At high elevations on the Greenland ice sheet meltwater percolates and refreezes in place, and hence does not contribute to mass loss. However, meltwater generation and associated surface runoff is occurring from increasingly higher altitudes, causing changes in firn stratigraphy that have led to the presence of near-surface ice slabs. These ice slabs force meltwater to flow laterally instead of percolating downwards. Here we present a simple, physics-based quasi-2-D model to simulate lateral meltwater runoff and superimposed ice (SI) formation on top of ice slabs. Using an Eulerian Darcy flow scheme, the model calculates how far meltwater can travel within a melt season and when it appears at the snow surface. Results show that lateral flow is a highly efficient runoff mechanism, as lateral outflow exceeds locally generated meltwater in all model gridcells, with total meltwater discharge sometimes reaching more than 30 times the average amount of in situ generated melt. SI formation, an important process in the formation and thickening of the ice slabs, can retain up to 40% of the available meltwater, and generally delays the appearance of visible runoff. Validating the model against field- or remote-sensing data remains challenging, but the results presented here are a first step towards a more comprehensive understanding and description of the hydrological system in the accumulation zone of the southwestern Greenland ice sheet.

Outlet glaciers in Greenland are undergoing retreat and diffusive thinning in response to external forcings, but the rates and magnitudes of these responses differ from glacier to glacier for unclear reasons. We test how changes in ice overburden pressure and basal lubrication affect diffusive thinning rates and their spatial patterns by conducting numerical experiments over various idealized Greenland-like glacier domains. We find that ~10 km frontal retreat over a decade can produce sustained thinning rates as large as 16 m a−1 due to ice overburden pressure changes, at outlet glaciers with high basal drag (>60 kPa) and lateral resistive stress (>70 kPa). Localized basal lubrication perturbations induce upstream thinning and downstream thickening up to 12 m a−1; the duration of the lubrication forcing generally has a greater effect than its intensity on induced thickness changes. Lastly, episodic grounding line retreats over a rough bed produce a stepped time series of thinning broadly consistent with observations of dynamic elevation change on multiple Greenland glaciers. Our findings highlight the critical role of the total grounding zone – not ice front position – through the resistive stress change in relation to total glacier thinning.

Rock glaciers support alpine biodiversity and may respond more slowly to warming than snow or glaciers. While responses of snow and glaciers to climate change are relatively well understood, a robust assessment of rock glacier environmental niche, future distributions of rock glaciers and potential for development of rock glaciers from current glaciers is lacking. Using process-relevant, high-resolution environmental descriptors, we develop a species distribution model of the topographic, geologic and hydroclimatic niche of rock glaciers that provides novel estimates of potential rock glacier distributions for different climates. We identify mean annual air temperature and headwall area as the dominant controls on rock glacier spatial distributions, with rock glaciers more likely to be found in areas with mean annual temperatures close to −5°C, little rain, northern aspects and broad headwalls. While rock glacier climate equilibration may take hundreds of years, we find that equilibration to present climate will result in a 50% reduction in rock glacier habitat and equilibration to late 21st-century climate under a high-end warming scenario will result in a 99% reduction in rock glacier habitat across the western USA. Under future conditions, we find limited potential for glacier to rock glacier transformation (3% of glacierized area), concentrated in cold, high elevation, moderate precipitation areas.

The future of tidewater glaciers in response to climate warming is one of the largest sources of uncertainty in the contribution of the Greenland ice sheet to global sea-level rise. In this study, we investigate the ability of an ice-sheet model to reproduce the past evolution of the velocity and surface elevation of a tidewater glacier, Upernavik Isstrøm, by prescribing front positions. To achieve this, we run two ensembles of simulations with a Weertman and a regularised-Coulomb friction law. We show that the ice-flow model has to include a reduction in friction in the first 15 km upstream of the ice front in fast-flowing regions to capture the trends observed during the 1985–2019 period. Without this process, the ensemble model overestimates the ice flow before the retreat of the front in 2005 and does not fully reproduce its acceleration during the retreat. This results in an overestimation of the total mass loss between 1985 and 2019 of 50% (300 vs 200 Gt). Using a variance-based sensitivity analysis, we show that uncertainties in the friction law and the ice-flow law have a greater impact on the model results than surface mass balance and initial surface elevation.

Rifts are full-thickness fractures that propagate laterally across an ice shelf. They cause ice-shelf weakening and calving of tabular icebergs, and control the initial size of calved icebergs. Here, we present a joint inverse and forward computational modeling framework to capture rifting by combining the vertically integrated momentum balance and anisotropic continuum damage mechanics formulations. We incorporate rift–flank boundary processes to investigate how the rift path is influenced by the pressure on rift–flank walls from seawater, contact between flanks, and ice mélange that may also transmit stress between flanks. To illustrate the viability of the framework, we simulate the final 2 years of rift propagation associated with the calving of tabular iceberg A68 in 2017. We find that the rift path can change with varying ice mélange conditions and the extent of contact between rift flanks. Combinations of parameters associated with slower rift widening rates yield simulated rift paths that best match observations. Our modeling framework lays the foundation for robust simulation of rifting and tabular calving processes, which can enable future studies on ice-sheet–climate interactions, and the effects of ice-shelf buttressing on land ice flow.

Mass loss from the Amundsen Sea Embayment of the West Antarctic Ice Sheet is a major contributor to global sea-level rise (SLR) and has been increasing over recent decades. Predictions of future SLR are increasingly modelled using ensembles of simulations within which model parameters and external forcings are varied within credible ranges. Accurately reporting the uncertainty associated with these predictions is crucial in enabling effective planning for, and construction of defences against, rising sea levels. Calibrating model simulations against current observations of ice-sheet behaviour enables the uncertainty to be reduced. Here we calibrate an ensemble of BISICLES ice-sheet model simulations of ice loss from the Amundsen Sea Embayment using remotely sensed observations of surface elevation and ice speed. Each calibration type is shown to be capable of reducing the 90% credibility bounds of predicted contributions to SLR by 34 and 43% respectively.

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.

Thwaites Glacier (TG) plays an important role in future sea-level rise (SLR) contribution from the West Antarctic Ice Sheet. Recent observations show that TG is losing mass, and its grounding zone is retreating. Previous modeling has produced a wide range of results concerning whether, when, and how rapidly further retreat will occur under continued warming. These differences arise at least in part from ill-constrained processes, including friction from the bed, and future atmosphere and ocean forcing affecting ice-shelf and grounding-zone buttressing. Here, we apply the Ice Sheet and Sea-level System Model (ISSM) with a range of specifications of basal sliding behavior in response to varying ocean forcing. We find that basin-wide bed character strongly affects TG's response to sub-shelf melt by modulating how changes in driving stress are balanced by the bed as the glacier responds to external forcing. Resulting differences in dynamic thinning patterns alter modeled grounding-line retreat across Thwaites' catchment, affecting both modeled rates and magnitudes of SLR contribution from this critical sector of the ice sheet. Bed character introduces large uncertainties in projections of TG under equal external forcing, pointing to this as a crucial constraint needed in predictive models of West Antarctica.

In this study, we investigate the differences between two transient, three-dimensional, thermomechanically coupled ice-sheet models, namely, a first-order approximation model (FOM) and a ‘full’ Stokes ice-sheet model (FSM) under the same numerical framework. For all numerical experiments, we take the FSM outputs as the reference values and calculate the mean relative errors in the velocity and temperature fields for the FOM over 100 years. Four different boundary conditions (ice slope, geothermal heat flux, basal topography and basal sliding) are tested, and by changing these parameters, we verify the thermomechanical behavior of the FOM and discover that the velocity and temperature biases of the FOM generally increase with increases in the ice slope, geothermal heat flux, undulation amplitude of the ice base, and with the existence of basal sliding. In addition, the model difference between the FOM and FSM may accumulate over time, and the spatial distribution patterns of the relative velocity and temperature errors are in good agreement.

Pigmented microalgae inhabiting snow and ice environments lower the albedo of glacier and ice-sheet surfaces, significantly enhancing surface melt. Our ability to accurately predict their role in glacier and ice-sheet surface mass balance is limited by the current lack of empirical data to constrain their representation in predictive models. Here we present new empirical optical properties for snow and ice algae and incorporate them in a radiative transfer model to investigate their impact on snow and ice surface albedo. We found ice algal cells to be more efficient absorbers than snow algal cells, but their blooms had comparable impact on surface albedo due to the different photic conditions of their habitats. We then used the model to reconstruct the effect of ice algae on bare ice albedo spectra collected at our field site in southern Greenland, where blooms dropped the albedo locally by between 3 and 43%, equivalent to 1–10 L m$^{-2}$ d$^{-1}$ of melted ice. Using the newly parametrized model, future studies could investigate biological albedo reduction and algal quantification from remote hyperspectral and multispectral imagery.

Mass loss at the Greenland Ice Sheet is influenced by atmospheric processes controlling its surface mass balance, and by submarine melt and calving where glaciers terminate in fjords. There, an ice mélange – a composite matrix of calved ice bergs and sea ice – may provide a buttressing force on a glacier terminus and control terminus dynamics. Kangerlussuaq Glacier is a major outlet of the Greenland Ice Sheet, for which recent major retreat events in 2004/2005 and 2016–2018 coincided with the absence of an ice mélange in Kangerlussuaq Fjord. To better understand the response of Kangerlussuaq Glacier to climatic and oceanic drivers, a 2D flowline model is employed. Results indicate that an ice mélange buttressing force exerts a major control on calving frequency and rapid retreat. When an ice mélange forms in Kangerlussuaq Fjord, it provides stabilising forces and conditions favourable for winter terminus re-advance. When it fails to form during consecutive years, model results indicate that Kangerlussuaq Glacier is primed to retreat into the large overdeepenings in Kangerlussuaq Fjord, and to terminus positions more than 30 km farther inland, implying that excessive mass loss from Kangerlussuaq Glacier by the year 2065 cannot be excluded.

Englacial water transport is an integral part of the glacial hydrologic system, yet the geometry of englacial structures remains largely unknown. In this study, we explore the excitation of fluid resonance by small amplitude waves as a probe of englacial geometry. We model a hydraulic network consisting of one or more tabular cracks that intersect a cylindrical conduit, subject to oscillatory wave motion initiated at the water surface. Resulting resonant frequencies and quality factors are diagnostic of fluid properties and geometry of the englacial system. For a single crack–conduit system, the fundamental mode involves gravity-driven fluid sloshing between the conduit and the crack, at frequencies between 0.02 and 10 Hz for typical glacial parameters. Higher frequency modes include dispersive Krauklis waves generated within the crack and tube waves in the conduit. But we find that crack lengths are often well constrained by fundamental mode frequency and damping rate alone for settings that include alpine glaciers and ice sheets. Branching crack geometry and dip, ice thickness and source excitation function help define limits of crack detectability for this mode. In general, we suggest that identification of eigenmodes associated with wave motion in time series data may provide a pathway toward inferring englacial hydrologic structures.

We develop a two-dimensional, plan-view formulation of ice-shelf flow and viscoelastic ice-shelf flexure. This formulation combines, for the first time, the shallow-shelf approximation for horizontal ice-shelf flow (and shallow-stream approximation for flow on lubricated beds such as where ice rises and rumples form), with the treatment of a thin-plate flexure. We demonstrate the treatment by performing two finite-element simulations: one of the relict pedestalled lake features that exist on some debris-covered ice shelves due to strong heterogeneity in surface ablation, and the other of ice rumpling in the grounding zone of an ice rise. The proposed treatment opens new venues to investigate physical processes that require coupling between the longitudinal deformation and vertical flexure, for instance, the effects of surface melting and supraglacial lakes on ice shelves, interactions with the sea swell, and many others.

Advances in analytical methods have made it possible to obtain high-resolution water isotopic data from ice cores. Their spectral signature contains information on the diffusion process that attenuated the isotopic signal during the firn densification process. Here, we provide a tool for estimating firn-diffusion rates that builds on the Community Firn Model. Our model requires two main inputs, temperature and accumulation, and it calculates the diffusion lengths for δ17O, δ18O and δD. Prior information on the isotopic signal of the precipitation is not a requirement. In combination with deconvolution techniques, diffusion lengths can be used in order reconstruct the pre-diffusion isotopic signal. Furthermore, the temperature dependence of the isotope diffusion and firn densification makes the diffusion length an interesting candidate as a temperature proxy. We test the model under steady state and transient scenarios and compare four densification models. Comparisons with ice core data provide an evaluation of the four models and indicate that there are differences in their performance. Combining data-based diffusion length estimates with information on past accumulation rates and ice flow thinning, we reconstruct absolute temperatures from three Antarctic ice core sites.

Streaming ice accounts for a major fraction of global ice flux, yet we cannot yet fully explain the dominant controls on its kinematics. In this contribution, we use an anisotropic full-Stokes thermomechanical flow solver to characterize how mechanical anisotropy and temperature distribution affect ice flux. For the ice stream and glacier geometries we explored, we found that the ice flux increases 1–3% per °C temperature increase in the margin. Glaciers and ice streams with crystallographic fabric oriented approximately normal to the shear plane increase by comparable amounts: an otherwise isotropic ice stream containing a concentrated transverse single maximum fabric in the margin flows 15% faster than the reference case. Fabric and temperature variations independently impact ice flux, with slightly nonlinear interactions. We find that realistic variations in temperature and crystallographic fabric both affect ice flux to similar degrees, with the exact effect a function of the local fabric and temperature distributions. Given this sensitivity, direct field-based measurements and models incorporating additional factors, such as water content and temporal evolution, are essential for explaining and predicting streaming ice dynamics.

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.

Wind-driven snow redistribution can increase the spatial heterogeneity of snow accumulation on ice caps and ice sheets, and may prove crucial for the initiation and survival of glaciers in areas of marginal glaciation. We present a snowdrift model (Snow_Blow), which extends and improves the model of Purves, Mackaness and Sugden (1999, Journal of Quaternary Science 14, 313–321). The model calculates spatial variations in relative snow accumulation that result from variations in topography, using a digital elevation model (DEM) and wind direction as inputs. Improvements include snow redistribution using a flux routing algorithm, DEM resolution independence and the addition of a slope curvature component. This paper tests Snow_Blow in Antarctica (a modern environment) and reveals its potential for application in palaeoenvironmental settings, where input meteorological data are unavailable and difficult to estimate. Specifically, Snow_Blow is applied to the Ellsworth Mountains in West Antarctica where ablation is considered to be predominantly related to wind erosion processes. We find that Snow_Blow is able to replicate well the existing distribution of accumulating snow and snow erosion as recorded in and around Blue Ice Areas. Lastly, a variety of model parameters are tested, including depositional distance and erosion vs wind speed, to provide the most likely input parameters for palaeoenvironmental reconstructions.

Subglacial hydrology plays a key role in many glaciological processes, including ice dynamics via the modulation of basal sliding. Owing to the lack of an overarching theory, however, a variety of model approximations exist to represent the subglacial drainage system. The Subglacial Hydrology Model Intercomparison Project (SHMIP) provides a set of synthetic experiments to compare existing and future models. We present the results from 13 participating models with a focus on effective pressure and discharge. For many applications (e.g. steady states and annual variations, low input scenarios) a simple model, such as an inefficient-system-only model, a flowline or lumped model, or a porous-layer model provides results comparable to those of more complex models. However, when studying short term (e.g. diurnal) variations of the water pressure, the use of a two-dimensional model incorporating physical representations of both efficient and inefficient drainage systems yields results that are significantly different from those of simpler models and should be preferentially applied. The results also emphasise the role of water storage in the response of water pressure to transient recharge. Finally, we find that the localisation of moulins has a limited impact except in regions of sparse moulin density.

Satellite observations of gravity anomalies, ice-surface elevation and glacier velocity show significant increases in net grounded-ice-mass loss over the past decade along the Bellingshausen Sea sector (BSS), West Antarctica, in areas where warm (>1°C) sea water floods the continental shelf. These observations provide compelling but indirect evidence that mass losses are driven primarily by reduced buttressing from the floating ice shelves caused by ocean-driven ice-shelf thinning. Here, we combine recent observations of ice velocity, thickness and thickness changes with an ice flow model to study the instantaneous dynamic response of BSS outlet glaciers to observed ice-shelf thinning, alone. Our model results show that multiple BSS outlet glaciers respond instantaneously to observed ice-shelf thinning, particularly in areas where ice shelves ground at discrete points. Increases in modeled and observed dynamic mass losses, however, account for ~5% of the mass loss rates estimated from gravity anomalies and changes in ice-surface elevation, suggesting that variations in surface mass balance may be key to understanding recent BSS mass loss. Our approach isolates the impact of ice-shelf thinning on glacier flow and shows that if ice-shelf thinning continues at or above current rates, total BSS mass loss will increase in the next decade.

Simple models of glacier volume evolution are important in understanding features of glacier response to climate change, due to the scarcity of data adequate for running more complex models on a global scale. Two quantities of interest in a glacier's response to climate changes are its response time and its volume sensitivity to changes in the equilibrium line altitude (ELA). We derive a simplified, computationally inexpensive model of glacier volume evolution based on a block model with volume–area–length scaling. After analyzing its steady-state properties, we apply the model to each mountain glacier worldwide and estimate regionally differentiated response times and sensitivities to ELA changes. We use a statistical method from the family of global sensitivity analysis methods to determine the glacier quantities, geometric and climatic, that most influence the model output. The response time is dominated by the climatic setting reflected in the mass-balance gradient in the ablation zone, followed by the surface slope, while volume sensitivity is mainly affected by glacier size, followed by the surface slope.