Most glaciers on the Tibetan Plateau are difficult to assess as they are located in remote regions at high altitude. This study focuses on the surface energy-balance (SEB) and mass-balance (MB) characteristics of Purogangri ice cap (PIC). A ‘COupled Snowpack and Ice surface energy and MAss balance model’ (COSIMA) is applied without observational data from the ground. The model is forced by a meteorological dataset from the High Asia Refined analysis. Model results for annual surface-elevation changes and MB agree well with the results of a previous remote-sensing estimate. Low surface velocities of 0.026 ± 0.012 m d−1 were measured by repeat-pass InSAR. This finding supports the validation of the steady-state COSIMA against satellite-derived surface changes. Overall MB of PIC for the period 2001–11 is nearly balanced (−44 kg m−2 a−1). Analysis of the model-derived SEB/MB components reveals that a significant amount of snowfall in spring is responsible for high surface albedo throughout the year. Thus, the average surface energy loss through net longwave radiation is larger than the energy gain through net shortwave radiation. The dry continental climate favours mass loss through sublimation, which accounts for 66% of the total mass loss.

A three-dimensional finite-element model is used to analyze field data collected as dirty basal ice flowed past an instrumented obstacle at the bed of Engabreen, a temperate glacier in northern Norway The ice is modeled as an incompressible power-law fluid, with viscosity , where ΠD is the second invariant of the stretching tensor, and B and n are two parameters. Using measurements obtained in 1996 and 1997, two values of B are obtained, one using the measured normal stress difference across the obstacle, and the other using the measured bed-parallel force over the instrument. These two values are not equal, probably owing to small frictional forces at the bed unaccounted for in the numerical model. Hence, B ranges between 1.9 × 107 and 3.2 × 107 Pa s1/3 in 1996, and between 2.2 × 107 and 4.1 × 107 Pa s1/3 in 1997. These values are smaller than measured elsewhere for clean glacier or laboratory ice. Field measurements of water content, fabric and texture of the basal ice suggest that unbound water between thin sediment layers and lamellae of clean ice may act as a lubricant and significantly weaken the ice. Near-isotropic fabrics indicate that preferred fabric orientation does not enhance the deformation.

A dynamic model of dry snow deformation is developed using a discrete-element technique to identify microstructural deformation mechanisms and simulate creep densification processes. The model employs grain-scale force models, explicit geometric representations of individual ice grains, and snow microstructure using assemblies of grains. Ice grains are randomly oriented cylinders of random length with hemispherical ends. Particle contacts are detected using a novel and efficient method based on the dilation operation in mathematical morphology. Grain-scale ice interaction algorithms, based on observed snow and ice microscale behavior, are developed and implemented in the model. These processes include grain contact sintering, grain boundary sliding and rotation at contacts, and grain contact deformation in tension, compression, shear, torsion and bending. Grain-scale contact force algorithms are temperature- and rate-dependent, with both elastic and viscous components. Grain bonds rupture when elastic stresses exceed ice tensile or shear strengths, after which intergranular friction and particle rearrangement control deformation until the snow compacts to its critical density. Simulations of creep settlement using 1000-grain model snow samples indicate the bulk viscosity of snow is controlled by the grain contact viscosity and area, grain packing and the increased number of frozen bonds that form during settlement. A linear relationship between contact viscosity and bulk snow viscosity at any specified density indicates that the linear model parameters can be accurately scaled, allowing simulations to be conducted for a broad range of dynamic and viscous creep deformation problems.

Despite their importance for mass-balance estimates and the progress in techniques based on optical and thermal satellite imagery, the mapping of debris-covered glacier boundaries remains a challenging task. Manual corrections hamper regular updates. In this study, we present an automatic approach to delineate glacier outlines using interferometrically derived synthetic aperture radar (InSAR) coherence, slope and morphological operations. InSAR coherence detects the temporally decorrelated surface (e.g. glacial extent) irrespective of its surface type and separates it from the highly coherent surrounding areas. We tested the impact of different processing settings, for example resolution, coherence window size and topographic phase removal, on the quality of the generated outlines. We found minor influence of the topographic phase, but a combination of strong multi-looking during interferogram generation and additional averaging during coherence estimation strongly deteriorated the coherence at the glacier edges. We analysed the performance of X-, C- and L- band radar data. The C-band Sentinel-1 data outlined the glacier boundary with the least misclassifications and a type II error of 0.47% compared with Global Land Ice Measurements from Space inventory data. Our study shows the potential of the Sentinel-1 mission together with our automatic processing chain to provide regular updates for land-terminating glaciers on a large scale.

We conducted a seismic and radar survey of the central part of midtre Lovénbreen, a small, polythermal valley glacier in Svalbard. We determined the physical properties of the material beneath the glacier by measuring the reflection coefficient of the bed by comparing the energy of the primary and multiple reflections, and deriving the acoustic impedance. By making reasonable assumptions about the properties of the basal ice, we determined the acoustic impedance of the bed material as (6.78 ± 1.53) × 106 kg m−2 s−1. We interpret the material beneath the glacier to be permafrost with up to 50% ice, and we speculate that the material may be frozen talus similar to a deposit observed directly by others beneath another Svalbard glacier. The implication for midtre Lovénbreen is that the basal material beneath the present glacier is not able to support fast flow. We conclude that midtre Lovénbreen has most likely had limited capability for faster flow in the past, with motion dominated by internal deformation. Midtre Lovénbreen is used as a ‘study glacier’ for the scientific community in Svalbard, and a large number of studies have been based there. Our results show that it cannot be used as an analogue for larger glaciers in Svalbard, having distinct basal boundary conditions.

Accurate knowledge of the spatial distribution of the mass balance of temperate glaciers is essential for a better understanding of the physical processes controlling the mass balance and for the monitoring of water resources. In relation to albedo variations, the shortwave radiation budget is a controlling variable of the surface energy balance of glaciers. Remotely sensed albedo observations are here assimilated in a snowpack model to improve the modeling of the spatial distribution of the glacier mass balance. The albedo observations are integrated in the snowpack simulation using a variational data assimilation scheme that modifies the surface grain conditions. The study shows that mesoscale meteorological variables and MODIS-derived albedo maps can be used to obtain a good reconstruction of the annual mass balance on Glacier de Saint-Sorlin, French Alps, on a 100 m × 100m grid. Five hydrological years within the 2000-10 decade are tested. The accuracy of the method is estimated from comparison with field measurements. Sensitivity to roughness lengths and winter precipitation fields is investigated. Results demonstrate the potential contribution of remote-sensing data and variational data assimilation to further improve the understanding and monitoring of the mass balance of snowpacks and temperate glaciers.

A history of the idea of transporting large icebergs to arid regions to provide a fresh-water source is presented and the problem is considered in four main parts: (1) Location of a supply of icebergs. Only in the Antarctic are supplies of large tabular icebergs available. Data on the size distribution of these icebergs are reviewed and it is concluded that icebergs of almost any desired size can readily be located. (2) Towing. Steady-state towing velocities of different sized icebergs are calculated based on estimates of the drag of the icebergs and the bollard pull of tugs. Because drag increases with velocity squared, large icebergs can only be towed at very slow velocities (<c. 0.5 m/s). However, tugs that can be built within the capabilities of current technology are capable of towing extremely large icebergs. (3) Melting in transit. Calculations of melting indicate that, although melting losses are significant and may be excessive for small icebergs, when large icebergs are towed, large amounts of ice are left when the iceberg arrives at its destination. Towing trajectories, travel times, and ice delivery rates are calculated for optimum routes between the Amery Ice Shelf and Western Australia (A–A) and the Ross Ice Shelf and the Atacama Desert (R–A). Forces included in these calculations are towing, air, water, gradient current and Coriolis. Transit times exceed 107 d (A–A) and 145 d (R–A) with over 50% of the initial ice delivered. (4) Economic feasibility. After total towing charges are paid, it is possible to deliver ice to Western Australia for 1.3 mills/m3 of water and to the Atacama Desert region for 1.9 mills/m3. These costs are appreciably less than the expected price of water delivered at these locations (8 mills/m3). The water delivered by the operation of one super-tug alone would irrigate 16 000 km2. Problems related to both iceberg transport and processing are reviewed and although substantial problems do exist, they appear to be within the capabilities of current technology.

It is suggested that the overall idea is indeed feasible and should be explored further by specific groups of experts.

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.

The stresses and strains in a limited region of a temperate glacier are approximated by polynomials. In this case it seems that we can replace Glen’s law by the more convenient law . We initially consider a plane problem with a flat glacier surface. In a simple example the theoretical possibility of very important deviations from the classical relation τxz = ρgz sin α is demonstrated. The calculation is then extended to the more general case when the surface of the glacier is no longer a plane (the contours remaining always parallel) and where the width of the glacier varies.

Starting from a precise survey of the surface and measurements of surface velocity, one can then obtain velocities and stresses at depth, and extrapolate the bedrock profile into regions inaccessible by seismic sounding. A provisional calculation has been made for the ice fall between the Glacier du Géant and the Glacier du Tacul (Mont-Blanc massif). In the lower part, the existence of a gorge near the right bank and the fact that the various ice streams partially superpose instead of flowing side by side, make the calculations uncertain.

In this way the law of friction can be determined experimentally. Proceeding down-glacier, the sliding velocity decreases from about 830 m/year to about 250 m/year, while the normal pressure increases from about 2.8 to about 18.5 bar. At the same time the friction increases from about 1.1 to about 4.3 bar, approximately proportional to the pressure, which seems to be in agreement with the author’s theory of friction.

Glacier-surface displacements produced by geothermal and volcanic activity beneath Vatnajökull ice cap in Iceland are described by field surveys of the surface topography combined with interferograms acquired from repeat-pass synthetic aperture radar images. A simple ice-flow model serves well to confirm the basic interpretation of the observations. The observations cover the period October 1996–January 1999 and comprise: (a) the ice-flow field during the infilling of the depressions created by the subglacial Gjálp eruption of October 1996, (b) the extent and displacement of the floating ice cover of the subglacier lakes of Grímsvötn and the Skaftá cauldrons, (c) surface displacements above the subglacier pathways of the jökulhlaups from the Gjálp eruption site and the Grímsvötn lake, (d) detection of areas of increased basal sliding due to lubrication by water, and (e) detection of spots of temporal displacement that may be related to altering subglacial volcanic activity. At the depression created by the Gjálp eruption, the maximum surface displacement rate away from the radar decreased from 27 cm d−1 to 2 cm d−1 over the period January 1997–January 1999. The observed vertical displacement of the ice cover of Grímsvötn changed from an uplift rate of 50 cm d−1 to sinking of 48 cm d−1, and for Skaftá cauldrons from 2 cm d to 25 cm d−1.

Glacier mass changes are considered to represent key variables related to climate variability. We have reconstructed a proxy for annual mass-balance changes in Grosse Aletschgletscher, Swiss Alps, back to AD 1500 using a non-linear back-propagation neural network (BPN). The model skill of the BPN performs better than reconstructions using conventional stepwise multiple linear regression. The BPN, driven by monthly instrumental series of local temperature and precipitation, provides a proxy for 20th-century mass balance. The long-term mass-balance reconstruction back to 1500 is based on a multi-proxy approach of seasonally resolved temperature and precipitation reconstructions (mean over a specific area) as input variables. The relation between the driving factors (temperature, precipitation) used and the reconstructed mass-balance series is discussed. Mass changes in Grosse Aletschgletscher are shown to be mainly influenced by summer (June–August) temperatures, but winter (December–February) precipitation also seems to contribute. Furthermore, we found a significant non-linear part within the climate–mass-balance relation of Grosse Aletschgletscher.

The size of firn crystals as a function of age has been investigated in thin sections to a depth of 49 m at the South Pole. Grain cross-sections increased in size from 0.24 mm2 at 0.1 m depth to 0.63 mm2 at 10 m. Crystals, as distinct from grains, increased in size from 0.18 to 0.43 mm2 over the same interval, implying that grains are generally composed of just one or two crystals rather than several as is frequently contended. The mean crystal cross-section increased linearly with the age of the firn at a rate of 0.0006 mm2 year−1; in 388 year old firn at 49 m the crystal size measured 0.63 mm2. Analysis of crystal-growth data from other locations in Antarctica and Greenland also revealed a strong linear relationship between the mean cross-sectional arcas (D2) of crystals (in mm2) and their ages in years (t), i.e. . The fact that the temperature dependence of the crystal growth rate K can be expressed very satisfactorily in an equation of the form K = K0 exp (E/RT) confirms predictions that crystal growth in firn is essentially analogous to grain growth in metallic and ceramic sinters. An extrapolation of available data indicates that crystal growth rates in dry firn could be expected to vary by two orders of magnitude (0.0003 to 0.03 mm2 year−1) over the temperature range −60° to −15°C. A method of utilizing crystal growth-mean annual temperature data to determine accumulation rates in snow is demonstrated.

This paper presents observations and measurements of debris characteristics and ice-shelf dynamics in the ablation region of the McMurdo Ice Shelf in the Ross Sea sector of Antarctica. Ice-shelf surface processes and dynamics are inferred from a combination of sedimentological descriptions, ground-penetrating radar investigations and through ablation, velocity and ice-thickness measurements. Field data show that in the study area the ice shelf moves relatively slowly (1.5–18.3ma–1), has high ablation rates (43–441 mm during 2003/04 summer) and is thin (6–22 m). The majority of debris on the ice shelf was originally transported into the area by a large and dynamic ice-sheet/ice-shelf system at the Last Glacial Maximum. This debris is concentrated on the ice-shelf surface and is continually redistributed by surface ablation (creating an ice-cored landscape of large debris-rich mounds), ice-shelf flow (forming medial moraines) and meltwater streams (locally reworking material and redistributing it across the ice-shelf surface). A conceptual model for supraglacial debris transport by contemporary Antarctic ice shelves is presented, which emphasizes these links between debris supply, surface ablation and ice-shelf motion. Low-velocity ice shelves such as the McMurdo Ice Shelf can maintain and sequester a debris load for thousands of years, providing a mechanism by which ice shelves can accumulate sufficient debris to contribute to sediment deposition in the oceans.

A substantial data set of digitally recorded radio echo-sounding data was collected over 44 ice masses in Spitsbergen and the ice caps on Nordaustlandet, Svalbard. These data have allowed quantitative analysis of bed and internal power-reflection coefficients. Substantial regional differences were observed and have been correlated with the presence of water and/or moraine at the bed and with the bulk thermal regime of the ice mass. Values of bed power-reflection coefficient varied between −40 ± 5 and −8 ± 6 dB. It is suggested that the ice caps in north-east Spitsbergen (possessing among the lowest reflection coefficients observed) are frozen to their beds as is much of Austfonna (in Nordaustlandet), and that such values imply the likelihood of a layer of debris-rich ice above the bedrock. It is proposed that significant quantities of water are present at the ice/bed interface of many of the glaciers in north-west Spitsbergen. Further, it is believed that two geological divides were detected. A number of extraordinary internal reflecting horizons are also discussed.

We analyse data on solar radiation measured with an automatic weather station on Morteratschgletscher, Switzerland, for the period 1 October 1995–30 September 1996. The station is in the lower ablation zone. Due to shading by surrounding mountains and atmospheric attenuation, only 49% of the annual extraterrestrial irradiance (mean: 292 W m−2) reaches the glacier surface. About 48% of this is absorbed at the surface (mean: 79 W m−2; annual albedo of 0.53).

We present a simple albedo scheme for use in glacier mass-balance models. We fit the model to the 1 year dataset by optimizing five control parameters (optimal values in brackets): albedo of snow (0.75), albedo of firn (0.53), albedo of ice (0.34), e-folding constant for effect of ageing on snow albedo (21.9 days) and e-folding constant for effect of snow depth on albedo (3.2 cm). The input consists of daily albedo, snow depth and dates of snowfall events. The correlation coefficient between observed and simulated albedo is 0.931, the corresponding rms difference being 0.067.

The Glacier Bay region of southeast Alaska, USA, and British Columbia, Canada, has undergone major glacier retreat since the Little Ice Age (LIA). We used airborne laser altimetry elevation data acquired between 1995 and 2011 to estimate the mass loss of the Glacier Bay region over four time periods (1995–2000, 2000–05, 2005–09, 2009–11). For each glacier, we extrapolated from center-line profiles to the entire glacier to estimate glacier-wide mass balance, and then averaged these results over the entire region using three difference methods (normalized elevation, area-weighted method and simple average). We found that there was large interannual variability of the mass loss since 1995 compared with the long-term (post-LIA) average. For the full period (1995–2011) the average mass loss was 3.93 ± 0.89 Gt a−1 (0.6 ± 0.1 m w.e. a−1), compared with 17.8 Gt a−1 for the post-LIA (1770–1948) rate. Our mass loss rate is consistent with GRACE gravity signal changes for the 2003–10 period. Our results also show that there is a lower bias due to center-line profiling than was previously found by a digital elevation model difference method.

Analysis of aerial photographs, GPS mapping and comparison of digital elevation models have been used to quantify the losses in extent and volume observed (1981–2005) in the glaciers of the Maladeta massif (Spanish Pyrenees). The data are examined in relation to different climatic (temperature, precipitation) and topographic factors that control glacial retreat both at the general and local scales. The evolution observed in the massif is characterized by the remarkable surface and volumetric shrinkage registered in all the glaciers: (1) glacial ice decreased in extent 35.7%, reducing from 240.9 ha to 155.0 ha; (2) losses in total ice volume reached 0.0137 km3 (75.6 m w.e.); (3) mean altitude of the studied glaciers increased 43.5 m. These changes seem to have been forced by climatic change (reduction in the snowfall contributions and increase in the maximum temperatures) during the past few decades in this Pyrenean region. In addition, local variables such as the orientation of each glacier, their altitude and their initial size seem to have induced significant spatial differences in the magnitude of the losses.

With the use of a numerical three-dimensional (3-D) model the flow dynamics of the confluence area of Unteraargletscher, Bernese Alps, Switzerland, are studied. Previous predictions, based on conceptual two-dimensional models, about flow characteristics at confluence areas are tested against results from the fully 3-D model. Measured winter velocities are used for model verification. Despite some consistent systematic differences, good overall agreement between measured and calculated surface velocities is obtained. The calculated vertical strain-rate variation with depth is in good agreement with available measurements from boreholes. The ice is found to be almost three times stiffer than standard estimates of rheological parameters for glacier ice would predict. The model predicts a complicated yet realistic pattern of vertical velocity variation along the surface. The most noticeable features of the vertical velocity distribution across the surface are listed, and their relation to topographic surface undulations and the overall dynamics of the confluence discussed. In accordance with previous results from analytical models, a strongly localized surface trough and a concomitant negative (downward orientation) vertical velocity anomaly develop at the junction point. Although depth-integrated strain rates are positive (extension), the basal layer is compressed vertically. The ice-cored medial moraine is formed by differential ablation. The flow mechanics of the confluence area play only an indirect role, by enabling transfer of debris-covered marginal ice towards the confluence center. In the absence of differential ablation, an elongated surface depression would be formed in the down-glacier direction from the junction point instead of an elevated ice-cored medial moraine.

Higher-order models represent a computationally less expensive alternative to the Stokes model for ice-sheet modeling. In this work, we develop linear and quadratic finite-element methods, implemented on parallel architectures, for the three-dimensional first-order model of Dukowicz and others (2010) that is based on the Blatter-Pattyn model, and for the depth-integrated model of Schoof and Hindmarsh (2010). We then apply our computational models to three of the ISMIP-HOM benchmark test cases (Pattyn and others, 2008). We compare results obtained from our models with those obtained using a reliable Stokes computational model, showing that our first-order model implementation produces reliable and accurate solutions for almost all characteristic length scales of the test geometries considered. Good agreement with the reference Stokes solution is also obtained by our depth-integrated model implementation in fast-sliding regimes and for medium to large length scales. We also provide a comprehensive comparison between results obtained from our first-order model implementation and implementations developed by ISMIP-HOM participants; this study shows that our implementation is at least as good as the previous ones. Finally, a comparison between linear and quadratic finite- element approximations is carried out, showing, as expected, the better accuracy of the quadratic finite-element method.

Fedchenko glacier is by far the largest glacier in the Pamir, Tajikistan. Owing to early accurate mapping of the glacier it is possible to evaluate glacier changes over eight decades, which is an exceptionally long time period for this remote mountain region. During this time a total volume loss of 5 km3 was observed on the main trunk of the glacier, while the total area changed by only 1.4%. It is observed that the volume loss migrates from the lower parts of the glacier towards the upper ablation zone. The comparatively small change in area is a result of the supraglacial debris cover on the glacier tongue, which decouples the area loss from the volume loss to a considerable degree. The observed velocities of the glacier do not reflect the volume changes up to now because the interannual variability is larger than possible long-term changes so far. The intra-annual velocity distribution in the central ablation zone probably reflects the evolution of the basal drainage system. Based on ice thickness measurements and simple ice-dynamic assumptions, the total volume of Fedchenko glacier is 123.4 ± 8 km3.