The flow of glacial ice is typically approximated as a nonNewtonian viscous fluid, with the momentum balance described by (an approximation to) the Stokes equations, and the nonlinear rheology described by a flow law. The most commonly used rheological law for glacial ice, Glen's flow law, yields infinite viscosity in the case of zero deformation, which can be the case at the ice surface. This poses a problem when solving the momentum balance numerically. We show that two commonly-used discretisation schemes for the boundary conditions at the ice surface and base, which yield proper numerical convergence when applied to simpler problems, produce poor numerical convergence and large errors, when used to solve the momentum balance with Glen's flow law. We show that a discretisation scheme based on the concept of ghost nodes, which substitutes the boundary conditions directly into the momentum balance equations, yields second-order numerical convergence and errors that can be up to four orders of magnitude smaller. These results are robust across different momentum balance approximations. We show that the improved boundary conditions are particularly useful for solving the 3-D higher-order Blatter-Pattyn Approximation (BPA). In general, this work underlines the importance of thoroughly verifying the numerical solvers used in ice-sheet models, before applying them to future projections of ice-sheet mass loss.

Monte Perdido Glacier, located in the central Pyrenees, is one of the southernmost glaciers in Europe. Due to climate change, this glacier is suffering an accelerated mass loss, especially in the last decades. If the current trends persist, this glacier is expected to disappear in the next 50 years. As part of the efforts of the scientific community to increase the knowledge about this glacier, this research presents the first microstructural characterization of the Monte Perdido Glacier, focused on a high-impurity concentration segment that belongs to an ice core drilled in 2017. The results reveal the ice has a layering defined by air bubbles and non-soluble impurities. The bubble-defined layering exhibits features of both a primary (sedimentary) and a secondary (strain-induced) origin. We found a clear inverse correspondence between the particle concentration and the grains' size and roundness index. A preliminary micro-Raman characterization of the particles shows the occurrence of atacamite, anatase (likely related to ancient mining activities in the vicinity of the glacier) and quartz. The latter could be an indicator of mineral dust, probably suggesting the arrival of dust-laden air masses from the north of the African continent.

Ice streams are regions of rapid ice sheet flow characterised by a high degree of sliding over a deforming bed. The shallow shelf approximation (SSA) provides a convenient way to obtain closed-form approximations of the velocity and flux in a rapidly sliding ice stream when the basal drag is much less than the driving stress. However, the validity of the SSA approximation breaks down when the magnitude of the basal drag increases. Here we find a more accurate expression for the velocity and flux in this transitional regime before vertical deformation fully dominates, in agreement with numerical results. The closed-form expressions we derive can be incorporated into wider modelling efforts to yield a better characterisation of ice stream dynamics, and inform the use of the SSA in large-scale simulations.

Floating ice shelves that fringe the coast of Antarctica resist the flow of grounded ice into the ocean. One of the key factors governing the amount of flow resistance an ice shelf provides is the rigidity (related to viscosity) of the ice that constitutes it. Ice rigidity is highly heterogeneous and must be calibrated from spatially continuous surface observations assimilated into an ice-flow model. Realistic uncertainties in calibrated rigidity values are needed to quantify uncertainties in ice sheet and sea-level forecasts. Here, we present a physics-informed machine learning framework for inferring the full probability distribution of rigidity values for a given ice shelf, conditioned on ice surface velocity and thickness fields derived from remote-sensing data. We employ variational inference to jointly train neural networks and a variational Gaussian Process to reconstruct surface observations, rigidity values and uncertainties. Applying the framework to synthetic and large ice shelves in Antarctica demonstrates that rigidity is well-constrained where ice deformation is measurable within the noise level of the observations. Further reduction in uncertainties can be achieved by complementing variational inference with conventional inversion methods. Our results demonstrate a path forward for continuously updated calibrations of ice flow parameters from remote-sensing observations.

Ice stream discharge responds to a balance between gravity, basal friction and lateral drag. Appreciable viscous heating occurs in shear margins between ice streams and adjacent slow-moving ice ridges, altering the temperature-dependent viscosity distribution that connects lateral drag to marginal strain rates and ice stream velocity. Warmer ice deforms more easily and accommodates faster flow, whereas cold ice supplied from ice ridges drives advective cooling that counteracts viscous heating. Here, we present a two-dimensional (three velocity component), steady-state model designed to explore the thermal controls on ice stream shear margins. We validate our treatment through comparison with observed velocities for Bindschadler Ice Stream and verify that calculated temperatures are consistent with results from previous studies. Sweeping through a parameter range that encompasses conditions representative of ice streams in Antarctica, we show that modeled steady-state velocity has a modest response to different choices in forcing up until temperate zones develop in the shear margins. When temperate zones are present, velocity is much more sensitive to changes in forcing. We identify key scalings for the emergence of temperate conditions in our idealized treatment that can be used to identify where thermo-mechanical feedbacks influence the evolution of the ice sheet.

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.

Basal ice of glaciers and ice sheets frequently contains a well-developed stratification of distinct, semi-continuous, alternating layers of debris-poor and debris-rich ice. Here, the nature and distribution of shear within stratified basal ice are assessed through the anisotropy of magnetic susceptibility (AMS) of samples collected from Matanuska Glacier, Alaska. Generally, the AMS reveals consistent moderate-to-strong fabrics reflecting simple shear in the direction of ice flow; however, AMS is also dependent upon debris content and morphology. While sample anisotropy is statistically similar throughout the sampled section, debris-rich basal ice composed of semi-continuous mm-scale layers (the stratified facies) possesses well-defined triaxial to oblate fabrics reflecting shear in the direction of ice flow, whereas debris-poor ice containing mm-scale star-shaped silt aggregates (the suspended facies) possesses nearly isotropic fabrics. Thus, deformation within the stratified basal ice appears concentrated in debris-rich layers, likely the result of decreased crystal size and greater availability of unfrozen water associated with high debris content. These results suggest that variations in debris-content over small spatial scales influence ice rheology and deformation in the basal zone.

We investigated the effects of microparticles and grain size on the microstructural evolutions and mechanical properties of polycrystalline ice. Uniaxial compression tests were conducted using fine-grained pure ice and silica-dispersed ice under various conditions. Deformation behavior of fine-grained ice was found to be characterized by stress exponent n ≈ 2 and activation energy Q ≈ 60 kJ mol−1. The derived strain rates of fine-grained ice were ≈ 1 order of magnitude larger than those of coarse-grained ice obtained in previous studies, and they were found to be independent of particle dispersion and dependent on the mean grain size of ice, with grain size exponent p ≈ 1.4. Work hardening was observed in dislocation creep, while the strain rate continued to decrease. These results indicate that the deformation mechanism of fine-grained ice is different from typical dislocation creep, often associated with n = 3. Although microparticles restricted grain growth, there was little direct effect on the deformation of fine-grained ice. Microstructural observations of the ice samples indicated that the grain boundaries were straight and that the subgrain boundary densities increased after deformation. Our experiments suggest that grain size and boundaries play important roles in the deformation processes of polycrystalline ice.

Ice rheology governs how glaciers flow and respond to environmental change. The rheology of glacier ice evolves in response to a variety of mechanisms, including damage, heating, melting and the development of crystalline fabric. The relative contributions of these rheological mechanisms are not well understood. Using remotely sensed data and physical models, we decouple the influence of each of the aforementioned mechanisms along the margins of Rutford Ice Stream, a laterally confined outlet glacier in West Antarctica. We show that fabric is an important control on ice rheology in the shear margins, with an inferred softening effect consistent with a single-maximum fabric. Fabric evolves to steady state near the onset of streaming flow, and ice progressively softens downstream almost exclusively due to shear heating. The rate of heating is sensitive to local shear strain rates, which respond to local changes in bed topography as ice is squeezed through the basal trough. The impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback – wherein faster ice flow leads to higher rates of shear heating, further softening the ice – is a fundamental control on glacier dynamics.

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.

The behavior of marine-terminating ice sheets, such as the West Antarctic ice sheet, is of interest due to the possibility of rapid grounding-line retreat and consequent catastrophic loss of ice. Critical to modeling this behavior is a choice of basal rheology, where the most popular approach is to relate the ice-sheet velocity to a power-law function of basal stress. Recent experiments, however, suggest that near-grounding line tills exhibit Coulomb friction behavior. Here we address how Coulomb conditions modify ice-sheet profiles and stability criteria. The basal rheology necessarily transitions to Coulomb friction near the grounding line, due to low effective stresses, leading to changes in ice-sheet properties within a narrow boundary layer. Ice-sheet profiles ‘taper off’ towards a flatter upper surface, compared with the power-law case, and basal stresses vanish at the grounding line, consistent with observations. In the Coulomb case, the grounding-line ice flux also depends more strongly on flotation ice thickness, which implies that ice sheets are more sensitive to climate perturbations. Furthermore, with Coulomb friction, the ice sheet grounds stably in shallower water than with a power-law rheology. This implies that smaller perturbations are required to push the grounding line into regions of negative bed slope, where it would become unstable. These results have important implications for ice-sheet stability in a warming climate.

We estimate the distribution of ice thickness for a Himalayan glacier using surface velocities, slope and the ice flow law. Surface velocities over Gangotri Glacier were estimated using sub-pixel correlation of Landsat TM and ETM+ imagery. Velocities range from ˜14–85 m a–1 in the accumulation region to ˜20–30 m a–1 near the snout. Depth profiles were calculated using the equation of laminar flow. Thickness varies from ˜540 m in the upper reaches to ˜50–60 m near the snout. The volume of the glacier is estimated to be 23.2 ± 4.2 km3.

Accurate modeling of calving glaciers relies on knowledge of many processes (ice flow, surface/submarine melting, calving, mélange interaction) and glacier-specific factors (air temperature, ocean circulation, precipitation rate, glacier geometry) that remain challenging to assess. Iceberg calving, especially, is important to glacier mass loss and difficult to resolve in currently-available models. Given these challenges facing even the most sophisticated models, there is value in simple, computationally-efficient models that can capture first-order effects. In this study we derive a simple model, extending Nye's perfect plastic approximation to include a yield surface at the calving front. With one climate-related input—either an upstream glacier thinning rate or glacier-wide accumulation—this model is able to simulate the advance and retreat of marine-terminating glaciers on annual to decadal scales. Our model requires knowledge of only two glacier-specific factors: glacier bed topography and basal shear strength, both reasonably constrained by laboratory and field observations. We apply the model to a case study of Columbia Glacier, Alaska and show that, despite its simplicity, the model succeeds in reproducing observed centerline profiles and rates of terminus retreat up to 2007.

In order to better understand the densification of polar firn, firn cores from the three sites within ~10 km of Dome Fuji, Antarctica, were investigated using surrogates of density: dielectric permittivities εv and εh at microwave frequencies with electrical fields in the vertical and horizontal planes respectively. Dielectric anisotropy Δε (=εv − εh) was then examined as a surrogate of the anisotropic geometry of firn. We find that layered densification is explained as a result of complex effects of two phenomena that commonly occur at the three sites. Basically, layers with initially smaller density and smaller geometrical anisotropy deform preferentially throughout the densification process due to textural effects. Second, layers having a higher concentration of Cl− ions deform preferentially during a limited period from the near surface depths until smoothing out of layered Cl− ions by diffusion. We hypothesize that Cl− ions dissociated from sea salts soften firn due to modulation of dislocation movement. Moreover, firn differs markedly across the three sites in terms of strength of geometrical anisotropy, mean rate of densification and density fluctuation. We hypothesize that these differences are caused by textural effects resulting from differences in depositional conditions within various spatial scales.