We present the first simulations of Jakobshavn Isbrae (Sermeq Kujalleq), west Greenland, using a 3D Stokes calving model that permits unrestricted advance and retreat. Using the position-based crevasse-depth calving law, the model is applied to simulate the calving dynamics of 2016–2017 season when Jakobshavn Isbrae is assumed to be stable because of the presence of a strong proglacial ice mélange. The calving law needs to be adjusted to avoid an underestimation of calving, but once adjusted the calving model simulates seasonal calving dynamics that reflect observed calving-driven retreat very well. We find that a crevasse penetration threshold of 94.5% best matches observations from satellite imagery. Additional, 2-year transient simulations show that although ice mélange is essential to the glacier's winter readvance, when removed, the glacier only retreats a couple of kilometres before reaching a stable position. While the backstress provided by the ice mélange allows the glacier to advance beyond this point, the retreated terminus position is determined by a combination of bed geometry and glacier dynamics. Ultimately, while the ice mélange allows winter readvance, cessation of the well-documented rapid retreat of Jakobshavn Isbrae will be influenced by the bed geometry.

Jostedalsbreen in western Norway is the mainland Europe's largest ice cap and a complex system of more than 80 glaciers. While observational records indicate a significant sensitivity to climate fluctuations, knowledge about ice-cap wide spatiotemporal mass changes and their drivers remain sparse. Here, we quantify the surface mass balance (SMB) of Jostedalsbreen from 1960 to 2020 using a temperature-index model within a Bayesian framework. We assimilate seasonal glaciological SMB to constrain accumulation and ablation, and geodetic mass balance to adjust model parameters for each glacier individually. Overall, we find that Jostedalsbreen has experienced a small mass loss of −0.07 m w.e. a−1 (−0.21 to +0.08 m w.e. a−1), but with substantial spatiotemporal variability. Our results suggest that winter SMB variations were the main control on annual SMB between 1960 and 2000, while increasingly negative summer SMB is responsible for substantial mass losses after 2000. Spatial variations in SMB between glaciers or regions of the ice cap are likely associated with local topography and its effect on orographic precipitation. We advocate for models to leverage the growing availability of observational resources to improve SMB predictions. We demonstrate an approach that incorporates complementary datasets, while addressing their inherent uncertainties, to constrain models and provide robust estimates of spatiotemporal SMB and associated uncertainties.

We present a new model for understanding ice cliff dynamics within a debris-covered glacier ablation zone. This simple energy-balance model incorporates a moving frame of reference, made necessary by the melt of the surrounding debris-covered ice. In so doing, this also formalises how different types of field measurements can be utilised and compared. Our predictions include showing: ice cliffs can endogenously select their own slope angles; that there should be an indifference between illuminated north- and south-facing ice cliff slopes; that ice cliffs grow steeper with thicker debris layers; that ice cliffs cannot stably exist below a certain critical debris thickness and that some modelling of ice cliffs (when not incorporating the moving frame) may incorrectly estimate ice mass losses. All of our results are produced using parametrisations from Baltoro Glacier, Karakoram.

Scenario–neutral methods are commonly used to rapidly compare system responses to changes in climate. Using glacier mass balance as a system response, we present a bottom-up, scenario–neutral method as an effective tool for preliminary and overview studies on glacier sensitivity and a complementary approach to traditional top–down methods. The method's main characteristic is its visual result: two–dimensional response surfaces depicting glacier mass balance. Their axes represent perturbations in temperature and precipitation relative to a baseline. The simplicity of our approach makes it applicable to all global glaciers. As a proof–of–concept, the Open Global Glacier Model (OGGM) is used to perform a scenario–neutral glacier sensitivity analysis for four glaciers. In addition, the integration with a top–down approach is demonstrated by overlaying temperature and precipitation from four Coupled Model Intercomparison Project Phase 6 (CMIP6) models, under four Shared Socioeconomic Pathways (SSP). Finally, the benefits of the method are discussed for decision–making and science communication. Assessing results shows that overall, this scenario–neutral method can provide useful information for the research of climate change impact on glacier mass, from aiding study design to science communication.

We present a new map of bed topography and ice thickness together with a corresponding ice volume estimate representative of the years ~2010 for all Scandinavian ice caps and glaciers. Starting from surface observations, we invert for ice thickness by iteratively running an innovative ice dynamics model on a distributed grid and updating bed topography until modelled and observed glacier dynamics as represented by their rate of surface elevation change (dh/dt) fields align. The ice flow model used is the instructed glacier model (Jouvet and Cordonnier, 2023, Journal of Glaciology 1–15), a generic physics-informed deep-learning emulator that models higher-order ice flow with high-computational efficiency. We calibrate the modelled thicknesses against >11 000 ice thickness observations, resulting in a final ice volume estimate of 302.7 km3 for Norway, 18.4 km3 for Sweden and 321.1 km3 for the whole of Scandinavia with an error estimate of ~$\pm 11\%$. The validation statistics computed indicate good agreement between modelled and observed thicknesses (RMSE = 55 m, Pearson's r = 0.87, bias = 0.8 m), outperforming all other ice thickness maps available for the region. The modelled bed shapes thus provide unprecedented detail in the subglacial topography, especially for ice caps where we produce the first maps that show ice-dynamically realistic flow features.

One fifth of Earth's volcanoes are covered by snow or ice and many have active geothermal systems that interact with the overlying ice. These glaciovolcanic interactions can melt voids into glaciers, and are subject to controls exerted by ice dynamics and geothermal heat output. Glaciovolcanic voids have been observed to form prior to volcanic eruptions, which raised concerns when such features were discovered within Job Glacier on Qw̓elqw̓elústen (Mount Meager Volcanic Complex), British Columbia, Canada. In this study we model the formation, evolution, and steady-state morphology of glaciovolcanic voids using analytical and numerical models. Analytical steady-state void geometries show cave height limited to one quarter of the ice thickness, while numerical model results suggest the void height h scales with ice thickness H and geothermal heat flux $\dot {Q}$ as $h/H = a H^b \dot {Q}^c$, with exponents b = −n/2 and c = 1/2 where n is the creep exponent. Applying this scaling to the glaciovolcanic voids within Job Glacier suggests the potential for total geothermal heat flux in excess of 10 MW. Our results show that relative changes in ice thickness are more influential in glaciovolcanic void formation and evolution than relative changes in geothermal heat flux.

Tropical Andean glaciers are highly sensitive to climate change and are impacted by the El Niño Southern Oscillation (ENSO). However, glaciological data are scarce, meaning that there are substantial knowledge gaps in the response of Andean glaciers to future anthropogenic and ENSO forcing and these are crucial to address, as glaciers represent a key water source for downstream populations and ecosystems. Here we integrated data from glaciological field studies, remote sensing, statistical analysis and glacier modelling to analyse the response of two Andean glaciers (Zongo and Shallap) to ENSO and their potential sensitivity to a range of climate forcing scenarios. Both glaciers retreated and experienced increasingly negative mass balance between the 1990s and the 2010s and responded strongly and rapidly to contemporary ENSO forcing, although this relationship evolved over time. Sensitivity experiments demonstrate that Shallap and Zongo are highly sensitive to ENSO forcing scenarios and the combination of ENSO and climate warming can cause rapid ice loss under the most extreme scenarios. Results also demonstrate the strong sensitivity of both glaciers to changes in the equilibrium line altitude, whereby rapid ice loss occurred when melt extended into present-day accumulation areas.

Subglacial hydrology models struggle to reproduce seasonal drainage patterns that are consistent with observed subglacial water pressures and surface velocities. We modify the standard sheet-flow parameterization within a coupled sheet–channel subglacial drainage model to smoothly transition between laminar and turbulent flow based on the locally computed Reynolds number in a physically consistent way (the ‘transition’ model). We compare the transition model to standard laminar and turbulent models to assess the role of the sheet-flow parameterization in reconciling observed and modelled water pressures under idealized and realistic forcing. Relative to the turbulent model, the laminar and transition models improve seasonal simulations by increasing winter water pressure and producing a more prominent late-summer water pressure minimum. In contrast to the laminar model, the transition model remains consistent with its own internal assumptions across all flow regimes. Based on the internal consistency of the transition model and its improved performance relative to the standard turbulent model, we recommend its use for transient simulations of subglacial drainage.

We investigate the physical basis of the crevasse-depth (CD) calving law by analysing relationships between glaciological stresses and calving behaviour at Sermeq Kujalleq (Store Glacier), Greenland. Our observations and model simulations show that the glacier has a stable position defined by a compressive arch between lateral pinning points. Ice advance beyond the arch results in calving back to the stable position; conversely, if melt-undercutting forces the ice front behind the stable position, it readvances because ice velocities exceed subaqueous melt rates. This behaviour is typical of self-organising criticality, in which the stable ice-front position acts as an attractor between unstable super-critical and sub-critical regimes. This perspective provides strong support for a ‘position-law’ approach to modelling calving at Sermeq Kujalleq, because any calving ‘rate’ is simply a by-product of how quickly ice is delivered to the critical point. The CD calving law predicts ice-front position from the penetration of surface and basal crevasse fields, and accurately simulates super-critical calving back to the compressive arch and melt-driven calving into the sub-critical zone. The CD calving law reflects the glaciological controls on calving at Sermeq Kujalleq and exhibits considerable skill in simulating its mean position and seasonal fluctuations.

Both submarine melt and calving are important for the overall mass balance of marine-terminating glaciers, but uncertainty is rife with regards to the magnitude of the processes. Modelling allows for these processes to be investigated without the need to visit inaccessible ice marginal zones. This study looks at the impact of different submarine melt and sea-ice back pressure scenarios on modelled calving activity and dynamics at Kronebreen, Svalbard, by running separate summer and winter simulations with various submarine melt parameterisations and sea-ice characteristics. It is found that submarine melt is an important driver of seasonal variation in modelled glacier dynamics and calving activity, with the choice of sliding law also exerting a significant influence on results.

The complex topography and size of High Mountain Asia (HMA) result in large differences in glacier mass-balance variability and climate sensitivity. Current understanding of these sensitivities is limited by simplifications in past studies’ model structure. This study overcomes this limitation by using a mass-balance model to investigate the climatic mass-balance variability and climate sensitivity of 16 glaciers covering major mountain ranges in HMA. Generally, glaciers in the southeast have higher mass turnover while glaciers at the margins of HMA show higher interannual mass-balance variability. All glaciers are most sensitive to temperature perturbations in summer. The climatic mass balance of 15 glaciers is most sensitive to precipitation perturbations in summer or spring and summer, even if the seasonal accumulation peak is not in summer. Only one glacier's mass balance (Chhota Shigri Glacier) is most sensitive to precipitation perturbations in winter. Glaciers with high mass turnover and high summer-precipitation ratio are more sensitive to temperature perturbations. Sensitivity experiments reveal that besides the non-linearity of mass-balance temperature sensitivity, mass-balance precipitation sensitivity is non-linear as well. Furthermore, resolving the diurnal cycle of albedo, (re)freezing and the differentiation between liquid and solid precipitation are important to assess climate sensitivity of glaciers in HMA.

Glaciological mass-balance measurements have been the backbone of internationally coordinated glacier monitoring. The resulting annual observations have been used to understand glacier reactions to climate change, and to assess both regional and global glacier mass changes and related contributions to runoff and sea-level rise. However, the comparability of annual observations is hampered by differences in survey periods and mass-balance amplitudes between glaciers, regions and hemispheres. This study presents a simple approach to temporally downscale glaciological mass balance using seasonal observations and sine functions. The proposed analytical model allows reconstruction of the seasonal course of glacier mass balance at weekly to monthly resolution from only annual or seasonal observations. Strengths and limitations of this analytical approach are discussed and compared with results from numerical mass-balance modelling. Potential applications include seasonal corrections of glaciological and geodetic observations and comparisons to monthly results from spaceborne gravimetry and altimetry.

Our limited knowledge of the climate prevailing over Europe during former glaciations is the main obstacle to reconstruct the past evolution of the ice coverage over the Alps by numerical modelling. To address this challenge, we perform a two-step modelling approach: First, a regional climate model is used to downscale the time slice simulations of a global earth system model in high resolution, leading to climate snapshots during the Last Glacial Maximum (LGM) and the Marine Isotope Stage 4 (MIS4). Second, we combine these snapshots and a climate signal proxy to build a transient climate over the last glacial period and force the Parallel Ice Sheet Model to simulate the dynamical evolution of glaciers in the Alps. The results show that the extent of modelled glaciers during the LGM agrees with several independent key geological imprints, including moraine-based maximal reconstructed glacial extents, known ice transfluences and trajectories of erratic boulders of known origin and deposition. Our results highlight the benefit of multiphysical coupled climate and glacier transient modelling over simpler approaches to help reconstruct paleo glacier fluctuations in agreement with traces they have left on the landscape.

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.

Hydrologic pathways beneath ice sheets and glaciers play an important role in regulating ice flow. Antarctica has experienced, and will continue to experience, changes in ice dynamics and geometry, but the associated changes in subglacial hydrology have received less attention. Here, we use the GlaDS subglacial hydrology model to examine drainage evolution beneath an idealised Antarctic glacier in response to steepening ice surface slopes, accelerating ice velocities and subglacial lake drainages. Ice surface slope changes exerted a dominant influence, redirecting basal water to different outlet locations and substantially increasing channelised discharge crossing the grounding line. Faster ice velocities had comparatively negligible effects. Subglacial lake drainage results indicated that lake refilling times play a key role in drainage system evolution, with lake flux more readily accommodated following shorter refilling times. Our findings are significant for vulnerable Antarctic regions currently experiencing dynamic thinning since subglacial water re-routing could destabilise ice shelves through enhanced sub-shelf melting, potentially hastening irreversible retreat. These changes could also affect subglacial lake activity. We, therefore, emphasise that including a nuanced and complex representation of subglacial hydrology in ice-sheet models could provide critical information on the timing and magnitude of sea-level change contributions from Antarctica.

The uncertainty of glacier change projections is largely influenced by glacier models. In this study, we focus on temperature-index mass-balance (MB) models and their calibration. Using the Open Global Glacier Model (OGGM), we examine the influence of different surface-type dependent degree-day factors, temporal climate resolutions (daily, monthly) and downscaling options (temperature lapse rates, temperature and precipitation corrections) for 88 glaciers with in-situ observations. Our findings indicate that higher spatial and temporal resolution observations enhance MB gradient representation due to an improved calibration. The addition of surface-type distinction in the model also improves MB gradients, but the lack of independent observations limits our ability to demonstrate the added value of increased model complexity. Some model choices have systematic effects, for example weaker temperature lapse rates result in smaller projected glaciers. However, we often find counter balancing effects, such as the sensitivity to different degree-day factors for snow, firn and ice, which depends on how the glacier accumulation area ratio changes in the future. Similarly, using daily versus monthly climate data can affect glaciers differently depending on the shifting balance between melt and solid precipitation thresholds. Our study highlights the importance of considering minor model design differences to predict future glacier volumes and runoff accurately.

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.

Glacier-bed characteristics that are poorly known and modeled are important in projected sea-level rise from ice-sheet changes under strong warming, especially in the Thwaites Glacier drainage of West Antarctica. Ocean warming may induce ice-shelf thinning or loss, or thinning of ice in estuarine zones, reducing backstress on grounded ice. Models indicate that, in response, more-nearly-plastic beds favor faster ice loss by causing larger flow acceleration, but more-nearly-viscous beds favor localized near-coastal thinning that could speed grounding-zone retreat into interior basins where marine-ice-sheet instability or cliff instability could develop and cause very rapid ice loss. Interpretation of available data indicates that the bed is spatially mosaicked, with both viscous and plastic regions. Flow against bedrock topography removes plastic lubricating tills, exposing bedrock that is eroded on up-glacier sides of obstacles to form moats with exposed bedrock tails extending downglacier adjacent to lee-side soft-till bedforms. Flow against topography also generates high-ice-pressure zones that prevent inflow of lubricating water over distances that scale with the obstacle size. Extending existing observations to sufficiently large regions, and developing models assimilating such data at the appropriate scale, present large, important research challenges that must be met to reliably project future forced sea-level rise.

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.