By fitting a very simple atmospheric impurity model to high-resolution data on ice accumulation and contaminant fluxes in the GISP2 ice core, we have estimated changes in the atmospheric concentrations of soluble major ions, insoluble particulates and 10Be during the transition from glacial to Holocene conditions. For many species, changes in concentration in the ice typically overestimate atmospheric changes, and changes in flux to the ice typically underestimate atmospheric changes, because times of increased atmospheric contaminant loading are also times of reduced snowfall. The model interpolates between the flux and concentration records by explicitly allowing for wet- and dry-deposition processes. Compared to the warm Preboreal that followed, we estimate that the atmosphere over Greenland sampled by snow accumulated during the Younger Dryas cold event contained on average four–seven times the insoluble particulates and nearly seven times the soluble calcium derived from continental sources, and about three times the sea salt but only slightly more cosmogenic 10Be.

The annual mean oxygen-isotope content of Antarctic snow is strongly influenced by the seasonal variability of accumulation. Since the annual mean δ18O value is frequently used to derive mean annual temperatures from ice cores, changes in atmospheric circulation pattern can lead to large errors in the deduced temperature record. At the German Antarctic wintering base, Neumayer, accumulation measurements have been carried out continuously over the last 16 years. Weekly readings of accumulation stakes combined with snow pits and shallow firn cores are used to investigate the influence of the seasonal variability of accumulation on the annual mean δ18O values and to estimate the possible error in the determination of annual mean temperatures from ice cores by using the oxygen-isotope record.

Ice-sheet models can be used to forecast ice losses from Antarctica and Greenland, but to fully quantify the risks associated with sea-level rise, probabilistic forecasts are needed. These require estimates of the probability density function (PDF) for various model parameters (e.g. the basal drag coefficient and ice viscosity). To infer such parameters from satellite observations it is common to use inverse methods. Two related approaches are in use: (1) minimization of a cost function that describes the misfit to the observations, often accompanied by explicit or implicit regularization, or (2) use of Bayes’ theorem to update prior assumptions about the probability of parameters. Both approaches have much in common and questions of regularization often map onto implicit choices of prior probabilities that are made explicit in the Bayesian framework. In both approaches questions can arise that seem to demand subjective input. One way to specify prior PDFs more objectively is by deriving transformation group priors that are invariant to symmetries of the problem, and then maximizing relative entropy, subject to any additional constraints. Here we investigate the application of these methods to the derivation of priors for a Bayesian approach to an idealized glaciological inverse problem.

The relationship between synoptic-scale atmospheric circulation and glacier mass balance in the Cordillera of south-western Canada is investigated. Objective synoptic typing techniques are applied to glaciometeorological data from Peyto Glacier, Alberta, and Sentinel Glacier, British Columbia, and to climatological data from nearby weather stations. Two scales of 500 mbar synoptic weather maps are analyzed and compared. One is smaller with high-wavenumber patterns, the other is larger with more general patterns.

The results demonstrate that the mass balance of Peyto and Sentinel Glaciers are related to the 500 mbar patterns. Synoptic types with cyclonic curvature favor glacier accumulation, while anticyclonic types inhibit build-up of the regional snow-pack. Ablation is suppressed by synoptic types associated with cloudy days and/or low temperatures, and is enhanced by types associated with warm, sunny days. Furthermore, findings suggest that both the accumulation and ablation of Sentinel Glacier are controlled by small-scale, high-wavenumber synoptic patterns. Conversely, Peyto Glacier accumulation is more closely associated with large-scale patterns, suggesting that high-frequency mid-tropospheric oscillations embedded within the slow-moving baroclinic zones associated with long-wave disturbances may be dampened by the rough topography of the Canadian Cordillera. Ablation is predicted poorly by both scales at Peyto.

The total air content (V) of ice has been measured along the Dome Summit South (DSS) core from Law Dome, East Antarctica. The main features of this record are the very well-preserved sub-annual fluctuations of V (down to at least 900 m depth) and the significant increase of the V values during the last deglaciation. The sub-annual variations reflect changes in close-off porosity, and we interpret the V seasonal peaks as tracers of depth-hoar layers. For the longer time-scale, the large V fluctuations observed are interpreted in terms of elevation and/or close-off porosity changes under different assumptions. We analyze the possible influence of a different global pressure field and/or a change in seasonal temperature and precipitation cycles during the last glacial period. Our estimates of surface elevation changes derived from the V data are then compared with independent reconstructions of past elevations.

Ice-shelf basal melting is tightly coupled to ice-shelf morphology. Ice shelves, in turn, are coupled to grounded ice via their influence on compressive stress at the grounding line (‘ice-shelf buttressing’). Here, we examine this interaction using a local parameterization that relates the basal melt rate to the ice-shelf thickness gradient. This formulation permits a closed-form solution for a steady-state ice tongue. Time-dependent numerical simulations reveal the spatial and temporal evolution of ice-shelf/ice-stream systems in response to changes in ocean temperature, and the influence of morphology-dependent melting on grounding-line retreat. We find that a rapid (<1 year) re-equilibration in upstream regions of ice shelves establishes a spatial pattern of basal melt rates (relative to the grounding line) that persists over centuries. Coupling melting to ice-shelf shape generally, but not always, increases grounding-line retreat rates relative to a uniform distribution with the same area- average melt rate. Because upstream ice-shelf thickness gradients and retreat rates increase nonlinearly with thermal forcing, morphology-dependent melting is more important to the response of weakly buttressed, strongly forced ice streams grounded on beds that slope upwards towards the ocean (e.g. those in the Amundsen Sea).

A finite-volume model is used to simulate 9 years (1995–2003) of snow temperatures at the South Pole. The upper boundary condition is skin-surface temperature derived from routine upwelling longwave radiation measurements, while the lower boundary condition is set to the seasonal temperature gradient at 6.5 m depth, taken from prior measurements at the South Pole. We focus on statistics of temperature, heat fluxes, heating rates and vapour pressures in the top metre of snow, but present results from the full depth of the model (6.5 m). The monthly mean net heat flux into the snow agrees with results from previous studies performed at the South Pole. On shorter timescales, the heating rates and vapour pressures show large variability. The net heat flux into the snow, which is between ±5 W m−2 in the monthly mean, can be greater than ±20 W m−2 on hourly timescales. On sub-daily timescales, heating rates exceed 40 K d−1 in the top 10 cm of the snow. Subsurface temperatures, and therefore heating rates, are more variable during winter (April–September) due to increased synoptic activity and the presence of a strong, surface-based, atmospheric temperature inversion. The largest vapour pressures (60–70 Pa) and vertical gradients of vapour pressure are found in the top metre of snow during the short summer (December–January). In contrast, during the long winter, the low temperatures result in very small vapour pressures and insignificant vapour-pressure gradients. The high summertime vapour-pressure gradients may be important in altering the isotopic composition of snow and ice on the Antarctic plateau.

In a two-dimensional (plane strain) glacier domain, gravity-driven ice flow is balanced by basal drag and the resistance associated with longitudinal stress gradients. The plane strain Stokes model accommodates both these resistances, whereas several simpler models only account for basal drag. Solving the Stokes equations is numerically challenging and computationally expensive, but simpler models may lead to unrealistic dynamical behaviour. Here, we propose a factor which can be introduced in shear-deformational flow models to yield results comparable to those from the plane strain Stokes model. As this factor adapts simpler models to capture the effects of missing dynamics, i.e. longitudinal stress gradients, we refer to it as the longitudinal stress (L-)factor. We assess the usefulness of this factor for idealized domains with complex basal topography and evolving geometry. We apply the model to Haig Glacier, Canadian Rockies, in order to present an illustration of how simulations of glacier response to climate forcing can be improved through the introduction of the L-factor in a shear-deformational flow model.

The relative permittivity and loss of zone-refined single crystals of hexagonal ice have been measured in the temperature range 200–271 K and frequency range 0.5 HZ–0.2 MHz, using brass, stainless steel, and gold-foil electrodes. The c-axis of the crystal was oriented parallel to the electric field in 14 samples and perpendicular to the field in 8 samples. The equilibrium relative permittivity of orientation polarization ϵ0, parallel and perpendicular to the c-axis, is 96.5±1 and the average relaxation time τay is 36 μs at 265±0.5K; ϵ0 = 124±1.5 and τav = 30 ms, at 210 K. The magnitude of the orientation polarization obeys the Curie-Weiss equation with T0= 15±2 K for both the orientations. These values are in contrast with the c. 17% difference in ϵo for the two orientations reported in the literature. The extrapolated limiting high-frequency relative permittivity ϵ∞, measured for both the orientations, is indistinguishable within 0.5%.

The logarithmic plot of the product of τav and temperature against the reciprocal temperature is linear in the range 210–271 K and gives an activation energy and a pre-exponential factor of 51±2 kJ mol–1 and 0.93±0.22 ps K respectively, for both the orientations of the c-axis with respect to the electric field. The decrease in activation energy which has been reported to occur in polycrystalline ice and in single crystal ice near 230 K is not found until a temperature of 210 K. Single crystals of ice stored in the dielectric cell, after the completion of measurements, for periods ranging from 1–11 weeks at 253±2 K showed no change in their ϵ0, τav, ϵ∞ that could be attributed to the effect of ageing on the orientation polarization.

Glacio-meteorological data obtained during the Greenland Ice Margin Experiment (GIMEX) investigations in West Greenland (the Søndre Strømfjord transect) have been used to test and calibrate energy-balance/mass-balance models for the ice/snow surface. The region is characterised by the development of a wide zone of low surface albedo in the course of the melting season. This zone was simulated in one of the energy-balance models by including the effect of surficial meltwater on albedo. Observed mass-balance and albedo data were used to constrain the models. Although all the models are capable of predicting the transect balance reasonably well, only the model with the meltwater albedo coupling, is able to reproduce the observed albedo pattern and mass-balance profile along the transect. By including the feedback between surficial meltwater and albedo in the model, the sensitivity of the specific balance to changes in air temperature is found to be greatest just below the equilibrium line (in contrast to what is generally found for valley glaciers). A 1 K warming of the air temperature would increase the mean ablation along the transect by 0.5 m w.e.year −1.

The Antarctic Ice Sheet loses mass via its ice shelves predominantly through two processes: basal melting and iceberg calving. Iceberg calving is episodic and infrequent, and not well parameterized in ice-sheet models. Here, we investigate the impact of hydrostatic forces on calving. We develop two-dimensional elastic and viscous numerical frameworks to model the ‘footloose’ calving mechanism. This mechanism is triggered by submerged ice protrusions at the ice front, which induce unbalanced buoyancy forces that can lead to fracturing. We compare the results to identify the different roles that viscous and elastic deformations play in setting the rate and magnitude of calving events. Our results show that, although the bending stresses in both frameworks share some characteristics, their differences have important implications for modeling the calving process. In particular, the elastic model predicts that maximum stresses arise farther from the ice front than in the viscous model, leading to larger calving events. We also find that the elastic model would likely lead to more frequent events than the viscous one. Our work provides a theoretical framework for the development of a better understanding of the physical processes that govern glacier and ice-shelf calving cycles.

Nivation is a collective noun identifying a set of geomorphic processes, comprised of an indeterminate number of elements and of unknown relative importance, for which there is little likelihood of ever producing a precise definition. Instead, attention should first be directed towards the relationships between snow-packs and individual geomorphic processes. The relationship between freezing amplitude in the bedrock, snow cover, and aspect at an Arctic site in northern Norway and an alpine site in the Front Range, Colorado, U.S.A. is complex. Comparison of field data and laboratory criteria permit several conflicting interpretations. If oscillations across 0°C, regardless of freezing amplitude, are critical, the alpine site is potentially a more active freeze-thaw weathering regime, with a primary springtime peak and a secondary fall peak. If a freezing amplitude of –5°C is required for effective freeze-thaw weathering then the alpine site is largely inactive and the Arctic active (but with only a single fall peak). Chemical weathering is much more important at snow-patch sites than has traditionally been recognized. Mass wasting at colluvial sites subject to snow patches is dominated by interaction between overland flow and solifluction when the site is unvegetated, and by solifluction when it is vegetated. Given contemporary knowledge of snow and glacial geomorphology, there appears to be no threshold, only differences of intensity. Resolution of the disruptive mechanism associated with bedrock freezing and its constraining temperature and moisture requirements is the most pressing present problem in the field of snow geomorphology.

This study investigates the evolution of Greenland ice sheet flux focusing on five of the main fast flowing regions (Petermann glacier, North East Greenland Ice Stream, Kangerdlugssuaq glacier, Helheim glacier and Jakobshavn glacier) in response to 20th and 21st century climate change. A hybrid (shallow ice and shallow shelf) ice-sheet model (ISM) is forced with the combined outputs of a set of seven CMIP5 models and the regional climate model MAR. The ISM simulates the present-day ice velocity pattern, topography and surface mass balance (SMB) in good agreement with observations. Except for the Kangerdlugssuaq glacier, over the 21st century all the fast-flowing areas have exhibited a decrease in ice flux as a result of a negative SMB rather than dynamical changes. Only the fronts of Kangerdlugssuaq and Helheim glaciers have shown an interannual variability driven by dynamical rather than climate changes. Finally, the results predict a substantial inland ice margin retreat by the end of the 21st century, especially along the northern coasts.

Wavelets transmitted by short-pulse radar are recovered from continuous profiles and used to determine interfacial dielectric contrasts within the englacial and basal ice at the terminus area of Matanuska Glacier, Alaska, U.S.A. The field studies were in the ablation region, where radar horizons could, at some point, be identified with interfaces between clear ice and air, water or basal ice, and were performed in early spring before drainage fully developed. The profiles used closely-spaced antennas with bandwidths centered near 50 and 400 MHz. Transmitted wavelets reflected from interfaces of known dielectric contrasts are used to establish a phase reference for other events from interfaces between unknown contrasts. Migration and Fourier-transform filtering are then applied to the profiles and shown to recover these wavelets from diffractions and reflections. Interfacial dielectric contrasts are determined from the relative phase of the wavelets. Near the terminus lake, some basal ice events above 8 m depth are interpreted as voids. Further up-glacier, most englacial events are interpreted as voids, but deeper localized reflectors and horizons to 90 m depth and within the basal zone are interpreted as voids, water or debris. Phase cannot be determined for the basal-substrate transition reflections. Recommendations are made for improving the wavelet recovery process and the quality of GPR migration.

A statistical analysis has been made of the annual balances collected during 16 consecutive years at 32 sites on the ablation area of the Glacier de Saint-Sorlin (French Alps). Only 38% of the 32 × 16 balances are known; moreover in 8 cases only the total balance for 2 consecutive years is known, and in one case the balance for 4 consecutive years. A comprehensive study of the errors leads us to assume the following linear model for the annual balance xjt at site j for year t:

where αj and βt are parameters depending upon the site and the year respectively, ηjt and η’jt are random errors with a Gaussian distribution and standard errors σ and σ’ respectively. Assuming some known value for σ’2/σ2 = ρ, the parameters αj and βt, their variance–covariance matrix, and the variance covariance matrix of the residuals are estimated in the most general case. The estimators being stable against variations in ρ, the value ρ = o may be assumed; this value docs not conflict with the behaviour of the estimates of the residuals. A test of the linear model derived from Tukey’s non-additivity test is positive. Although a much more general, non-linear model

gives a better representation of 13 × 6 balances forming a complete table of data, the linear model with σ ≈ 0.20 m is good enough to be used in theoretical studies or in routine work.

The snow surface roughness at centimetre and millimetre scales is an important parameter related to wind transport, snowdrifts, snowfall, snowmelt and snow grain size. Knowledge of the snow surface roughness is also of high interest for analyzing the signal from radar sensors such as SAR, altimeters and scatterometers. Unfortunately, this parameter has seldom been measured over snow surfaces. The techniques used to measure the roughness of other surfaces, such as agricultural or sand soils, are difficult to implement in polar regions because of the harsh climatic conditions. In this paper we develop a device based on a laser profiler coupled with a GPS receiver on board a snowmobile. This instrumentation was tested successfully in midre Lovénbreen, Svalbard, in April 2006. It allowed us to generate profiles of 3 km sections of the snow-covered glacier surface. Because of the motion of the snowmobile, the roughness signal is mixed with the snowmobile signal. We use a distance/frequency analysis (the empirical mode decomposition) to filter the signal. This method allows us to recover the snow surface structures of wavelengths between 4 and 50 cm with amplitudes of >1 mm. Finally, the roughness parameters of snow surfaces are retrieved. The snow surface roughness is found to be dependent on the scales of the observations. The retrieved RMS of the height distribution is found to vary between 0.5 and 9.2 mm, and the correlation length is found to be between 0.6 and 46 cm. This range of measurements is particularly well adapted to the analysis of GHz radar response on snow surfaces.

Global positioning system (GPS) campaigns were conducted during the 2003 and 2004 austral summer seasons to obtain insight into the velocity and strain-rate distribution on Schirmacher Glacier, central Dronning Maud Land, East Antarctica. GPS data were collected at 21 sites and analyzed to estimate the site coordinates, baselines and velocities. The short-term precision of the base station, MAIT, is estimated from the daily coordinate repeatability solutions during the two years. All GPS points on the glacier were constrained with respect to MAIT and nearby International GPS Service stations. Horizontal velocities of the glacier sites lie between 1.89 ± 0.01 and 10.88 ± 0.01 ma−1 to the north-northeast, with an average velocity of 6.21 ± 0.01 m a−1. The principal strain rates provide a quantitative measurement of extension rates, which range from (0.11 ± 0.01) × 10−3 to (1.48 ± 0.85) × 10−3a−1, and shortening rates, which range from (0.04 ± 0.02) × 10−3 to (0.96 ± 0.16) × 10−3a−1. The velocity and strain-rate distributions across the GPS network in Schirmacher Glacier are spatially correlated with topography, subsurface undulations, fracture zones/crevasses and the partial blockage of the flow by nunataks and the Schirmacher Oasis.

The use of well known simple periodic solutions of the two-dimensional biharmonic stress equation for studying the flow over undulations of an ice mass of small surface slope is examined. The model considered is one in which most of the shear (deformation or. sliding) takes place near the base and the upper part moves largely as a block, with longitudinal strain-rates varying linearly with the longitudinal stress deviations. For bedrock perturbations of a given wavelength the steady-state surface shape consists of similar waves but out of phase by ½π, such that the steepest slope occurs over the highest bedrock; and the amplitude is reduced by a “damping factor”, depending on the speed, viscosity, ice thickness and wavelength.

Minimum damping occurs for λm ≈ 3.3 times the ice thickness, while waves much longer or much shorter than this are almost completely damped out. The energy dissipation and the resistance to the ice flow is also a maximum for an undulation scale of several times the ice thickness, whereas the effects of small basal irregularities die out exponentially with distance into the ice, and only have an effect in so far as the average basal stress is related to the average surface slope. As a result of this a revision of present glacier sliding theories becomes possible.

Various predictions of the theory have been confirmed from spectral analysis of surface and bedrock profiles of ice caps.

Knowledge of ice flow and strain rate in the vicinity of the Taylor Dome (East Antarctica) ice-core site enhances interpretation of the paleoclimate information from the ice core. We measured surface ice motion by repeated optical and GPS surveys of a network of 253 markers. We developed a robust data reduction method that uses least squares based on singular value decomposition, to simultaneously calculate positions and velocities of these markers in a geocentric coordinate system. Constrained by these surface velocities, we used a finite-element model to compute the modern ice velocity field at depth. As the geometry of Taylor Dome appears to have been steady through the Holocene, we used particle paths from a steady-state model to track ice particles to the ice core from their points of origin on the surface. By removing the effects of path-dependent vertical strain, we derived past accumulation rates at the origin points of those particle paths from measured layer thicknesses in the ice core. Comparison with accumulation rates estimated from concentrations of 10Be and SO4 in the core suggests that significant amounts of snow were lost by wind scouring during the Last Glacial Maximum and at ~50kyr BP.