Results from the Heinrich Event Intercomparison (HEINO) topic of the Ice-Sheet Model Intercomparison Project (ISMIP) are presented. ISMIP HEINO was designed to explore internal large-scale ice-sheet instabilities in different contemporary ice-sheet models. These instabilities are of interest because they are a possible cause of Heinrich events. A simplified geometry experiment reproduces the main characteristics of the Laurentide ice sheet, including the sedimented region over Hudson Bay and Hudson Strait. The model experiments include a standard run plus seven variations. Nine dynamic/thermodynamic ice-sheet models were investigated; one of these models contains a combination of the shallow-shelf (SSA) and shallow-ice approximation (SIA), while the remaining eight models are of SIA type only. Seven models, including the SIA–SSA model, exhibit oscillatory surges with a period of ∼1000 years for a broad range of parameters, while two models remain in a permanent state of streaming for most parameter settings. In a number of models, the oscillations disappear for high surface temperatures, strong snowfall and small sediment sliding parameters. In turn, low surface temperatures and low snowfall are favourable for the ice-surge cycles. We conclude that further improvement of ice-sheet models is crucial for adequate, robust simulations of cyclic large-scale instabilities.

Here we report a laboratory study of the effects of debris thickness, diurnally cyclic radiation and rainfall on melt rates beneath rock-avalanche debris and sand (representing typical highly permeable supraglacial debris). Under continuous, steady-state radiation, sand cover >50 mm thick delays the onset of ice-surface melting by >12 hours, but subsequent melting matches melt rates of a bare ice surface. Only when diurnal cycles of radiation are imposed does the debris reduce the longterm rate of ice melt beneath it. This is because debris >50 mm thick never reaches a steady-state heat flux, and heat acquired during the light part of the cycle is partially dissipated to the atmosphere during the nocturnal part of the cycle, thereby continuously reducing total heat flux to the ice surface underneath. The thicker the debris, the greater this effect. Rain advects heat from high-permeability supraglacial debris to the ice surface, thereby increasing ablation where thin, highly porous material covers the ice. In contrast, low-permeability rock-avalanche material slows water percolation, and heat transfer through the debris can cease when interstitial water freezes during the cold/night part of the cycle. This frozen interstitial water blocks heat advection to the ice–debris contact during the warm/day part of the cycle, thereby reducing overall ablation. The presence of metre-deep rock-avalanche debris over much of the ablation zone of a glacier can significantly affect the mass balance, and thus the motion, of a glacier. The length and thermal intensity of the diurnal cycle are important controls on ablation, and thus both geographical location and altitude significantly affect the impact of debris on glacial melting rates; the effect of debris cover is magnified at high altitude and in lower latitudes.

Ice originating near the inland ice divide of the ice sheet can reappear as marginal ice at the surface near the ice terminal in the ablation area. We have analyzed δ18O values and ion concentrations of the Skallen, Skarvsnes and Hamna terminal ice sections, located along the estuary line in the Sôya drainage basin, East Antarctica. The data suggest that the upper part of the Skallen terminal ice section could have originated from inland precipitation on the Shirase drainage basin during marine isotope stage (MIS) 5e, while the upper part of Skarvsnes and Hamna terminal ice sections could have originated from inland precipitation on the Sôya drainage basin. We calculate past elevation maps for the Antarctic ice sheet using the three-dimensional model, SICOPOLIS. This model suggests that the upstream portion of the Sôya drainage basin during the glacial period (MIS 2, 3 or 4) was located to the northeast of its present location. A flow history is proposed wherein ice from the inland Shirase drainage area flowed over the present ice-divide line from the Shirase to the Sôya drainage basin during the glacial period. The ice in the Sôya drainage basin then flowed to the marginal part of the sheet after the ice divide had assumed its present position.

Three-dimensional geometric descriptions of microstructure are indispensable to obtain the structure–property relationships of snow. Because snow is a random heterogeneous material, it is often helpful to construct stochastic geometric models that can be used to model physical and mechanical properties of snow. In the present study, the Gaussian random field-based stochastic reconstruction of the sieved and sintered dry-snow sample with grain size less than 1 mm is investigated. The one- and two-point correlation functions of the snow samples are used as input for the stochastic snow model. Several statistical descriptors not used as input to the stochastic reconstruction are computed for the real and reconstructed snow to assess the quality of the reconstructed images. For the snow samples and the reconstructed snow microstructure, we also estimate the mechanical properties and the size of the associated representative volume element using numerical simulations as additional assessment of the quality of the reconstructed images. The results indicate that the stochastic reconstruction technique used in this paper is reasonably accurate, robust and highly efficient in numerical computations for the high-density snow samples we consider.

Using RADARSAT synthetic aperture radar data, we have mapped the flow velocity over much of the Greenland ice sheet for the winters of 2000/01 and 2005/06. These maps provide a detailed view of the ice-sheet flow, including that of the hundreds of glaciers draining the interior. The focused patterns of flow at the coast suggest a strong influence of bedrock topography. Differences between our two maps confirm numerous early observations of accelerated outlet glacier flow as well as revealing previously unrecognized changes. The overall pattern is one of speed-up accompanied by terminus retreat, but there are also several instances of surge behavior and a few cases of glacier slowdown. Comprehensive mappings such as these, at regular intervals, provide an important new observational capability for understanding ice-sheet variability.

Strong ground motions caused by earthquakes can induce catastrophic avalanches. Massive snow avalanching has also been observed on slopes near quarries and underground mines where ground motions are produced by explosives. To address a lack of information regarding seismogenic snow avalanches, we have compiled an inventory to document case histories. For the period 1899–2010, 22 cases are identified worldwide, related to natural or artificial seismicity with magnitudes of 1.9 ≤ Mw ≤ 9.2 and source-to-site distances of ∼0.2–640 km. In the extreme case, many thousands of simultaneously released large-scale avalanches have been reported. The obtained distribution and variety of parameters are discussed and compared with earthquake-induced landslides and ice avalanches; the results are similar among these three types of failure events, although all data derived from statistical analyses (i.e. non-witnessed cases) represent outliers, suggesting a significant reduction in the threshold magnitudes proposed for landslides. This proposal could be verified by the collection of additional data.

We conducted experiments on the stability of snow, subjecting snow to vibrations, with the aim of improving our understanding of poorly studied mechanisms behind the triggering of avalanches during earthquakes. Most experiments were carried out on a specially constructed shaking table using artificial snowpacks containing a weak layer. Accelerations in the snow samples were measured using high-frequency sensors, enabling calculation of vibration-induced stresses within the snow at the moment of fracture. We used a high-speed camera to film different types of fracturing. In all cases, the vibrations caused failure of the snow by fracturing along the weak layer or at the base of the snow sample. An additional inertial stress induced by accelerations normal to the shear plane was quantified. We find that this stress can be related to smaller values of the shear strength in snow.

Long rifts near the front of the Ronne Ice Shelf, Antarctica, are observed to begin as fractures along the lateral boundaries of outlet streams feeding the shelf. These flaws eventually become the planes along which tabular icebergs calve. The fractures propagate laterally as they advect through the shelf, with orientations that can be explained by the glaciological stress field. Fracture length remains constrained over much of the advective path, and locations of crack tip arrest are observed to coincide with structural boundaries, such as suture zones between ice from adjacent outlet glaciers. Geomechanical principles and numerical models demonstrate that in the absence of these suture zones crack tips are unlikely to arrest in these locations. We conclude that lateral inhomogeneity in the ice plays an important role in fracture mechanics through most of the ice shelf. Only near the shelf front are these local structural effects overcome such that the large rifts required for tabular iceberg production develop.

The effect of thermal conductivity on ice friction is studied systematically for different metallic slider materials over a wide range of temperatures, and sliding velocities. By thermally insulating the slider with fiberglass, the isolated effect of thermal conductivity on ice friction is investigated. A decrease of the friction coefficient in the boundary friction regime and an earlier onset of the mixed friction regime in terms of sliding velocity are found. Furthermore, the dependence of the ice friction coefficient on sliding velocity is compared for different sliding materials. It is found that the influence and importance of thermal conductivity decreases with increasing sliding velocity.

The formulation of a physical problem in terms of a variational (or action) principle conveys significant advantages for the analytical formulation and numerical solution of that problem. One such problem is ice-sheet dynamics as described by non-Newtonian Stokes flow, for which the variational principle can be interpreted as stating that a measure of heat dissipation, due to internal deformation and boundary friction, plus the rate of loss of total potential energy is minimized under the constraint of incompressible flow. By carrying out low-aspect-ratio approximations to the Stokes flow problem within this variational principle, we obtain approximate dynamical equations and boundary conditions that are internally consistent and preserve the analytical structure of the full Stokes system. This also allows us to define an action principle for the popular first-order or ‘Blatter–Pattyn’ shallow-ice approximation that is distinct from the action principle for the Stokes problem yet preserves its most important properties and elucidates various details about this approximation. Further approximations within this new action functional yield the standard zero-order shallow-ice and shallow-shelf approximations, with their own action principles and boundary conditions. We emphasize the specification of boundary conditions, which are problematic to derive and implement consistently in approximate models but whose formulation is greatly simplified in a variational setting.

Ice-sheet modelers tend to be more familiar with the Newtonian, vectorial formulation of continuum mechanics, in which the motion of an ice sheet or glacier is determined by the balance of stresses acting on the ice at any instant in time. However, there is also an equivalent and alternative formulation of mechanics where the equations of motion are instead found by invoking a variational principle, often called Hamilton’s principle. In this study, we show that a slightly modified version of Hamilton’s principle can be used to derive the equations of ice-sheet motion. Moreover, Hamilton’s principle provides a pathway in which analytic and numeric approximations can be made directly to the variational principle using the Rayleigh–Ritz method. To this end, we use the Rayleigh–Ritz method to derive a variational principle describing the large-scale flow of ice sheets that stitches the shallow-ice and shallow-shelf approximations together. Numerical examples show that the approximation yields realistic steady-state ice-sheet configurations for a variety of basal tractions and sliding laws. Small parameter expansions show that the approximation reduces to the appropriate asymptotic limits of shallow ice and shallow stream for large and small values of the basal traction number.

Spaceborne microwave radiometers are an attractive tool for observing Antarctic climate because their measurements are related to the snow temperature. However, the conversion from microwave emission to snow temperature is not simple and strongly depends on the emissivity through snow properties. This difficulty in predicting the snow property profile for Antarctic conditions is the main bottleneck in the retrieval of accurate climate information from microwave radiometers. We attempt to explain the vertically polarized emissivity at 19.3 and 37 GHz derived from brightness temperatures acquired by the Special Sensor Microwave/Imager (SSM/I) and physical temperature from the ERA-40 re-analysis. In Antarctica the snow emissivities at 19.3 and 37 GHz are nearly equal, although a decrease with frequency is expected. To explain this, we consider various profiles of snow grain size and density and predict their emissivity using a dense-medium radiative transfer (DMRT) model. The results show that the emissivities cannot be explained by constant profiles of grain size and density. Heterogeneous snowpacks need to be considered. We first test random variations of snow density and grain radius with depth and then monotonic and continuous variations in the snow grain radius. In both cases, we show that an overall increase of the snow grain radius with depth is required to match the observed emissivity in Antarctica. In addition, two parameters characterizing the snow grain profiles are retrieved and compared with (1) in situ measurements of grain size at various locations in East Antarctica, (2) grain size estimated using visible spaceborne radiometers and (3) a semi-empirical relationship for grain growth.

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.

A linear two-level atmospheric model is employed to study the influence of ice-sheet topography on atmospheric stationary waves. In particular, the stationary-wave-induced temperature anomaly is considered locally over a single ice-sheet topography, which is computed using the plastic approximation. It is found that stationary waves induce a local cooling which increases linearly with the ice volume for ice sheets of horizontal extents smaller than ∼1400 km. Beyond this horizontal scale, the dependence of stationary-wave-induced cooling on the ice volume becomes gradually weaker. For a certain ice-sheet size, and for small changes of the surface zonal wind, it is further shown that the strength of the local stationary-wave-induced cooling is proportional to the basic state meridional temperature gradient multiplied by the vertical stratification in the atmosphere. These results are of importance for the nature of the feedback between ice sheets and stationary waves, and may also serve as a basis for parameterizing this feedback in ice-sheet model simulations (e.g. through the Pleistocene glacial/interglacial cycles).

We use ice-penetrating radar data across grounding lines of Siple Dome and Roosevelt Island, Antarctica, to measure the spatial pattern, magnitude and duration of sub-ice-shelf melting at these locations. Stratigraphic layers across the grounding line show, in places, a large-amplitude downwarp at, or slightly downstream of, the grounding line due to sub-ice-shelf basal melting. Localized downwarping indicates that melting is transient; melt rates, or the grounding line position, have changed within a few hundred years in order to produce the observed stratigraphy. Elsewhere, no melt-related stratigraphic signature is preserved. In part, heterogeneity in the amount of sub-ice-shelf melt is due to regional circulation patterns in the sub-shelf cavity, but local (on the order of tens of kilometers) heterogeneity in the melt pattern may reflect small differences in the shape of the ice-shelf base at the grounding line. We find that all of the grounding lines crossed have been in place for at most ∼400 years.