Assessment of the importance of ice‐shelf buttressing to ice‐sheet flow

GEOPHYSICAL RESEARCH LETTERS, VOL. 32, L04503, doi:10.1029/2004GL022024, 2005 Assessment of the importance of ice-shelf buttressing to ice-sheet flow T. K. Dupont and R. B. Alley Department of Geosciences and EMS Earth and Environmental Systems Institute, The Pennsylvania State University, University Park, Pennsylvania, USA Received 17 November 2004; revised 5 January 2005; accepted 19 January 2005; published 25 February 2005. [ 1 ] Reduction or loss of a restraining ice shelf will cause speed-up of flow from contiguous ice streams, contributing to sea-level rise, with greater changes from ice streams that are wider, have stickier beds, or have higher driving stress. Loss of buttressing offsetting half of the tendency for ice- stream/ice-shelf spreading for an ice stream similar to Pine Island Glacier, West Antarctica is modeled to contribute at least 1 mm of sea-level rise over a few decades. These results come from a new, simple model that includes relevant stresses in a boundary-layer formulation, and allows rapid estimation of ice-shelf impacts for a wide range of configurations. Citation: Dupont, T. K., and R. B. Alley (2005), Assessment of the importance of ice-shelf buttressing to ice-sheet flow, Geophys. Res. Lett., 32, L04503, doi:10.1029/2004GL022024. 1. Introduction [ 2 ] The non-floating portions of the Antarctic and Green- land ice sheets represent the largest potential sources of sea- level rise on time-scales of human economies. Response times to some environmental forcings are reassuringly long [e.g., Alley and Whillans, 1984], but recent observations from numerous regions show short-time-scale changes (few-annual and shorter) with potential to affect sea level rapidly [Zwally et al., 2002; Anandakrishnan et al., 2003; Thomas et al., 2004; Scambos et al., 2004; Rignot et al., 2004; Joughin et al., 2004; Shepherd et al., 2004]. Of particular importance is the ice-sheet response to changes in their floating extensions, called ice shelves. Shearing of ice shelves past slower-moving ice or rock causes a back- stress [Thomas and MacAyeal, 1982], so ice-shelf thinning or loss leads immediately (stress transmission at the speed of sound) to acceleration of ice-sheet flow contributing to sea-level rise. Ice shelves can be affected rapidly by environmental changes, including increase in basal melting of O(10 m/year) for warming of sub-ice-shelf waters by 1°C [Shepherd et al., 2004], and very rapid collapse (order of days or less) when meltwater wedges open crevasses. Speed-up of ice flow in response to ice-shelf changes is strongly implicated in changes now occurring in places including Jakobshavn Isbrae in Greenland, the former site of the Larsen B ice shelf along the Antarctic Peninsula, and the glaciers draining the West Antarctic ice sheet into Pine Island Bay. [ 3 ] We have developed a simple, fast tool for assessing the importance of ice-shelf buttressing to inland-ice behav- ior, and the early stages of response to loss of that buttress- ing. For a reference case similar to the Pine Island Glacier Copyright 2005 by the American Geophysical Union. 0094-8276/05/2004GL022024 (P.I.G.) ice stream, West Antarctica, loss of buttressing offsetting half of the tendency for ice-stream/ice-shelf spreading leads to sea-level rise of about 1 mm from the ice stream itself, with a response time of about a decade. Response will be greater for ice streams with more buttress- ing, less side drag, more basal drag, and higher driving stress. 2. Model Description [ 4 ] We use a mass- and momentum-balance model of a coupled ice-stream/ice-shelf system, loosely following MacAyeal [1989] as derived by Dupont [2004], solved using what we believe is a glaciologically novel Petrov- Galerkin approach [Dupont, 2004] providing high accuracy rapidly. All variables are non-dimensional unless otherwise noted, with dimensional scales listed in Table 1. The primary variables solved for are the ice thickness h(x, t) and along-flow velocity u(x, t). As shown in Figure 1, the ice stream flows from x = 0 to x = 1 from left to right, through a parallel-sided, unit-width channel. Lateral thick- ness variation is neglected, so that ice is always the same thickness on the sides and in the stream. Side and basal drags are applied in boundary layers, with basal shear replaced by water pressure where ice is afloat. [ 5 ] The elevation of the channel’s bed z r is specified as z r ð x Þ ¼ Ar sw þ b ð x A 1 Þ where r sw is the ratio of the density of seawater to ice, and b is the gradient in bed elevation. Note that given this bed elevation, the flotation thickness h f is h f ð x Þ ¼ 1 þ r sw b ð 1 A x Þ This is the maximum floating-ice thickness, such that ice is grounded if h > h f , and floating otherwise. 2.1. Momentum Balance [ 6 ] We model the momentum balance following MacAyeal [1989], as derived by Dupont [2004, equation (2.65)] with specified channel bed elevation: A @ x 2hn@ x u A h 2 A G s hu n h f h h f This non-dimensional, width-averaged and depth-integrated stress-equilibrium equation is appropriate for thin, channe- lized flow within ice streams and shelves. A fundamental L04503 1 of 4