Todd K. Dupont

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

Acceleration of Pine Island and Thwaites Glaciers, West Antarctica

Abstract Recent satellite investigations revealed that in the 1990s the grounding line of Pine Island and Thwaites Glaciers, West Antarctica, retreated several km, the ice surface on the interior of the basins lowered 10 cm a–1, and Pine Island Glacier thinned 1.6 ma–1. These observations, however, were not sufficient to determine the cause of the changes. Here, we present satellite radar interferometry data that show the thinning and retreat of Pine Island Glacier are caused by an acceleration of ice flow of about 18 ± 2% in 8 years. Thwaites Glacier maintained a nearly constant flow regime at its center, but widened along the sides, and increased its 30 ± 15% mass deficit by another 4% in 4 years. The combined mass loss from both glaciers, if correct, contributes an estimated 0.08 ± 0.03 mma–1 global sea-level rise in 2000.

Effect of Sedimentation on Ice-Sheet Grounding-Line Stability

Sedimentation filling space beneath ice shelves helps to stabilize ice sheets against grounding-line retreat in response to a rise in relative sea level of at least several meters. Recent Antarctic changes thus cannot be attributed to sea-level rise, strengthening earlier interpretations that warming has driven ice-sheet mass loss. Large sea-level rise, such as the ≈100-meter rise at the end of the last ice age, may overwhelm the stabilizing feedback from sedimentation, but smaller sea-level changes are unlikely to have synchronized the behavior of ice sheets in the past.

Access of surface meltwater to beds of sub-freezing glaciers: preliminary insights

Abstract Sufficiently deep water-filled fractures can penetrate even cold ice-sheet ice, but glaciogenic stresses are typically smaller than needed to propagate water-filled fractures that are less than a few tens of meters deep, as shown by our simplified analytical treatment based on analogous models of magmatic processes. However, water-filled fractures are inferred to reach the bed of Greenland through >1 km of ice and then collapse to form moulins, which are observed. Supraglacial lakes appear especially important among possible crack ‘nucleation’ mechanisms, because lakes can warm ice, supply water, and increase the pressure driving water flow and ice cracking.

A simple law for ice-shelf calving.

A major problem for ice-sheet models is that no physically based law for the calving process has been established. Comparison across a diverse set of ice shelves demonstrates that iceberg calving increases with the along-flow spreading rate of a shelf. This relation suggests that frictional buttressing loss, which increases spreading, also leads to shelf retreat, a process known to accelerate ice-sheet flow and contribute to sea-level rise.

Sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions: A model study

We use a finite-element model of coupled ice-stream/ice-shelf flow to study the sensitivity of Pine Island Glacier, West Antarctica, to changes in ice-shelf and basal conditions. By tuning a softening coefficient of the ice along the glacier margins, and a basal friction coefficient controlling the distribution of basal shear stress underneath the ice stream, we are able to match model velocity to that observed with interferometric synthetic aperture radar (InSAR). We use the model to investigate the effect of small perturbations on ice flow. We find that a 5.5 13% reduction in our initial ice-shelf area increases the glacier velocity by 3.5 10% at the grounding line. The removal of the entire ice shelf increases the grounding-line velocity by > 70%. The changes in velocity associated with ice-shelf reduction are felt several tens of km inland. Alternatively, a 5% reduction in basal shear stress increases the glacier velocity by 13% at the grounding line. By contrast, softening of the glacier side margins would have to be increased a lot more to produce a comparable change in ice velocity. Hence, both the ice-shelf buttressing and the basal shear stress contribute significant resistance to the flow of Pine Island Glacier.

Conditions for the reversal of ice/air surface slope on ice streams and shelves: a model study

Abstract Reversals in the ice/air surface slope are important in geomorphic and glaciological contexts, thus motivating consideration of the conditions under which they form. Surface slope reversals are seen in numerous places, such as ice rumples on ice shelves, as surficial lakes, and at the down-glacier end of Vostok lake, Antarctica. Such slope reversals can reduce or reverse the subglacial hydrological gradient, thereby rerouting subglacial water transport and possibly leading to the creation of subglacial lakes. Supraglacial lakes produced by slope reversals in ablation zones may aid in driving water-filled cracks that allow surface water access to the bed. Surface slope reversals, in the absence of a concomitant reversal in ice flow, indicate a local violation of the so-called ‘shallow-ice’ approximation, and in this circumstance the longitudinal deviatoric stress becomes critical in the stress equilibrium. Using a simple numerical model, we have explored the conditions under which surface slope reversals form for certain simple scenarios. The results indicate that ice which initially possesses a normal slope will tend toward a reversed slope if the ice is thinned, the bed is strengthened or the downstream buttressing is increased.