The Cryosphere, 7, 1721–1740, 2013 Open Access www.the-cryosphere.net/7/1721/2013/ doi:10.5194/tc-7-1721-2013 The Cryosphere © Author(s) 2013. CC Attribution 3.0 License. Potential subglacial lake locations and meltwater drainage pathways beneath the Antarctic and Greenland ice sheets S. J. Livingstone1, C. D. Clark1, J. Woodward2, and J. Kingslake3 1Department of Geography, University of Shefeld, Shefeld, S10 2TN, UK 2Department of Geography, Engineering and Environment, Northumbria University, Newcastle-Upon-Tyne, NE1 8ST, UK 3British Antarctic Survey, Madingley Road, Cambridge, UK Correspondence to: S. J. Livingstone ([email protected]) Received: 5 March 2013 – Published in The Cryosphere Discuss.: 21 March 2013 Revised: 7 October 2013 – Accepted: 15 October 2013 – Published: 11 November 2013 Abstract. We use the Shreve hydraulic potential equation 1 Introduction as a simplied approach to investigate potential subglacial lake locations and meltwater drainage pathways beneath the Antarctic and Greenland ice sheets. We validate the method Understanding the drainage of meltwater beneath ice is fun- by demonstrating its ability to recall the locations of > 60 % damental to resolving ice-ow dynamics because water pres- of the known subglacial lakes beneath the Antarctic Ice sure inuences both the strength of the subglacial sedi- Sheet. This is despite uncertainty in the ice-sheet bed ele- ment and the frictional interaction between ice and its sole vation and our simplied modelling approach. However, we (Clarke, 2005; Schoof, 2010). However, subglacial meltwater predict many more lakes than are observed. Hence we sug- drainage is dynamic in space and time and varies in a com- gest that thousands of subglacial lakes remain to be found. plicated manner coupled to ice mechanics (e.g. Fountain and Applying our technique to the Greenland Ice Sheet, where Walder, 1998; Nienow et al., 1998; Bartholomew et al., 2010; very few subglacial lakes have so far been observed, recalls Kingslake and Ng, 2013). Possible meltwater networks at the 1607 potential lake locations, covering 1.2 % of the bed. Our ice–bed interface are thought to include (i) discrete tunnel results will therefore provide suitable targets for geophys- systems (e.g. Röthlisberger, 1972; Walder and Hallet, 1979; ical surveys aimed at identifying lakes beneath Greenland. Nienow et al., 1998); (ii) distributed networks of passage- We also apply the technique to modelled past ice-sheet con- ways and cavities (e.g. Lliboutry, 1979; Kamb, 1987; Sharp gurations and nd that during deglaciation both ice sheets et al., 1989); (iii) thin water lms (e.g. Hallet, 1979; Lappe- likely had more subglacial lakes at their beds. These lakes, gard et al., 2006); and (iv) Darcian ow through sediments inherited from past ice-sheet congurations, would not form (e.g. Hubbard et al., 1995). These drainage congurations under current surface conditions, but are able to persist, sug- evolve on daily to millennial timescales as basal conditions gesting a retreating ice-sheet will have many more subglacial are perturbed (Hubbard et al., 1995; Bartholomew et al., lakes than advancing ones. We also investigate subglacial 2010). drainage pathways of the present-day and former Greenland The identication of subglacial lakes beneath the Antarc- and Antarctic ice sheets. Key sectors of the ice sheets, such tic Ice Sheet (AIS) (Robin et al., 1970) has altered our per- as the Siple Coast (Antarctica) and NE Greenland Ice Stream ception of how meltwater drains and is stored beneath large system, are suggested to have been susceptible to subglacial ice masses (e.g. Smith et al., 2009). Indeed, subglacial lakes drainage switching. We discuss how our results impact our beneath the AIS are now known to comprise a crucial compo- understanding of meltwater drainage, basal lubrication and nent of the subglacial environment, capable of actively inter- ice-stream formation. acting with the surrounding hydrological network and trans- mitting large volumes of meltwater between lakes and to- wards the grounding line (e.g. Wingham et al., 2006; Fricker et al., 2007; Smith et al., 2009). An inventory of over 380 Published by Copernicus Publications on behalf of the European Geosciences Union. 1722 S. J. Livingstone et al.: Potential subglacial lake locations and drainage pathways known subglacial lakes has been compiled recently for the which is a function of the elevation potential and water pres- AIS (Wright and Siegert, 2012), and thus, unlike the sub- sure (Shreve, 1972): glacial hydrological system as a whole (i.e. the pathways and networks), we have a decent (and rapidly improving) un- 8 = ρwgh + Pw, (1) derstanding of the spatial distribution and geometry of sub- −3 glacial lakes. They are therefore a valuable resource for con- where ρw is the density of water (1000 kgm ), g is the ac- straining and testing glacial models (Pattyn, 2010). celeration due to gravity, h is the bed elevation and Pw is Despite theoretical advances in how we understand sub- the water pressure. The subglacial water pressure can be ex- glacial hydrology, relatively little is known about the dis- pressed as a function of the ice overburden pressure and ef- tribution of subglacial water and the form of the drainage fective pressure, N: system. And although subglacial lakes are being identied Pw= ρ gH − N, (2) beneath the AIS, they have only been posited under other i (palaeo-)ice sheets (e.g. Livingstone et al., 2012, 2013). One −3 where ρi is the density of ice (917 kgm ) and H is the ice method of investigating the subglacial hydrological network thickness. Subglacial water pressures vary in a complex way is to calculate the hydraulic potential from the bed and ice- due to temporally and spatially varying drainage-pathway ca- surface topographies (Shreve, 1972), and then to use sim- pacities and the lling and drainage of lakes. However, lim- ple routing techniques to derive rst-order approximations ited borehole observations suggest that Pw is close to the ice of meltwater ow paths and subglacial lakes (e.g. Evatt overburden pressure (e.g. Kamb, 2001). As our aim is to esti- et al., 2006; Siegert et al., 2007; Wright et al., 2008). This mate the average, large-scale behaviour of drainage systems method has potential application in predicting and investi- we can therefore assume that N=0, allowing us to re-write gating subglacial hydrological systems in both contemporary Eq. (1) as and palaeo-settings, and it is therefore important to verify how well it can reproduce known subglacial drainage cong- 8 = ρwgh + ρigH, (3) urations. In this paper, potential subglacial lake locations and melt- We evaluate 8 in a GIS using the Shreve equation and grid- water drainage pathways are calculated both for the present- ded data pertaining to h and H. This produces a hydraulic day Antarctic and Greenland ice sheets, and over the last potential surface over which water is routed using a rout- 20 000 yrs of their evolution. The inventory of subglacial ing algorithm from the ArcHydro package (part of the GIS lakes for the AIS (Wright and Siegert, 2012) is used to test software ArcMap) to estimate the large-scale structure of the whether the hydraulic potential can be used to recall the pat- subglacial drainage systems of the Greenland and Antarctic tern of known present-day subglacial lakes. Because much ice sheets. At each GIS grid cell the algorithm calculates the of the ice thickness and bed topography are derived from hydraulic potential gradient in each direction, then routes wa- radar data that represent the surface of subglacial lakes at the ter in the direction of the largest hydraulic gradient. Drainage bed, the hydraulic potential surface will include a represen- pathways are calculated by dening the cumulative number tation of the surface of known lakes. This may preclude their of all cells that ow into each downslope cell. Output cells identication. If known subglacial lakes can be recalled our with a high ow accumulation represent concentrated sub- approach will allow us to locate subglacial lakes that have glacial meltwater ow and are therefore potential subglacial not been observed yet. Derived subglacial meltwater ow meltwater pathways (see also Siegert et al., 2007; Wright paths provide information on hydrological connections, the et al., 2008). Another algorithm in the ArcHydro package structure of the drainage system and their association with was used to identify minima in the hydraulic potential sur- ice streams (see Siegert et al., 2007). Subglacial meltwater face. Following previous authors (e.g. Evatt et al., 2006; Liv- pathways and lakes calculated at time slices through the past ingstone et al., 2013), we associate these minima with likely deglaciation, of the Antarctic and Greenland ice sheets, using locations of subglacial lakes by lling them to their lip. the output of independent models (not coupled to our simple Equation (3) can be re-arranged to demonstrate the well- hydrological model) allow an assessment of the sensitivity known result that the contribution of the ice-surface gradient of subglacial hydrological pathways and subglacial lakes to to the hydraulic potential is a factor of ≈ 10 times that of large-scale ice-sheet evolution (e.g. Wright et al., 2008). the bed gradient. Thus, the ice surface, which is capable of rapid changes in elevation and slope, is the primary driver of subglacial water. However, the weaker inuence of the bed 2 Methods is partially offset by its greater relief and spatial variability (Wright et al., 2008). 2.1 Calculating subglacial water ow and storage Using the Shreve equation to derive rst-order potential subglacial lake locations and meltwater drainage pathways The ow and storage of meltwater under ice masses is prin- is simple and quick to implement but has a number of limi- cipally governed by gradients in the hydraulic potential (8), tations.