The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects.

Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.

We use a mathematical model to investigate the effect of basal topography and ice surface slope on transport and deposition of sediment within a water-filled subglacial channel. In our model, three zones of different behaviour occur. In the zone furthest upstream, variations in basal topography lead to sediment deposition under a wide range of conditions. In this first zone, even very small and gradually varying basal undulations (~5 m amplitude) can lead to the deposition of sediment within a modelled channel. Deposition is concentrated on the downstream gradient of subglacial ridges, and on the upstream gradient of subglacial troughs. The thickness and steepness of the ice sheet has a substantial impact on deposition rates, with shallow ice profiles strongly promoting both the magnitude and extent of sediment deposition. In a second zone, all sediment is transported downstream. Finally, a third zone close to the ice margin is characterised by high rates of sediment deposition. The existence of these zones has implications for esker formation and the dynamics of the subglacial environment.

The mathematical theory of heat conduction is applied to the analysis of ice segregation processes in soil. A diffusion equation is first employed for the flow of soil moisture. Two new quantities, the rate of ice segregation,σ and the segregation efficiency, E, are introduced. The first is the rate of ice growth measured as mass per area per time. The latter is defined as E = σL/(K1∂T1/∂x−K2∂T2/∂x), where L is the latent heat of fusion of ice, T1and K1are the temperature and thermal conductivity of frozen soil, and T2 and K2 are the temperature and thermal conductivity of unfrozen soil. Three types of soil freezing can be classified in terms of E: freezing of non-frost-susceptible soil (E = 0), perfect segregation (E = 1) and imperfect segregation (0 < E < 1). Finally, the mathematical boundary conditions at an advancing frost line are obtained in freezing, frost-susceptible soil (E ≠ 0). Two parameters related to the structure of soil are pointed out, which seem to be valid criteria of frost susceptibility. The amount of frost-heaving is derived under special conditions.

The quantification of snow transport, both in wind tunnels and the field, apply particle counting methods limited to punctual sampling of relatively small volumes. Particle counting can only capture horizontal mass fluxes, failing to measure snow erosion or deposition. Herein, we present a novel low-cost sensor tool, based on a Microsoft Kinect, adapted to capture snow surface changes during snow drifting at unprecedented spatial and temporal resolutions. In the wind tunnel setting of these experiments we observe a balance between erosion and deposition at low wind speeds, while erosion is dominant at higher wind speeds. Significant differences in power spectral densities of surface mass flux and horizontal particle mass flux are observed. We show that for the saltation-length-scale parameter λ = 1, the integrated particle flux can be used to estimate the total surface mass flux in the wind tunnel. This provides an important basis to interpret mass flux measurements in the field.

During the summer of 1983 a 2 kW array of solar voltaic panels was used to power a drill which collected two cores of 154 m and 163 m length to bedrock on the Quelccaya ice cap in Peru. The operation and performance of this array are discussed, considering the need for future requirements in remote pristine areas of the world.

Surface height changes above three previously undetected subglacial lakes in northeastern Greenland are documented using CryoSat, DEMs and ICESat-2. Between 7 February and 6 March 2012, the central ice region (22.6 km2) above the largest lake dropped by ~37 m followed by a further drop of 12 m in the following 29 days. This implies a subglacial water outflow, or jökulhlaup, of at least 1 km3 at rates of hundreds of cubic meters per second. A comparable outflow occurred again between 23 July and 15 September 2019, with smaller outflows in the fall of 2014 and 2016. In contrast, a second smaller subglacial lake at a higher elevation had two subglacial outbursts of ~0.3 km3 in 2012 and 2019 but the lake filling was gradual and not strongly seasonal or episodic. Water remained in both lakes after the outflows but this may not be the case for the third smallest and lowest subglacial lake. While there appears to be some hydrological link between the three lakes, the flux of water moving under the ice in this area appears to be larger than would be expected from local summer melt. However, the source of the excess water remains uncertain.

Equations and a graph are presented for calculating gravity anomalies on a two-dimensional glacier model having a horizontal upper boundary and a lower boundary which is a parabola with a vertical axis of symmetry.

On the Kamchatka Peninsula in the Russian Far East, 405 glaciers with an estimated total mass of 49 Gt were reported in the 1970s. These have been retreating at an accelerated rate since the start of the 21st century. Because glacier studies in this region are scarce, ice loss and its influence on sea level rise and regional environments is poorly understood. In this study, we analyzed satellite data to quantify glacier mass change from 2000 to 2016 in six major glacier-covered regions on the peninsula. The mean rate of the glacier mass change over the study period was −0.46 ± 0.01 m w.e. a−1 (total mass change was −4.9 ± 0.1 Gt, −304.2 ± 9.1 Mt a−1), which is slightly lower than other regions in mid-latitude and subarctic zones. The mass loss accelerated from >−0.33 ± 0.02 m w.e. a−1 in the period 2000–2006/2010 to <−1.65 ± 0.12 m w.e. a−1 in 2006/2010–2015/16. The increase in mass loss is attributed to a rise in average decadal summer temperatures observed in the region (+0.68°C from 1987–99 to 2000–13). Moreover, a recent trend in Pacific decadal oscillation suggests future acceleration of mass loss due to a decline in winter precipitation.

Formulae for calculating temperature profiles in steady-state ice sheets are derived in terms of the horizontal and vertical velocities of the surface ice, and of the variation in surface temperature along the flow lines. Two models are considered: parallel flow and radial flow. In each case the result consists of a “stationary” term (equivalent to Robin's equation), a term dependent on the horizontal velocity, and a term arising from the temperature variations. This last term produces reversals in the temperature field such as are measured in practice.

A method is described for measuring the thermal conductivity of ice in the temperature range from 0.5 to 5.0 K using a 3He apparatus. The results from our first experiments are not too far from the theoretical law for the low-temperature thermal conductivity of ice . Measurements at still lower temperatures are necessary to confirm our results.

A model, relating spatial patterns of snow accumulation in the alpine belt of major mountain ranges to the angular relationship which exists among terrain features such as cirque basins, mean storm-path trajectories, and incident solar radiation, is presented together with a limited amount of relevant empirical data. It is suggested that an “orientation gradient” exists in both the temporal and spatial variation of accumulation and ablation in the alpine terrain, the importance of which varies as some function of the relative control exerted by wind redistribution of snow and of direct incident solar radiation on the accumulation and ablation processes. The data obtained to date suggest that the importance of the orientation gradient varies widely among the mountain ranges studied, being a good predictor of snow distribution patterns in the Front Range of the Colorado Rockies and the Snowy Range in southern Wyoming, both of which are relatively windswept, while in the much less windy Bridger Range, in south-western Montana, both orientation and elevation appear to contribute on an almost equal basis. An indirect method of estimating relative amounts of annual mass turnover, using eleven glaciers located in the Wind River of west central Wyoming, is presented.

A 198.8 m deep borehole was drilled through ice to subglacial bedrock in the northwestern marginal part of Princess Elizabeth Land, ~12 km south of Zhongshan Station, in January–February 2019. Three years later, in February 2022, the borehole temperature profile was measured, and the geothermal heat flow (GHF) was estimated using a 1-D time-dependent energy-balance equation. For a depth corresponding to the base of the ice sheet, the GHF was calculated as 72.6 ± 2.3 mW m−2 and temperature −4.53 ± 0.27°C. The regional averages estimated for this area based, generally, on tectonic setting vary from 55 to 66 mW m−2. A higher GHF is interpreted to originate mostly from the occurrence of metamorphic complexes intruded by heat-producing elements in the subglacial bedrock below the drill site.

An interacting continua framework is adopted to model a dry snow park, which is viewed as a three-constituent mixture composed of an ice matrix whose pore space is occupied by water vapour and dry air. We focus on the response of a one-dimensional vertical snowpack to changes in pressure and temperature at its surface. The time-scale of the surface forcing is assumed to be much longer than the time-scale for thermal transfers and phase change to take place. The constituents are, therefore, in thermal equilibrium with a common temperature Τ which is governed by a single bulk-energy balance. In addition, each constituent satisfies a mass and momentum balance. The constitutive postulates and external prescriptions necessary to close the system of equations are discussed in detail. Non-dimensional variables are then introduced formally to draw out the major balances in the equations and construct a reduced system that accurately models the dominant features in the snowpack. It is shown how the effects of phase change enter the leading-order balance. An iterative procedure is constructed to solve the system. Illustrations for the case of a sinusoidal annual temperature gradient imposed at the surface are presented.

Slab avalanches are shown to be released by brittle fracture. An analogy is drawn in which the snow-pack is considered to be a macroscopic, molecular model of glass. The analogy is examined qualitatively from two viewpoints: the Griffith fracture criterion, and stress concentration theory. The details of fracture propagation in a layered snow-pack are explained by means of stress concentration theory, and many details of slab avalanches are shown to be consistent with the proposed mechanism. The significance of various fracture surface markings is pointed out.

Computing predictions of future sea level that include well-defined uncertainty bounds requires models that are capable of robustly simulating the evolution of ice sheets and glaciers. Ice flow behaviour is known to be sensitive to the location and geometry of dynamic ice boundaries such as the grounding line (GRL), terminus position and ice surface elevation, so that any such model should track these interfaces with a high degree of accuracy. To address this challenge, we implement a numerical approach that uses the level-set method (LSM) that accurately models the evolution of the ice–air and ice–water interface as well as capturing topological changes in ice-sheet geometry. This approach is evaluated by comparing simulations of grounded and marine-terminating ice sheets to various analytical and numerical benchmark solutions. A particular advantage of the LSM is its ability to explicitly track the moving margin and GRL while using a fixed grid finite-difference scheme. Our results demonstrate that the LSM is an accurate and robust approach for tracking the ice surface interface and terminus for advancing and retreating ice sheets, including the transient marine ice-sheet interface and GRL positions.