A physically based energy-balance model with improved parameterization of solar radiation for a sloped ice surface has been developed to estimate the backwasting rate of an ice cliff in a debris-covered area. The model has been tested against observations between 5 August and 5 September 2008 on 38 ice cliffs in the debris-covered area of Koxkar glacier, Tuomuer mountain, China. We calculated that the energy-balance model gave a good estimate of the backwasting rates, with errors in the range ±1.96 cm d−1 and root-mean-square errors of 0.99 cm d−1. Errors arising from setting of surface albedo and turbulent flux parameterization were limited. We found that shortwave radiation is the most important heat source for ice-cliff ablation, contributing about 76% of the total heat available for ice melt, while the sensible heat flux provides nearly 24% of the total heat for ice-cliff wastage. The latent heat flux and net longwave radiation are comparatively small according to the model calculation. The mean backwasting rate of ice cliffs in the debris-covered area of Koxkar glacier is estimated at 7.64 m a−1 when the winter ablation is neglected. With this annual backwasting rate and given a mean slope angle of 46.4°, the backwasting of ice cliffs produces about 1.60 × 106 m3 of meltwater, accounting for about 7.3% of the total melt runoff from the debris-covered area.

The association between basal hydrology and glacier sliding has become nearly synonymous with the early work of Almut Iken and colleagues. Their research published in the Journal of Glaciology from 1981 to 1986 made an indelible impact on the study of glacier hydromechanics by documenting strong correlations between basal water pressure and short-term ice-flow variations. With a passion for elucidating the physics of glacier-bed processes, Iken herself made fundamental contributions to our theoretical and empirical understanding of the sliding process. From the theoretical bound on basal shear stress, to the inferences drawn from detailed horizontal and vertical velocity measurements, the work of Iken and colleagues continues to inform the interpretation of data from alpine glaciers and has found increasing relevance to observations from the ice sheets.

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.

Ortles mountain (3905 m a.s.l.), South Tyrol, Italy, is the highest mountain of the Eastern European Alps, and its upper glacier, Alto dell’Ortles, presents a unique opportunity to obtain the first paleoenvironmental record from an ice core in this area. To study the suitability of this glacier as a drilling site, in 2009 we performed the first preliminary study of its glaciological characteristics at ˜3830 m a.s.l. The maximum thickness is ˜75 m, and lamination of the exposed ice layers is excellent down to bedrock. Firn and ice lenses were observed in a 10 m shallow core, and the firn/ice transition was below ˜24m. The seasonal chemical signal is clearly preserved only within the uppermost 2008 and 2009 snow/firn. A simple mass-balance model, the incipient ‘smoothing’ of the chemical record, and the observed ice lenses provide evidence that melting, infiltration and refreezing cycles occurred within the firn layers formed before 2008. Nevertheless, the mass balance of the upper part of Alto dell’Ortles was positive (˜800mma_1) during the last few years. We suggest that an environmental history is likely to be well preserved only within the ice layers formed before ˜1980, when summer air temperature was ˜2°C colder than today in this area. Clearly the continued warming trend predicted to occur over the next few decades, and the consequent increase in frequency and/or intensity of infiltration processes, will endanger the preservation of the glacial archive conserved in the deep ice layers of Ortles mountain.

Four firn cores were retrieved in 2007 at two ridges in the area of the Ekström Ice Shelf, Dronning Maud Land, coastal East Antarctica, in order to investigate the recent regional climate variability and the potential for future extraction of an intermediate-depth core. Stable water-isotope analysis, tritium content and electrical conductivity were used to date the cores. For the period 1981–2006 a strong and significant correlation between the stable-isotope composition of firn cores in the hinterland and mean monthly air temperatures at Neumayer station was (r = 0.54−0.71). No atmospheric warming or cooling trend is inferred from our stable-isotope data for the period 1962–2006. The stable-isotope record of the ice/firn cores could expand well beyond the meteorological record of the region. No significant temporal variation of accumulation rates was detected. However, decreasing accumulation rates were found from coast to hinterland, as well as from east (Halvfarryggen) to west (Søråsen). The deuterium excess (d) exhibits similar differences (higher d at Søråsen, lower d at Halvfarryggen), with a weak negative temporal trend on Halvfarryggen (0.04‰ a−1), probably implying increasing oceanic input. We conclude that Halvfarryggen acts as a natural barrier for moisture-carrying air masses circulating in the region from east to west.

Ice types, albedos and impurity content are characterized for the ablation zone of the Greenland ice sheet in Kronprinz Christians Land (80° N, 24° W). Along this ice margin the width of the ablation zone is only about 8 km. The emergence and melting of old ice in the ablation zone creates a surface layer of dust that was originally deposited with snowfall high on the ice sheet. This debris cover is augmented by locally derived wind-blown sediment. Subsequently, the surface dust particles often aggregate together to form centimetre-scale clumps that melt into the ice, creating cryoconite holes. The debris in the cryoconite holes becomes hidden from sunlight, raising the area-averaged albedo relative to surfaces with uniform debris cover. Spectral and broadband albedos were obtained for snow, ice hummocks, debris-covered ice, cryoconite-studded ice and barren tundra surfaces. Broadband ice albedos varied from 0.2 (for ice with heavy loading of uniform debris) to 0.6 (for ice hummocks with cryoconite holes). The cryoconite material itself has albedo 0.1 when wet. Areal distribution of the major surface types was estimated visually from a transect video as a function of distance from the ice edge (330 m a.s.l.). Ablation rates were measured along a transect from the ice margin to the slush zone 8 km from the margin (550 m a.s.l.), traversing both Pleistocene and Holocene ice. Ablation rates in early August averaged 2 cm d−1. Impurity concentrations were typically 4.3 mg L−1 in the subsurface ice. Surface concentrations were about 16 g m−2 on surfaces with low impurity loading, and heavily loaded surfaces had concentrations as high as 1.4 kg m−2. The mineralogical composition of the cryoconite material is comparable with that of the surrounding soils and with dust on a snowdrift in front of the ice margin, implying that much of the material is derived from local sources. A fine mode (clay) is present in the oldest ice but not in the nearby soil, suggesting that its origin is from wind deposition during Pleistocene glaciation.

The theory of channelized water flow through glaciers, most commonly associated with the names of Hans Röthlisberger and Ron Shreve and their 1972 papers in the Journal of Glaciology, was developed at a time when interest in glacier-bed processes was expanding, and the possible relationship between glacier sliding and water at the bed was becoming of keen interest. The R-channel theory provided for the first time a physically based conceptual model of water flow through glaciers. The theory also marks the emergence of glacier hydrology as a glaciological discipline with goals and methods distinct from those of surface-water hydrology.

In mountain environments, longwave radiation provides large amounts of melt energy for high-albedo snow surfaces and can dominate in the energy balance of snow or glacier surfaces under cloudy skies. This study examines the atmospheric controls of sky longwave radiation at Glaciar Zongo, Bolivia (16°15’ S, 5060 ma.s.l.) over an entire year to derive a parameterization suitable for melt studies. Tropical glaciers are characterized by a pronounced seasonality of longwave radiation, due to cloud emissions during the wet season that strongly enhance the small emissivity of the thin and dry clear-sky atmosphere at very high altitudes. Clear-sky radiation is well simulated as a function of air temperature and humidity, but changes in humidity atmospheric profiles from daytime to night-time entail different optimized coefficients for hourly and daily data. Cloud emission, which enhances clear-sky emissivity by up to 55%, with an average of 20%, is estimated using daily atmospheric transmissivity for solar radiation. Partial correlations show that in high mountains cloud emissions control the variations of longwave radiation, far more than clear-sky emissivity and temperature of the emitting atmosphere. An independent test on Glaciar Antizana in the humid tropics of Ecuador (0°280 S, 4860ma.s.l.) indicates that the parameterization is robust for the Central Andes.

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.

Extensive field measurements and historical data have been used to re-analyse the cause of the outburst flood from Glacier de Tête Rousse that devastated the village of Saint-Gervais–Le Fayet, French Alps in 1892, causing 175 fatalities. The origin of this disaster was the rupture of an intraglacial cavity in Glacier de Tête Rousse that released 200 000 m3 of water and ice. All previous studies have concluded that the intraglacial cavity was formed from a crevasse that was filled and enlarged by meltwater. The re-analysis presented here suggests that the reservoir of the upper cavity did not originate as an enlarging crevasse. The origin of the meltwater reservoir was more likely a supraglacial lake formed before 1878 during a period of negative mass balance. Following a period of positive mass balance after 1878, the lake was hidden until the outburst flood of 1892. This means that such hazards may be detected by checking regularly for the formation of a lake on the surface of the glacier before it is hidden.

The sensitivity of glaciers to climatic change is key information in assessing the response and sea-level implications of projected future warming. New Zealand glaciers are important globally as an example of how maritime glaciers will contribute to sea-level rise. A spatially distributed energy-balance model is applied to Brewster Glacier, New Zealand, in order to calculate glacier mass balance, run-off and sensitivity to climate change. The model successfully simulates four annual mass-balance cycles. Close to half (52%) of the energy available for melt on the glacier is supplied by turbulent heat fluxes, with radiation less important, except during the winter. Model sensitivity to temperature change is one of the largest reported on Earth, at −2.0 m w.e. a−1 °C−1. In contrast, a 50% change in precipitation is required to offset the mass-balance change resulting from a 1 °C temperature change. Meltwater runoff sensitivity is also very high, increasing 60% with a 1°C warming. The extreme sensitivity of mass balance to temperature change suggests that significant ice loss will occur with even moderate climate warming.

Supraglacial dust (cryoconite) is an important but poorly understood component of the glacial system. There is a lack of primary data on cryoconite form, extent and dynamics. Here we present a suite of rapid, low-cost methodologies for quantification of granule geometry and supraglacial cryoconite coverage using image data captured by commercially available digital cameras. We develop robust, transferable protocols for analysis of (1) cryoconite granule geometry (major axis, Feret diameter, circularity); (2) centimetre–metre scale supraglacial extent (m2cryoconite m−2surface); and (3) temporal change in supraglacial extent at hourly intervals over several days. Image-processing methodologies were developed using the public domain software ImageJ. Manual (supervised) controls were used to estimate sources of error, and measurements then automated using simple scripting tools (macros). Fully automated processing successfully identified ∼90% of a sample of isolated granules ranging between 2.5 and 39.2 mm, with uncertainties of <20%. Particle sphericity (inferred from circularity) decreased as particle size increased. Supraglacial cryoconite extent was obtained with a mean uncertainty of 37% and 22% for data from field sites in Greenland and Svalbard, respectively. These methods will facilitate acquisition and analysis of datasets for cryoconite across a range of spatial scales, supporting research into cryoconite impacts on supraglacial hydrological connections, nutrient and carbon cycling, and initiation of primary succession in deglaciating environments.

Observations of glacier flow and explanations of its origin started as early as the 18th century. Several mechanisms were suggested before gravity-driven viscous flow became the accepted theory of glacier flow in the 1950s, the early years of the Journal of Glaciology. Since the viscosity of ice is strongly temperature-dependent, the topic of glacier and ice-sheet dynamics became essentially a fluid-dynamical problem. The availability of growing computing power turned the field of glacier mechanics and thermodynamics into a field of numerical modelling with increasing sophistication.

The southernmost glaciers in Europe are located on the Iberian, Apennine and Balkan Peninsulas in mid-latitudes between 41° N and 44° N at altitudes ranging from 2000 to 3000 m a.s.l. All these glaciers are a legacy of the Little Ice Age (LIA). They survive in a relatively warm environment (mean annual temperature 0°C to +1°C) due to local topographic controls and high levels of accumulation as a result of avalanche and wind-blown snow. In the Pirin Mountains, Bulgaria, Snezhnika glacieret has been cored, providing an archive of recent climate change. Small glaciers such as this respond quickly to climatic extremes. Since the LIA maximum during the 19th century, all southern European glaciers have retreated, losing 30–100% of their volume. However, despite the trend towards warmer years since the late 1970s, some glaciers still survive, even after some of the hottest summers on record. Predicted future warming, especially in summer, and drier conditions in the Mediterranean basin may result in the disappearance of all glacier features at these latitudes in Europe within the next few decades.

Passive-microwave 37 GHz vertically polarized (V) brightness temperature (Tb) measurements from the Advanced Microwave Scanning Radiometer for Earth Observing System (AMSR-E) are used to monitor the extent and timing of snowmelt on the Southern Patagonia Icefield (SPI) in Chile and Argentina. Twice daily Tb’s for 2002–08 for high-elevation (>1200 m a.s.l.) pixels exhibit a bimodal histogram, typical of snow-covered regions in Yukon, Alaskan icefields and the Greenland ice sheet. The low count between the two populations represents the Tb threshold for melt (252 K). This Tb value with the ±18 K diurnal amplitude variation threshold quantifies onset and duration of the spring melt–refreeze period and is used to identify melt regimes and seasonal Tb signals. Tb histograms for pixels west of the Andean divide have a normal distribution above the melt threshold. We interpret the Tb histogram as controlled by surface moisture; the shape and position with respect to Tb are retained with changes in both latitude and elevation, and the region is known to have a moist climate. Tb is not driven by seasonal temperature changes in the northwest sector of the icefield because the Tb threshold is exceeded 75% of the time. For all pixels, the spring melt–refreeze period has shortened by a mean of 10 days a−1 and a mean of 16 days a−1 for pixels with bimodal distributions between 2002 and 2008.

The temporary storage and subsequent release of water at glacial margins can cause severe flooding in downstream areas and substantially impact glacier dynamics. Alpine subglacial lakes may not be identified until they become subaerially exposed or release a jokulhlaup. We use interferometric synthetic aperture radar (InSAR) to identify and characterize three dynamic alpine subglacial lakes of Brady Glacier, Alaska, USA. We quantify changes in vertical displacement of the glacier surface and lake volumes from September 1995 through March 1996 using European Remote-sensing Satellite-1/-2 (ERS- 1/-2) tandem data. In the autumn, subsidence ranged from 4 to 26cmd-1 and the volume of water discharged ranged from 22 000 ± 2000 to 243 000 ± 14 000m3d-1. Subsidence and discharge rates declined significantly during the winter and continued at a lesser rate through March. Application of this technique may allow researchers to locate alpine subglacial lakes years or decades before they begin to release hazardous outburst floods and substantially impact glacier dynamics.

We use topographic maps, historical data, multispectral satellite data and real-time kinematic GPS data to analyze glacier area, length and ice-elevation changes of two glaciers in the central Qilian Shan, China, between 1956 and 2007. We find that the fronts of Yanglonghe glacier No. 1 (5Y432A1) and Yanglonghe glacier No. 5 (5Y432A5) have retreated by 266.5 ± 37.1 m (5.2 ± 0.73 m a−1) and 181.4 ± 37.1 m (3.6 ± 0.73 m a−1) respectively, and that this retreat accelerated after 1999. During the study period, the glacier areas decreased by ∼4.1% and 15.9% respectively. In addition, spatially non-uniform thinning, which averaged 20.2 ± 11 m (0.4 ± 0.22 m a−1) and 16.9 ± 11 m (0.33 ± 0.22 m a−1) in the ablation areas of 5Y432A1 and 5Y432A5 respectively, is observed using digital elevation models constructed using data from 1956, 1977 and 2007. The ice-volume depletion from 5Y432A1 (2.91 × 107 m3) was 2.7 times greater than from the smaller 5Y432A5 (1.08 × 107 m3). Based on records from nearby Tuole weather station, increasing annual temperatures are principally responsible for the observed glacier thinning and retreat.

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.

We describe a portable low-frequency impulse radar system intended for ground-based surveys that employs off-the-shelf hardware integrated with custom-designed software. The hardware comprises a 1–200 MHz transmitter, digitizer, computer and GPS receiver, which together weigh ∼1.5 kg. The entire system, including waterproof enclosures and batteries suited for >8 hours of continuous operation, weighs <10 kg plus the weight of the antenna housing. The system design is flexible, permitting hardware components such as the digitizer or navigation device to be exchanged. The software includes acquisition parameter control, real-time visual ice-depth rendering and data management capabilities using a hierarchical data format. The system described here has been successfully used to sound polythermal ice up to ∼220 m thick in ski-based surveys in the Yukon, Canada, and temperate ice up to ∼550 m thick in machine-based surveys in Iceland.

The thermal conductivity of snow determines, to a large extent, ground heat flux and snow metamorphism. One common method of measuring the thermal conductivity of snow is with a needle probe. We measured the microstructural changes in the snow around a typical needle using micro- computed tomography. The insertion of the needle probe caused structural changes up to a radial distance of 0.5-1 mm. Using a commercial needle probe with short (30 s) heating time, we measured thermal conductivity values in snow that were 50% lower than the conductivity measured using a calibrated guarded hot-plate apparatus. Numerically simulated time-temperature curves with an introduced air gap that simulated the needle damage reproduced the observed needle-probe results well, confirming that poor contact resistance between the needle and the snow will lead to measurement discrepancies and a large bias. While most measurements in snow have been done using a long heating time and are not subject to this error, the thermal conductivity of snow measured with needle probes with short measurement times should be avoided. This same effect is probably observed in other brittle and highly porous materials, a condition that may not be widely appreciated.