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Traveling supraglacial lakes on George VI Ice Shelf, Antarctica

2011; American Geophysical Union; Volume: 38; Issue: 24 Linguagem: Inglês

10.1029/2011gl049970

1944-8007

C. H. LaBarbera, Douglas R. MacAyeal,

Landslides and related hazards

Geophysical Research LettersVolume 38, Issue 24 The CryosphereFree Access Traveling supraglacial lakes on George VI Ice Shelf, Antarctica C. H. LaBarbera, C. H. LaBarbera Department of Geology, Cornell College, Mount Vernon, Iowa, USASearch for more papers by this authorD. R. MacAyeal, D. R. MacAyeal [email protected] Department of Geophysical Sciences, University of Chicago, Chicago, Illinois, USASearch for more papers by this author C. H. LaBarbera, C. H. LaBarbera Department of Geology, Cornell College, Mount Vernon, Iowa, USASearch for more papers by this authorD. R. MacAyeal, D. R. MacAyeal [email protected] Department of Geophysical Sciences, University of Chicago, Chicago, Illinois, USASearch for more papers by this author First published: 28 December 2011 https://doi.org/10.1029/2011GL049970Citations: 16AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Abstract [1] We describe a sequence of supraglacial lakes on the George VI Ice Shelf, Antarctica, that migrate along the boundary of the ice shelf with Alexander Island in the manner of a traveling wave, with a velocity that differs from the local ice-shelf flow in both magnitude and direction. These lakes are arrangeden échelonalong a grounding line of the ice shelf where the flow displays the atypical feature of being directed toward land. A simple model presented here suggests that the propagating lakes form in the depressions of a viscous-buckling wave associated with compressive ice-shelf stresses and ice-flow directed obliquely toward the coastline. The existence of these lakes and their propagation gives rise to the implication that other ice-shelf surface features (e.g., patterns of swells and depressions, surface lakes, and drainage) can be organized by large-scale viscous buckling behavior, when ice-shelf flow is strongly compressive. Key Points We discover a type of supraglacial lake that propagates as a wave These waves result from large-scale stress regime Thus, large-scale stress regime may determine how lakes mediate shelf stability 1. Introduction [2] George VI Ice Shelf (Figure 1) stands apart from other Antarctic ice shelves as a result of an atypical flow regime. Within the central part of the long, channel-like and double ice-fronted ice shelf, flow is largely transverse to the channel – from the Antarctic Peninsula toward Alexander Island [Sugden and Clapperton, 1981; Pearson and Rose, 1983; Reynolds and Hambrey, 1988; Humbert, 2007; Rignot et al., 2011]. Where the ice shelf pushes against the shoreline of Alexander Island, a unique en-échelon sequence of meltwater lakes [Reynolds and Hambrey, 1988] of unusual geometric uniformity is found (Figures 1a–1c). Figure 1Open in figure viewerPowerPoint Propagating en échelonlakes along the Alexander Island boundary of George VI Ice Shelf. (a) DigitalGlobe image from 29 December 2008 during period of relatively meltwater-free conditions. (b) Close-up of box in Figure 1a.(c) DigitalGlobe image from 24 January 2011 showing extensive standing surface meltwater. (Imagery provided by the NGA Commercial Imagery Program.) (d) Location map of George VI Ice Shelf. Red box indicates area of Figures 1a and 1c. [3] The en-échelonlakes are notable for their propagation in a direction and with a velocity that differs from the ice-shelf flow–a fact which we shall establish here. These lakes move parallel to the ice-shelf grounding line as a traveling wave, with a phase velocity that differs in both magnitude and direction from the velocity of the underlying ice (see Figure S1 and Animation S1 in theauxiliary materialfor additional demonstration of the propagation of these lakes). In the present study, we describe the kinematics of this propagation, and present measurements that may be useful in eventually understanding the dynamics of this unusual form of glaciological wave, which we believe to be associated with a previously described ice-shelf phenomena known as pressure rolls [Hattersley-Smith, 1957; Kehle, 1964; Collins and McCrae, 1985]. The motivation for our study stems from the desire to understand surface hydrology of ice shelves, which is a factor in determining the stability of ice shelves [e.g., Scambos et al., 2003; van den Broeke, 2005; Glasser and Scambos, 2008; Scambos et al., 2009]. The lakes are located at the downstream end of an ice-shelf surface water-flow system that includes several quasi-perennial surface streams such as shown inFigure 1c [Wager, 1972; Reynolds, 1981; Reynolds and Hambrey, 1988]. Understanding the physical processes which control the unusual properties of these lakes may also yield understanding of various other types of ice-shelf surface meltwater features. 2. Observations [4] Using Landsat 7ETM+ enhanced thematic mapper imagery between January 2001 to December 2010, we compiled 10 cloud-free images of the Alexander Island/George VI Ice Shelf boundary. After georeferencing the images, outlines of 11 lakes were digitized by noting lake shorelines in the ablation season or superimposed lake ice cover (i.e., giving a rough surface appearance) when visible meltwater was absent. A summary of the digitization is shown inFigure 2a. Figure 2Open in figure viewerPowerPoint Comparison of lake-propagation velocity (this study) and ice-shelf velocity [Rignot et al., 2011]. (a) Digitization of individual pear-shape lakes over a sequence of images. Initial (light blue) and final (red) positions of digitized lake areas from 12 Landsat images ranging from 22 January 2001 to 1 December 2010. The digitized lake areas are superimposed on a Landsat image from 22 January 2001. Inset shows digitized boundary from each of the 12 images for the lake indicated by the arrow. The headland located in the lower right portion of the figure is identified as the source of propagating lakes. (b) Magnitude (m a−1, colors) and direction (vectors) of ice-shelf velocity from multiple satellite interferometric synthetic-aperture radar data, acquired from 2007 to 2009 and compiled byRignot et al. [2011] (refer to their paper for description of uncertainty). Inset: close up of the study area. The white boxes indicate the location of the Landsat images studied in Figure 2a. [5] In Figure 2, a comparison is made between the observed propagation of the digitized lakes and the ice shelf velocity derived from the satellite interferometric synthetic-aperture data compiled byRignot et al. [2011]. The average speed of lake propagation varies between 300 m a−1 and 760 m a−1 depending on location along the coastline. The average for the entire group of 11 lakes is 450 m a−1. Error in observed propagation speed is related to errors in the manual digitization process, approximately 30 m, and to fluctuations in lake water level from year to year, which causes the center of area of successive representations of a given lake to fluctuate of the order of 100 m. We estimate overall error in the average lake propagation speed to be to be approximately 60 m a−1. The magnitude of ice-shelf velocity does not exceed 175 m a−1 in the study area depicted in Figure 2a, and decreases to 0 m a−1 at the coastline (uncertainty of ice velocity shown in Figure 2 is given by Rignot et al. [2011]). The direction of lake propagation follows the trend of the coastline, not the direction of ice flow, and can differ from the local ice flow direction by as much as 60°. 3. Buckle-Wave Model [6] We have developed a simple qualitative model of lake propagation that is based purely on kinematical considerations, and offer it as a working hypothesis for use in exploring the dynamics of these lakes. Previous studies of compressive stress regimes on ice shelves are relatively rare, as ice-shelf flow is generally divergent in the horizontal plane [e.g.,Thomas, 1979]; however, work has been done where flow is directed toward shorelines on Ellesmere Island ice shelves [Hattersley-Smith, 1957], the McMurdo Ice Shelf [Collins and McCrae, 1985] and the Ross Ice Shelf near the Little America Station [Kehle, 1964]. These studies have motivated the concept of a viscous-buckling wave, or pressure roller, that can produce a sinusoidal flexure profile in the ice shelf parallel to the direction of compressive stress. (Such phenomena are also described in the tectonics literature, and have been referred to as sinuous boudinage [e.g., seeSmith, 1977].) A well known property of viscous buckling [Ribe, 2003] is that the sinusoidal waves typically decay exponentially away from boundaries where they form. Applying the concept of a viscous buckle wave, we hypothesize that exponentially damped sinusoidal buckle waves are present on the George VI Ice Shelf and reach their maximum amplitude along the boundary of the ice shelf with Alexander Island. We show a schematic diagram of this damped sinusoid in Figure 3a. The troughs of the sinusoid are indicated by bold parallel lines that impinge on the coast obliquely. Where the troughs of the sinusoidal waves are sufficiently amplified by having come sufficiently close to the coast, they fill with surface meltwater to form a lake. Figure 3Open in figure viewerPowerPoint Wave kinematics along a coastline. (a) If the amplitude of the viscous-buckle wave decays with distance from coastline, and if lakes are expressed (visible) where troughs are within a boundary zone (between the coast and the dashed line) determined by this decay distance, lakes will appear to migrate along the coastline as advancing troughs impinge obliquely on the coast. Inset: 5 roots of the dispersion relation for the viscous-buckle wave equation when = 0. (b) The lines of constant phase (i.e., troughs containing surface meltwater) impinge on the coastline obliquely, the apparent propagation of the phase along the coastline, c = V/sin θ, will be larger than the speed, V, with which the troughs advance by the ice flow, because sin θ < 1. [7] We further assume that the coastline is nearly, but not exactly, parallel to the direction of ice flow axis, as shown in Figure 3b. If the angle, θ, between wave troughs and the coastline is small, the apparent phase velocity, c, of the wave troughs (where lakes will form) will advance along the coastline at a rate that is much larger than the ice flow velocity, V. Figure 3b provides a construction that illustrates this assertion. If we take a value of c ≈ 450 m/a for lake propagation, and a value for θ ≈ 8° determined from the angle the lakes step out from the boundary, we compute a value of V ≈ 63 m/a. This value of V is consistent with the observed ice velocity in the vicinity of the coastline shown in Figure 2b. [8] We propose that viscous buckling generates the phenomena described above. Following the development by Ribe [2003], we examine the viscous buckling equation (in its low order form that assumes small ice thickness to horizontal scale) to determine properties of the vertical deflection of the ice shelf, η(x, y, t), in response to loads, where, ∇4is the bi-harmonic operator involving two horizontal coordinatesx and y, ρ is ice density, g is the acceleration of gravity, P and S represent the vertically integrated horizontal (x, y)-plane stresses,P represents a compressive longitudinal stress in the x direction, where x is taken to be the horizontal coordinate in the direction of flow, S represents a shear stress along the boundary (assumed to be in the y-direction),ρwgd is an applied meltwater load, assuming standing water depth of d and water density ρw, and is the viscous buckling constant, where νis the effective ice-shelf viscosity, andhis the ice-shelf thickness. For now, we treat ice as a viscous fluid. The deflection rate,W, is defined to be the material time derivative of the vertical deflection, η. Allowing for ice-shelf flow toward the boundary with vertically homogeneous velocityV [Ribe, 2003]: Dimensional Analysis [9] We define the following non-dimensional variables:x = Lx′, y = Ly′, η = Aη′, and t = t′, where L is a horizontal length scale, A is the amplitude (which we take to be unity) of the vertical deflection, and V is the velocity scale, and use them to express the homogeneous (where there is no meltwater loading) form of the viscous buckling equation: where and We have assumed S = 0 in equation (4), because the ice flow is directed predominantly toward the coastline, thereby producing little shear (Figure 2b). If we assume = 1, i.e., a balance between vertical force induced by viscous deformation of the ice shelf (the first term on the left hand side of equation (4)) with that of buoyancy (the second term on the left hand side of equation (4)) we deduce a length scale for the horizontal width of the viscous buckles (and lakes that they subsequently create): Choosing scales: ν = 1015 Pa s, h = 102 m, V = 100 m/a, ρg = 104 Pa m−1, gives L = 243 m. This scale is consistent with the perpendicular to coastline variable width of the lakes observed in the imagery, which ranges from 0 m to 500 m in the imagery studied. [10] Pearson and Rose [1983] observed a compressive strain rate of roughly 5 × 10−3 a−1 along the coast of Alexander island. This, and the other values of assumed scales given above gives P ≈ 0.5. If we assume a traveling plane wave of the form, where i = , k is a complex wave number, and τ = x′ + t′ is a phase variable, we obtain the following dispersion relation for k: We have examined the above dispersion relation for a range of surrounding 0.5, and have found that at least two roots, k, representing waves of a damped sinusoid form continue to exist. When P = 0 and = 0 zero compressive stress in the ice shelf against the boundary, the dispersion relation becomes The 5 roots for k are shown in the inset of Figure 3a. Three of these roots can be discarded as unphysical leading to exponential increase of amplitude away from a boundary or, as in the case of the purely imaginary root, no exponential decay. The remaining two roots, circled in the inset of Figure 3a, provide physically acceptable solutions. Both have exponential decay of the order of the length scale L. 4. Conclusion [11] The George IV Ice Shelf (Figure 1d) is notable for its widespread and long-persisting system of seasonal surface meltwater lakes and channels [e.g.,Wager, 1972; also T. O. Holt, personal communication, 2011]. On other ice shelves, standing surface water features can lead to catastrophic break-up [e.g.,Scambos et al., 2003; van den Broeke, 2005; Glasser and Scambos, 2008; Scambos et al., 2009]. The apparent stability of the George IV Ice Shelf in spite of the longstanding presence of surface water sets the ice shelf apart from others on the Antarctic Peninsula. This stability is considered to be a consequence of the atypical flow regime leading to strong compressive strain rates in parts of the ice shelf most subject to surface meltwater ponding [Humbert, 2007]. [12] The purposes of the present paper have been to 1) present evidence for traveling lakes along the boundary of the George VI Ice Shelf, and 2) develop a simple kinematic model of the waves. We close by asking what the existence of these waves implies for ice-shelf stability and grounding-line dynamics. Clearly, the fact that these lakes are formed by aspects of ice dynamics involving wave-like viscous deformation motivates the proposition that other surface lakes on ice shelves may also be organized in this way. If indeed lakes outside of the boundary layer along a compressive coastline are influenced by viscous buckling, we may expect that ice-shelf vulnerability to the presence of standing meltwater bodies may also be mediated by viscous effects. We do not test this proposition here, but remark that the observations presented here motivate further study on this proposition. [13] The viscous bending associated with the lakes is one example of the more general problem of viscous flow across a grounding line [e.g., Schoof, 2011]. However, it is essential to remind that the lakes studied here are the physical expression of an atypical ice-shelf flow regime. However, the prominent role of viscous bending in our example may serve to highlight viscous bending near grounding lines under a more typical (i.e., extensional and directed away from land) ice-shelf flow regime. The grounding zone where traveling lakes form on George VI Ice Shelf may represent a useful testing ground for theories of grounding line behavior over a wide range of parameters, not necessarily limited to the atypical landward flow exhibited over parts of the George VI Ice Shelf. Acknowledgments [14] Funding for this project was provided by the U.S. National Science Foundation (ANT0944248). We thank Mac Cathles, Kristopher Darnell, Jason Amundson, Linghan Li, Helen Fricker, Olga Sergienko, John Reynolds, Anja Slim, M. Mahadevan, Jeremy Bassis, David Sugden, Michael Bentley, Tom Holt and various attendees of the British Branch Meeting of the IGS held in 2011 for helpful discussions and guidance. Bernd Scheuchl and the Editor provided access to the comprehensive Antarctic ice velocity data used in this study. We thank referees Neil Glasser and Ian Willis for reviews that significantly improved the paper. [15] The Editor thanks Neil Glasser and Ian Willis for their assistance in evaluating this paper. Supporting Information Auxiliary material for this article contains a figure and an animation that illustrate the propagation of en echelon lakes using Landsat 7 imagery. Auxiliary material files may require downloading to a local drive depending on platform, browser, configuration, and size. To open auxiliary materials in a browser, click on the label. To download, Right-click and select “Save Target As…” (PC) or CTRL-click and select “Download Link to Disk” (Mac). Additional file information is provided in the readme.txt. Filename Description grl28770-sup-0001-readme.txtplain text document, 1.2 KB readme.txt grl28770-sup-0002-fs01.pdfPDF document, 797 KB Figure S1. Propagating en echelon lakes along the Alexander Island boundary of George VI Ice Shelf. grl28770-sup-0003-ms01.mp4MPEG-4 video, 35.4 KB Animation S1. Time-lapse animation of Landsat imagery showing propagation of en echelon lakes. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article. References Collins, I. F., and I. R. McCrae (1985), Creep buckling of ice shelves and the formation of pressure rollers, J. Glaciol., 31(109), 242– 252. Glasser, N. F., and T. A. Scambos (2008), A structural glaciological analysis of the 2002 Larsen B ice-shelf collapse, J. Glaciol., 54(184), 3– 16. Hattersley-Smith, G. (1957), The rolls on the Ellesmere Ice Shelf, Arctic, 10(1), 32– 44. Humbert, A. (2007), Numerical simulations of the ice flow dynamics of George VI Ice Shelf, Antarctica, J. Glaciol., 53(183), 659– 664. 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