The shallow ice approximation for glaciers and ice sheets is a degenerate model in which the ice surface slope at the margin may be infinite. This result is due to the neglect of the otherwise small longitudinal stress terms. Here we derive a corrected approximation for the basal shear stress, and show that the resulting model provides an explanation for the observed finite slope margins.

Theory and observation show that glacier-flow regimes characterized by high basal slip enhance the projection of topographic detail to the surface, motivating this investigation into the efficacy of using glacier surges to improve bed estimation. Here we adapt a Bayesian inversion scheme and apply it to real and synthetic data as a proof of concept. Synthetic tests show a reduction in mean RMSE between true and inferred beds by more than half, and an increase in the mean correlation coefficient of ~0.5, when data from slip- versus deformation-dominated regimes are used. Multi-epoch inversions, which partition slip- and deformation-dominated regimes, are shown to outperform inversions that average over these flow regimes thereby squandering information. Tests with real data from a surging glacier in Yukon, Canada, corroborate these results, while highlighting the challenges of limited or inconsistent data. With the growing torrent of satellite-based observations, fast-flow events such as glacier surges offer potential to improve bed estimation for some of the world's most dynamic glaciers.

This study presents the first dataset of physical and textural properties of sea ice collected in the South Atlantic and Indian Ocean sector of the Antarctic marginal ice zone (MIZ). Observations of sea ice from this region in the austral spring 2019, including sea-ice core temperature, salinity, crystal size, texture, oxygen isotopes and stratigraphy, were used in conjunction with a Lagrangian back-tracking algorithm and atmospheric reanalyses. This method relates the reconstructed synoptic conditions to sea-ice growth along the transect. A significant difference was found between the stratigraphy of consolidated pack ice samples collected at the same latitude and spanning over 550 km eastwards. The eastward group was found to have more disturbances in their stratigraphy which is attributed to the highly variable atmospheric and sea-ice conditions together with varying wave penetration through the sea-ice pack, notably during the passage of an intense polar cyclone, while the westward group showed no signs of disturbance or deformation. These results indicate that consolidated Antarctic sea-ice floes of similar thickness and from the same latitude in the MIZ have distinct stratigraphic properties, which will influence their physical and biogeochemical features.

During Cook's 1772–75 Antarctic circumnavigation on the HMS Resolution, he recorded the positions of hundreds of icebergs. This paper compares Cook's observations and those of Halley in 1700, Bouvet in 1739 and Riou in 1789, with the Brigham Young University/National Ice Center (BYU/NIC) and the Alfred Wegener Institute datasets. Cook's description of the iceberg plume east of the Amery Ice Shelf and the iceberg distributions in the Weddell, Ross and Amundsen Seas agree with modern data. In January 1774, Cook reached his farthest south on the shelf of the Amundsen Sea Embayment, the site of the current International Thwaites Glacier Collaboration field study. Cook's largest iceberg had a 2.5 km diameter, where power-law models show that icebergs of this size or smaller comprise 92% of their total number. In the eastern Weddell, Cook's observation of a sea-ice tongue with a much greater extent than in satellite imagery remains unexplained. Although Riou's icebergs lie 1000 km east of the BYU/NIC trajectories, application of the England and others (2020) fracture and drift model to the trajectories removes the discrepancy and means that all the ship observations are consistent with modern observations and theory.

To investigate the mechanisms driving recent changes in outlet glaciers in Antarctica, we measured the glacier front position, flow velocity and surface elevation of five outlet glaciers flowing into Lützow-Holm Bay in East Antarctica. After a steady advance from 2008 to 2015, all the glaciers synchronously retreated by 0.4–6.0 km between 2016 and 2018. The initiation of the retreat coincided with the breakup of land-fast sea ice in Lützow-Holm Bay in 2016, which resulted in the largest sea-ice loss in the region since 1998. Similar flow variations and surface elevation changes were observed near the grounding line of Shirase, Skallen and Telen glaciers. The slowdown in 2011–15 (by 13%) and the speedup in 2016–18 (by 7%) coincided with the respective increase and decrease in surface elevation. Simultaneous retreat and acceleration after the land-fast sea-ice breakup implies that sea ice has a significant influence on glacier dynamics. Thickening/thinning observed near the grounding line was attributed to a reduced/enhanced stretching flow regime during the deceleration/acceleration period. Our results demonstrate that land-fast sea ice affects not only terminus positions, but also the flow speed and ice thickness of the Antarctic glaciers.

The magnitude and azimuth of horizontal ice flow at Camp Century, Greenland have been measured several times since 1963. Here, we provide a further two independent measurements over the 2017–21 period. Our consensus estimate of horizontal ice flow from four independent satellite-positioning solutions is 3.65 ± 0.13 m a−1 at an azimuth of 236 ± 2°. A portion of the small, but significant, differences in ice velocity and azimuth reported between studies likely results from spatial gradients in ice flow. This highlights the importance of restricting inter-study comparisons of ice flow estimates to measurements surveyed within a horizontal distance of one ice thickness from each other. We suggest that ice flow at Camp Century is stable on seasonal to multi-decadal timescales. The airborne and satellite laser altimetry record indicates an ice thickening trend of 1.1 ± 0.3 cm a−1 since 1994. This thickening trend is qualitatively consistent with previously inferred ongoing millennial-scale ice thickening at Camp Century. The ice flow divide immediately north of Camp Century may now be migrating southward, although the reasons for this divide migration are poorly understood. The Camp Century flowlines presently terminate in the vicinity of Innaqqissorsuup Oqquani Sermeq (Gade Gletsjer) on the Melville Bay coast.

Wet-snow avalanches are triggered by the infiltration of liquid water which weakens the snowpack. Wet-snow avalanches are among the most destructive avalanches, yet their release mechanism is not sufficiently understood for a process-based prediction model. Therefore, we followed a data-driven approach and developed a random forest model, depending on slope aspect, to predict the local wet-snow avalanche activity at the locations of 124 automated weather stations distributed throughout the Swiss Alps. The input variables were the snow and weather data recorded by the stations over the past 20 years. The target variable was based on manual observations over the same 20-year period. To filter out erroneous reports, we defined the days with wet-snow avalanches in a stringent manner, selecting only the most extreme active or inactive days, which reduced the size of the dataset but increased the reliability of the target variable. The model was trained with weather variables and variables computed from simulated snow stratigraphy in 38$^\circ$ slopes facing the 4 cardinal directions. While model development and validation were done in nowcast mode, we also studied model performance in 24-hour forecast mode by using input variables computed from a numerical weather prediction (NWP) model. Overall, the performance was good in both nowcast and forecast mode (f1-score around 0.8). To assess model performance beyond the stringent definition of wet-snow avalanche days, we compared model predictions to wet-snow avalanche activity over the entire Swiss Alps, based on the raw data over 8 winters. We obtained a Spearman correlation coefficient of 0.71. Hence, our model represents a step toward the application of support tools in operational wet-snow avalanche forecasting.

Glaciers in the Russian High Arctic have undergone accelerated mass loss due to atmospheric and oceanic warming in the Barents–Kara Sea region. Most studies have concentrated on the western Barents–Kara sector, despite evidence of accelerating mass loss as far east as Severnaya Zemlya. However, long-term trends in glacier change on Severnaya Zemlya are largely unknown and this record may be complicated by surge-type glaciers. Here, we present a long-term assessment of glacier change (1965–2021) on Severnaya Zemlya and a new inventory of surge-type glaciers using declassified spy-satellite photography (KH-7/9 Hexagon) and optical satellite imagery (ASTER, Sentinel-2A, Landsat-4/5 TM and 8 OLI). Glacier area reduced from 17 053 km2 in 1965 to 16 275 in 2021 (−5%; mean: −18%, max: −100%), with areal shrinkage most pronounced at land-terminating glaciers on southern Severnaya Zemlya, where there is a recent (post-2010s) increase in summer atmospheric temperatures. We find that surging may be more widespread than previously thought, with three glaciers classified confirmed as surge-type, eight as likely to have surged and nine as possible, comprising 11% of Severnaya Zemlya's 190 glaciers (37% by area). Under continued warming, we anticipate accelerated retreat and increased likelihood of surging as basal thermal regimes shift.

Numerical glacier and ice-sheet models compute evolving ice geometry and velocity fields using various stress-balance approximations and boundary conditions. At high spatial resolution, with horizontal mesh/grid resolutions of a few kilometers or smaller, these models usually require time steps shorter than climate-coupling time scales because they update ice thickness after each velocity solution. High-resolution performance is degraded by the stability restrictions of such explicit time-stepping. This short note, which considers the shallow ice approximation and Stokes models as stress-balance end members, clarifies the scaling of numerical model performance by quantifying simulation cost per model year in terms of mesh resolution and the number of degrees of freedom. The performance of current-generation explicit time-stepping models is assessed, and then compared to the prospective performance of implicit schemes. The main results highlight the key roles played by the algorithmic scaling of stress-balance solvers and coupled, implicit-step solvers.

In Southeast Greenland, summer melt and high winter snowfall rates give rise to firn aquifers: vast stores of meltwater buried beneath the ice-sheet surface. Previous detailed studies of a single Greenland firn aquifer site suggest that the water drains into crevasses, but this is not known at a regional scale. We develop and use a tool in Ghub, an online gateway of shared datasets, tools and supercomputing resources for glaciology, to identify crevasses from elevation data collected by NASA's Airborne Topographic Mapper across 29000 km2 of Southeast Greenland. We find crevasses within 3 km of the previously mapped downglacier boundary of the firn aquifer at 20 of 25 flightline crossings. Our data suggest that crevasses widen until they reach the downglacier boundary of the firn aquifer, implying that crevasses collect firn-aquifer water, but we did not find this trend with statistical significance. The median crevasse width, 27 meters, implies an aspect ratio consistent with the crevasses reaching the bed. Our results support the idea that most water in Southeast Greenland firn aquifers drains through crevasses. Less common fates are discharge at the ice-sheet surface (3 of 25 sites) and refreezing at the aquifer bottom (1 of 25 sites).

We present the first systematic inventory of surge-type glaciers for the whole of Greenland compiled from published datasets and multitemporal satellite images and digital elevation models. The inventory allows us to define the spatial and climatic distribution of surge-type glaciers and to analyse the timing of surges from 1985 to 2019. We identified 274 surge-type glaciers, an increase of 37% compared to previous work. Mapping surge-type glacier distribution by temperature and precipitation variables derived from ERA5-Land reanalysis data shows that the west and east clusters occur in well-defined climatic envelopes. Analysis of the timing of surge active phases during the periods ~1985 to 2000 (T1) and ~2000 to 2019 (T2) suggests that overall surge activity is similar in T1 and T2, but there appears to be a reduction in surging in the west cluster in T2. Our climate analysis shows a coincident increase in mean annual and mean winter air temperature between T1 and T2. We suggest that as glaciers thin under current warming, some surge-type glaciers in the west cluster may be being prevented from surging due to (1) their inability to build-up sufficient mass and (2) a switch from a polythermal to a largely cold-based thermal regime.

Initialising model glaciers such that they match well with their real counterparts and are thus able to make more accurate predictions is an ongoing challenge in glacier modelling. We set out a data-assimilation approach using an ensemble Kalman filter in a 2D flowline example that provides one possible solution to this problem. We show that our approach is valid across a range of parameters and scenarios, including deliberately data-deficient or inaccurate ones, and leads to robust retrieval of the glacier bed. We also provide some suggestions for how best to use data assimilation within a mountain-glacier context.

Empirical glacier mass-balance models are commonly used in assessments of glacier and runoff evolution. Recent satellite-borne geodetic mass-balance observations of global coverage facilitate large-scale model calibration that previously relied on sparse in situ observations of glacier mass change. Geodetic observations constitute temporally aggregated mass-balance signals with significant uncertainty, raising questions about the role of observations with different temporal resolutions and uncertainties in constraining model parameters. We employ a Bayesian approach and demonstrate the sensitivity of parameter values to commonly used mass-balance observations of seasonal, annual and decadal resolution with uncertainties characteristic to in situ and satellite-borne observations. For glaciers along a continentality gradient in Norway, the use of annual mass balances results in around 20% lower magnitude of modelled ablation and accumulation (1960–2020), compared to employing seasonal balances. Decadal mass balance also underestimates magnitudes of ablation and accumulation, but parameter values are strongly influenced by the prior distribution. The datasets yield similar estimates of annual mass balance with different margins of uncertainty. Decadal observations are afflicted with considerable uncertainty in mass-balance sensitivity due to high parameter uncertainty. Our results highlight the importance of seasonal observations when model applications require accurate magnitudes of ablation, e.g. to estimate meltwater runoff.

Links between proglacial lakes and glacier dynamics are poorly understood but are necessary to predict how mountain glaciers will react to a warmer, wetter climate, where such lakes are expected to increase both in number and volume. Here, we examine a long-term (~120 year) record of terminus retreat, thinning and surface velocities from in-situ and remote sensing observations at the terminus of Kaskawulsh Glacier, Yukon, Canada, and determine the impact of a local proglacial hydrological reorganisation on glacier dynamics. After an initial deceleration during the late 1990s, terminus velocities increased at a rate of 3 m a−2 from 2000–12, while proglacial Slims Lake area increased simultaneously. The rapid drainage of the lake in May 2016 substantially altered the velocity profile, decreasing annual velocities by 48% within 3 km of the terminus between 2015 and 2021, at an average rate of ~ 12.5 m a−2. A key cause of the rapid drop in glacier motion was a reduction in flotation of the lower part of the glacier terminus after lake drainage. This has important implications for glacier dynamics and provides one of the first assessments of the impacts of a rapid proglacial lake drainage event on local terminus velocities.

Progress in our understanding of wave–ice interactions is currently hindered by the lack of in situ observations and information of sea-ice properties, including the elastic modulus. Here, we estimate the effective elastic modulus of sea ice using observations of waves in ice through the deployment of three open-source geophone recorders on landfast sea ice. From observations of low-frequency dispersive waves, we obtain an estimate of the effective elastic modulus in the range of 0.4–0.7 GPa. This is lower than the purely elastic modulus of the ice estimated at 1 GPa as derived from in situ beam experiments. Importantly, our experimental observation is significantly lower than the default value currently in use in wave models. While our estimate is not representative for all sea ice, it does indicate that considerably more measurements are required to provide confidence in the development of parameterizations for this complex sea-ice property for wave models.