The volume- and area-change evolution of glaciers can be obtained by employing the volume–area scaling approach during mass-balance modelling. This method usually requires information on the initial surface area and ice volume to adjust the volume–area relation to the specific ice body. However, absolute volumetric data on glaciers are very rare, so the applicability of volume–area scaling is limited. In order to use volume–area scaling on glaciers for which only limited information is available, a new method is presented to calibrate the volume–area relation without prior knowledge of this relation by using glacier extent information from different times. To validate the method and illustrate its practicability, we model the range of probable future changes in ice volume and surface area of ‘Glaciar Noroeste’, an outlet glacier of Gran Campo Nevado ice cap, southern Chilean Patagonia, during the 21st century, based on IPCC SRES scenarios B1 and A2.

‘Extrusion flow’ describes any velocity field where maximum horizontal velocity occurs below the surface. By 1914, viscous flow and basal sliding over rough beds were accepted concepts. Between the world wars, there was little communication between naturalists describing complicated ice sheets, and physicists studying fundamental processes controlling flow. Max Demorest brought concepts from mechanics into glaciology and glacial geology; however, his extrusion flow theory, to explain how ice flowed out of central Greenland, overlooked force imbalance. Rudolf Streiff-Becker found an apparent large imbalance between ice flux discharged through a gate and net accumulation in the upstream catchment at Claridenfirn, Switzerland. Because he underestimated uncertainty in ice depth, he had to propose a strong undercurrent (extrusion flow) to evacuate the excess mass. Reassessment of his assumptions shows that extrusion was actually unnecessary. However, confluence of two lines of evidence for extrusion flow added stature to the concept. In 1952, John Nye showed that free extrusion flow was impossible due to force imbalance. Two forms of extrusion flow survive: capped extrusion flow is possible on local scales where longitudinal stress gradients allow upper ice to move slowly, and rigid- body rotational flow can allow deeper ice to move faster without strain.

We present results from numerical ice-flow models that include calving criteria based on penetration of surface and basal crevasses, which in turn is a function of longitudinal strain rates near the glacier front. The position of the calving front is defined as the point where either (1) surface crevasses reach the waterline (model CDw), or (2) surface and basal crevasses penetrate the full thickness of the glacier (model CD). For comparison with previous studies, results are also presented for a height-above-buoyancy calving model. Qualitatively, both models CDw and CD produce similar behaviour. Unlike previous models for calving, the new calving criteria are applicable to both grounded termini and floating ice shelves and tongues. The numerical ice-flow model is applied to an idealized geometry characteristic of marine outlet glaciers. Results indicate that grounding-line dynamics are less sensitive to basal topography than previously suggested. Stable grounding-line positions can be obtained even on a reverse bed slope with or without floating termini. The proposed calving criteria also allow calving losses to be linked to surface melt and therefore climate. In contrast to previous studies in which calving rate or position of the terminus is linked to local water depth, the new calving criterion is able to produce seasonal cycles of retreat and advance as observed for Greenland marine outlet glaciers. The contrasting dynamical behaviour and stability found for different calving models suggests that a realistic parameterization for the process of calving is crucial for any predictions of marine outlet glacier change.

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.

Due to a lack of in situ measurements, model-based studies of glacier mass balance in the Tibetan Plateau are very limited. An energy-balance model is applied to analyse the mass-balance sensitivity of Xibu glacier, in the Nyainqêntanglha mountain range, to climatic change. A sensitivity calculation shows that a temperature change of ±1°C or a precipitation change of ±35% changes the equilibrium-line altitude (ELA) by 140 ± 125 m. We use a clustering method to link local weather parameters, including wet-season temperatures, to weather types observed over the period 1955–2006. Modelled variability of the Xibu glacier mass balance seems to be controlled by air-temperature variations during the wet season (May–September) and by a long-term warming trend that is unrelated to weather type. The observed wet-season temperature trend of 0.23°C (10 a)−1 leads to an estimated lengthening of the ablation season by 8 days at the glacier terminus (5000 m a.s.l.) and by 23 days at the ELA (5590 m a.s.l.) over the period 1966–2005. The calculated rise in the ELA was 49 m (10 a)−1.

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.

Assessing snow stability requires a holistic approach, relying on avalanche, snowpack and weather observations. Part of this assessment utilizes stability tests, but these tests can be unreliable due in part to the spatial variability of test results. Conducting more than one test can help to mitigate this uncertainty, though it is unclear how far apart to space tests to optimize our assessments. To address this issue we analyze the probability of sampling two relatively strong test results over 25 spatial datasets collected using a variety of stability tests. Our results show that the optimal distance for spacing stability tests varies by dataset, even when taking the sampling scheme and stability-test type into account. This suggests that no clear rule currently exists for spacing stability tests. Our work further emphasizes the spatial complexity of snow stability measurements, and the need for holistic stability assessments where stability tests are only one part of a multifaceted puzzle.

Borehole optical stratigraphy (BOS) is a borehole video system and processing routine for investigating polar firn. BOS records brightness variations in the firn and is effective at identifying stratigraphic markers. BOS brightness logs have been used to count annual layers and measure vertical strain, even though a specific cause of the brightness variations has not been determined. Here we combine two models of light transport to examine potential errors with BOS and identify improvements which will allow the system to estimate optical grain size. We use a Monte Carlo radiative transfer model to estimate the influence of firn microstructure variations on borehole reflectance. We then use a ray-tracing algorithm to model the multiple reflections within the borehole that cause measured brightness variations. Multiple reflections cause the brightness measured at a point on the borehole wall to not necessarily be equal to the local wall reflectance. The ray tracing further shows that wall imperfections or variations in the camera position can produce brightness variations that are unrelated to changes in firn properties. Smooth walls and good stabilization of the camera help ensure that brightness variations result from variations in firn properties, and thus are a measure of firn stratigraphy, rather than artifacts.

A simple circuit has been developed to allow measurement of brief subglacial water-pressure pulses. This circuit continuously powers a pressure transducer and captures the peak output of the transducer during each measurement interval, thus allowing determination of the maximum pressure attained during the interval. This circuit provides an alternative to setting a data logger to perform rapid repeated measurements, and overcomes some key limitations imposed by rapid measurement. Benefits include significantly lower demands on the data-logger microprocessor, which allows additional instruments to be monitored simultaneously, reduced memory usage and moderately lower power consumption. The reduced microprocessor and memory loads allow older and slower logger models, many of which are still in common use, to be used to obtain data that compare favourably with high-frequency data obtained using newer data loggers.

For 40 years Anonymous (J. Glaciol., 8(52), 1969) has been the effective standard of glacier mass-balance terminology. It grew out of a concern for clarity in the communication of information, and has guided thinking about mass balance in many ways. Certain ambiguities and gaps in its conceptualization have become more evident with the passage of time, and some have been aggravated by ad hoc extensions of and deviations from the standard. Methodological progress means that a review of the terminology of Anonymous (1969) is now timely, and a forthcoming glossary to be published by the International Association of Cryospheric Sciences addresses this need. There are good reasons for being concerned about clear terminology, but consistent usage by the members of a large community cannot be secured other than by consensus.

Polar ice is known to be one of the most anisotropic natural materials. For a given fabric the polycrystal viscous response is strongly dependent on the actual state of stress and strain rate. Within an ice sheet, grounded-ice parts and ice shelves have completely different stress regimes, so one should expect completely different impacts of ice anisotropy on the flow. The aim of this work is to quantify, through the concept of enhancement factors, the influence of ice anisotropy on the flow of grounded ice and ice shelves. For this purpose, a full-Stokes anisotropic marine ice-sheet flowline model is used to compare isotropic and anisotropic diagnostic velocity fields on a fixed geometry. From these full-Stokes results, we propose a definition of enhancement factors for grounded ice and ice shelves, coherent with the asymptotic models used for these regions. We then estimate realistic values for the enhancement factors induced by ice anisotropy for grounded ice and ice shelves.

We have constructed a new digital elevation model (DEM) of the 1995 surface of Black Rapids Glacier, a surge-type glacier in the central Alaska Range, using ERS-1/-2 repeat-pass interferometry. We isolated the topographic phase from three interferograms with contrasting perpendicular baselines. Numerous phase-unwrapping errors caused by areas of poor coherence were corrected in all three interferograms, using a novel, iterative, semi-automated approach that capitalizes on the multi-baseline nature of the dataset. Comparison of our DEM with a 1949 US Geological Survey DEM and with 1973–95 ground survey data shows the gradual return of Black Rapids Glacier to a pre-surge hypsometry following a surge in 1936/37. Maximum elevation changes along the glacier center line in the ablation and accumulation areas are, respectively, −249 and +63 m (−5.4 and +1.4 m a−1). Maximum elevation changes of survey points at nearby locations are −4.9 m a−1 (1975–84) and +0.5 m a−1 (1975–85). Center-line thickening of +62 m between 1949 and 1995 (+1.4 m a−1), just above the Loket tributary in the upper part of the ablation zone, indicates dynamic thickening following the 1936/37 surge.

We present results from ground-penetrating radar (GPR) and seismic surveys for the Mullins Valley debris-covered glacier (Mullins Glacier), Antarctica, that yield local ice-thickness estimates of 80–110 m in upper Mullins Valley and 150 m in upper Beacon Valley. Englacial debris in upper Mullins Glacier occurs as scattered cobbles and as discrete layers. One extensive englacial debris layer, which appears as a coherent reflector dipping 40–45° up-valley, intersects the ground surface within an ∼8 m high ice-cored ridge, the largest of several ridges that mark the glacier surface. Field excavations reveal that this englacial interface consists of multiple debris bands that can be directly correlated with ridge microtopography. Englacial debris layers most probably originate as concentrated rockfall in ice accumulation zones and/or as surface lags that form as dirty ice sublimes during periods of negative mass balance. A similar pattern of surface ridges on Friedman Glacier (∼2.5 km west of Mullins Glacier) suggests regional environmental changes are involved in ridge formation. These observations carry implications for evaluating debris entrainment and surface ridge formation mechanisms in cold-based, debris-covered glaciers and provide a glaciological framework for evaluating and interpreting paleoclimate records from Mullins Glacier.

The study of jökulhlaups has advanced from describing them qualitatively to measuring systematically on site their discharge curves and source geometry, as well as investigating conditions when particular floods were initiated. In the early days of this science, hypotheses were formulated which attempted to explain the processes responsible for unstable flood growth. The general theory of time-dependent turbulent water flow through intraglacial conduits marked a breakthrough in understanding jökulhlaup hydraulics and has since remained a classical foundation for jökulhlaup studies. This theory described flood evolution in terms of water input into the upper end of a tunnel leading from a reservoir, taking account of sensible stored lake heat and geometry. Such a tunnel expands by positive feedback, since its ice walls melt through frictional heat produced by the flowing water. While this model successfully described jökulhlaups in which the discharge hydrograph increases more or less exponentially over time, other floods were observed which are in stark contrast. In them, pressurized floodwater propagates in a turbulent subglacial water sheet which opens and expands a system of conduits, with an extremely rapid linear rise in discharge. The rushing water enlarges its subglacial pathway not only by melting the ice around it but also by lifting, deforming and fracturing it. Subsequent drainage is nourished by two different sources, with conduit growth being controlled not only by water input at the upper end of the flood path but also by further water joining in, all the way to the edge of the glacier. Moreover, the trigger for releasing meltwater from glacial lakes has been seen to be either of two conduit opening mechanisms, which also determine whether a turbulent subglacial water sheet will result or not. On the one hand, drainage may begin by expanding already existing conduits, in which case the pressure remains lower than that of the ice overburden at the dam and the conduits grow slowly. On the other hand, lake levels may rise until flotation of the ice dam, abruptly opening a sufficient gap for water to propagate as a sheet flow. In order to explain which of these two initiation mechanisms will act, further studies are required into the structure of hydrological drainage systems under ice dams and into their linkage with these two mechanisms. Although current theoretical models of jökulhlaups drainage have managed to reproduce the observed discharge patterns, inconsistencies with the observed behaviour of subglacial drainage systems along the flood path demand further exploration of the actual hydraulic and glaciodynamic processes of jökulhlaups.

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 seismic refraction surveys in the upper ablation area of Storglaciären, a small valley glacier located in Swedish Lapland. We estimated seismic-wave attenuation using the spectral-ratio method on the energy travelling in the uppermost ice with an average temperature of approximately −1 °C. Attenuation values were derived between 100 and 300 Hz using the P-wave quality factor, QP, the inverse of the internal friction. By assuming constant attenuation along the seismic line we obtained mean QP = 6 ± 1. We also observed that QP varies from 8 ± 1 to 5 ± 1 from the near-offset to the far-offset region of the line, respectively. Since the wave propagates deeper at far offsets, this variation is interpreted by considering the temperature profile of the study area; far-offset arrivals sampled warmer and thus more-attenuative ice. Our estimates are considerably lower than those reported for field studies in polar ice (∼500–1700 at −28°C and 50–160 at −10°C) and, hence, are supportive of laboratory experiments that show attenuation increases with rising ice temperature. Our results provide new in situ estimates of QP for glacier ice and demonstrate a valuable method for future investigations in both alpine and polar ice.

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.

Meltwater runoff is an important component of the mass balance of the Greenland ice sheet (GrIS) and contributes to eustatic sea-level rise. In situ measurements of river runoff at the ˜325 outlets are nonexistent due to logistical difficulties. We develop a novel methodology using satellite observations of sediment plumes as a proxy for the onset, duration and volume of meltwater runoff from a basin of the GrIS. Sediment plumes integrate numerous poorly constrained processes, including meltwater refreezing and supra- and englacial water storage, and are formed by meltwater that exits the GrIS and enters the ocean. Plume characteristics are measured in Moderate Resolution Imaging Spectroradiometer (MODIS, band 1, 250 m) satellite imagery during the 2001-08 melt seasons. Plume formation and cessation in Kangerlussuaq Fjord, West Greenland, are positively correlated (r2 = 0.88, n = 5, p < 0.05; r2 = 0.93, n = 5, p < 0.05) with ablation onset and cessation at the Kangerlussuaq Transect automatic weather station S5 (490 ma.s.l., 6 km from the ice margin). Plume length is positively correlated (r2 = 0.52, n = 35, p < 0.05) with observed 4 day mean Watson River discharge throughout the 2007 and 2008 melt seasons. Plume length is used to infer instantaneous and annual cumulative Watson River discharge between 2001 and 2008. Reconstructed cumulative discharge values overestimate observed cumulative discharge values for 2007 and 2008 by 15% and 29%, respectively.

Following three decades of relative stability, Jakobshavn Isbræ, West Greenland, underwent dramatic thinning, retreat and speed-up starting in 1998. To assess the amount of ice loss, we analyzed 1985 aerial photos and derived a 40 m grid digital elevation model (DEM). We also obtained a 2007 40 m grid SPOT DEM covering the same region. Comparison of the two DEMs over an area of ∼4000 km2 revealed a total ice loss of 160 ± 4 km3, with 107 ± 0.2 km3 in grounded regions (0.27 mm eustatic sea-level rise) and 53 ± 4 km3 from the disintegration of the floating tongue. Comparison of the DEMs with 1997 NASA Airborne Topographic Mapper data indicates that this ice loss essentially occurred after 1997, with +0.7 ± 5.6 km3 between 1985 and 1997 and −160 ± 7 km3 between 1997 and 2007. The latter is equivalent to an average specific mass balance of −3.7 ± 0.2 m a−1 over the study area. Previously reported thickening of the main glacier during the early 1990s was accompanied by similar-magnitude thinning outside the areas of fast flow, indicating that the land-based ice continued reacting to longer-term climate forcing.

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.