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.

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.

From 2017 to 2020, three significant calving events took place on Pine Island Glacier, West Antarctica. Ice-shelf velocities changed over this period and the calving events have been suggested as possible drivers. However, satellite observations also show significant changes in the areal extent of fracture zones, especially in the marginal areas responsible for providing lateral support to the ice shelf. Here, we conduct a model study to identify and quantify drivers of recent ice-flow changes of the Pine Island Ice Shelf. In agreement with recent studies, we find that the calving events caused significant velocity changes over the ice shelf. However, calving alone cannot explain observed velocity changes. Changes in the structural rigidity, i.e. ice damage, further significantly impacted ice flow. We suggest that ice damage evolution of the ice-shelf margins may have influenced recent calving events, and these two processes are linked.

Convolutional neural networks (CNN) trained from high-order ice-flow model realisations have proven to be outstanding emulators in terms of fidelity and computational performance. However, the dependence on an ensemble of realisations of an instructor model renders this strategy difficult to generalise to a variety of ice-flow regimes found in the nature. To overcome this issue, we adopt the approach of physics-informed deep learning, which fuses traditional numerical solutions by finite differences/elements and deep-learning approaches. Here, we train a CNN to minimise the energy associated with high-order ice-flow equations within the time iterations of a glacier evolution model. As a result, our emulator is a promising alternative to traditional solvers thanks to its high computational efficiency (especially on GPU), its high fidelity to the original model, its simplified training (without requiring any data), its capability to handle a variety of ice-flow regimes and memorise previous solutions, and its relatively simple implementation. Embedded into the ‘Instructed Glacier Model’ (IGM) framework, the potential of the emulator is illustrated with three applications including a large-scale high-resolution (2400x4000) forward glacier evolution model, an inverse modelling case for data assimilation, and an ice shelf.

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.

One of the largest contributors to uncertainty in predictions of sea-level rise from ice-sheet models is a lack of knowledge about the bed topography beneath ice sheets. Bed topography maps are normally made by interpolating between linear radar surveys using methods that include kriging, mass conservation and flowline diffusion, all of which may miss influential mesoscale (2–30 km) bedforms. Previous works have explored an Ice-Flow Perturbation Analysis (IFPA) approach for estimating bed topography using the surface expression of these mesoscale bedforms. Using regions of Pine Island Glacier that have been intensively surveyed by ice-penetrating radar as test sites, and a refined IFPA methodology, we find that IFPA detects bedforms capable of influencing ice flow which are not represented in Bedmachine Antarctica and other interpolated bed products. We further explore the ability of IFPA to estimate relative bed slipperiness, finding higher slipperiness in the main trunk and tributaries. Alongside other methods which estimate ice thickness, bed topography maps from IFPA have the potential to constrain projections of future sea-level rise, especially where radar data are sparse.

As part of the Coupled Model Intercomparison Project Phase 6 (CMIP6), the Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) was devised to assess the likely sea-level-rise contribution from the Earth's ice sheets. Here, we construct an ensemble of climate forcings for Antarctica until the year 2300 based on original ISMIP6 forcings until 2100, combined with climate indices from simulations with the MIROC4m climate model until 2300. We then use these forcings to run simulations for the Antarctic ice sheet with the SICOPOLIS model. For the unabated warming pathway RCP8.5/SSP5-8.5, the ice sheet suffers a severe mass loss, amounting to ~ 1.5 m SLE (sea-level equivalent) for the fourteen-experiment mean, and ~ 3.3 m SLE for the most sensitive experiment. Most of this loss originates from West Antarctica. For the reduced emissions pathway RCP2.6/SSP1-2.6, the loss is limited to a three-experiment mean of ~ 0.16 m SLE. The means are approximately two times larger than what was found in a previous study (Chambers and others, 2022, doi:10.1017/jog.2021.124) that assumed a sustained late-21st-century climate beyond 2100, demonstrating the importance of post-2100 climate trends on Antarctic mass changes in the 22nd and 23rd centuries.

Future projections of sea-level rise under strong warming scenarios are dominated by mass loss in the marine-grounded sectors of West Antarctica, where thinning shelves as a result of warming oceans can lead to reduced buttressing. This consequently leads to accelerated flow from the upstream grounded ice. However, the relation between warming oceans and increased melt rates under the shelves is very uncertain, especially when interactions with the changing shelf geometry are considered. Here, we compare six widely used, highly parameterised formulations relating sub-shelf melt to thermal forcing. We implemented them in an ice-sheet model, and applied the resulting set-up to an idealised-geometry setting, as well as to the Antarctic ice sheet. In our simulations, the differences in modelled ice-sheet evolution resulting from the choice of parameterisation, as well as the choice of numerical scheme used to apply sub-shelf melt near the grounding line, generally are larger than differences from ice-dynamical processes such as basal sliding, as well as uncertainties from the forcing scenario of the model providing the ocean forcing. This holds for the idealised-geometry experiments as well as for the experiments using a realistic Antarctic topography.

Sea level rise contributions from the Pine Island Glacier (PIG) are strongly modulated by the backstress that its floating extension – Pine Island Ice Shelf (PIIS) – exerts on the adjoining grounded ice. The front of PIIS has recently retreated significantly via calving, and satellite and theoretical analyses have suggested further retreat is inevitable. As well as inducing an instantaneous increase in ice flow, retreat of the PIIS front may result in increased ocean melting, by relaxing the topographic barrier to warm ocean water that is currently provided by a prominent seabed ridge. Recently published research (Bradley and others, 2022a) has shown that PIIS may exhibit a strong melting response to calving, with melting close to the PIG grounding line always increasing with ice front retreat. Here, we summarise this research and, additionally, place the results in a glaciological context by comparing the impact of melt-induced and ice-dynamical changes in the ice shelf thinning rate. We find that while PIG is expected to experience rapid acceleration in response to further ice front retreat, the mean instantaneous thinning response is set primarily by changes in melting, rather than ice dynamics. Overall, further ice front retreat is expected to lead to enhanced ice-shelf thinning, with potentially detrimental consequences for ice shelf stability.

Subglacial hydrology is an important component of the ice dynamic system in Antarctica but is challenging to investigate due to the large spatial scales of the catchment systems, the ice thickness, and remote location. Here I discuss key discoveries about Antarctic subglacial hydrology from the Glacier Drainage System (GlaDS) model, including the presence of long, often high-pressure, subglacial channels. These channels pump tens of cubic metres per second of freshwater into ice-shelf cavities and directly affect melt rates at the critical grounding zone regions. Future ice dynamics and ice-shelf cavity models should take subglacial hydrology into account if they are to accurately predict future behaviour of the Antarctic Ice Sheet.

A conceptual model, based on field observations and assumed physics of a perennial firn aquifer near Helheim Glacier (southeast Greenland), is evaluated via steady-state 2-D simulation of liquid water flow and energy transport with phase change. The simulation approach allows natural representation of flow and energy advection and conduction that occur in vertical meltwater recharge through the unsaturated zone and in lateral flow within the saturated aquifer. Agreement between measured and simulated aquifer geometry, temperature, and recharge and discharge rates confirms that the conceptual field-data-based description of the aquifer is consistent with the primary physical processes of groundwater flow, energy transport and phase change. Factors that are found to control simulated aquifer configuration include surface temperature, meltwater recharge rate, residual total-water saturation and capillary fringe thickness. Simulation analyses indicate that the size of perennial firn aquifers depends primarily on recharge rates from surface snowmelt. Results also imply that the recent aquifer expansion, likely due to a warming climate, may eventually produce lakes on the ice-sheet surface that would affect the surface energy balance.

Basal crevasses are macroscopic structural discontinuities at the base of ice sheets and glaciers that arise by fracture. Motivated by observations and by the mechanics of elastic fracture, we hypothesise that spatial variations in basal stress (in the presence of basal water pressure) can promote and localise basal crevassing. We quantify this process in the theoretical context of linear elastic fracture mechanics. We develop a model evaluating the effect of shear-stress variation on the growth of basal crevasses. Our results indicate that sticky patches promote the propagation of basal crevasses, increase their length of propagation into the ice and, under some conditions, give them curved trajectories that incline upstream. A detailed exploration of the parameter space is conducted to gain a better understanding of the conditions under which sticky-patch-induced basal crevassing is expected beneath ice sheets and glaciers.

Mass loss from ice shelves is a strong control on grounding-line dynamics. Here we investigate how calving and submarine melt parameterizations affect steady-state grounding-line positions and their stability. Our results indicate that different calving laws with the same melt parameterization result in more diverse steady-state ice-sheet configurations than different melt parameterizations with the same calving law. We show that the backstress at the grounding line depends on the integrated ice-shelf mass flux. Consequently, ice shelves are most sensitive to high melt rates in the vicinity of their grounding lines. For the same shelf-averaged melt rates, different melt parameterizations can lead to very different ice-shelf configurations and grounding-line positions. If the melt rate depends on the slope of the ice-shelf draft, then the positive feedback between increased melting and steepening of the slope can lead to singular melt rates at the ice-shelf front, producing an apparent lower limit of the shelf front thickness as the ice thickness vanishes over a small boundary layer. Our results illustrate that the evolution of marine ice sheets is highly dependent on ice-shelf mass loss mechanisms, and that existing parameterizations can lead to a wide range of modelled grounding-line behaviours.

We conduct extended versions of the ISMIP6 future climate experiments for the Greenland ice sheet until the year 3000 with the model SICOPOLIS. Beyond 2100, the climate forcing is kept fixed at late-21st-century conditions. For the unabated warming pathway RCP8.5/SSP5-8.5, the ice sheet suffers a severe mass loss, which amounts to ~ 1.8 m SLE (sea-level equivalent) for the 12-experiment mean, and ~ 3.5 m SLE (~ 50% of the entire mass) for the most sensitive experiment. For the reduced emissions pathway RCP2.6/SSP1-2.6, the mass loss is limited to a two-experiment mean of ~ 0.28 m SLE. Climate-change mitigation during the next decades will therefore be an efficient means for limiting the contribution of the Greenland ice sheet to sea-level rise in the long term.

Ice-sheet simulations of Antarctica extending to the year 3000 are analysed to investigate the long-term impacts of 21st-century warming. Climate projections are used as forcing until 2100 and afterwards no climate trend is applied. Fourteen experiments are for the ‘unabated warming’ pathway, and three are for the ‘reduced emissions’ pathway. For the unabated warming path simulations, West Antarctica suffers a much more severe ice loss than East Antarctica. In these cases, the mass loss amounts to an ensemble average of ~3.5 m sea-level equivalent (SLE) by the year 3000 and ~5.3 m for the most sensitive experiment. Four phases of mass loss occur during the collapse of the West Antarctic ice sheet. For the reduced emissions pathway, the mean mass loss is ~0.24 m SLE. By demonstrating that the consequences of the 21st century unabated warming path forcing are large and long term, the results present a different perspective to ISMIP6 (Ice Sheet Model Intercomparison Project for CMIP6). Extended ABUMIP (Antarctic BUttressing Model Intercomparison Project) simulations, assuming sudden and sustained ice-shelf collapse, with and without bedrock rebound, corroborate a negative feedback for ice loss found in previous studies, where bedrock rebound acts to slow the rate of ice loss.

This paper examines the effect of basal topography and strength on the grounding-line position, flux and stability of rapidly-sliding ice streams. It does so by supposing that the buoyancy of the ice stream is small, and of the same order as the longitudinal stress gradient. Making this scaling assumption makes the role of the basal gradient and accumulation rate explicit in the lowest order expression for the ice flux at the grounding line and also provides the transcendental equation for the grounding-line position. It also introduces into the stability condition terms in the basal curvature and accumulation-rate gradient. These expressions revert to well-established expressions in circumstances in which the thickness gradient is large at the grounding line, a result which is shown to be the consequence of the non-linearity of the flow. The behaviour of the grounding-line flux is illustrated for a range of bed topographies and strengths. We show that, when bed topography at a horizontal scale of several tens of ice thicknesses is present, the grounding-line flux and stability have more complex dependencies on bed gradient than that associated with the ‘marine ice-sheet instability hypothesis’, and that unstable grounding-line positions can occur on prograde beds as well as stable positions on retrograde beds.

Bulk directional enhancement factors are determined for axisymmetric (girdle and single-maximum) orientation fabrics using a transversely isotropic grain rheology with an orientation-dependent non-linear grain fluidity. Compared to grain fluidities that are simplified as orientation independent, we find that bulk strain-rate enhancements for intermediate-to-strong axisymmetric fabrics can be up to a factor of ten larger, assuming stress homogenization over the polycrystal scale. Our work thus extends previous results based on simple basal slip (Schmid) grain rheologies to the transversely isotropic rheology, which has implications for large-scale anisotropic ice-flow modelling that relies on a transversely isotropic grain rheology. In order to derive bulk enhancement factors for arbitrary evolving fabrics, we expand the c-axis distribution in terms of a spherical harmonic series, which allows the rheology-required structure tensors through order eight to easily be calculated and provides an alternative to current structure-tensor-based modelling.

Antarctica's ice shelves modulate the grounded ice flow, and weakening of ice shelves due to climate forcing will decrease their ‘buttressing’ effect, causing a response in the grounded ice. While the processes governing ice-shelf weakening are complex, uncertainties in the response of the grounded ice sheet are also difficult to assess. The Antarctic BUttressing Model Intercomparison Project (ABUMIP) compares ice-sheet model responses to decrease in buttressing by investigating the ‘end-member’ scenario of total and sustained loss of ice shelves. Although unrealistic, this scenario enables gauging the sensitivity of an ensemble of 15 ice-sheet models to a total loss of buttressing, hence exhibiting the full potential of marine ice-sheet instability. All models predict that this scenario leads to multi-metre (1–12 m) sea-level rise over 500 years from present day. West Antarctic ice sheet collapse alone leads to a 1.91–5.08 m sea-level rise due to the marine ice-sheet instability. Mass loss rates are a strong function of the sliding/friction law, with plastic laws cause a further destabilization of the Aurora and Wilkes Subglacial Basins, East Antarctica. Improvements to marine ice-sheet models have greatly reduced variability between modelled ice-sheet responses to extreme ice-shelf loss, e.g. compared to the SeaRISE assessments.