No single flow model can simulate all possible glaciers and ice sheets without violating fundamental tenets of computational science. The root cause is not one of numerical sophistication, precision or accurate initial conditions. Instead, using flow and transport as data transmission, glaciers inadvertently function as information processors. This computational capability confers a level of complexity that inherently limits our ability to accurately and efficiently predict glacier flow and therefore, for example, to forecast those aspects of climate systems that depend on glaciers. In particular, even with considerable future advancements in glacier physics, computational theory shows that no dramatic improvements in numerical speed are likely when compared to today’s glacier models. Therefore, to increase speed and resolution, the next generation of climate and sea-level models must rely on simulations tailored to specific ice-sheet geometries rather than general-purpose glacier flow models. However, because glaciers process information, entirely new computation-theoretic advances in glaciology are possible, and concepts from information entropy may help to define new glacier scaling relationships and identify which geometries will be most problematic for modeling.

The loss of methanesul phonic acid (MSA) from stored ice cores can be significant over typical storage times, with diffusion to the ice-core surface controlling the loss. Methods for minimizing this loss are discussed and it is shown how measurements can be corrected by calculating the amount of MSA lost. A revised diffusion coefficient for MSA in solid ice, (4.1 × 10−13) ± (2.5 × 10−14) m2 s−1, is derived to improve such MSA loss corrections.

In 2003–07 summer balance was measured at altitudes between 1700 and 3382 m a.s.l. on two glaciers on Mount Rainier, Washington State, USA (46.85° N,121.72° W; 4400 m a.s.l.): south-facing Nisqually Glacier and east-northeast-facing Emmons Glacier. Upper-air temperatures at the nearest gridpoint in the NCEP/NCAR reanalysis database are used in a distributed (over altitude) positive-degreeday (PDD) model. For each glacier the model used the same coefficients at all altitudes, for all years. The rms model error was 0.65 (r2 = 0.87) and 0.78 m a−1 w.e. (r2 = 0.93) for Nisqually and Emmons Glaciers, respectively. Although PDD work generally uses different coefficients for snow and ice surfaces, and the duration of exposure of those surfaces varies with altitude, error in this single-coefficient model is nearly uncorrelated with altitude. Values of coefficients obtained are within the range of those found in other PDD work. The degree-day coefficient, however, differs markedly between the two glaciers, and is shown to be controlled by the difference between them in vertical gradient of measured summer balance. It is smaller for Nisqually Glacier, where solar radiation is a stronger contributor to melt; and larger for Emmons Glacier, where it is a weaker contributor. Over 1948–2007, when the model calibrated over 2003–07 was applied to the upper-air temperatures, estimated summer balance was ∼0.4 m a−1 less negative over 1962–83 than before and ∼0.6 m a−1 less negative than after, corresponding roughly with changes of the northeast Pacific sea-surface temperatures.

A recently developed dating method for glacier ice, based on the analysis of radiocarbon in carbonaceous aerosol particles, is thoroughly investigated. We discuss the potential of this method to achieve a reliable dating using examples from a mid- and a low-latitude ice core. Two series of samples from Colle Gnifetti (4450 m a.s.l., Swiss Alps) and Nevado Illimani (6300 m a.s.l., Bolivian Andes) demonstrate that the 14C ages deduced from the water-insoluble organic carbon fraction represent the age of the ice. Sample sizes ranged between 7 and 100 μg carbon. For validation we compare our results with those from independent dating. This new method is thought to have major implications for dating non-polar ice cores in the future, as it provides complementary age information for time periods not accessible with common dating techniques.

This paper presents a newly derived velocity field of the Brunt Ice Shelf and Stancomb-Wills Ice Tongue in East Antarctica. Velocity is derived using automated feature-tracking techniques on RADARSAT-1 imagery from the 1997 Antarctic Mapping Mission-1 (AMM-1) and 2000 Modified Antarctic Mapping Mission (MAMM). We measure velocities up to 1350 m a−1 at the ice front. Closer investigation of the velocity field and radar images reveals an obvious divergence of contemporary flowlines from relict flow stripes along a portion of Stancomb-Wills Ice Tongue. Analysis of relict flow stripes can reveal glacial events in the past. Assuming relatively steady flow since the event occurred, we utilize the current velocity field to reconstruct former stripe configuration. We believe the flowline deviation points to a change in dynamics that occurred approximately 140 years ago, perhaps due to thinning and an associated shift in grounding-line position. This seems to be supported by historic observations and bottom topography data.

The first three-dimensional properties of polar firn obtained by X-ray microtomography are used to study the microstructure of snow on a 15 m deep firn core from West Antarctica. The snow is found to undergo coarsening down to approximately 2.5 m depth before grain growth and densification become the prevalent mechanisms of microstructure change. In contrast to previous assumptions, distinct anisotropy of the ice and pore geometry is observed throughout the profile, with a maximum at 2.5 m depth. The air permeability and the degree of anisotropy vary with depth and can be linked to short-term changes in accumulation rate via the residence time for which a certain snow layer stays in the uppermost 2.5 m. Patterns of the degree of anisotropy and air permeability of buried polar firn are relative indicators of past accumulation rates.

The resistance to sliding and the extent of till deformation beneath soft-bedded glaciers depend on the spatially averaged level of effective stress , which is controlled by the distribution of water pressure at the bed. Major subglacial conduits that facilitate large-scale water transport are expected to be predominantly aligned with the direction of maximum hydraulic gradient, which is normally parallel to the slope of the glacier surface. When the basal heat flow promotes net melting or freezing, seepage transport can enable water exchange between these conduits and the rest of the basal surface area. For a simple glacier geometry with subglacial conduits that are aligned parallel to a uniform slope, the seepage transport is driven primarily by gradients in effective stress. Balance equations determine how varies with conduit spacing and the heat-flow regime. Considerations of thermodynamic equilibrium require that ice penetrates the pore space at high effective stress. Even when the glacier base experiences net melting, for a given heat-flow regime there are limits on the conduit spacing that can be attained before a finite till layer becomes partially frozen throughout. During net freezing, the resistance to flow through partially frozen sediments limits the steady-state conduit spacing. The partially frozen zone can actually be restricted to smaller thicknesses when the freezing rate is greater.

A flowline model, coupled with a surface mass-balance model forced by climate data from Bergen, was used to simulate future frontal changes of Briksdalsbreen, a western outlet glacier from Jostedalsbreen, western Norway, under various future climate scenarios. The model was used to calculate the time-lag of frontal response to a sudden and short change in the mass balance. According to the model, the front has a time-lag for maximum advance rate of 4–5 years, in close agreement with previous studies. The response time for Briksdalsbreen was calculated by running the model for 200 years with different mass-balance perturbations. For mass-balance perturbations of +0.3 and +0.6 m w.e. the model yields response times of 52 and 60 years, respectively. We ran the model from 1963 to 2007 with measured mass-balance data, and from 2007 to 2085 using calculated mass balances from 12 different climate scenarios. The model predicts retreat up the steep valley from the lake inlet, with a total frontal retreat of 2.5–5.0 km by 2085. A spectacular icefall, one of the main tourist attractions in western Norway, may thus disappear and the glacier may become a plateau glacier that will gradually melt down.

In situ field measurements of an active polynya in Storfjorden, Svalbard, during April 2006 are presented. A surface heat flux, estimated to be 400 W m−2, produced frazil ice that was advected away from the fast ice edge during the end of a polynya event driven by cold winds from the northeast. Conductivity, temperature and depth casts from the fast ice edge of the polynya were calibrated by accompanying water samples, and reveal a supercooling event that lasted for 3 days in a 5 m deep water column. Surface salinity reached 35.9 psu from brine release during ice growth. The maximum supercooling measured was 0.037 ± 0.005°C below the in situ freezing point near the surface and 0.016 ± 0.005°C at the bottom; the mean supercooling gradient was 0.020 ± 0.005°C between the surface and the bottom. These measurements are consistent with results from a one-dimensional frazil ice model, confirming that such supercooling levels can be expected. Frazil ice concentrations in the water were modeled to be lower than 0.02 g L−1, due to advection in the surface layer. Seven frazil/grease ice samples taken from a place where advection was blocked along the fast ice edge showed a mean salinity of 26.2 psu, indicating 25% frazil ice and 75% sea water in the grease ice. The water-column salinity decreased during the measurement period due to less saline water replacing newly formed brine-enriched shelf water flowing down to deeper parts of Storfjorden. The supercooling ceased when the wind direction turned to the east, with higher air temperatures and warmer and less saline water being pushed into Storfjorden by the northward Ekman transport. These are the first in situ observations from an active Arctic polynya with concurrent sampling of hydrography and frazil ice, and the supercooling is the maximum observed in recent years with modern and accurate instrumentation.

Dry-snow slab avalanches initiate from a failure in a weak snow layer below a cohesive slab. Snow is considered as a porous ice structure, and the strength distribution of the single elements of this structure, i.e. grains and bonds between grains, shows a high degree of disorder. On the bond or microstructural level, the failure process is believed to start if the fracturing of bonds between snow grains is not balanced by the formation of new bonds. We use a statistical fracture model – a fibre bundle model – to study the failure process in a weak snow layer. The model consists of fibres of various strengths representing single snow grains between two rigid plates which represent the slab above and the substratum below the weak layer. The fibres deform in a linear elastic manner and break instantly at their rupture strength. Broken fibres may sinter (re-bond) and regain strength after a finite sintering time. We show that the different characteristic times for breaking and sintering lead to the rate dependence of snow strength. This is, to our knowledge, the first statistical model to reproduce the ductile-to-brittle transition which snow exhibits with increasing strain rate. When the model is applied to simulate experimental stress–strain curves for different strain rates, the model and experimental results are in fair agreement.

Historically, dry-snow metamorphism has been classified by the thermal environment and thermodynamic processes in a snowpack. Snow experiencing predominantly macroscopic isothermal conditions develops different microstructure than snow subjected to large temperature gradients. As such, much previous research has been categorized by and limited to specific thermal conditions. The current research expands a generalized approach for the movement of heat and mass to include a snow crystal kinetic growth model. An existing spiral defect propagation theory for kinetic growth on simple faceted geometry is utilized. Primary crystal habit as a function of temperature is incorporated. A model of heat and mass transfer through an ice and pore structure is coupled with phase-change thermodynamics during kinetic growth. A kinetic growth microstructure model is developed and integrated into heat and mass transfer representations, which are solved using finite-difference techniques. The kinetic morphology model approximates frequently observed hopper-type crystals. The snow microstructure is allowed to change at every step, resulting in a transient description of kinetic growth metamorphism. Variable kinetic growth rates are demonstrated based on temperature and on crystallographic orientation relative to a temperature gradient. Crystals preferentially aligned with the temperature gradient have significantly higher growth rates, supporting previous observations of predominant crystal habits developing under temperature gradient conditions. Grain-size dispersion increase with time is demonstrated and supported experimentally in the literature. A dominant grain growth theory based on crystallographic orientation that has been previously postulated is supported. A broad range of metamorphic geometric parameters and thermal conditions may now be simulated with a single model.

Two diagnostic, dynamic/thermodynamic ice-shelf models are applied to the Brunt Ice Shelf/Stancomb-Wills Ice Tongue system, located off Caird Coast, Coats Land, Antarctica. The Brunt Ice Shelf/Stancomb-Wills Ice Tongue system is characterized as a thin, unbounded ice shelf with an atypical and highly heterogeneous structure. In contrast to other ice shelves, a composite mass of icebergs that calved at the grounding line and were then locked within fast (sea) ice exists between the fast-moving Stancomb-Wills Ice Stream and the slow-moving Brunt Ice Shelf. We simulate the present flow regime of the ice shelf that results from the ice-thickness distribution and the inflow at the grounding line with two different models, and compare the model results with feature tracking and InSAR flow velocities. We then incorporate two observed features, a rift and a shear margin, into the models with two different approaches, and demonstrate the effects of variations in numerical values for the shear strength and viscosity in these zones on the simulated velocity field. A major result is that both kinds of implementation of the rifts lead to similar effects on the entire velocity field, while there are discrepancies in the vicinity of the rifts.

Wind-blown mineral aerosol dust derived from the crustal surface is an important atmospheric component affecting the Earth’s radiation budget. Deposition of water-insoluble dust was determined in snow deposited on Ürümqi glacier No. 1, Haxilegen glacier No. 51 and Miaoergou glacier, eastern Tien Shan, China. Analysis of the horizontal distribution of snow depth and concentration, and flux of dust particles in the snow cover suggests that dust deposition differs on each of these glaciers as the atmospheric environment changes from west to east. Mean mass concentrations of micro-particles in the size range 0.57–26 μm diameter at the three locations are respectively 969, 1442 and 3690 μg kg−1, with an increasing trend from west to east. Dust layers in the snow cover contain Na- and Ca-rich materials typically found in central Asian dust particles. Volume size distributions of dust particles in the snow showed single-modal structures having volume median diameters of 3–22 μm. Dust profiles in the snow cover over the past 4 years reveal frequent, sporadic high dust concentrations with a large year-to-year variability, implying that dust deposition in the eastern Tien Shan is very sensitive to atmospheric environment change.

Debris cover over glaciers greatly affects their rate of ablation and is a sensitive indicator of glacier health. This study focuses on estimation of debris cover over Samudratapu glacier, Chenab basin, Himalaya, using optical remote-sensing data. Remote-sensing image data of IRS-1C LISS-III (September 2001), IRS-P6 AWiFS (September 2004) and Terra ASTER (September 2004) along with Survey of India topographical maps (1963) were used in the study. Supervised classification of topographically corrected reflectance image data was systematically conducted to map six land-cover classes in the glacier terrain: snow, ice, mixed ice and debris, debris, valley rock, and water. An accuracy assessment of the classification was conducted using the ASTER visible/near-infrared data as the reference. The overall accuracies of the glacier-cover maps were found to range from 83.7% to 89.1%, whereas the individual class accuracy of debris-cover mapping was found to range from 82% to 95%. This shows that supervised classification of topographically corrected reflectance data is effective for the extraction of debris cover. In addition, a comparative study of glacier-cover maps generated from remote-sensing data (supervised classification) of September 2001 and September 2004 and Survey of India topographical maps (1963) has highlighted the trends of glacier depletion and recession. The glacier snout receded by about 756 m from 1963 to 2004, and the total glacier area was reduced by 13.7 km2 (from 110 km2 in 1963). Further, glacier retreat is found to be accompanied by a decrease in mixed ice and debris and a marked increase in debris-cover area. The area covered by valley rock is found to increase, confirming an overall decrease in the glacier area. The results from this study demonstrate the applicability of optical remote-sensing data in monitoring glacier terrain, and particularly mapping debris-cover area.

We use models constrained by remotely sensed data from Pine Island and Thwaites Glaciers, West Antarctica, to infer basal properties that are difficult to observe directly. The results indicate strong basal melting in areas upstream of the grounding lines of both glaciers, where the ice flow is fast and the basal shear stress is large. Farther inland, we find that both glaciers have ‘mixed’ bed conditions, with extensive areas of both bedrock and weak till. In particular, there are weak areas along much of Pine Island Glacier’s main trunk that could prove unstable if it retreats past the band of strong bed just above its current grounding line. In agreement with earlier studies, our forward ice-stream model shows a strong sensitivity to small perturbations in the grounding line position. These results also reveal a large sensitivity to the assumed bed (sliding or deforming) model, with non-linear sliding laws producing substantially greater dynamic response than earlier simulations that assume a linear-viscous till rheology. Finally, comparison indicates that our results using a plastic bed are compatible with the limited observational constraints and theoretical work that suggests an upper bound exists on maximum basal shear stress.

Visualization and quantification of snow structures at a scale of a few millimetres is important in understanding the mechanical, thermal and electromagnetic properties of snow. Surface sections and, to an even greater degree, three-dimensional (3-D) reconstructions of cast snow samples are difficult to prepare, and automatic image processing is notoriously difficult and often requires manual evaluation. Here, we present a new method to measure the 3-D structure of cast snow samples. Snow samples cast with diethyl phthalate (DEP) and frozen are cut to a sample size a few centimetres in diameter and up to 10 cm in height. The ice of these samples is then sublimated in high vacuum and the remaining negative structure (replica) is imaged using X-ray microtomography (micro-CT). The accuracy of the method is demonstrated by comparing micro-CT scans of the original snow structure and the replica. The method described here allows easy transportation of samples, requires little manual interaction, has a very high spatial resolution of up to 10 μm and is environmentally friendly.

Information on snow-cover stability is important for predicting avalanche danger. Traditionally, stability evaluation is based on manual observations of snow stratigraphy and stability tests, which are time-consuming. The SnowMicroPen (SMP) is a high-resolution, constant-speed penetrometer to measure penetration resistance. We have analysed the resistance signal to derive snow stability. The proposed stability algorithm was developed by comparing 68 SMP force–distance profiles with the corresponding manual profiles, including stability tests. The algorithm identifies a set of four potentially weak layers by taking into account changes in structure and rupture strength of microstructural elements that make up snow layers as derived from the SMP signal. In 90% of the cases, one of the four potentially weak layers proposed by the algorithm coincided with the failure layer observed in the stability test. To select the critical layer from the four potential weaknesses was more difficult. With fully automatic picking of the critical layer, agreement with the failure layer observed in the stability test was reached in 60% of the cases. To derive a stability classification, we analysed weak-layer as well as slab properties. These predictor variables allow the SMP signal to be classified into two stability classes, poor and fair-to-good, with an accuracy of ∼75% when compared with observed stability. The SMP, in combination with the proposed algorithm, shows high potential for providing snow-cover stability information at high resolution in time and space.

In order to develop and evaluate a method for the determination of glacier volume from ice-thickness data, the volume of Schaufelferner, Austria, is calculated (1) by manual interpolation of ground-penetrating radar (GPR) data based on measurements at 36 locations in 1995, (2) by manual interpolation of 144 GPR measurements acquired for a higher-resolution estimate in 2003 and 2006, (3) by multiplying the mean of the measured ice-thickness data by the glacier area, (4) by automatic kriging of the 1995 GPR data and (5) by application of area/volume scaling algorithms to the Austrian glacier inventory data of 1969, 1997 and 2006. The so determined glacier volumes are compared with the ice-volume changes calculated from digital elevation models (DEMs) of the Austrian glacier inventories. The manually interpolated volumes based on the 1995 and 2003/06 GPR data yielded a volume loss only slightly different from volume loss calculated from the glacier inventories of 1997 and 2007. Other methods were not able to reproduce the volume losses of the glacier inventory DEMs. To assess the accuracy of deriving ice-thickness changes with GPR, repeated ice-thickness measurements at the same locations were carried out between 2005 and 2008.

We investigate the transferability of an enhanced temperature-index melt model that was developed and tested on Haut Glacier d’Arolla, Switzerland, in the 2001 season. The model’s empirical parameters (temperature factor, TF, and shortwave radiation factor, SRF) are recalibrated for: (1) other locations on Haut Glacier d’Arolla; (2) subperiods of distinct meteorological conditions; (3) different years on Haut Glacier d’Arolla; and (4) other glaciers in different years. The model parameters are optimized against simulations of an energy-balance model validated against ablation observations. Results are compared with those obtained with the original parameters. The model works very well when applied to other sites, seasons and glaciers, with the exception of overcast conditions. Differences are due to underestimation of high melt rates. The parameter values are associated with the prevailing energy-balance conditions, showing that high SRF are obtained on clear-sky days, whereas higher TF are typical of locations where glacier winds prevail and turbulent fluxes are high. We also provide a range of parameters clearly associated with the site’s location and its meteorological characteristics that could help to assign parameter values to sites where few data are available.

We use a simple energy-conservation model and a model based on Röthlisberger’s theory for steady-state water flow in a subglacial conduit to model water movement between lakes in the Adventure subglacial trench region of East Antarctica during a 1996–98 jökulhlaup. Using available field evidence to constrain the models suggests that water flow would likely be accommodated in a tunnel with a cross-sectional area of 36 m2 and a value for k (the reciprocal of Manning’s roughness parameter) larger than the 12.5 m1/3 s−1 previously calculated. We also use Nye’s theory for time-dependent conduit water flow to model the temporal evolution of conduit discharge, cross-sectional area, water pressure and lake draining and filling during the flood. We initially assume one source and one sink lake. We perform sensitivity tests on the input parameter set, matching modeled source- and sink-lake depth changes with measured surface elevation data. Using a simple function for vertical ice deformation in which surface deformation scales linearly to the lake depth change, we find the scaling factor is of the order 4 × 10−3 of the ice thickness. The most likely value of k lies in the range 55–68 m1/3 s−1, and the ratio of source to sink-lake radii is approximately 1 : 1.4. Finally, we experiment using Nye’s theory to model water movement between one source and three sink lakes. The model fails to produce the observed patterns of water movement as indicated by the surface deformation data.