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Large parts of the Antarctic ice sheet lying on bedrock below sea level may be vulnerable to marine-ice-sheet instability (MISI), a self-sustaining retreat of the grounding line triggered by oceanic or atmospheric changes. There is growing evidence that MISI may be underway throughout the Amundsen Sea embayment (ASE), which contains ice equivalent to more than a metre of global sea-level rise. If triggered in other regions, the centennial to millennial contribution could be several metres. Physically plausible projections are challenging: numerical models with sufficient spatial resolution to simulate grounding-line processes have been too computationally expensive to generate large ensembles for uncertainty assessment, and lower-resolution model projections rely on parameterizations that are only loosely constrained by present day changes. Here we project that the Antarctic ice sheet will contribute up to 30 cm sea-level equivalent by 2100 and 72 cm by 2200 (95% quantiles) where the ASE dominates. Our process-based, statistical approach gives skewed and complex probability distributions (single mode, 10 cm, at 2100; two modes, 49 cm and 6 cm, at 2200). The dependence of sliding on basal friction is a key unknown: nonlinear relationships favour higher contributions. Results are conditional on assessments of MISI risk on the basis of projected triggers under the climate scenario A1B (ref. 9), although sensitivity to these is limited by theoretical and topographical constraints on the rate and extent of ice loss. We find that contributions are restricted by a combination of these constraints, calibration with success in simulating observed ASE losses, and low assessed risk in some basins. Our assessment suggests that upper-bound estimates from low-resolution models and physical arguments (up to a metre by 2100 and around one and a half by 2200) are implausible under current understanding of physical mechanisms and potential triggers.

Fast-flowing glaciers and ice streams are pathways for ice discharge from the interior of the Antarctic Ice Sheet to ice shelves, at rates controlled by conditions at the ice-bed interface. Using recently compiled high-resolution data sets and a standard inverse method, we computed basal shear stress distributions beneath Pine Island and Thwaites Glaciers, which are currently losing mass at an accelerating rate. The inversions reveal the presence of riblike patterns of very high basal shear stress embedded within much larger areas with zero basal shear stress. Their colocation with highs in the gradient of hydraulic potential suggests that subglacial water may control the evolution of these high-shear-stress ribs, potentially causing migration of the grounding line by changes in basal resistance in its vicinity.

Changes at the grounding line of ice streams have consequences for inland ice dynamics and hence sea level. Despite substantial evidence documenting upstream propagation of frontal change, the mechanisms by which these changes are transmitted inland are not well understood. In this vein, the frequency response of an idealized ice stream to periodic forcing in the downstream strain rate is examined for basally and laterally resisted ice streams using a one-dimensional, linearized membrane stress approximation. This reveals two distinct behavioural branches, which we find to correspond to different mechanisms of upstream velocity and thickness propagation, depending on the forcing frequency. At low frequencies (centennial to millennial periods), slope and thickness covary hundreds of kilometres inland, and the shallow-ice approximation is sufficient to explain upstream propagation, which occurs through changes in grounding-line flow and geometry. At high frequencies (decadal to sub-decadal periods), penetration distances are tens of kilometres; while velocity adjusts rapidly to such forcing, thickness varies little and upstream propagation occurs through the direct transmission of membrane stresses. Propagation properties vary significantly between 29 Antarctic ice streams considered. A square-wave function in frontal stress is explored by summing frequency solutions, simulating some aspects of the dynamical response to sudden ice-shelf change.

Rapid warming over the past 50 years on the Antarctic Peninsula is associated with the collapse of a number of ice shelves and accelerating glacier mass loss. In contrast, warming has been comparatively modest over West Antarctica and significant changes have not been observed over most of East Antarctica, suggesting that the ice-core palaeoclimate records available from these areas may not be representative of the climate history of the Antarctic Peninsula. Here we show that the Antarctic Peninsula experienced an early-Holocene warm period followed by stable temperatures, from about 9,200 to 2,500 years ago, that were similar to modern-day levels. Our temperature estimates are based on an ice-core record of deuterium variations from James Ross Island, off the northeastern tip of the Antarctic Peninsula. We find that the late-Holocene development of ice shelves near James Ross Island was coincident with pronounced cooling from 2,500 to 600 years ago. This cooling was part of a millennial-scale climate excursion with opposing anomalies on the eastern and western sides of the Antarctic Peninsula. Although warming of the northeastern Antarctic Peninsula began around 600 years ago, the high rate of warming over the past century is unusual (but not unprecedented) in the context of natural climate variability over the past two millennia. The connection shown here between past temperature and ice-shelf stability suggests that warming for several centuries rendered ice shelves on the northeastern Antarctic Peninsula vulnerable to collapse. Continued warming to temperatures that now exceed the stable conditions of most of the Holocene epoch is likely to cause ice-shelf instability to encroach farther southward along the Antarctic Peninsula.

Membrane stresses act along thin bodies which are relatively well lubricated on both surfaces. They operate in ice sheets because the bottom is either sliding, or is much less viscous than the top owing to stress and heat softening of the basal ice. Ice streams flow over very well lubricated beds, and are restrained at their sides. The ideal of the perfectly slippery bed is considered in this paper, and the propagation of mechanical effects along an ice stream considered by applying spatially varying horizontal body forces. Propagation distances depend sensitively on the rheological index, and can be very large for ice-type rheologies.A new analytical solution for ice-shelf profiles and grounded tractionless stream profiles is presented, which show blow up of the profile in a finite distance upstream at locations where the flux is non-zero. This is a feature of an earlier analytical solution for a floating shelf.The length scale of decay of membrane stresses from the grounding line is investigated through scale analysis. In ice sheets, such effects decay over distances of several tens of kilometres, creating a vertical boundary layer between sheet flow and shelf flow, where membrane stresses adjust. Bounded, physically reasonable steady surface profiles only exist conditionally in this boundary layer. Where bounded steady profiles exist, adjacent profile equilibria for the whole ice sheet corresponding to different grounded areas occur (neutral equilibrium). If no solution in the boundary layer can exist, the ice-sheet profile must change.The conditions for existence can be written in terms of whether the basal rate factor (sliding or internal deformation) is too large to permit a steady solution. The critical value depends extremely sensitively on ice velocity and the back stress applied at the grounding line. High ice velocity and high stress both favour the existence of solutions and stability. Changes in these parameters can cause the steady solution existence criterion to be traversed, and the ice-sheet dynamics to change.A finite difference model which represents both neutral equilibrium and the dynamical transition is presented, and preliminary investigations into its numerical sensitivity are carried out. Evidence for the existence of a long wavelength instability is presented through the solution of a numerical eigenproblem, which will hamper predictability.

The problem of forecasting the future behaviour of the Antarctic ice sheet is considered. We describe a method for optimizing this forecast by combining a model of ice sheet flow with observations. Under certain assumptions, a linearized model of glacial flow can be combined with observations of the thickness change, snow accumulation, and ice-flow, to forecast the Antarctic contribution to sea-level rise. Numerical simulations show that this approach can potentially be used to test whether changes observed in Antarctica are consistent with the natural forcing of a stable ice sheet by snowfall fluctuations. To make predictions under less restrictive assumptions, improvements in models of ice flow are needed. Some of the challenges that this prediction problem poses are highlighted, and potentially useful approaches drawn from numerical weather prediction are discussed.