Comparison of numerically computed solutions to exact (analytical) time-dependent solutions, when possible, is superior to intercomparison as a technique for verification of numerical models. At least two sources of such exact solutions exist for the isothermal shallow ice-sheet equation: similarity solutions and solutions with ‘compensatory accumulation’. In this paper, we derive new similarity solutions with non-zero accumulation. We also derive exact solutions with (i) sinusoidal-in-time accumulation and (ii) basal sliding. A specific test suite based on these solutions is proposed and used to verify a standard explicit finite-difference method. This numerical scheme is shown to reliably track the position of a moving margin while being characterized by relatively large thickness errors near the margin. The difficulty of approximating the margin essentially explains the rate of global convergence of the numerical method. A transformed version of the ice-sheet equation eliminates the singularity of the margin shape and greatly accelerates the convergence. We also use an exact solution to verify an often-used numerical approximation for basal sliding and we discuss improvements of existing benchmarks.

Recent snow accumulation rate is a key quantity for ice-core and mass-balance studies. Several accumulation measurement methods (stake farm, fin core, snow-radar profiling, surface morphology, remote sensing) were used, compared and integrated at eight sites along a transect from Terra Nova Bay to Dome C, East Antarctica, to provide information about the spatial and temporal variability of snow accumulation. Thirty-nine cores were dated by identifying tritium/b marker levels (1965_66) and non-sea-salt (nss) SO42_ spikes of the Tambora (Indonesia) volcanic event (1816) in order to provide information on temporal variability. Cores were linked by snow radar and global positioning system surveys to provide detailed information on spatial variability in snow accumulation. Stake-farm and ice-core accumulation rates are observed to differ significantly, but isochrones (snow radar) correlate well with ice-core derived accumulation. The accumulation/ablation pattern from stake measurements suggests that the annual local noise (metre scale) in snow accumulation can approach 2 years of ablation and more than four times the average annual accumulation, with no accumulation or ablation for a 5 year period in up to 40% of cases. The spatial variability of snow accumulation at the kilometre scale is one order of magnitude higher than temporal variability at the multi-decadal/secular scale. Stake measurements and firn cores at Dome C confirm an approximate 30% increase in accumulation over the last two centuries, with respect to the average over the last 5000 years

This paper reports detailed textural and gas measurements conducted in cold basal ice (–17°C from the margin of Taylor Glacier, an outlet glacier of the East Antarctic ice sheet. The analyzed samples were retrieved from a basal ice sequence excavated at the end of a subglacial tunnel dug near the glacier snout. The basal sequence exhibits two contrasting ice facies, defined as the englacial and stratified facies. On the one hand, analysis of ice crystal textures from the basal ice sequence provides evidence for localized ductile deformation, especially within the stratified facies where significant dynamic recrystallization was detected. On the other hand, high-resolution gas analyses reveal that strong changes in gas composition occurred at the structural interfaces of the stratified facies. These gas composition changes are typical of melting–refreezing processes but are not associated with any significant loss of gas volume. Given the specific subglacial thermal conditions at the margin of Taylor Glacier, we interpret this phenomenon as resulting from microscopic phase changes involving selective gas redistribution through the pre-melt phase. It is argued that such processes may play an important role in the post-genetic geochemical evolution of cold debris-laden ice and may be enhanced through intense strain conditions.

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.

We derive work dissipation functionals for granular snow avalanches flowing in simple shear. Our intent is to apply constructive theorems of non-equilibrium thermodynamics to the snow avalanche problem. Snow chute experiments show that a bi-layer system consisting of a non-yielded flow plug overriding a sheared fluidized layer can be used to model avalanche flow. We show that for this type of constitutive behaviour the dissipation functionals are minimum at steady state with respect to variations in internal velocity; however, the functionals must be constrained by subsidiary mass- continuity integrals before the equivalence of momentum balance and minimal work dissipation can be established. Constitutive models that do not satisfy this equivalence are henceforth excluded from our consideration. Fluctuations in plug and slip velocity depend on the roughness of the flow surface and viscosity of the granular system. We speculate that this property explains the transition from flowing avalanches to powder avalanches. Because the temperature can safely be assumed constant, we demonstrate within the context of non-equilibrium thermodynamics that granular snow avalanches are irreversible, dissipative systems, minimizing – in space – entropy production. Furthermore, entropy production is linear both near and far from steady-state non-equilibrium because of the mass-continuity constraint. Finally, we derive thermodynamic forces and conjugate fluxes as well as expressing the corresponding phenomenological Onsager coefficients in terms of the constitutive parameters.

Surface melting rarely occurs across most of the Antarctic ice sheet, away from the warmer coastal regions. Nonetheless, isolated melt features are preserved in the firn and ice in response to infrequent and short-lived melting events. An understanding of the formation and occurrence of these melt layers will help us to interpret records of past melt occurrences from polar ice cores such as the Siple Dome ice-core record from West Antarctica. A search in the near-surface firn in West Antarctica found that melt features are extremely rare, and consist of horizontal, laterally continuous, one to a few millimeter thick, ice layers with few air bubbles. The melt layers found date from the 1992/93 and 1991/92 summers. Field experiments to investigate changes in stratigraphy taking place during melt events reproduced melt features as seen in the natural stratigraphy. Melting conditions of varying intensity were created by passively heating the near-surface air for varying lengths of time inside a clear plastic hotbox. Melt layers formed due entirely to preferential flow and subsequent refreezing of meltwater from the surface into near-surface, fine-grained, crust layers. Continuous melt layers were formed experimentally when positive-degree-day values exceeded 1ºC-day, a value corresponding well with air-temperature records from automatic weather station sites where melt layers formed in the recent past.

Data from the mouth of the decelerating Whillans Ice Stream (WIS), West Antarctica, spanning 42 years are reviewed. Deceleration has continued, with local areas of both thinning and thickening occurring. The mean thinning rate is 0.48 ± 0.77 ma–1. No consistent overall pattern is observed. Ice thickens immediately upstream of Crary Ice Rise where deceleration and divergence are strongest, suggesting expanded upstream influence of the ice rise. Thinning is prevalent on the Ross Ice Shelf. Grounding-line advance at a rate of 0.3 km a–1 is detected in a few locations. Basal stresses vary across an ice-stream transect with a zone of enhanced flow at the margin. Marginal shear is felt at the ice-stream center. Mass-balance values are less negative, but larger errors of earlier measurements mask any possible temporal pattern. Comparisons of the recent flow field with flow stripes suggest WIS contributes less ice to the deep subglacial channel carved by Mercer Ice Stream and now flows straighter. The general lack of geometric changes suggests that the regional velocity decrease is due to changing basal conditions.

Assuming a channelized drainage system in steady state, we investigate the influence of enhanced surface melting on the water pressure in subglacial channels, compared to that of changes in conduit geometry, ice rheology and catchment variations. The analysis is carried out for a specific part of the western Greenland ice-sheet margin between 66° N and 66°30′N using new high-resolution digital elevation models of the subglacial topography and the ice-sheet surface, based on an airborne ice-penetrating radar survey in 2003 and satellite repeat-track interferometric synthetic aperture radar analysis of European Remote-sensing Satellite 1 and 2 (ERS-1/-2) imagery, respectively. The water pressure is calculated up-glacier along a likely subglacial channel at distances of 1, 5 and 9 km from the outlet at the ice margin, using a modified version of Röthlisberger’s equation. Our results show that for the margin of the western Greenland ice sheet, the water pressure in subglacial channels is not sensitive to realistic variations in catchment size and mean surface water input compared to small changes in conduit geometry and ice rheology.

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.

This paper considers the role of structural glaciology in debris entrainment, transport and deposition at Haut Glacier d’Arolla, a temperate valley glacier in Valais, Switzerland. Sedimentological descriptions and cIast anaIysis have been used to identify reIationships between ice structure and debris transport. Relationships identified are (1) debris associated with crevasse traces, (2) the folding of rockfall material incorporated within primary stratification to form medial moraines and (3) dirt cones and engIaciaI debris Iayers associated with reactivated crevasse traces. A conceptuaI modeI is introduced to summarize the manner in which ice structures at Haut Glacier d’Arolla control entrainment and deposition of debris.

We report on analysis of meteorological data for the period 27 May–20 August 2004, from two automatic weather stations on McCall Glacier, Alaska, USA, aimed at studying the relationship between climate and ablation. One station is located on a mountain ridge and the other in the ablation area where we also analyzed the energy balance. The weather station on the glacier measured an average temperature of 5.3°C (at 2 m height above surface) and wind speed of 3.1 m s−1 (at 3 m height). A sonic height ranger and ablation stakes indicate a specific mass balance of –1.94 ± 0.09 m w.e between 15 June and 20 August. The specific mass balance calculated from the surface energy balance, –2.06 ± 0.18 m w.e., is in close correspondence to this. The latter is the sum of 0.12 m w.e. of snowfall, 0.003 m w.e. of deposition and –2.18 m w.e. of melt. Net radiation contributes 74% of the melt energy. Compared to ablation measurements in the early 1970s, summer ablation was large. This increase is explained by a combination of a relatively higher net radiation, a lower albedo and larger turbulent heat fluxes that led to more energy being available for melting. No single meteorological variable can be isolated as being the principal reason for the high ablation, however. The lower ice albedo (0.19) is possibly due to ash deposits from forest fires.

In the summers of 2001 and 2002, glacio-climatological research was performed at 4110–4120 m a.s.l. on the Belukha snow/firn plateau, Siberian Altai. Hundreds of samples from snow pits and a 21 m snow/firn core were collected to establish the annual/seasonal/monthly depth–accumulation scale, based on stable-isotope records, stratigraphic analyses and meteorological and synoptic data. The fluctuations of water stable-isotope records show well-preserved seasonal variations. The δ18O and δD relationships in precipitation, snow pits and the snow/firn core have the same slope to the covariance as that of the global meteoric water line. The origins of precipitation nourishing the Belukha plateau were determined based on clustering analysis of δ18O and d-excess records and examination of synoptic atmospheric patterns. Calibration and validation of the developed clusters occurred at event and monthly timescales with about 15% uncertainty. Two distinct moisture sources were shown: oceanic sources with d-excess <12‰, and the Aral–Caspian closed drainage basin sources with d-excess >12‰. Two-thirds of the annual accumulation was from oceanic precipitation, of which more than half had isotopic ratios corresponding to moisture evaporated over the Atlantic Ocean. Precipitation from the Arctic/Pacific Ocean had the lowest deuterium excess, contributing one-tenth to annual accumulation.

We investigate velocity changes occurring along Whillans Ice Stream (WIS) by comparing velocities derived from repeat aerial photographs acquired in 1985-89 (average date of 1987) to interferometric satellite radar (InSAR) velocities collected in 1997. Three different analysis methods are applied to the velocity data. First, temporal and spatial changes in velocities are correlated to identifiable features (flowlines, shear margins, bed features) visible on the 1997 RADARSAT Antarctic Mapping Project mosaic. Second, we relate velocity gradients to stresses via the flow law and, along with surface topography and ice-thickness data, apply the force-budget technique to determine the relative importance of driving stress, side drag and basal drag over time. Finally, the mass balance of the main part of WIS is determined for 1987 and 1997. Our results are consistent with previous studies that show an overall deceleration resulting in downstream thickening of the ice stream (Whillans and others, 2001; Joughin and others, 2002).

Replicate ice cores have been drilled about 10 m apart for the top 790 m of the ice sheet at Dome C, Antarctica. This provides an opportunity to examine inter-core variation of the signal for identical events, based on dielectric profile (DEP) comparisons. Comparison of the signal from the same core (a section 48 m long), measured 1 year apart, showed good reproducibility, with peak heights varying by around 10% between the two measurements. For the two replicate cores, identical peaks were matched and showed variability between cores of typically a factor 1.5. This can be explained based on the likelihood of significant time periods of missing accumulation in any single core at sites with such low snow accumulation rate. To synchronize core depths by matching peaks, it is essential to use the pattern of peaks, rather than just widely spaced individual strong peaks. To derive a quantitative volcanic index from these low-accumulation rate sites, it will be necessary to combine or average the results from several closely spaced parallel cores.

Five statistical techniques to determine peaks in ice-core time series are presented and compared. The ice-core time series, representing different signal characteristics, comprise electrical conductivity measurements (ECM), dielectric properties (DEP) and sulphate. Three techniques (I–III) utilize all the data in the time series to estimate significant thresholds for identifying peaks. Technique IV applies a moving window and conducts a statistical inference within the defined window. In technique V, a family of smoothed estimates of the ice-core time series is produced, and statistical tests are performed on the significant changes in the derivative of the estimates. The correction of the significance level, α, due to multiple tests is introduced and implemented in techniques II–V. The threshold obtained by techniques I–III is determined by the influence of the error term on the global variance estimate, whereas the threshold of IV is determined by the data within the window. The success of identifying peaks with technique V is dependent on the redundancy in the data, i.e. the sampling rate. It is concluded that techniques II and III are superior to the other techniques due to their simplicity and robustness.

Synchrotron-based micro-X-ray fluorescence (μXRF) equipment has been used to analyze impurities in polar ice. A customized sample holder has been developed and the μXRF equipment has been adapted with a thermal control system to keep samples unaltered during analyses. Artificial ice samples prepared from ultra-pure water were analyzed to investigate possible contamination and/or experimental artefacts. Analyses of polar ice from Antarctica (Dome C and Vostok) confirm this μXRF technique is non-destructive and sensitive. Experiments can be reproduced to confirm or refine results by focusing on interesting spots such as crystal grain boundaries or specific inclusions. Integration times and resolution can be adjusted to optimize sensitivity. Investigation of unstable particles is possible due to the short analysis time. In addition to identification of elements in impurities, μXRF is able to determine their speciations. The accuracy and reliability of the results confirm the potential of this technique for research in glaciology.

North–south and east–west differences in firn-line altitude, equilibrium-line altitude or middle altitudes of glaciers can be separated by regression on the cosine and sine of glacier aspect (accumulation area azimuth). Allowing for regional trends in altitude, the north–south differences expected from radiation and shade effects can be reliably quantified from World Glacier Inventory (WGI) data. The north–south differences are greater in sunnier climates, mid-latitudes and steeper relief. Local altitude differences between north- and south-facing glaciers are commonly 70–320 m. Such asymmetry is near-universal, although weak in the Arctic and tropics. East–west contrasts are less, and found mainly in the tropics and areas most exposed to strong winds. Altitude, latitude, glacier gradient and height range, calculable from most of the WGI data, are potential controls on the degree of north–south contrast, as well as surrogates for climatic controls (temperature, precipitation, radiation and cloudiness). An asymmetric sine–cosine power model is developed to describe the variation of north–south contrast with latitude. Multiple regression over 51 regions shows altitude and latitude to be the strongest controls of this contrast. Aspect–altitude analysis for former glaciers provides new evidence of cloudiness.

We describe an instrument developed to make in situ measurements of salinity and solid- fraction profiles in growing sea ice. The vertical resolution of the measurements is up to a few millimeters, with a temporal resolution of up to fractions of a second. The technique is based on impedance measurements between platinum wires around which sea ice grows. Data obtained using this instrument in laboratory experiments are in good agreement with theoretical predictions. In a field test in the Arctic, the bulk salinity of growing sea ice has been measured in situ throughout the whole depth of the ice layer. The data are compared with bulk salinities obtained from ice cores, and confirm the general understanding that the bulk salinity in ice-core studies is significantly underestimated in the lower parts of the cores. The approach can also be used in other glaciological applications and for general studies of two-phase, two-component porous media.