Any model of snow avalanches must be able to reproduce velocity profiles. This is a key problem in avalanche science because the profiles are the result of a multitude of snow/ice particle interactions that, in the fend, define the rheology of flowing snow. Recent measurements on real-scale avalanches show that the velocity profiles change from a highly sheared profile at the avalanche front to a plug-like profile at the avalanche tail, preventing the application of a single, simple rheology to the avalanche problem. In this paper, we model not only the velocity profiles but also the evolution of the velocity profiles, by taking into account the production and decay of the kinetic energy of the random motion of the snow granules. We find that the generation of this random energy depends on the distribution of viscous shearing within the avalanche. Conversely, the viscous shearing depends on the magnitude of the random energy and therefore its collisional dissipation. Thus, there is a self–consistency problem that must be resolved in order to predict the amount of random energy and therefore the velocity profiles. We solve this problem by stating equations that describe the production and decay of random energy in avalanches. An important guide to the form of these equations is that the generation of random energy is irreversible. We show that our approach successfully accounts for measured profiles in natural avalanches.

A linear stability analysis of a two-dimensional flow of an isothermal ice sheet interacting with the ocean is considered. The set of boundary conditions determining motion of the grounding line is adopted to describe hydrostatic equilibrium of ice in water and a cubic dependence of the mass flow rate on ice thickness. The numerical analysis shows that the zero-growth (zero-eigenvalue) mode found for linear bed slopes and constant accumulation rates indeed determines neutral equilibrium and separates stable and unstable solutions. It is also argued that, provided some conditions of regularity of the solutions are satisfied, finding only one stable and one unstable solution would be enough to ascertain that the condition determining a zero eigenvalue also determines neutral equilibrium. This supports the intuitive understanding of ice-sheet stability: ice sheets are stable on bed slopes that ensure that the mass flow rate at the grounding line increases faster than the cumulative ice accumulation rate at the surface when the grounding line is perturbed; and ice sheets are unstable otherwise.

From 1999 to 2001 a 724 m deep ice core was drilled on Akademii Nauk ice cap, Severnaya Zemlya, to gain high-resolution proxy data from the central Russian Arctic. Despite strong summertime meltwater percolation, this ice core provides valuable information on the regional climate and environmental history. We present data of stable water isotopes, melt-layer content and major ions from the uppermost 57 m of this core, covering the period 1883–1998. Dating was achieved by counting seasonal isotopic cycles and using reference horizons. Multi-annual δ18O values reflect Eurasian sub-Arctic and Arctic surface air-temperature variations. We found strong correlations to instrumental temperature data from some stations (e.g. r = 0.62 for Vardø, northern Norway). The δ18O values show pronounced 20th-century temperature changes, with a strong rise about 1920 and the absolute temperature maximum in the 1930s. A recent decrease in the deuterium-excess time series indicates an increasing role of the Kara Sea as a regional moisture source. From the multi-annual ion variations we deduced decreasing sea-salt aerosol trends in the 20th century, as reflected by sodium and chloride, whereas sulphate and nitrate are strongly affected by anthropogenic pollution.

We use an empirically validated high-resolution three-dimensional ice-sheet model to investigate the mass-balance regime, flow mechanisms and subglacial characteristics of a simulated Younger Dryas Stadial ice cap in Scotland, and compare the resulting model forecasts with geological evidence. Input data for the model are basal topography, a temperature forcing derived from GRIP δ18O fluctuations and a precipitation distribution interpolated from modern data. The model employs a positive-degree-day scheme to calculate net mass balance within a domain of 112500 km2, which, under the imposed climate, gives rise to an elongate ice cap along the axis of the western Scottish Highlands. At its maximum, the ice cap is dynamically and thermally zoned, reflecting topographic and climatic controls, respectively. In order to link these palaeoglaciological conditions to geological interpretations, we calculate the relative balance between sliding and creep within the simulated ice cap, forecast areas of the ice cap with the greatest capacity for basal erosion and predict the likely pattern of subglacial drainage. We conclude that ice flow in central areas of the ice cap is largely due to internal deformation, and is associated with geological evidence of landscape preservation. Conversely, the distribution of streamlined landforms is linked to faster-flowing ice whose velocity is predominantly the result of basal sliding. The geometry of the main ice mass focuses subglacial erosion in the mid-sections of topographic troughs, and produces glaciohydraulic gradients that favour subglacial drainage through low-order arterial routes.

In situ field measurements of an active polynya in Storfjorden, Svalbard, during April 2006 are presented. A surface heat flux, estimated to be 400 W m−2, produced frazil ice that was advected away from the fast ice edge during the end of a polynya event driven by cold winds from the northeast. Conductivity, temperature and depth casts from the fast ice edge of the polynya were calibrated by accompanying water samples, and reveal a supercooling event that lasted for 3 days in a 5 m deep water column. Surface salinity reached 35.9 psu from brine release during ice growth. The maximum supercooling measured was 0.037 ± 0.005°C below the in situ freezing point near the surface and 0.016 ± 0.005°C at the bottom; the mean supercooling gradient was 0.020 ± 0.005°C between the surface and the bottom. These measurements are consistent with results from a one-dimensional frazil ice model, confirming that such supercooling levels can be expected. Frazil ice concentrations in the water were modeled to be lower than 0.02 g L−1, due to advection in the surface layer. Seven frazil/grease ice samples taken from a place where advection was blocked along the fast ice edge showed a mean salinity of 26.2 psu, indicating 25% frazil ice and 75% sea water in the grease ice. The water-column salinity decreased during the measurement period due to less saline water replacing newly formed brine-enriched shelf water flowing down to deeper parts of Storfjorden. The supercooling ceased when the wind direction turned to the east, with higher air temperatures and warmer and less saline water being pushed into Storfjorden by the northward Ekman transport. These are the first in situ observations from an active Arctic polynya with concurrent sampling of hydrography and frazil ice, and the supercooling is the maximum observed in recent years with modern and accurate instrumentation.

Two diagnostic, dynamic/thermodynamic ice-shelf models are applied to the Brunt Ice Shelf/Stancomb-Wills Ice Tongue system, located off Caird Coast, Coats Land, Antarctica. The Brunt Ice Shelf/Stancomb-Wills Ice Tongue system is characterized as a thin, unbounded ice shelf with an atypical and highly heterogeneous structure. In contrast to other ice shelves, a composite mass of icebergs that calved at the grounding line and were then locked within fast (sea) ice exists between the fast-moving Stancomb-Wills Ice Stream and the slow-moving Brunt Ice Shelf. We simulate the present flow regime of the ice shelf that results from the ice-thickness distribution and the inflow at the grounding line with two different models, and compare the model results with feature tracking and InSAR flow velocities. We then incorporate two observed features, a rift and a shear margin, into the models with two different approaches, and demonstrate the effects of variations in numerical values for the shear strength and viscosity in these zones on the simulated velocity field. A major result is that both kinds of implementation of the rifts lead to similar effects on the entire velocity field, while there are discrepancies in the vicinity of the rifts.

On uncrevassed regions of polythermal glaciers, englacial conduits can form by incision of supraglacial stream channels followed by roof closure. The origin and evolution of examples in Longyearbreen, Svalbard, and Khumbu Glacier, Nepal, were determined by speleological survey. The development of perennial incised channels requires that incision is significantly faster than glacier surface ablation, and thus will be favoured by high meltwater discharges in combination with cool climatic conditions or thick debris cover. Incised canyons can become blocked by drifted winter snow, refrozen meltwater, ice rafting from non-local sources (allochthonous breccias) and roof collapses (autochthonous breccias). Conduit closure can also occur in response to ice creep, particularly at depth. Following isolation from the surface, englacial conduits continue to evolve by vadose incision down to local base level. In the case of Longyearbreen, incision allowed the channel to reach the glacier bed, but on Khumbu Glacier deep incision is prevented because an effectively impermeable terminal moraine provides a high base level for the glacier drainage system. During our period of observations, deeper parts of the Longyearbreen conduit became blocked by a combination of ice accumulation and creep, causing the stream course to be re-routed to higher levels. On that glacier, incision, blockage and upward re-routing are cyclic. We conclude that ‘cut and closure’ is the dominant mechanism of englacial conduit formation on uncrevassed regions of polythermal glaciers.

We report impedance measurements of the complex dielectric permittivity ε = ε′ − jε″ of sea ice and laboratory-grown NaCl single crystals using 50 MHz Stevens Water Monitoring Systems Hydra Probes. Temperature cycling of the single-crystal samples shows hydrohalite precipitation, and hysteresis in ε′ and ε″ qualitatively consistent with the expected evolution of brine-inclusion microstructure. Measurements parallel and perpendicular to intra-crystalline brine layers show weak (<10%) anisotropy in ε′ and a 20–40% difference in ε″ due to enhanced d.c. conductivity along the layers. Measurements in landfast, first-year ice near Barrow, Alaska, USA, indicate brine motion in warming ice as the brine volume fraction vb increases above 5%. Plots of vb derived from salinity profiles against ε′ and ε″ for these and previous measurements display too much variability between datasets for unguided inversion of vb. Contributing to this variability are intrinsic microstructural dependence, uncertainties in vb, and sub-representative sample volumes. A standard model of sea-ice permittivity is inverted to derive the apparent brine-inclusion aspect ratio and bulk d.c. conductivity at a spatial scale complementary to previous measurements. We assess Hydra Probe performance in high-salinity environments and conclude that they are not generally suited for autonomous sea-ice salinity measurements, partly due to the range of relevant brine pocket inclusion length scales.

Near-surface air temperature (2 m) over the Greenland ice sheet (GrIS) is parameterized using data from automatic weather stations located on land and on the ice sheet. The parameterization is expressed in terms of mean annual temperatures and mean July temperatures, both depending linearly on altitude, latitude and longitude. The temperature parameterization is compared to a previous study and is shown to be in better agreement with observations. The temperature parameterization is tested in a positive degree-day model to simulate the present (1996–2006) mean melt area extent of the GrIS. The model accounts for firn warming, rainfall and refreezing of meltwater, with different degree-day factors for ice and snow under warm and cold climate conditions. The simulated melt area extent is found to have reasonable agreement with satellite-derived observations.

Photogrammetric processing of archival stereo imagery offers the opportunity to reconstruct glacier volume changes for regions where no such data exist, and to better constrain the contribution to sea-level rise from small glaciers and ice caps. The ability to derive digital elevation model (DEM) measurements of glacier volume from photogrammetry relies on good-quality, well-distributed ground reference data, which may be difficult to acquire. This study shows that ground-control points (GCPs) can be identified and extracted from point-cloud airborne lidar data and used to control photogrammetric glacier models. The technique is applied to midtre Lovénbreen, a small valley glacier in northwest Svalbard. We show that the amount of ground control measured and the elevation accuracy of GCP coordinates (based on known and theoretical error considerations) has a significant effect on photogrammetric model statistics, DEM accuracy and the subsequent geodetic measurement of glacier volume change. Models controlled with fewer than 20 lidar control points or GCPs from sub-optimal areas within the swath footprint overestimated volume change by 14–53% over a 2 year period. DEMs derived from models utilizing 20–25 or more GCPs, however, gave volume change estimates within ∼4% of those from repeat lidar data (−0.51 m a−1 between 2003 and 2005). Our results have important implications for the measurement of glacier volume change from archival stereo-imagery sources.

Inclusions affect the behavior of ice, and their characteristics help us understand the formation history of the ice. Recently, a low-temperature magnesium sulfate salt was discovered. This paper describes this naturally occurring MgSO4·11H2O mineral, meridianiite, derived from salt inclusions in sea ice of Lake Saroma, Japan and in Antarctic continental core ice. Its occurrence is confirmed by using micro-Raman spectroscopy to compare Raman spectra of synthetic MgSO4·11H2O with those of the inclusions.

Melt factors for snow (ks) and ice (ki) were derived from specific mass-balance data and regionally interpolated daily air-temperature series at nine glaciers in the western Cordillera of Canada. Fitted ks and ki were relatively consistent across the region, with mean values (standard deviations) of 3.04 (0.38) and 4.59 (0.59) mm d−1 °C−1, respectively. The interannual variability of melt factors was investigated for two long-term datasets. Calculated annually, snow- and ice-melt factors were relatively stable from year to year; standard deviations for snowmelt factors were 0.48 (17%) and 0.42 (18%) at Peyto and Place Glaciers, respectively, while standard deviations of ice-melt factors were 1.17 (25%) and 0.81 (14%). While fitted values of ks are comparable to those presented in previous observational and modeling studies, fitted ki are substantially and consistently lower across the region. Fitted melt factors were sensitive to the choice of lapse rate used in the air-temperature interpolation. Melt factors fitted to mass-balance data from a single site (Place Glacier) provided reasonable summer balance predictions at most other sites representing both maritime and continental climates, although there was a tendency for under-prediction at several sites. The combination of regionally interpolated air temperatures and a degree-day model appears capable of generating first-order estimates of regional summer balance, which can provide a benchmark against which to judge the predictive ability of more complex (e.g. energy balance) models applied at a regional scale. Mass-balance sensitivity analyses indicate that a temperature increase of 1 K will increase summer ablation in the region by 0.51 m w.e. a−1 on average.

Deep, pervasive shear deformation of the bed to high strains (>100) may have been primarily responsible for flow and sediment transport of the Lake Michigan lobe of the Laurentide ice sheet. To test this hypothesis, we sampled at 0.2 m increments a basal till from one advance of the lobe (Batestown till) along vertical profiles and measured fabrics due to both anisotropy of magnetic susceptibility and sand-grain preferred orientation. Unlike past fabric studies, interpretations were guided by results of laboratory experiments in which this till was deformed in simple shear to high strains. Fabric strengths indicate that more than half of the till sampled has a <5% probability of having been sheared to moderate strains (7–30). Secular changes in fabric azimuth over the thickness of the till, probably due to changing ice-flow direction as the lobe receded, indicate that the bed accreted with time and that the depth of deformation of the bed did not exceed a few decimeters. Orientations of principal magnetic susceptibilities show that the state of strain was commonly complex, deviating from bed-parallel simple shear. Deformation is inferred to have been focused in shallow, temporally variable patches during till deposition from ice.

Aircraft laser-altimeter surveys during the 1990s showed near-coastal parts of the Greenland ice sheet to be thinning; despite slow thickening at higher elevations, the ice sheet lost mass to the ocean. Many outlet glaciers thinned more rapidly than could be explained by increased melting during the recent warmer summers, indicating dynamic imbalance between glacier velocity and upstream snow accumulation. Results from more recent surveys, presented here, show that thinning rates have increased in most coastal regions. For almost half of the surveys, these increases might have resulted from increases in summer melting, but rapid thinning on others is indicative of dynamic changes that increased with time. In particular, thinning rates on the three fastest glaciers increased to tens of m a−1 after 2000, and other observations show an approximate doubling in their velocities. The deep beds of these glaciers appear to have a strong influence on rates of grounding-line retreat and thickness change, with periods of glacier acceleration and rapid thinning initiated by flotation and break-up of lightly grounded glacier snouts or break-up of floating ice tongues. Near-simultaneous thinning of these widely separated glaciers suggests that warming of deeper ocean waters might be a common cause. Nearby glaciers without deep beds are thinning far more slowly, suggesting that basal lubrication as a result of increased surface melting has only a marginal impact on Greenland outlet-glacier acceleration

An investigation was made to estimate the variance, measurement errors and sampling error in currently accepted practices for manual snow density measurement carried out as part of snow profile observations using the available variety of density cutters. A field experiment in dry snow conditions was conducted using a randomized block design to account for layer spatial variability. Cutter types included a 500 cm3 aluminium tube, 200 and 100 cm3 stainless-steel box types, 200 cm3 stainless-steel wedge types and a 100 cm3 stainless-steel tube. Without accounting for variation due to weighing devices, the range of values for ‘accepted practice’ determined in this study included variation within individual cutters of 0.8–6.2%, variation between cutters of 3–12%, variation between cutter means and layer means of 2–7%, and under-sampling errors of 0–2%. The results of a statistical analysis suggest that snow density measurements taken using various density cutters are significantly different from each other. Without adjustment for under-sampling, and given that the mean of all measurements is the accepted true value of the layer density, variation exclusively between cutter types provides ‘accepted practice’ measurements that are within 11% of the true density.

As an ice sheet evolves, there are ice elements near the surface only recently subjected to stress following deposition, and others that have been subjected to stress over many ranges of time. The constant stress and constant strain-rate responses of ice in uniaxial compressive stress exhibit non-viscous behaviour, that is, the strain rate is not fixed by the stress (and conversely) but both vary with time. At constant stress the initial primary strain rate decreases with time to a minimum, described as secondary creep. It then increases and approaches an asymptotic limit, described as tertiary creep. Analogously, at constant strain rate the initial stress increases to a maximum then decreases to an asymptotic limit. These responses are used to construct a simple viscoelastic fluid constitutive law of differential type. Such a time-dependent law, with timescales changing widely with temperature, can be expected to yield a flow field in an ice sheet that is very different from that obtained from the viscous law. Only comparison solutions for both constitutive laws can determine the differences and significance of the non-viscous behaviour, and the simple law constructed would be a candidate for such comparisons.

A number of scientists have already warned against the risks of interpreting paleoclimate records without an adequate understanding of the diffusion of relevant chemical traces in deep ice cores (Gow, 1971; Ikeda and others, 1999; Bender, 2002; Faria and others, in press, and references therein). Particularly critical is the formation – either prior to drilling or during ice-core storage – of micro-inclusions such as solid inclusions, microscopic bubbles and plate-like inclusions (PLIs).

Dome A is the highest ice feature in Antarctica, at over 4000 m a.s.l., and overlies the Gamburtsev mountains. It is believed that deep ice-core drilling in this area may reveal the oldest ice in Antarctica, providing an unparalleled paleoclimate record in excess of 1 Ma, and perhaps going back as far as 1.2 Ma (Xiao and others, 2008). However, little is known about this area because its height and distance from the coast and scientific stations makes access difficult.