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.

Changes in water pressure at the beds of glaciers greatly modify their sliding rate, affecting rates of ice mass loss and sea level change. However, there is still no agreement about the physics of subglacial sliding or how water affects it. Here, we present a new simplified physical model for the effect of transient subglacial hydrology on basal ice velocity. This model assumes that a fraction of the glacier bed is connected by an active hydrologic system that, when averaged over an appropriate scale, is governed by two parameters with limited spatial variability. The sliding model is reminiscent of Budd's empirical sliding law but with fundamental differences including a dependence on the fractional area of the active hydrologic system. With periodic surface meltwater forcing, the model displays classic diffusion-wave behavior, with a downstream time lag and decay of subglacial water pressure perturbations. Testing the model against Greenland observations suggests that, despite its simplicity, it captures key features of observed proglacial discharges and ice velocities with reasonable physical parameter values. Given these encouraging findings, including this sliding model in predictive ice-sheet models may improve their ability to predict time-evolving velocities and associated sea level change and reduce the related uncertainties.

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.

Owing to drifting snow processes, snow accumulation and surface density in polar environments are variable in space and time. We present new field data of manual measurements, repeat terrestrial laser scanning and snow micro-penetrometry from Dronning Maud Land, Antarctica, showing the density of new snow accumulations. We combine these data with published drifting snow mass flux observations, to evaluate the performance of the 1-D, detailed, physics-based snow cover model SNOWPACK in representing drifting snow and surface density. For two sites in East Antarctica with multiple years of data, we found a coefficient of determination for the simulated drifting snow of r2 = 0.42 and r2 = 0.50, respectively. The field observations show the existence of low-density snow accumulations during low wind conditions. Successive high wind speed events generally erode these low-density layers while producing spatially variable erosion/deposition patterns with typical length scales of a few metres. We found that a model setup that is able to represent low-density snow accumulating during low wind speed conditions, as well as subsequent snow erosion and redeposition at higher densities during drifting snow events was mostly able to describe the observed temporal variability of surface density in the field.

This paper presents and discusses the results of constant deformation-rate tests on laboratory-prepared polycrystalline ice. Strain-rates ranged from 10−7 to 10−1s−1, grain–size ranged from 1.5 to 5.8 mm, and the test temperature was −5°C.

At strain-rates between 10−7 and 10−3 s−1, the stress-strain-rate relationship followed a power law with an exponent of n = 4.3 calculated without regard to grain-size. However, a reversal in the grain-size effect was observed: below a transition point near 4 × 10−6 s−1 the peak stress increased with increasing grain-size, while above the transition point the peak stress decreased with increasing grain-size. This latter trend persisted to the highest strain-rates observed. At strain-rates above 10−3 s−1 the peak stress became independent of strain-rate.

The unusual trends exhibited at the lower strain-rates are attributed to the influence of the grain-size on the balance of the operative deformation mechanisms. Dynamic recrystallization appears to intervene in the case of the finer-grained material and serves to lower the peak stress. At comparable strain-rates, however, the large-grained material still experiences internal micro-fracturing, and thin sections reveal extensive deformation in the grain-boundary regions that is quite unlike the appearance of the strain-induced boundary migration characteristic of the fine-grained material.

Global warming is causing glaciers in the Caucasus Mountains and around the world to lose mass at an accelerated pace. As a result of this rapid retreat, significant parts of the glacierized surface area can be covered with debris deposits, often making them indistinguishable from the surrounding land surface by optical remote-sensing systems. Here, we present the DebCovG-carto toolbox to delineate debris-covered and debris-free glacier surfaces from non-glacierized regions. The algorithm uses synthetic aperture radar-derived coherence images and the normalized difference snow index applied to optical satellite data. Validating the remotely-sensed boundaries of Ushba and Chalaati glaciers using field GPS data demonstrates that the use of pairs of Sentinel-1 images (2019) from identical ascending and descending orbits can substantially improve debris-covered glacier surface detection. The DebCovG-carto toolbox leverages multiple orbits to automate the mapping of debris-covered glacier surfaces. This new automatic method offers the possibility of quickly correcting glacier mapping errors caused by the presence of debris and makes automatic mapping of glacierized surfaces considerably faster than the use of other subjective methods.

Lichens were found growing on some of the supraglacial debris of six small, active, retreating valley glaciers in southern Norway. The circumstances permitting their growth are discussed, as is the possibility of their surviving pro-glacial deposition under current and past conditions. Their occurrence does not appear to present a problem to careful lichenometric surveys of Holocene glacial and fluvio-glacial deposits.

Flow at ice divides, their shape, size and internal structure depend not only on local conditions, but also on the flow regimes and past histories of the surrounding ice masses. Here we use field data from Kealey Ice Rise, Ellsworth Land, West Antarctica, in combination with flow modelling to investigate any possible signs of transients in the flow of the surrounding ice masses. Kealey Ice Rise shows linear surface features running parallel to its ridge in satellite imagery and a conspicuous layering in the ground-penetrating radar data known as double-peaked Raymond bumps. Through numerical modelling, by using an anisotropic full-Stokes thermomechanical flow solver, we analyse the evolution of Kealey Ice Rise and the timescales involved. We conclude that the features observed in the stratigraphy of Kealey Ice Rise require at least 3 ka of near-stationary flow conditions. However, we cannot exclude the possibility of a recent flow reorganization in the last century. We stress that the signs of stationary flow in radar stratigraphy observed in Kealey Ice Rise have been observed in other ice divides in the East Ellsworth Land area, suggesting stationary flow conditions over a millennial timescale in the region.

A set of internally consistent mass budget terms is proposed for consideration. Vertically measured, water-equivalent components of accumulation, ablation, and net budget are defined for points on a glacier (specific quantities) or as area-integrated totals for the whole glacier (total quantities). The budget year is defined as the time between two minima of net budget. Additional terms involving specific and total rates of accumulation, ablation, net budget, and various subdivisions of the glacier area are developed. Mass budget quantities can be separated into steady-state and budget imbalance terms. Net budgets can be calculated by simplified means when the variation of budget with altitude is known. It is suggested that the term “firn” be applied to layers which have survived one summer’s ablation season.

In the afternoon of 30 January 2017, a catastrophic outburst flood occurred in the Larsemann Hills (Princess Elizabeth Land, East Antarctica). The rapid drainage of both a thin supraglacial layer of water (near Boulder Lake) and Lake Ledyanoe into the englacial Lake Dålk provoked its overfill and outburst. As a result, a depression of 183 m × 220 m was formed in the place where Lake Dålk was located. This study summarises and clarifies the current state of knowledge on the flood that occurred in 2017. We present a phenomenological model of depression formation. We specify the reasons for the outburst of the system of lakes Boulder, Ledyanoe and Dålk. In addition, we carry out mathematical modelling of the outburst of each of the three lakes and estimate the flood severity. Outburst hydrographs, channel diameters, volume and duration of floods were calculated. Particular simulation results were validated with field data. In conclusion, we give an overview of the new outburst cycle of the lake system, which began in 2020 with the drainage of the lakes Boulder and Ledyanoe, and the new formation of Lake Dålk. Further research is required to improve our understanding of the lake system responses to changing external factors.

Samples of snow and firn from accumulation zones on Clark, Commonwealth, Blue and Victoria Upper Glaciers in the McMurdo Dry Valleys (∼77–78º S, 161–164º E), Antarctica, are evaluated chemically and isotopically to determine the relative importance of local (site-specific) factors vs regional-scale influences in defining glaciochemistry. Spatial variation in snow and firn chemistry confirms documented trends within individual valleys regarding major-ion deposition relative to elevation and to distance from the coast. Sodium and methylsulfonate (MS–), for example, follow a decreasing gradient with distance from the coast along the axis of Victoria Valley (350–119 µg L−1 for Na+; 33–14 µg L−1 for MS–); a similar pattern exists between Commonwealth and Newall Glaciers in the Asgaard Range. When comparing major-ion concentrations (e.g. Na+, MS−, Ca2+) or trace metals (e.g. Al, Fe) among different valleys, however, site-specific exposures to marine and local terrestrial chemical sources play a dominant role. Because chemical signals at all sites respond to particulates with varying mixtures of marine and terrestrial sources, each of these influences on site glaciochemistry must be considered when drawing temporal climate inferences on regional scales.

A draw-wire sensor has successfully been used to measure surface lowering due to net ablation of a glacier. A thin steel wire attached to a weight is inserted and frozen into a borehole in the ice. The draw-wire sensor, installed on a tetrahedron on the surface, retracts the wire as the snow or ice melts. Relative surface lowering of the melting surface is recorded in a data logger and may be converted to mass loss. The instrument continuously logs net ablation over several melt seasons and has the potential to be used extensively in future studies of glacier melt, whenever high temporal resolution and precision are required.

This study tests novel methods for automatically identifying annual layers in a shallow Antarctic ice core (WDC05Q) using images that were collected with an optical scanner at the US National Ice Core Laboratory. A new method of optimized variance maximization (OVM) modeled the density-related changes in annual layer thickness directly from image variance. This was done by using multi-objective complex (MOCOM) parameter optimization to drive a low-pass filtering scheme. The OVM-derived changes in annual layer thickness corresponded well with the results of an independent glaciochemical interpretation of the core. Individual annual cycles in image brightness were then identified by using OVM results to apply a depth-varying low-pass filter and fitting a second-order polynomial to a locally detrended neighborhood. The resulting map of annual cycles agreed to within 1% of the overall annual count of the glaciochemical interpretation. Agreement on the presence of specific annual layer features was 96%. It was also shown that the MOCOM parameter optimization could calibrate the image-based results to match directly the date of a specific volcanic marker.

We investigate the major sources of backscatter at 5.3 GHz, within the superimposed ice and firn areas of a polythermal glacier. Two ground-penetrating radar systems, an 800 MHz impulse system and a polarimetric 5.3 GHz frequency-modulated continuous-wave system, are used to acquire along-glacier profiles in the accumulation area of Kongsvegen, Svalbard. The 800 MHz response is used to map reflection horizons in the glacier. Using cores from the superimposed ice and firn areas, the causes of these reflection horizons, in terms of snow, firn and ice layers, are investigated. Superimposing the reflection horizons on the co-polarized and cross-polarized 5.3 GHz profile, we are able to determine how the 5.3 GHz frequency responds to the different media. Scattering at rough interfaces and volume scattering occur in the superimposed ice area and are apparently caused by air-bubble number, size and distribution. In the firn the strongest return originates from below the previous summer surface, consistent with previous findings. At approximately the same depth, strong incoherent scattering begins. The rapid decrease in coherent reflections indicates the significance of scattering in the firn.

We simulate the ice dynamics of the San Rafael Glacier (SRG) in the Northern Patagonia Icefield (46.7°S, 73.5°W), using glacier geometry obtained by airborne gravity measurements. The full-Stokes ice flow model (Elmer/Ice) is initialized using an inverse method to infer the basal friction coefficient from a satellite-derived surface velocity mosaic. The high surface velocities (7.6 km a−1) near the glacier front are explained by low basal shear stresses (<25 kPa). The modelling results suggest that 98% of the surface velocities are due to basal sliding in the fast-flowing glacier tongue (>1 km a−1). We force the model using different surface mass-balance scenarios taken or adapted from previous studies and geodetic elevation changes between 2000 and 2012. Our results suggest that previous estimates of average surface mass balance over the entire glacier (Ḃ) were likely too high, mainly due to an overestimation in the accumulation area. We propose that most of SRG imbalance is due to the large ice discharge (−0.83 ± 0.08 Gt a−1) and a slightly positive Ḃ (0.08 ± 0.06 Gt a−1). The committed mass-loss estimate over the next century is −0.34 ± 0.03 Gt a−1. This study demonstrates that surface mass-balance estimates and glacier wastage projections can be improved using a physically based ice flow model.

The increased availability of high-resolution and high-quality digital elevation models (DEMs) allows for the investigation of small-scale glaciological changes and improved precision in geodetic mass-balance estimates. However, high precision and careful methodological choices are required to retrieve glacier-wide mass changes at annual to seasonal time scales. Here, we used a 7-year time series of 12 DEMs of the Glacier d'Argentière, in the French Alps, derived from the Pléiades optical satellites to assess the ability of sub-metre stereoscopic satellite images to retrieve annual-to-seasonal mass balances. We found good agreement between the five annual and the four winter mass-balance values estimated using a geodetic method and those of in situ glaciological measurements: mean values via the geodetic method are −0.66 m w.e. and 1.47 m w.e. for annual and winter balances, respectively; mean absolute discrepancies are 0.25 m w.e. (annual) and 0.36 m w.e. (winter). Our study identified three main limitations of this methodology: (i) the intrinsic DEM precision; (ii) the lack of control over the satellite acquisition dates; and (iii) the density assumption. The consistency between the methods demonstrates the potential of short time-scale glacier mass-balance monitoring using very high-resolution satellite images.

Three basic areas of ice accretion are discussed: (i) the motion of the (supercooled) droplets in air up to collision with the icing object, (ii) the net growth rates, and (iii) the heat balance of an icing cylinder. The weakness of presently used approaches to establish collision efficiency and possible improvements are outlined. Experimental evidence on the icing of cylinders is then reviewed which establishes that the growth rates by icing are farless than expected because up to 80% and more of the initially accreted water can bounce off or be lost by shedding at air temperatures of –20°C. The reduced growth rates have a considerable effect on the heat balance of the icing object, whose temperature and water-phase mixture are controlled by the temperature and phme of the lost water-substance. These latter properties are completely unknown and require further studies. In conclusion the scientific aspects of icing are far from being understood; empirical findings may have to provide guidance for applications.

Continuous records have been made during the passage of dry–snow avalanches of both seismic signals, which allows the avalanche speed to be estimated, and impact pressures on load cells with surface areas of 645 and 6 450 mm2. The impact pressure recordings show an initial peak followed by a base pressure. The observed initial and base pressures vary strongly within avalanches and from one avalanche to another, but, on average, they can be correlated with the frontal speed and the density of the deposited avalanche snow. It is concluded that well–developed dry–snow avalanches have an unsteady wave motion similar to the slug flow observed in ultra–rapid flow of water, and that they consist of three stratified components: dense flowing snow at the bottom, light flowing snow, and powder snow.

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.

Three types of glacier margin are found along the edge of the Greenland ice sheet near Thule: ice cliffs, ramps and ice-cored moraines. Where the glacier margin is perpendicular to prevailing katabatic winds, drifting snow accumulates along it in stagnant wind-drill ice wedges. Upward flow of active ice behind these wedges causes ice originally near the base of the glacier to rise to the surface. Where this basal ice is free of debris, a gently sloping ramp develops. However, where the basal ice contains sufficient debris, a layer of till accumulates on the glacier surface. Ice beneath the till is insulated and a debris-capped ice ridge or ice-cored moraine forms, Ice cliffs occur where the ice-sheet margin is parallel to prevailing winds and is thus swept clear of drifting snow. Although the ice sheet in the Thule area appears to have had a negative mass balance for many years, all three types of glacier margin are believed to be equilibrium forms that can develop and persist on a glacier with a balanced mass budget.

Foliation in wind-drift ice wedges generally dips down-glacier but foliation in active ice dips up-glacier. It is inferred that foliation in the wedges was once sedimentary stratification that has been tipped upward and locally overturned.