Sound knowledge of the ice volume and ice-thickness distribution of a glacier is essential for many glaciological applications. However, direct measurements of ice thickness are laborious, not feasible everywhere and necessarily restricted to a small number of glaciers. In this paper, we present a method to estimate the ice-thickness distribution and the total ice volume of alpine glaciers. This method is based on glacier mass turnover and principles of ice-flow mechanics. The required input data are the glacier surface topography, the glacier outline and a set of borders delineating different ‘ice-flow catchments’. Three parameters describe the distribution of the ‘apparent mass balance’, which is defined as the difference between the glacier surface mass balance and the rate of ice-thickness change, and two parameters define the ice-flow dynamics. The method was developed and validated on four alpine glaciers located in Switzerland, for which the bedrock topography is partially known from radio-echo soundings. The ice thickness along 82 cross-profiles can be reproduced with an average deviation of about 25% between the calculated and the measured ice thickness. The cross-sectional areas differ by less than 20% on average. This shows the potential of the method for estimating the ice-thickness distribution of alpine glaciers without the use of direct measurements.

We present spatial patterns of glacier fluctuations from the Cordillera Blanca, Peru, (glacier area, terminus elevations, median elevations and hypsography) at decadal timescales derived from 1970 aerial photography, 2003 SPOT5 satellite data, Geographic Information Systems (GIS) and statistical analyses. We derived new glacier outlines from the 2003 SPOT images, and ingested them in the Global Land and Ice Measurements from Space (GLIMS) glacier database. We examined changes in glacier area on the eastern and western side of the Cordillera in relation to topographic and climate variables (temperature and precipitation). Results include (1) an estimated glacierized area of 569.6 ± 21 km2 in 2003, (2) an overall loss in glacierized area of 22.4% from 1970 to 2003, (3) an average rise in glacier terminus elevations by 113 m and an average rise in the median elevation of glaciers by 66 m, showing a shift of ice to higher elevations, especially on the eastern side of the Cordillera, and (4) an increase in the number of glaciers, which indicates disintegration of ice bodies. Annual air temperature showed a significant upward trend in the last 30 years, with larger temperature increases at lower elevations. There was a slight but not significant decrease in precipitation. Our results are consistent with glacier retreat and warming trends noted in the last three decades in the tropics.

The characteristics and sensitivities of a cold-based glacier on the Tibetan Plateau, where the summer monsoon provides most of the mass input to glaciers, are discussed using an energy-balance model incorporating the process of water refreezing. The model accurately represents the observational results related to the mass balance of Xiao Dongkemadi glacier on the central plateau during 1992/93. Our data revealed that the mass balance of cold glaciers cannot simply be described by the surface mass/heat balances, because about 20% of infiltrated water is refrozen and thus does not run off from the glacier. Model calculations demonstrate that glaciers in an arid environment can maintain their mass since the monsoon provides precipitation during the melting season. Snowfall in summer keeps surface albedo high and largely restrains ablation. Nevertheless, the calculations also make clear that glaciers on the plateau are more vulnerable than those of other regions because of summer accumulation. In the monsoon climate, warming would cause not only a decrease in accumulation, but also a drastic increase in ablation in combination with surface-albedo lowering. Therefore, although glaciers on and around the plateau can be sustained by summer accumulation, they are more vulnerable to warming than winter-accumulation-type glaciers.

This study evaluates the impact of a recent upgrade in the physics package of the regional atmospheric climate model RACMO2 on the simulated surface mass balance (SMB) of the Antarctic ice sheet. The modelled SMB increases, in particular over the grounded ice sheet of East Antarctica (+44 Gt a–1), with a small change in West Antarctica. This mainly results from an increase in precipitation, which is explained by changes in the cloud microphysics, including a new parameterization for ice cloud supersaturation, and changes in large-scale circulation patterns, which alter topographically forced precipitation. The spatial changes in SMB are evaluated using 3234 in situ SMB observations and ice-balance velocities, and the temporal variability using GRACE satellite retrievals. The in situ observations and balance velocities show a clear improvement of the spatial representation of the SMB in the interior of East Antarctica, which has become considerably wetter. No improvements are seen for West Antarctica and the coastal regions. A comparison of model SMB temporal variability with GRACE satellite retrievals shows no significant change in performance.

Little is known about the Himalayan glaciers, although they are of particular interest in terms of future water supply, regional climate change and sea-level rise. In 2002, a long-term monitoring programme was started on Chhota Shigri Glacier (32.2° N, 77.5° E; 15.7 km2, 6263–4050 ma.s.l., 9 km long) located in Lahaul and Spiti Valley, Himachal Pradesh, India. This glacier lies in the monsoon–arid transition zone (western Himalaya) which is alternately influenced by Asian monsoon in summer and the mid-latitude westerlies in winter. Here we present the results of a 4 year study of mass balance and surface velocity. Overall specific mass balances are mostly negative during the study period and vary from a minimum value of –1.4 m w.e. in 2002/03 and 2005/06 (equilibrium-line altitude (ELA) ∼5180 m a.s.l.) to a maximum value of +0.1 m w.e. in 2004/05 (ELA 4855 m a.s.l.). Chhota Shigri Glacier seems similar to mid-latitude glaciers, with an ablation season limited to the summer months and a mean vertical gradient of mass balance in the ablation zone (debris-free part) of 0.7mw.e.(100 m)–1, similar to those reported in the Alps. Mass balance is strongly dependent on debris cover, exposure and the shading effect of surrounding steep slopes.

A large portion of the recent increase in the rate of mass loss from the Greenland ice sheet is from increased outlet glacier discharge along its southeastern margin. While previous investigations of the region’s two largest glaciers suggest that acceleration is a dynamic response to thinning and retreat of the calving front, it is unknown whether this mechanism can explain regional acceleration and what forcing is responsible for initiating rapid thinning and retreat. We examine seasonal and interannual changes in ice-front position, surface elevation and flow speed for 32 glaciers along the southeastern coast between 2000 and 2006. While substantial seasonality in front position and speed is apparent, nearly all the observed glaciers show net retreat, thinning and acceleration, with speed-up corresponding to retreat. The ratio of retreat to the along-flow stress-coupling length is proportional to the relative increase in speed, consistent with typical ice-flow and sliding laws. This affirms that speed-up results from loss of resistive stress at the front during retreat, which leads to along-flow stress transfer. Large retreats were often preceded by the formation of a flat or reverse-sloped surface near the front, indicating that subsequent retreats were influenced by the reversed bed slope. Many retreats began with an increase in thinning rates near the front in the summer of 2003, a year of record high coastal-air and sea-surface temperatures. This anomaly was driven in part by recent warming, suggesting that episodes of speed-up and retreat may become more common in a warmer climate.

Surveys were conducted seaward of all the major drainage outlets of the Antarctic ice sheet from the Pennell Coast, north Victoria Land, to Marguerite Bay, Antarctic Peninsula. The results show that the ice sheet extended onto the outer shelf. Glacial troughs occur offshore of all major glacial outlets. Where the substrate is crystalline bedrock, ice flow tended to follow the structural grain of the bedrock, deposited little sediment and eroded the underlying bedrock. Where ice flowed over relatively soft, more easily eroded, sedimentary strata, the direction of ice flow was more directly offshore, and depositional features characterize the sea-floor. In these areas the signature of the grounded ice consists of till deposits and large-scale geomorphic features. Drumlins occur within the region of contact between crystalline and sedimentary substrates. The different geological substrates are interpreted to have exerted a fundamental control on the behavior of past ice sheets. The troughs in the areas of bedrock composed of sedimentary substrate are interpreted to have been occupied by relatively fast-flowing ice, ice streams, and the troughs in the areas of crystalline substrate are interpreted to have been occupied by slower-moving ice. The area between these two zones was characterized by ice acceleration and is marked by drumlins.

A degree-day model is used to assess the sensitivity of the mass balance of five Swiss glaciers to temperature changes. The model uses temperature data extrapolated from nearby climate stations, and is tuned by varying precipitation to make the model fit the observed distribution of mass balance with altitude. Once the model is tuned, the effect of temperature change is simulated by recalculating the mass balance with the same parameters as before, but with a temperature increase of 1°C throughout the year. The largest mass-balance changes, involving increased ablation of > 1 m w.e. a−1 °C−1, occur at the snout, with a progressively smaller increase with altitude. The area-averaged sensitivities for the five glaciers are −0.7 to −0.9 m w.e. a−1 °C−1. If annual precipitation also increased by 20% it would partly offset the effect of the 1°C higher temperatures but could not compensate for it.

We present a generalized version of SnowTran-3D (version 2.0), that simulates wind-related snow distributions over the range of topographic and climatic environments found globally. This version includes three primary enhancements to the original Liston and Sturm (1998) model: (1) an improved wind sub-model, (2) a two-layer sub-model describing the spatial and temporal evolution of friction velocity that must be exceeded to transport snow (the threshold friction velocity) and (3) implementation of a three-dimensional, equilibrium-drift profile sub-model that forces SnowTran-3D snow accumulations to duplicate observed drift profiles. These three sub-models allow SnowTran-3D to simulate snow-transport processes in variable topography and different snow climates. In addition, SnowTran-3D has been coupled to a high-resolution, spatially distributed meteorological model (MicroMet) to provide more realistic atmospheric forcing data. MicroMet distributes data (precipitation, wind speed and direction, air temperature and relative humidity) obtained from meteorological stations and/or atmospheric models located within or near the simulation domain. SnowTran-3D has also been coupled to a spatially distributed energy- and mass-balance snow-evolution modeling system (SnowModel) designed for application in any landscape and climate where snow is found. SnowTran-3D is typically run using temporal increments ranging from 1 hour to 1 day, horizontal grid increments ranging from 1 to 100 m and time-spans ranging from individual storms to entire snow seasons.

Ten ice-sheet models are used to study sensitivity of the Greenland and Antarctic ice sheets to prescribed changes of surface mass balance, sub-ice-shelf melting and basal sliding. Results exhibit a large range in projected contributions to sea-level change. In most cases, the ice volume above flotation lost is linearly dependent on the strength of the forcing. Combinations of forcings can be closely approximated by linearly summing the contributions from single forcing experiments, suggesting that nonlinear feedbacks are modest. Our models indicate that Greenland is more sensitive than Antarctica to likely atmospheric changes in temperature and precipitation, while Antarctica is more sensitive to increased ice-shelf basal melting. An experiment approximating the Intergovernmental Panel on Climate Change’s RCP8.5 scenario produces additional first-century contributions to sea level of 22.3 and 8.1 cm from Greenland and Antarctica, respectively, with a range among models of 62 and 14 cm, respectively. By 200 years, projections increase to 53.2 and 26.7 cm, respectively, with ranges of 79 and 43 cm. Linear interpolation of the sensitivity results closely approximates these projections, revealing the relative contributions of the individual forcings on the combined volume change and suggesting that total ice-sheet response to complicated forcings over 200 years can be linearized.

Four tributaries of Panmah Glacier have surged in less than a decade, three in quick succession between 2001 and 2005. Since 1985, 13 surges have been recorded in the Karakoram Himalaya, more than in any comparable period since the 1850s. Ten were tributary surges. In these ten a full run-out of surge ice is prevented, but extended post-surge episodes affect the tributary and main glacier. The sudden concentration of events at Panmah Glacier is without precedent and at odds with known surge intervals for the glaciers. Interpretations must consider the response of thermally complex glaciers, at exceptionally high altitudes and of high relief, to changes in a distinctive regional climate. It is suggested that high-altitude warming affecting snow and glacier thermal regimes, or bringing intense, short-term melting episodes, may be more significant than mass-balance change.

Estimates of glacier mass balance using geodetic methods can differ significantly from estimates using direct glaciological field-based measurements. To determine if such differences are real or methodological, there is a need to improve uncertainty estimates in both methods. In this paper, we focus on the uncertainty of geodetic methods and describe a geostatistical technique that takes into account the spatial correlation of the elevation differences when calculating spatially averaged elevation changes. We apply this method to the western Svartisen ice cap, Norway, using elevation differences from the surrounding bedrock derived from stereophotogrammetry. We show that the uncertainty is not only dependent on the standard error of the individual elevation differences but is also dependent on the size of the averaging area and the scale of the spatial correlation. To assess if the geostatistical analysis made over bedrock is applicable to glacier surfaces, we use concurrent photogrammetrical and laser scanning data from bedrock and a range of glacier surfaces to evaluate the dependency of the geostatistical analysis on the surface type. The estimated geodetic mass balance, and its uncertainty, is −2.6 ± 0.9 m w.e. for the period 1968–85, and −2.0 ± 2.2 m w.e. for 1985–2002.

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.

Polythermal conditions are ubiquitous among glaciers, from small valley glaciers to ice sheets. Conventional temperature-based ‘cold-ice’ models of such ice masses cannot account for that portion of the internal energy which is latent heat of liquid water within temperate ice, so such schemes are not energy-conserving when temperate ice is present. Temperature and liquid water fraction are, however, functions of a single enthalpy variable: a small enthalpy change in cold ice is a change in temperature, while a small enthalpy change in temperate ice is a change in liquid water fraction. The unified enthalpy formulation described here models the mass and energy balance for the threedimensional ice fluid, for the surface runoff layer and for the subglacial hydrology layer, together in a single energy-conserving theoretical framework. It is implemented in the Parallel Ice Sheet Model. Results for the Greenland ice sheet are compared with those from a cold-ice scheme. This paper is intended to be an accessible foundation for enthalpy formulations in glaciology.

Analysis of the likely behavior of a water system developed between ice and an unconsolidated glacier bed suggests that, in the absence of channelized sources of melt water, the system will approximate a film of varying thickness. The effective pressure in such a film will be proportional to the basal shear stress but inversely proportional to the fraction of the bed occupied by the film. These hypotheses allow calculation of the sliding and bed-deformation velocities of a glacier from the water supply and basal shear stress, as discussed in the second and third papers in this series.

Twenty-seven studies on the thermal conductivity of snow (Keff) have been published since 1886. Combined, they comprise 354 values of Keff, and have been used to derive over 13 regression equation and predicting Keff vs density. Due to large (and largely undocumented) differences in measurement methods and accuracy, sample temperature and snow type, it is not possible to know what part of the variability in this data set is the result of snow microstructure. We present a new data set containing 488 measurements for which the temperature, type and measurement accuracy are known. A quadratic equation,

where ρ is in g cm−3, and Keff is in W m−1K−1, can be fit to the new data (R2 = 0.79). A logarithmic expression,

can also be used. The first regression is better when estimating values beyond the limits of the data; the second when estimating values for low-density snow. Within the data set, snow types resulting from kinetic growth show density-independent behavior. Rounded-grain and wind-blown snow show strong density dependence. The new data set has a higher mean value of density but a lower mean value of thermal conductivity than the old set. This shift is attributed to differences in snow types and sample temperatures in the sets. Using both data sets, we show that there are well-defined limits to the geometric configurations that natural seasonal snow can take.

Remote sensing offers local, regional and global observations of seasonal snow, providing key information on snowpack processes. This brief review highlights advancements in instrumentation and analysis techniques that have been developed over the past decade. Areas of advancement include improved algorithms for mapping snow-cover extent, snow albedo, snow grain size, snow water equivalent, melt detection and snow depth, as well as new uses of instruments such as multiangular spectroradiometers, scatterometry and lidar. Limitations and synergies of the instruments and techniques are discussed, and remaining challenges such as multisensor mapping, scaling issues, vegetation correction and data assimilation are identified.

Recent studies indicate that the dynamics of fast-flowing, marine-terminating outlet glaciers of the Greenland ice sheet may be sensitive to climate and ocean forcing on sub-annual timescales. Observations of seasonal behavior of these glaciers at such high temporal resolution, however, are currently few. Here we present observations of front position, flow speed, near-surface air temperature and ocean conditions for six large marine-terminating glaciers in the Uummannaq region of West Greenland, to investigate controls on short-term glacier dynamics. As proposed by other studies, we find that seasonal front advance and retreat correlates with the formation and disappearance of an ice melange. Our data suggest that high sea-surface temperature, anomalously low sea-ice concentration and reduced melange formation in early 2003 have triggered multi-year retreat of several glaciers in the study area, which is consistent with other regions in Greenland. Of the stable glaciers, only Rink Isbræ exhibits a seasonal speed variation that correlates with variations in front position, with the others undergoing mid-summer deceleration that indicates the effects of subglacial meltwater discharge and drainage system evolution. Drainage of supraglacial lakes and water-filled crevasses results in substantial decreases in speed (40–60%) on fast-flowing glaciers. Our results demonstrate that attempts to model ice-sheet evolution must take into account short-timescale flow dynamics resulting from drainage events and oceanographic conditions.

This study provides a detailed structural glaciological analysis of changes in surface structures on the Larsen B ice shelf on the Antarctic Peninsula prior to its collapse in February–March 2002. Mapped features include the ice-shelf front, rifts, crevasses, longitudinal linear surface structures and meltwater features. We define domains on the ice shelf related to glacier source areas and demonstrate that, prior to collapse, the central Larsen B ice shelf consisted of four sutured flow units fed by Crane, Jorum, Punchbowl and Hektoria/Green/Evans glaciers. Between these flow units were ‘suture zones’ of thinner ice where the feeder glaciers merged. Prior to collapse, large open-rift systems were present offshore of Foyn Point and Cape Disappointment. These rifts became more pronounced in the years preceding break-up, and ice blocks in the rifts rotated because of the strong lateral shear in this zone. Velocity mapping of the suture zones indicates that the major rifts were not present more than about 20 years ago. We suggest that the ice shelf was preconditioned to collapse by partial rupturing of the sutures between flow units. This, we believe, was the result of ice-shelf front retreat during 1998–2000, reducing the lateral resistive stress on the upstream parts of the shelf and glacier flow units, ice-shelf thinning and pre-shelf-break-up glacier acceleration.