Richard C. A. Hindmarsh

Recent Antarctic Peninsula warming relative to Holocene climate and ice-shelf history

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.

A numerical comparison of approximations to the Stokes equations used in ice sheet and glacier modeling

A computational analysis of the accuracy of different approximations to the Stokes equations for momentum balance used in ice sheet modeling is performed by solving a particular tractable form of the equations appropriate for small perturbations of the ice surface, describing the uniform flow of ice with a Glen rheology on an infinitely long and broad section. The approximants comprise the shallow ice approximation and various schemes for incorporating longitudinal stresses and, in one case, the horizontal gradient of the horizontal plane shear stresses. The simplifications lead to a vertically one-dimensional numerical problem, whose solution can be computed rapidly. The relaxation rate of perturbations as well as other response descriptors for the stable full system and approximants are compared. Compared with the shallow ice approximation, the inclusion of longitudinal stresses increases accuracy at shorter wavelengths, but accuracy is poor at wavelengths around or less than the ice sheet thickness. Even though analysis shows that the horizontal gradients of the horizontal plane shear stresses are of similar magnitude to longitudinal stress effects, computations show, in agreement with glaciological belief, that longitudinal stress effects are more significant and need to be corrected for first in practice. Two schemes, a multilayer scheme and a one-layer scheme, are particularly good and should be investigated further in cases where perturbations from uniformity are large. Some other apparently plausible approximations introduce nonphysical instabilities. New schemes need to be assessed in the way described in this paper before being used in real ice sheet models.

Widespread low rates of Antarctic glacial isostatic adjustment revealed by GPS observations

Bedrock uplift in Antarctica is dominated by a combination of glacial isostatic adjustment (GIA) and elastic response to contemporary mass change. Here, we present spatially extensive GPS observations of Antarctic bedrock uplift, using 52% more stations than previous studies, giving enhanced coverage, and with improved precision. We observe rapid elastic uplift in the northern Antarctic Peninsula. After considering elastic rebound, the GPS data suggests that modeled or empirical GIA uplift signals are often over?estimated, par t icularly the magnitudes of the signal maxima. Our observation that GIA uplift is misrepresented by modeling (weighted root?meansquares of observation?model differences: 4.9–5.0 mm/yr) suggests that, apart from a few regions where large ice mass loss is occurring, the spatial pattern of secular ice mass change derived from Gravity Recovery and Climate Experiment (GRACE) data and GIA models may be unreliable, and that several recent secular Antarctic ice mass loss estimates are systematically biased, mainly too high.

Dynamical processes involved in the retreat of marine ice sheets

Marine ice sheets with mechanics described by the shallow-ice approximation by definition do not couple mechanically with the shelf. Such ice sheets are known to have neutral equilibria. We consider the implications of this for their dynamics and in particular for mechanisms which promote marine ice-sheet retreat. The removal of ice-shelf buttressing leading to enhanced flow in grounded ice is discounted as a significant influence on mechanical grounds. Sea-level rise leading to reduced effective pressures under ice streams is shown to be a feasible mechanism for producing postglacial West Antarctic ice-sheet retreat but is inconsistent with borehole evidence. Warming thins the ice sheet by reducing the average viscosity but does not lead to grounding-line retreat. Internal oscillations either specified or generated via a MacAyeal-Payne thermal mechanism promote migration. This is a noise-induced drift phenomenon stemming from the neutral equilibrium property of marine ice sheets. This migration occurs at quite slow rates, but these are sufficiently large to have possibly played a role in the dynamics of the West Antarctic ice sheet after the glacial maximum. Numerical experiments suggest that it is generally true that while significant changes in thickness can be caused by spatially uniform changes, spatial variability coupled with dynamical variability is needed to cause margin movement.

Potential sea-level rise from Antarctic ice-sheet instability constrained by observations

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.

Deforming beds: Viscous and plastic scales of deformation

Small scale field and laboratory observations of sub-glacial sediment deformation suggest that failure is the predominant method of sediment deformation, while large scale modelling studies using a viscous model of till deformation have been reasonably successful in predicting the geological consequences of ice sheet action. This suggests that the cross-over scale between viscous and plastic deformation occurs at a much larger scale than the grain-grain interaction scale previously thought to be appropriate to deforming till. Sediment deformation and the drainage of sub-glacial areas are considered at different scales, and how these interact to produce failure and viscous behaviour is discussed. A fluctuation length scale is proposed, whose horizontal dimensions are of the order of the depth of the base of deformation (1–10 m). On this length scale, the glacier/deforming bed system is highly variable in time as well as in space. Till deformation occurring at this length scale is plastic, happening though failure events. Three other specific scales are proposed, whose different properties depend on the relative spatial variability of static and seepage pressures and topography. The key theoretical problem which has yet to be solved is how multiple small scale failure events combine into a viscous type flow. This is discussed in the context of self-organised criticality. It is argued that the length scales appropriate for some drainage features are not appreciably larger than the scale for plastic failure events, implying that modelling sub-glacial drainage channels by balancing erosion rates against viscous closure of the channel is misconceived. The outlines of an alternative model involving percolation theory are presented. Certain key questions which can only be settled through observations by glaciologists and glacial geologists are discussed. It is suggested that the difference between lodgement tills and deformation tills reflects the rate of motion of till by deformation, and that lodgement from the ice is unimportant.

Time-step limits for stable solutions of the ice-sheet equation

Various spatial discretizations for the ice sheet are compared for accuracy against analytical solutions in one and two dimensions. The computational efficiency of various iterated and non-iterated marching schemes is compared. The stability properties of different marching schemes, with and without iterations on the non-linear equations, are compared. Newton-Raphson techniques permit the largest time steps. A new technique, which is based on the fact that the dynamics of unstable iterated maps contain information about where the unstable root lies, is shown to improve substantially the performance of Picard iteration at a negligible computational cost.

The stability of a viscous till sheet coupled with ice flow, considered at wavelengths less than the ice thickness

A turbation method is used to analyse the stability of a thin till layer overlain by a deep ice layer. Ice is modelled as a linearly viscous fluid, while the till viscosity has power-law dependence on stress and effective pressure. A linearized set of equations yields descriptions of the coupling of the ice flow with the sediment flow and reveals parameter ranges where the till-perturbation amplitude can grow. This shect-flow instability is an essential part of any theory of drumlin formation and shows that viscous models of till have the ability to explain typical deforming-bed features. This is of great significance for large-scale ice-shect modelling.

Full Stokes modeling of marine ice sheets: influence of the grid size

Abstract Using the finite-element code Elmer, we show that the full Stokes modeling of the ice-sheet/ice-shelf transition we propose can give consistent predictions of grounding-line migration. Like other marine ice-sheet models our approach is highly sensitive to the chosen mesh resolution. However, with a grid size down to <5 km in the vicinity of the grounding line, predictions start to be robust because: (1) whatever the grid size (<5 km) the steady-state grounding-line position is sensibly the same (6 km standard deviation), and (2) with a grid-size refinement in the vicinity of the grounding line (200 m), the steady-state solution is independent of the applied perturbation in fluidity, provided this perturbation remains monotonic.

The role of membrane-like stresses in determining the stability and sensitivity of the Antarctic ice sheets: back pressure and grounding line motion.

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.