Robert J. Arthern

Extensive dynamic thinning on the margins of the Greenland and Antarctic ice sheets

Many glaciers along the margins of the Greenland and Antarctic ice sheets are accelerating and, for this reason, contribute increasingly to global sea-level rise. Globally, ice losses contribute ∼1.8 mm yr-1 (ref. 8), but this could increase if the retreat of ice shelves and tidewater glaciers further enhances the loss of grounded ice or initiates the large-scale collapse of vulnerable parts of the ice sheets. Ice loss as a result of accelerated flow, known as dynamic thinning, is so poorly understood that its potential contribution to sea level over the twenty-first century remains unpredictable. Thinning on the ice-sheet scale has been monitored by using repeat satellite altimetry observations to track small changes in surface elevation, but previous sensors could not resolve most fast-flowing coastal glaciers. Here we report the use of high-resolution ICESat (Ice, Cloud and land Elevation Satellite) laser altimetry to map change along the entire grounded margins of the Greenland and Antarctic ice sheets. To isolate the dynamic signal, we compare rates of elevation change from both fast-flowing and slow-flowing ice with those expected from surface mass-balance fluctuations. We find that dynamic thinning of glaciers now reaches all latitudes in Greenland, has intensified on key Antarctic grounding lines, has endured for decades after ice-shelf collapse, penetrates far into the interior of each ice sheet and is spreading as ice shelves thin by ocean-driven melt. In Greenland, glaciers flowing faster than 100 m yr-1 thinned at an average rate of 0.84 m yr-1, and in the Amundsen Sea embayment of Antarctica, thinning exceeded 9.0 m yr-1 for some glaciers. Our results show that the most profound changes in the ice sheets currently result from glacier dynamics at ocean margins.

Antarctic snow accumulation mapped using polarization of 4.3‐cm wavelength microwave emission

Different parts of Antarctica receive different amounts of snowfall each year. In this paper we map the variations of the mean annual snow accumulation across the ice sheet. We also quantify the uncertainty in our estimates more objectively than has been possible for earlier maps. The new map is produced using observations from satellites and ground-based measurements. After a logarithmic transformation, these are combined using the geostatistical method of continuous-part universal kriging to give an estimate of the snow accumulation within each cell of a rectangular grid covering Antarctica. We also derive spatial averages over the major drainage systems of the ice sheet, along with their confidence intervals. We obtain a value of 143 ± 4 kg m−2 a−1 for the average rate of snow accumulation upon the grounded ice sheet of Antarctica.

Initialization of ice-sheet forecasts viewed as an inverse Robin problem

As simulations of 21st-century climate start to include components with longer timescales, such as ice sheets, the initial conditions for those components will become critical to the forecast. This paper describes an algorithm for specifying the initial state of an ice-sheet model, given spatially continuous observations of the surface elevation, the velocity at the surface and the thickness of the ice. The algorithm can be viewed as an inverse procedure to solve for the viscosity or the basal drag coefficient. It applies to incompressible Stokes flow over an impenetrable boundary, and is based upon techniques used in electric impedance tomography; in particular, the minimization of a type of cost function proposed by Kohn and Vogelius. The algorithm can be implemented numerically using only the forward solution of the Stokes equations, with no need to develop a separate adjoint model. The only requirement placed upon the numerical Stokes solver is that boundary conditions of Dirichlet, Neumann and Robin types can be implemented. As an illustrative example, the algorithm is applied to shear flow down an impenetrable inclined plane. A fully three-dimensional test case using a commercially available solver for the Stokes equations is also presented.

Mapping Greenland accumulation rates using observations of thermal emission at 4.5‐cm wavelength

Accurate predictions of sea level rise over the coming century will require improved knowledge of the processes controlling accumulation on the great ice sheets. The sparsity of accumulation rate observations, both temporally and spatially, hinder development of this understanding. We introduce a new method to observe accumulation rates (averaged over roughly a decade) using satellite observations of microwave emission at 4.5-cm wavelength, focusing in this paper on Greenland. At this wavelength, scattering by the grain fabric in firn is unimportant relative to quasi-reflection from density (and thus dielectric permittivity) stratification. We show observationally a strong link between random firn density stratification, on scales of millimeters to centimeters, and accumulation rate. We then show theoretically how the observed density stratification can produce and is consistent with observations of polarization of 4.5-cm-wavelength emission. We employ observations from the Scanning Multichannel Microwave Radiometer (SMMR) and previously published ground observations of accumulation rates in Greenland to complete specification of the relationship between accumulation rate and polarization. The relationship is sufficiently accurate to serve as a basis for mapping accumulation rate fields. We compare our satellite-derived maps with previously published maps based on syntheses of ground data. We find broad agreement between the two types of maps, though the satellite-derived map indicates more strongly the importance of topography and prevailing weather patterns in determining detailed accumulation rate patterns. Finally, we discuss possible refinements and the prospects for improved satellite-derived maps based on a new generation of sensors about to be launched.

Flow speed within the Antarctic ice sheet and its controls inferred from satellite observations

Accurate dynamical models of the Antarctic ice sheet with carefully specified initial conditions and well-calibrated rheological parameters are needed to forecast global sea level. By adapting an inverse method previously used in electric impedance tomography, we infer present-day flow speeds within the ice sheet. This inversion uses satellite observations of surface velocity, snow accumulation rate, and rate of change of surface elevation to estimate the basal drag coefficient and an ice stiffness parameter that influences viscosity. We represent interior ice motion using a vertically integrated approximation to incompressible Stokes flow. This model represents vertical shearing within the ice and membrane stresses caused by horizontal stretching and shearing. Combining observations and model, we recover marked geographical variations in the basal drag coefficient. Relative changes in basal shear stress are smaller. No simple sliding law adequately represents basal shear stress as a function of sliding speed. Low basal shear stress predominates in central East Antarctica, where thick insulating ice allows liquid water at the base to lubricate sliding. Higher shear stress occurs in coastal East Antarctica, where a frozen bed is more likely. Examining Thwaites glacier in more detail shows that the slowest sliding often coincides with elevated basal topography. Differences between our results and a similar adjoint-based inversion suggest that inversion or regularization methods can influence recovered parameters for slow sliding and finer scales; on broader scales we recover a similar pattern of low basal drag underneath major ice streams and extensive regions in East Antarctica that move by basal sliding.

Frequency response of ice streams.

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.

Optimal estimation of changes in the mass of ice sheets

We describe a new approach for estimating changes in ice sheet mass. Two methods are in common use: the ice budget and geodetic methods. The first makes use of separate estimates of the mass fluxes into and out of a domain, differencing them to obtain the local mass balance. The second estimates mass balance directly, using measurements of the change in surface elevation, often from aircraft or satellites. Here we combine ice budget and geodetic approaches to obtain an optimal estimate of mass balance. We seek maximum likelihood solutions for three terms: (1) the rate of change of surface elevation, (2) the rate of snow accumulation, and (3) the local divergence of the ice flux. These estimates are constrained to obey the continuity equation. We allow the location and temporal averaging interval of the estimates to be chosen arbitrarily. This approach can use all relevant measurements. The fidelity of any measurement is lowered by measurement error, and by fluctuations in each of the three terms driven by random year-to-year snowfall variations. We take full account of both error sources, weighting the data so as to minimize the confounding effect of these influences. Realistic covariance between randomly forced fluctuations are provided by a linearized model of ice sheet flow. We test the approach by applying the algorithm to synthetically generated measurements. The method performs better than either ice budget or geodetic methods applied in isolation, and has the important advantage that good estimates may still be derived when measurements appropriate to either technique are lacking or inaccurate.

Determining the contribution of Antarctica to sea-level rise using data assimilation methods

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.

Diverse landscapes beneath Pine Island Glacier influence ice flow

The retreating Pine Island Glacier (PIG), West Antarctica, presently contributes ~5–10% of global sea-level rise. PIG’s retreat rate has increased in recent decades with associated thinning migrating upstream into tributaries feeding the main glacier trunk. To project future change requires modelling that includes robust parameterisation of basal traction, the resistance to ice flow at the bed. However, most ice-sheet models estimate basal traction from satellite-derived surface velocity, without a priori knowledge of the key processes from which it is derived, namely friction at the ice-bed interface and form drag, and the resistance to ice flow that arises as ice deforms to negotiate bed topography. Here, we present high-resolution maps, acquired using ice-penetrating radar, of the bed topography across parts of PIG. Contrary to lower-resolution data currently used for ice-sheet models, these data show a contrasting topography across the ice-bed interface. We show that these diverse subglacial landscapes have an impact on ice flow, and present a challenge for modelling ice-sheet evolution and projecting global sea-level rise from ice-sheet loss.Projecting the future retreat and thus global sea level contributions of Antarctica’s Pine Island Glacier is hampered by a poor grasp of what controls flow at the ice base. Here, via high-resolution ice-radar imaging, the authors show diverse landscapes beneath the glacier fundamentally influence ice flow.

The sensitivity of West Antarctica to the submarine melting feedback.

We use an ice sheet model with realistic initial conditions to forecast how the Amundsen Sea sector of West Antarctica responds to recently observed rates of submarine melting. In these simulations, we isolate the effects of a positive feedback, driven by submarine melt in new ocean cavities flooded during retreat, by allowing the present climate, calving front and melting beneath existing ice shelves to persist over the 21st century. Even without additional forcing from changes in climate, ice shelf collapse, or ice cliff collapse, the model predicts slow, sustained retreat of West Antarctica, driven by the marine ice sheet instability and current levels of ocean-driven melting. When observed rates of melting are included in new subglacial ocean cavities, the simulated sea level contribution increases, and for sufficiently intense melting it accelerates over time. Conditional Bayesian probabilities for sea level contributions can be derived but will require improved predictions of ocean heat delivery.