We address the usefulness of the unstable manifold correction (UMC) in a Picard iteration for the solution of the velocity field in higher-order ice-flow models. We explain under- and overshooting and how one can remedy them. We then discuss the rationale behind the UMC, initially developed to remedy overshooting, and how it was previously introduced in a Picard iteration to calculate the velocity field in higher-order models. Using a laminar-flow experiment with two higher-order model implementations, we demonstrate that it is not overshooting, but undershooting, that is the main problem when using a proper implementation for the calculation of the velocity field in higher-order models. We also consider a variant of the original UMC algorithm that often enables a relatively fast solution, but is theoretically less sound. Therefore, neither the variant nor the original algorithm is suited for these problems. We present a more appropriate, stable and simple relaxed Picard algorithm and demonstrate that, compared to the true Picard iteration and the variant of the original UMC algorithm, it results in a faster solution of the velocity field in higher-order models for problems with real data.

Digital elevation models (DEMs) of the ablation area of Hailuogou glacier, China, produced from Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) data obtained in 2009, differential GPS (DGPS) data surveyed in 2008 and aerial photographs acquired in 1966 and 1989 are differenced to estimate long- and short-term glacier surface elevation change (dh/dt). The mean dh/dt of the ablation area over 43 years (1966–2009) is −1.1 ± 0.4 m a−1. Since 1989 the thinning has accelerated significantly. Ice velocities measured by DGPS at 28 fixed stakes implanted in the ablation area increase with distance from the glacier terminus, ranging from 41.0 m a−1 approaching the glacier terminus to a maximum of 205.0 m a−1 at the base of an icefall. Our results reveal that the overall average ice velocity in the ablation area has undergone significant temporal variability over the past several decades. Changes in glacier surface elevation in the ablation area result from the combined effects of climate change and glacier dynamics, which are driven by different factors for different regions and periods.

Spaceborne interferometric synthetic aperture radar (InSAR) techniques for measuring ice flow velocity and topography have developed rapidly over the last decade and a half, revolutionizing the study of ice dynamics. Spaceborne interferometry has contributed to major progress in many areas of glaciological study by: providing the first comprehensive measurements of ice-stream flow velocity over the major outlets of Greenland and Antarctica; revealing that ice-stream and outlet-glacier flow can change rapidly (months to years); improving understanding of several ice-sheet and ice-shelf processes; providing velocity for flux-gate based mass-balance assessment; mapping flow of mountain glaciers; and capturing the geomorphic traces of past ice flow. We review the basic technique development, the measurement characteristics, and the extensive set of results yielded by these measurements.

We propose a general framework for iceberg-calving models that can be applied to any calving margin. The framework is based on mass continuity, the assumption that calving rate and terminus velocity are not independent and the simple idea that terminus thickness following a calving event is larger than terminus thickness at the event onset. The theoretical, near steady-state analysis used to support and analyze the framework indicates that calving rate is governed, to first order, by ice thickness, thickness gradient, strain rate, mass-balance rate and backwards melting of the terminus; the analysis furthermore provides a physical explanation for a previously derived empirical relationship for ice-shelf calving (Alley and others, 2008). In the calving framework the pre- and post-calving terminus thicknesses are given by two unknown but related functions. The functions can vary independently of changes in glacier flow and geometry, and can therefore account for variations in calving behavior due to external forcings and/or self-sustaining calving processes (positive feedbacks). Although the calving framework does not constitute a complete calving model, any thickness-based calving criterion can easily be incorporated into the framework. The framework should be viewed as a guide for future attempts to parameterize calving.

Basal water lubricates and enables the fast flow of the West Antarctic ice streams which exist under low gravitational driving stress. Identification of sources and rates of basal meltwater production can provide insight into the dynamics of ice streams and the subglacial hydrology, which remain insufficiently described by glaciological theory. Combining measurements and analytic modeling, we identify two regions where basal meltwater is produced beneath Whillans Ice Stream, West Antarctica. Downstream of the onset of shear crevasses, strong basal melt (20–50 mm a−1) is concentrated beneath the relatively narrow shear margins. Farther upstream, melt rates are consistently 3–7 mm a−1 across the width of the ice stream. We show that the transition in melt-rate patterns is coincident with the onset of shear margin crevassing and streaming flow and related to the development of significant lateral shear resistance, which reorganizes the resistive stress regime and induces a concentration of basal resistance adjacent to the shear margin. Finally, we discuss how downstream freeze-on in the ice-stream center coupled with melt beneath the shear margin might result in a slowing but widening ice stream.

Deposition of snow from precipitation and wind events creates layering within seasonal snowpacks. The thickness and horizontal continuity of layers within seasonal snowpacks can be highly variable, due to snow blowing around topography and vegetation, and this has important implications for hydrology, remote sensing and avalanche forecasting. In this paper, we present practical field and post-processing protocols for recording lateral variations in snow stratigraphy using near-infrared (NIR) photography. A Fuji S9100 digital camera, modified to be sensitive to NIR wavelengths, was mounted on a rail system that allowed for rapid imaging of a 10 m long snow trench excavated on the north side of Toolik Lake, Alaska (68°38′ N, 149°36′ W). Post-processing of the images included removal of lens distortion and vignetting. A tape measure running along the base of the trench provided known locations (control points) that permitted scaling and georeferencing. Snow layer heights estimated from the NIR images compared well with manual stratigraphic measurements made at 0.2 m intervals along the trench (n = 357, R2 = 0.97). Considerably greater stratigraphic detail was captured by the NIR images than in the manually recorded profiles. NIR imaging of snow trenches using the described protocols is an efficient tool for quantifying continuous microscale variations in snow layers and associated properties.

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 air–sea-ice CO2 flux was measured in the ice-covered Saroma-ko, a lagoon on the northeastern coast of Hokkaido, Japan, using a chamber technique. The air–sea-ice CO2 flux ranged from −1.8 to +0.5 mg C m−2 h−1 (where negative values indicate a sink for atmospheric CO2). The partial pressure of CO2 (pCO2) in the brine of sea ice was substantially lower than that of the atmosphere, primarily because of the influence of the under-ice plume from the Saromabetsu river located in the southeastern part of the lagoon. This suggests that the brine had the ability to take up atmospheric CO2 into the sea ice. However, the snow deposited over the sea ice and the superimposed ice that formed from snowmelting and refreezing partially blocked CO2 diffusion, acting as an impermeable medium for CO2 transfer. Our results suggest that the air–sea-ice CO2 flux was dependent not only on the difference in pCO2 between the brine and the overlying air, but also on the status of the ice surface. These results provide the necessary evidence for evaluation of the gas exchange processes in ice-covered seas.

An overview is given of the relatively short history, important issues and primary challenges of research on permafrost in cold mountain regions. The systematic application of diverse approaches and technologies contributes to a rapidly growing knowledge base about the existence, characteristics and evolution in time of perennially frozen ground at high altitudes and on steep slopes. These approaches and technologies include (1) drilling, borehole measurement, geophysical sounding, photogrammetry, laser altimetry, GPS/SAR surveying, and miniature temperature data logging in remote areas that are often difficult to access, (2) laboratory investigations (e.g. rheology and stability of ice-rock mixtures), (3) analyses of digital terrain information, (4) numerical simulations (e.g. subsurface thermal conditions under complex topography) and (5) spatial models (e.g. distribution of permafrost where surface and microclimatic conditions are highly variable spatially). A sound knowledge base and improved understanding of governing processes are urgently needed to deal effectively with the consequences of climate change on the evolution of mountain landscapes and, especially, of steep mountain slope hazards as the stabilizing permafrost warms and degrades. Interactions between glaciers and permafrost in cold mountain regions have so far received comparatively little attention and need more systematic investigation.

The basal melting and freezing rates under the Amery Ice Shelf, East Antarctica, are evaluated, and their spatial distributions mapped. Ice velocity, surface elevation and accumulation rate datasets are employed in the analysis, along with a column-averaged ice density model. Our analysis shows that the total area of basal melting is 34 700 km2, with a total annual melt of 62.5 ± 9.3 Gt and an average melting rate of 1.8 ± 0.3 m a−1. Basal freezing mainly occurs in the northwestern part of the ice shelf, over a total area of 26 100 km2 and with a maximum freezing rate of 2.4 ± 0.4 m a−1. The total marine ice that accretes to the ice-shelf base is estimated to be 16.2 ± 2.4 Gt a−1. Using a redefined grounding line and geometry of the Amery Ice Shelf, we estimate the net melt over the ice-shelf base is about 46.4 ± 6.9 G ta−1, which is higher than previous modeling and oceanographic estimates. Net basal melting accounts for about half of the total ice-shelf mass loss, with the rest being from iceberg discharge. Our basal melting and freezing distribution map provides a scientific basis for quantitative analysis of ice–ocean interaction at the ice-shelf–ocean interface.

We consider an idealized problem of a sphere of ice growing symmetrically in a spherical cavity within a porous rock in order to identify and quantify different physical mechanisms that can result in fracturing the rock. We show that if the permeability of the rock is very small then high pressures can develop in the cavity as the water inside it expands on freezing. However, given typical permeabilities of most rocks, the pressure is relieved by flow out of the cavity through the rock pores. When ice fills the cavity, there remains a microscopic film of water separating the ice from the rock, owing to disjoining forces, and these forces can stress the rock and have the potential to fracture it. The elastic pressure in the rock depresses the freezing temperature, which can limit the potential for fracturing. This simple example reveals the important interactions between disjoining forces, elasticity and fluid flow in determining the pressure exerted during freezing of water-saturated cavities in rocks.

Solar visible radiation can penetrate 2–30 cm (e-folding depth) into snowpacks and photolyse nitrate anions and hydrogen peroxide contained in the snow. Photolysis rate coefficients, J, for NO3− and H2O2 photolysis are presented for a melting and a fresh snowpack at Ny-Ålesund, Svalbard. Calculations of (a) transfer velocities, υ, and molecular fluxes of gaseous NO2 from the snowpack and (b) depth-integrated production rates of OH radicals within the snowpack are presented. The results show the importance of considering the depth dependence, i.e. not just the snow surface, when modelling snowpack photochemistry. Neglecting photochemistry under the snow surface can result in an apparent larger molecular flux of NO2 from NO3− photolysis than the melting snowpack. However, when the depth-resolved molecular fluxes of NO2 within the snowpack are calculated, a larger NO2 flux may be apparent in the melting snowpack than the fresh snowpack. For solar zenith angles of 60°, 70° and 80° the modelled molecular fluxes of NO2 from fresh snowpack are 11.6, 5.6 and 1.7 nmol m−2 h−1, respectively, and those for melting snowpack are 19.7, 9.1 and 2.9 nmol m−2 h−1, respectively.

Previous studies using Fourier transformation (FT) methods to analyze subglacial roughness have shown promise for distinguishing between different types of subglacial landscape from raw subglacial elevation data. We derive a two-parameter FT roughness index {ξ, η}, where • is based on the FT of elevation (as previously considered in isolation), and η is based on both the FT of elevation and the FT of bed-slope profile. In this way, we take account of both vertical and horizontal irregularities in subglacial surfaces. We demonstrate the statistical veracity of using {ξ, η} to consider roughness in terms of obstacle amplitudes and spacing, and consider the use of {ξ, η} in studies of ice dynamics and subglacial geomorphological interpretation. We show that {ξ, η} can be linked to basal sliding rates on the metre scale, and can be used to differentiate further than single-parameter roughness indices between different classes of subglacial landscape, in particular between erosional and depositional settings.

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.

Supraglacial Lac de Rochemelon was formed 50 years ago behind an ice dam and grew steadily until 2004. In October 2004, the volume of the lake reached 650 000 m3, bringing its surface within 0.2 m of the top of the ice dam. To eliminate the threat to towns located below in the event of an overflow, the lake was drained artificially in October 2004 and during the summer of 2005. Once the volume had been reduced to 250 000 m3 by siphoning, a channel was dug with explosives and the remaining water overflowed naturally. This offered a very good opportunity to investigate the breaching of an ice dam accompanied by thermal erosion of the drainage channel. Extensive field measurements were carried out during drainage. Analysis of the energy dissipated in the channel reveals that only half of the available energy was used for breach erosion. A numerical model was used to simulate the evolution of a number of variables during drainage and to study the sensitivity of discharge and ice erosion to different parameters, revealing a high sensitivity to water temperature. Model simulations indicate that natural drainage of this lake at the beginning of October 2004 would have led to a peak discharge of <6 m3 s−1.

Using micro-Raman spectroscopy, we identified the chemical forms of methanesulfonate salt particles in reference samples of the Dome Fuji (Antarctica) ice core. We found only (CH3SO3)2Mg nH2O among methanesulfonate salts, and this salt particle is most prevalent in the Last Glacial Maximum (LGM) ice. We suggest that during the LGM, (CH3SO3)2Mg nH2O may have formed in the atmosphere through the chemical reaction of CH3SO3H with sea salts, but probably not in the firn and ice due to the neutralization of acid in LGM ice of inland Antarctica.

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.

Major advances in understanding the plasticity of ice have been made during the past 60 years with the development of studies of the flow of glaciers and, recently, with the analysis of deep ice cores in Antarctica and Greenland. Recent experimental investigations clearly show that the plastic deformation of the ice single crystal and polycrystal is produced by intermittent dislocation bursts triggered by long-range interaction of dislocations. Such dislocation avalanches are associated with the formation of dislocation patterns in the form of slip lines and slip bands, which exhibit long-range correlations and scale invariance. Long-range dislocation interactions appear to play an essential role in primary creep of polycrystals and dynamic recrystallization. The large plastic anisotropy of the ice crystal is at the origin of large strain and stress heterogeneities within grains. The use of full- field approaches is now a compulsory proceeding to model the intracrystalline heterogeneities that develop in polycrystals. Ice is now highly regarded among the materials science community. It is considered a model material for understanding deformation processes of crystalline materials and polycrystal modeling.

Snow penetrometers are being developed to detect stratigraphy indicative of slab avalanches. Results are presented here from experiments performed to assess the relationship between the velocity of a round-tipped penetrometer through uniform snow and the resulting force response. The range of velocities used is commensurate with that used to drive a manually driven penetrometer through the snow. A characteristic spike is noted in profiles during the initial stage of deformation, which appears to be more pronounced for the harder snow layers tested. An investigation of snow deformation using video analysis of a split-axis rod deforming snow against a clear plastic window indicates that the spike in the force signal corresponds to the development of a compaction zone below the penetrometer tip. Once shear forces that develop in the compacted snow are overcome, deformation proceeds in a steady state and there is little or no relationship between the force response and velocity over the velocity range of our experiments.

Gornergletscher, Switzerland, is located adjacent to the marginal lake Gornersee, which periodically drains. We measured glacier ice-flow velocities during two drainage events of the lake, in 2004 and 2006. The common feature of these events was that, during both, Gornersee filled to its maximum level and then overflowed. The events differed in that in 2004 Gornersee rapidly drained via a sudden subglacial connection, whereas in 2006 the lake water continued to overflow and slowly discharged into a nearby moulin. We analysed the changes in ice-flow velocities in the vicinity of Gornersee during the two drainage events, using a three-dimensional ice-flow model which is able to (1) simulate locally variable enhanced basal motion of the ice and (2) account for the load and release of water pressure exerted on the ice margin. We demonstrate that the key features of the observed flow changes can be reproduced adequately in the numerical model by considering these two effects as the main mechanisms. We interpret the 2006 flow changes to be dominated by the release of lake water pressure acting on the ice during the lake drainage. The 2004 ice-flow changes can be explained by enhanced basal motion, and the impact of the lake water pressure provides certain clues to some observations insufficiently explained by enhanced basal motion.