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Fluid Mech. 357, 29±57 (1998). 12. Shiikhmurzaev, Y. D. On cusped interfaces. J. Fluid Mech 359, 313±328 (1998). 13. Sherwood, J. D. Tip streaming from slender drops in a nonlinear extensional ¯ow. J. Fluid Mech. 144, 281±295 (1984). 14. Smith, P. G. & Van de Ven, T. G. M. Shear induced deformation and rupture of suspended solid/liquid clusters. Colloids Surf. 15, 191±210 (1985). 15. Stone, H. A. Dynamics of drop deformation and breakup in viscous ¯uids. Annu. Rev. Fluid Mech. 26, 65±102 (1994). 16. Eggers, J. Nonlinear dynamics and breakup of free-surface ¯ows. Rev. Mod. Phys. 69, 865±929 (1997). 17. de Bruijn, R. A. Tip streaming of drops in simple shear ¯ows. Chem. Eng. Sci. 48, 277±284 (1993). 18. Siegal, M. In¯uence of surfactant on rounded and pointed bubbles in 2-D Stokes ¯ow. SIAM J. Appl. Math. 59, 1998±2007 (1999). Acknowledgements We thank R. Slagle (Oxford Lasers, Inc.) for help in obtaining the high-speed images displayed in Figs 2 and 4, and C. Pozrikidis for helpful comments on an earlier version of the manuscript. Correspondence and requests for materials should be addressed to P. G. S. (e-mail: pgs@bell-labs.com). letters to nature NATURE | VOL 403 | 10 FEBRUARY 2000 | www.nature.com 643 ................................................................. Water exchange between the subglacial Lake Vostok and the overlying ice sheet Martin J. Siegert*, Ron Kwok², Christoph Mayer³ & Bryn Hubbard§ * Bristol Glaciology Centre, School of Geographical Sciences, University of Bristol, Bristol BS8 1SS, UK ² California Institute of Technology, Jet Propulsion Laboratory, Pasadena, California 91109, USA ³ Alfred-Wegener-Institute for Polar and Marine Research, Department of Geophysics, Bremerhaven, Germany § Centre for Glaciology, Institute of Geography and Earth Sciences, University of Wales, Aberystwyth SY23 3DB, UK .............................................................................................................................................. It has now been known for several years that a 200-km-long lake, called Lake Vostok, lies beneath the ice sheet on which sits Vostok Station in Antarctica 1±5 . The conditions at the base of the ice sheet above this subglacial lake can provide information about the environment within the lake, including the likelihood that it supports life 2 . Here we present an analysis of the ice-sheet structure from airborne 60-MHz radar studies, which indicates that distinct zones of basal ice loss and accretion occur at the ice± water interface. Subglacial melting and net ice loss occur in the north of the lake and across its 200-km-long western margin, whereas about 150 m of ice is gained by subglacial freezing in the south. This indicates that signi®cant quantities of water are exchanged between the base of the ice sheet and the lake waters, which will enrich the lake with gas hydrates, cause sediment deposition and encourage circulation of the lake water. Three 60-MHz radar lines are aligned parallel to the general direction of ice ¯ow, as indicated by interferometric-SAR (InSAR) data (Fig. 1). These transects run across the northwestern margin of the lake (Fig. 2a), the southern central region of the lake (Fig. 2b), and from the southwestern margin of the lake to Vostok Station (Fig. 2c). InSAR data show the ice-velocity ®eld above the lake, and along each of the transects, in metres per year (Fig. 1b). Several isochronous internal radar layers, extracted from the raw 60-MHz radar data, were traced across each transect. The vertical distance between the highest and lowest traceable internal layers, and that between the lowest layer and the ice-sheet base, were both then measured along these transects. The resulting data (Fig. 3) clearly indicate marked, spatially-coherent deviations in the dip of the basal radar layers away from parallelism with the ice-sheet base. Such deviations could be caused by a number of processes. For example, basal topography is commonly translated into the over- lying ice column. However, such topography is negligible over Lake Vostok. The ice base in contact with the lake surface is characterized by a small (0.002) but steady gradient from the north of the lake where the ice is ,4,200 m in thickness, to the south where the ice is ,3,800 m thick. There is very little variation in ice thickness across the lake from west to east. This situation is therefore analogous to an ice shelf, where the absence of basal shear stress prevents deformation of internal layers. For the same reason, the in¯uence of compressive ¯ow, which would force internal layers apart, and extending ¯ow, which would bring them closer together, is con- sidered unlikely except near the lake margins, where an abrupt transition in basal drag is expected. Independent evidence for a relatively uniform stress ®eld across the lake is provided by the InSAR data (Fig. 1b), which indicate a smooth divergence of ice, similar to that in ¯oating ice shelves. Dipping internal layers could, however, still re¯ect oblique topographic in¯uences inherited from grounded sections of the ice sheet located up-¯ow of the transect under consideration. In this case, the observed dip will vary with the sine of the angle between the transect and the ice ¯ow direction. Inherited dip will therefore be zero where transects are aligned parallel to ice ¯ow. Since no transect in the present study is aligned exactly parallel to the ice ¯ow (Fig. 1), this argument cannot be used to constrain inherited layering precisely. However, the in¯uence may be evaluated where two transects cross the same ice-¯ow path at different angles. Here, a similar pattern of inherited internal layering will be present in both transects, and the amplitude of the pattern will vary with the sine of the angle that each transect makes with the ice ¯ow direction. Finally, basal ice melting and accretion as the ice sheet passes over the lake surface will cause ¯ow-parallel internal layers to dip downwards and upwards respectively. We believe that at least three approximately ¯ow-parallel transects indicate that such processes operate on a signi®cant scale above Lake Vostok. In transect AB when ice is grounded (Fig. 2a, Fig. 3a), four traceable internal layers are observed to run parallel to the ice sheet base, and are separated from each other by a relatively constant thickness along the transect. However, as ice ¯ows over the western margin of the lake, the distance between the ®rst and fourth internal layers increases by 200 m over a horizontal distance of 8 km, while that between the layer and the ice base decreases by 300 m (Fig. 3b). The rate of change of basal ice thickness with distance along the transect is greatest (-140 m km -1 ) at 1 km downstream of the ice grounding line, decreasing to only a few metres per kilometre at 8 km from the grounding line (Fig. 3c). Since high basal relief is absent over the lake area, we interpret this thinning in terms of ice loss by basal melting. Here, the melt rate may be calculated from the InSAR-derived ice-surface velocities, since two-dimensional numerical modelling of ice ¯ow over the lake indicates negligible change in horizontal ice velocity down the vertical ice column 6 . This model also calculates a vertical ice-velocity pro®le consistent with the dipping of our internal layers (Fig. 2a), where the thickness between layers increases down the ¯owline. Concurrent with this englacial thickening, the model predicts ice loss between the lowest layer and the ice base only if sub-ice melting is accounted for. The