interval, fluxes and volume ranges within less than 5 % of one another. The most
significant difference was that the model ran six times faster on the idealized domain and appeared to be more stable. We
suspect the slower performance of the model over the realistic domain is due to undulations in
Outputs such as timing, magnitude, and high stand relative to floatation height were all shown to be quite variable in response changes in both flow path geometry and input parameters. We divide our sensitivities into classes of tests relating to sediment properties, flow path geometry, model inputs, and low sensitivity parameters.
The parameters to which the model shows the greatest sensitivity all relate to the properties of the sediments: channel
geometry, grain size and till pressure (
We experimented with flow path geometry by multiplying bed elevation and hydraulic potential, while keeping the
At lower
Although we assume that
Any factor which affected the relationship between sheet thickness and
The amount of sheet flow necessary to initiate channelization
There were two model parameters that seemed to affect primarily how fast the model ran:
Although previous work by Carter et al. (2013) has shown that the filling rates for subglacial lakes vary considerably over
time, we were able to roughly reproduce the elevation change time series using a constant value for
Given the sensitivity of timing and drainage magnitude to parameters relating to the sediment properties, running the model at constant inflow may be a reasonable approximation for tuning those parameters. The assumption of constant inflow may even serve as a workable approximation in the absence of reliable data on lake activity upstream. Close reproduction of filling and drainage cycles will require precise and time varying inflow, which is outside the scope of this paper.
The T-channel model reproduces observations in the Whillans/Mercer ice stream better then the R-channel model, and performs sufficiently well for us to believe that it is realistic. The modification of channels being incised into the sediment rather than the ice has two major implications: (i) many active lakes are shallow and only exist in the presence of saturated sediment, which could explain why these lakes are not detectable using radar sounding; and (ii) the process of lake drainage for such lakes is sensitive to the composition and strength of the underlying till, which suggests that it is sensitive to properties of the till, which indicates that models could be improved with a realistic treatment of sediment – interfacial water exchange. It also casts some doubt on the interpretation of the origin of channels observed under ice shelves (Le Brocq et al., 2013), which assumes that channels are carved into the basal ice. We expand on some of these implications in the following discussion.
There have been several recent inventories of Antarctic subglacial lakes as well as several other works (e.g. Smith et al., 2009; Siegert et al., 2013; Wright and Siegert, 2012; Wright et al., 2014), and all have noted a significant discrepancy between the locations of “RES lakes” and “active lakes”. While we attribute some of this discrepancy to the limitations of the distinct methods used for lake detection, our modeling work offers a plausible explanation: for areas where the regional surface slope (and resultant hydraulic gradient) is low, the only mechanism by which a self-enlarging conduit capable of siphoning substantial amounts of water several meters below the seal floatation height to points downstream can exist is if the channel it is incised into the sediment. The observed volume change reported for active lakes (Fricker et al., 2007, 2014; Fricker and Scambos, 2009; Smith et al., 2009) requires ice to be underlain by widespread, deformable saturated sediments. The presence of saturated sediments would inhibit positive identification of these lakes using the criteria of the Carter et al. (2007) radar classification strategy, such as specularity and brightness relative to surroundings. The angle of repose for these sediments would imply low basal slopes and shallow lakes. In shallow lakes, radar reflections off the lake bottom would impair the specularity criteria (Gorman and Siegert, 1999). A lake surrounded by saturated sediments might not be significantly brighter than its surroundings as the reflection coefficient between ice and for saturated sediments is very close to that that of ice and lake water (Schroeder et al., 2013).
A number of recent models for ice flow have begun to predict the formation of subglacial lakes in local hydraulic potential minima (e.g. Sergienko and Hulbe, 2011; Goeller et al., 2013; Livingstone et al., 2013; Fried et al., 2014). These models all assume that these lakes simply fill until the water level reaches the floatation height of the “static seal” at which point they drain steadily through a distributed network at the ice bed interface. Although we cannot comment on lakes surrounded by bedrock, our models results suggest that subglacial lakes surrounded by saturated sediments will undergo cyclical pattern of filling and draining. This finding along with recent observations of ice velocity change in response to subglacial lake drainage (Stearns et al., 2008; Scambos et al., 2011; Fricker et al., 2014; Siegfried et al., 2015), indicate that this process needs to be explored more deeply, especially for ice sheet models of areas where lakes and sediments are known to exist such as the Siple Coast.
Ice sheet models would be limited in their ability to precisely reproduce observed lake drainage patterns due to issues
relating to the spatial resolution of the ice surface and bedrock topography as well as the sensitivity of the lake drainage
process to small changes in sediment composition and strength. With the sensitivities however comes the interesting possibility
that subglacial lakes might form and be “active” in subglacial sediments under only limited circumstances. In particular the
exchange of water between the till and the basal interface has been shown to affect till strength on timescales of less than
a decade (e.g. Christoffersen et al., 2014; Bougamont et al., 2014). If a model can fill enclosed basins in the hydraulic
potential and predict till strength evolution over timescales longer than the current observational record (10
Spatial variations in basal traction in areas of fast flow have previously been proposed as a mechanism for forming lakes (Sergienko and Hulbe, 2011), with lakes forming in the lee of local traction highs. More recently inversions of basal traction have inferred bands of stiff till impounding water in areas of moderate to fast flow, but usually outside the regions where active lakes are found (Sergienko et al., 2014). It may be these two different mechanisms of water storage, one stable and the other unstable, owe their existence to subtle changes in till properties. This along with findings of multiple other mechanisms of water storage beneath the Antarctic ice sheet (Ashmore and Bingham, 2014) indicate that simply modeling the filling an enclosed depression in the hydraulic potential, while an important first step, is not sufficient to simulate the full nature and impact of lake dynamics in an ice sheet model.
Where active lakes are present, their tendency to drain primarily via a channelized system rather than a distributed one suggests that the formation and drainage of subglacial lakes in regions of fast flow actually results in net slowdown relative to lake free regions rather than acceleration over the longer term. Regions of the ice sheet underlain by active subglacial lakes, will however exhibit more variability in flow rate with peak ice velocity coinciding with peak distributed flow and peak lake volume. In chains of lakes, however the lubrication will be spatially variable over time as shown in Siegfried et al. (2015). The exact degree to which lake drainage accelerates ice flow is, however, highly dependent on longitudinal stresses, which is outside the scope of this paper.
Recent work by Le Brocq et al. (2013) has suggested that a number of channel-like features in the surface and base of ice shelves may have originated when water thermally eroded grounded ice, showing how many of these linear features appear to correlate with locations where ice sheet subglacial water models predict outflow into the ice shelf cavity. While this correlation has interesting implications for the offshore evolution of subglacial outflow and its interaction with the ice shelf, our study casts doubt on the origin of such channels as hypothesized in the Le Brocq et al. (2013) paper. We have shown that even in temperate ice as is implicit in out model, that the low amounts of turbulent heat generated by water flowing down relatively gentle hydraulic gradients is insufficient to erode the ice fast enough to explain the observed lake volume change in a location like the Whillans/Mercer ice streams. If we assume polar ice (Hooke and Fastook, 2007) or factor in the adverse bed slopes (Fig. 3b and c) and associated supercooling that water exiting many of these lakes might encounter (e.g. Alley et al., 1998; Creyts et al., 2010; Carter et al., 2009) then the feasibility of channel incision into the overlying ice upstream of the grounding line is even less likely. If any thermal erosion is taking place it would be the result of tidal inflow (e.g. Horgan et al., 2013), not subglacial outflow. Although the evolution of ice and subglacial water seaward of the grounding line is beyond the scope of this work, we do provide constraints on the mechanisms by which such features on the ice shelf surface might form.
We have developed a new model for subglacial lake drainage in the Antarctic ice streams in which channels are mechanically eroded into deformable subglacial sediment, and compared it to a previously-accepted model for an “R-channel” incised into the base of the ice through melting. Using the “T-channel” model we have been able to reproduce the timing and magnitude of subglacial lake drainage events in one of the better-studied regions of Antarctica, the Whillans/Mercer ice stream system. Due to effective pressure differences between the lake center and the “seal” lake drainage begins well before lake levels reaches floatation height, and accelerates once flow is sufficient to initiate erosion into the sediment. Peak distributed flow correlated with lake level, while channelization is dominant when the rate of volume loss is highest.
The time series output by the model is highly sensitive to small changes in the properties of the subglacial sediments, in particular those related to till water content. Given recent work on the exchange of water between sediment pores and the interfacial flow system taking place over time frames of years to decades, it is likely that there are substantial changes in till strength over the filling/drainage cycle of a subglacial lake.
The requirement of sediments for active lakes appears to explain why such lakes often fail classic radar detection criteria as lakes in such environments are often neither deep and therefore not specular (Gorman and Siegert, 1999), nor are such lakes brighter than their surroundings (Carter et al., 2007). Our results also cast some doubt on the interpretation of the origin of channels observed under ice shelves (Le Brocq et al., 2013), which relies on incision into the basal ice.
Funding for this research was provided by the Antarctic Integrated Systems Science (AISS) program of the National Science Foundation, through the WISSARD project and by the Cryospheric Sciences program at NASA.
Work also benefitted from conversations with: Geir Moholdt, David Heezel, Fernando Paolo, Adrian Borsa, Andrew Fowler, Mauro Werder, Stephen Livingstone, Ted Scambos, Dustin Schroeder, Duncan Young, Slawek Tulaczyk, Richard Alley, Jonathan Kingslake, Tim Creyts, Christian Schoof, and Ian Hewitt, and the WISSARD Team members.
List of all symbols used in this paper with definitions.
Continued.
List of parameters used for each of the experiments.
Map of study area showing
Schematic diagram showing the basic principles of our model.
Ice surface elevation, hydraulic potential, and ice base elevation along the
Results of steady inflow model on idealized and realistic domains (see Fig. 3a and b respectively).
Results of a sensitivity study testing how model output varies in response to changes in
Variation of model output in response to changes in model geometry:
Sensitivity of
Sensitivity of modelled volume change to
Plot of modelled and observed lake evolution showing mean lake surface elevation (observed and modelled), and outflow
via distributed and channelized systems (modelled) for constant