Glaciers provide critical ecosystem services, including water resources, biodiversity, cultural value and climate signals. But what makes a glacier a glacier? And when is a glacier no longer a glacier? Different glacier definitions can conflict. While a common definition emphasizes ‘past or present flow’, practical applications involve criteria like observable ice flow, crevassing, minimum thickness, minimum area, surficial features related to hydrology and/or debris cover and/or relative size. Increasingly, glacier inventories apply multiple criteria, acknowledging the nuanced, continuous nature of glacier retreat rather than a binary status. In the context of increasingly melting, shrinking and vanishing glaciers, as glaciologists consider when to declare a glacier lost, disappeared or dead, it is important to explore glacier definitions and their application. Ultimately, the glacier definition applied depends on the specific context, purpose and audience. This also highlights the need for careful language choice, clear communication and localized expertise in considering glacier loss.

Ice sheets and glaciers flow through basal sliding and internal deformation, each governed by physical laws commonly expressed as power-law relations. These formulations include coefficients—the sliding coefficient and rate factor—whose values and units depend on the respective exponents. This dependency complicates the systematic exploration of parameter space, especially in ensemble simulations. To address this, we propose dimensionless formulations of both sliding and flow laws, in which the coefficients are of order unity and decoupled from the exponents. This separation simplifies sensitivity studies and parameter variations. The dimensionless laws are straightforward to implement in existing models; we demonstrate this with the SICOPOLIS ice-sheet model using three test simulations in an idealized set-up. These simulations illustrate that independent variation of exponents and coefficients is feasible and practical, supporting the use of dimensionless laws in efforts to better constrain ice dynamics in past and future climate scenarios.

Ice shelves regulate ice sheet dynamics, with their stability influenced by horizontal flow and vertical flexure. MacAyeal and others (2021) developed the theoretical foundation for a coupled flow-flexure model (the “M21 model”), combining the Shallow Shelf Approximation with thin-beam flexure, providing a computationally efficient tool for studying phenomena like ice shelf rumpling and lake drainage. However, the M21 model relies on proprietary software, is unstable under compressive flow conditions, and does not incorporate fracture processes critical for capturing ice-shelf damage evolution. We present an open-source version of the M21 model addressing these limitations. Using the free Python libraries Firedrake and icepack, we introduce a plastic failure mechanism, effectively limiting bending stresses and thereby stabilizing the model. This enhancement expands the viscous M21 model into a viscoplastic flow-flexure-fracture (3F) framework. We validate the 3F model through test cases replicating key ice shelf phenomena, including marginal rumpling and periodic surface meltwater drainage. By offering this tool as open-source software, we aim to enable broader adoption, with the ultimate aim of representing surface meltwater induced flow-flexure-fracture processes in large-scale ice sheet models.

Recent ice cores from the Allan Hills, a blue ice area in Antarctica, are nearly 3 million years old. These cores extend ice core chronologies, enabling new insight into key climate periods such as the Mid-Pleistocene Transition. The interpretation of these climate records is complex because of the disturbed stratigraphy in this ice. Here, we present a new three-dimensional multitrack electrical conductivity measurement method (3D ECM) to resolve layer structure. We demonstrate this technique on a cumulative 60 m of two large-diameter (241 mm) ice cores, ALHIC2201 and ALHIC2302. Measurements were taken on the upper section of both cores due to better ice core quality in this shallow ice. We find well-defined and dipping layering in both cores, averaging 29° in ALHIC2201 and 69° in ALHIC2302 from horizontal. We observe a slight decrease in dip with depth in both cores, although it only achieves statistical significance in ALHIC2302. We discuss how this new method can be applied to enable accurate, high-resolution multi-proxy record development even in ice cores with steeply dipping layers. 3D ECM improves interpretation of blue ice area cores by providing accurate, non-destructive constraints on stratigraphy.

Sít’ Tlein (Malaspina Glacier), located in Southeast Alaska, has a complex flow history. This piedmont glacier, the largest in the world, is fed by three main tributaries that all exhibit similar flow patterns, yet with varying surge cycles. The piedmont lobe is dramatically reshaped by surges that occur at approximately decadal timescales. By combining historical accounts with modern remote sensing data, we derive a surge history over the past century. We leverage the Stochastic Matrix Factorization, a novel data analysis and interpolation technique, to process and interpret large datasets of glacier surface velocities. A variant of the Principal Component Analysis allows us to uncover spatial and temporal patterns in ice dynamics. We show that Sít’ Tlein displays a wide range of behaviors, spanning quiescence to surge with seasonal to decadal variations of ice flow direction and magnitude. We find that in the lobe, surges dominate the velocity dataset’s variance (spanning 1984–2021), while seasonal variations represent a much smaller part of the variance. However, despite the regular surge pulses, the glacier lobe is far from equilibrium, and widespread retreat of the glacier is inevitable, even without further climate warming.

Glacier ice flux is a key indicator of mass balance; therefore, accurate monitoring of ice dynamics is essential. Satellite-based methods are widely used for glacier velocity measurements but are limited by satellite revisit frequency. This study explores using seismic station internal GPS data to track glacier movement. While less accurate than differential GPS, this method offers high-temporal resolution as a by-product where seismic stations are deployed. Using a seismic station on Borebreen, Svalbard, we show that internal GPS provides reliable surface velocity measurements. When compared with satellite-inferred velocities, the results show a strong correlation, suggesting that the internal GPS, despite its inherent uncertainty, can serve as an efficient tool for glacier velocity monitoring. The high-temporal sampling reveals short-term dynamics of speed-up events and underscores the role of meltwater in driving these processes. This approach augments glacier observation networks at no additional cost.

Fast glacier motion is facilitated by slip at the ice-bed interface. For slip over rigid beds, areas of ice-bed separation (cavities) can exert significant control on slip dynamics. Analytic models of these systems assume that cavities instantaneously adjust to changes in slip and effective pressure forcings, but recent studies indicate transient forcings violate this—and other—underlying assumptions. To assess these incongruities, we conducted novel experiments emulating hard-bedded slip with ice-bed separation under periodic effective pressure transients. We slid an ice-ring over a sinusoidal bed while varying the applied overburden stress to emulate subglacial effective pressure cycles observed in nature and continuously recorded mechanical and geometric system responses. We observed characteristic lags and nonlinearities in system responses that were sensitive to forcing periodicity and trajectory. This gave rise to hysteresis not predicted in analytic theory, which we ascribed to a combination of geometric, thermal and rheologic processes. This framework corroborates other studies of transient glacier slip and we used it to place new constraints on transient phenomena observed in the field. Despite these divergences, average system responses converged toward model predictions, suggesting that analytic theory remains applicable for modeling longer-term behaviors of transiently forced slip with ice-bed separation.

The Ice-sheet and Sea-level System Model (ISSM) provides numerical solutions for ice sheet dynamics using finite element and fine mesh adaption. However, considering ISSM is compatible only with central processing units (CPUs), it has limitations in economizing computational time to explore the linkage between climate forcings and ice dynamics. Although several deep learning emulators using graphic processing units (GPUs) have been proposed to accelerate ice sheet modeling, most of them rely on convolutional neural networks (CNNs) designed for regular grids. Since they are not appropriate for the irregular meshes of ISSM, we use a graph convolutional network (GCN) to replicate the adapted mesh structures of the ISSM. When applied to transient simulations of the Pine Island Glacier (PIG), Antarctica, the GCN successfully reproduces ice thickness and velocity with a correlation coefficient of approximately 0.997, outperforming non-graph models, including fully convolutional network (FCN) and multi-layer perceptron (MLP). Compared to the fixed-resolution approach of the FCN, the flexible-resolution structure of the GCN accurately captures detailed ice dynamics in fast-ice regions. By leveraging 60–100 times faster computational time of the GPU-based GCN emulator, we efficiently examine the impacts of basal melting rates on the ice sheet dynamics in the PIG.

The momentum conservation equation for glacier flow can be described through minimization of an action functional. Several software packages for glacier flow modeling use this action principle in the design of numerical solution procedures. We derive here an equivalent dual action principle for the shallow stream approximation and implement this model using the finite element method. The key feature of the dual action is that the flow law and friction law are both inverted, which changes the character of the non-linearities. This altered character makes it possible to implement numerical solvers for the dual form that work even when the ice thickness or strain rate are exactly equal to zero. Solvers for the primal form typically fail on such input data and require regularization of the problem. This robustness makes it possible to implement iceberg calving in a simple way: the modeler sets the ice thickness to zero in the desired area. We provide several demonstrations and a reference implementation.

There follows the open discussion which took place at the IGS symposium on ‘The Edges of Glaciology’, in July 2023. The discussion was curated by Doug Benn. The time of speaking in minutes and seconds into the Panopto recording is given in bold figures. The recording itself is provided as electronic supplementary material. It has been transcribed and edited by Andrew Fowler, with much (and much-needed) assistance from the participants. Footnotes (mostly references) are editorial intrusions.

The time-evolution of glacier basal motion remains poorly constrained, despite its importance in understanding the response of glaciers to climate warming. Athabasca Glacier provides an ideal site for observing changes in basal motion over long timescales. Studies from the 1960s provide an in situ baseline dataset constraining ice deformation and basal motion. We use two complementary numerical flow models to investigate changes along a well-studied transverse profile and throughout a larger study area. A cross-sectional flow model allows us to calculate transverse englacial velocity fields to simulate modern and historical conditions. We subsequently use a 3-D numerical ice flow model, Icepack, to estimate changes in basal friction by inverting known surface velocities. Our results reproduce observed velocities well using standard values for flow parameters. They show that basal motion declined significantly (30–40%) and this constitutes the majority (50–80%) of the observed decrease in surface velocities. At the same time, basal resistive stress has remained nearly constant and now balances a much larger fraction of the driving stress. The decline in basal motion over multiple decades of climate warming could serve as a stabilizing feedback mechanism, slowing ice transport to lower elevations, and therefore moderating future mass loss rates.

Ice-contact lakes modify glacier geometry and dynamics by shifting the majority of mass loss from the ice surface to the terminus. Lake-terminating glaciers are known to experience greater thinning rates and higher velocities than land-terminating glaciers, but the controls on variability in surface elevation change and ice flow between lake-terminating glaciers in different regions remain poorly explored. We combined existing datasets of glacier velocity, surface elevation change and glacial lake area to characterise the evolution of 352 lake-terminating and land-terminating glaciers within three Himalayan sub-regions between 2000 and 2019. These analyses show that the influence of ice-contact lakes propagates up-glacier across only the lowermost 30% of the hypsometric distribution, even where lakes are well established. We find that ice-contact lakes only affect glacier behaviour when the lakes reach an advanced evolutionary stage; most clearly manifested in the Eastern Himalaya by statistically robust differences in glacier-wide surface elevation change between lake-terminating (–0.68 ± 0.05 m a–1) and land-terminating (–0.54 ± 0.04 m a–1) glaciers. These differences are driven by the presence of a greater number of well-developed ice-contact lakes in the Eastern Himalaya compared to in the Western and Central Himalaya, resulting from greater mass loss rates to date.

Upernavik Isstrøm, the largest contributor to sea-level rise in northwest Greenland, has experienced complex and contrasting ice-flow-speed changes across its five outlets over the last two decades. In this study, we present a detailed remote-sensing analysis of the ice dynamics at Upernavik's outlets from 2000 to 2021 to evaluate the details of these changes. Previous research suggested that the presence or absence of floating ice tongues strongly influences Upernavik's ice dynamics. We use several lines of evidence to document the presence of floating ice tongues, and find that, while several outlets experienced ice-tongue formation and/or loss during the study period, these changes do not explain observed fluctuations in ice-flow velocity. Further exploration of ice-dynamic forcings using a flowline model suggests that changes in basal slipperiness near the terminus have a strong impact on upstream ice dynamics and can explain the velocity variations. Our results suggest that speed fluctuations at Upernavik's outlets may be seasonally and interannually controlled by bed conditions near the terminus, and highlight the need for further research on the influence of basal conditions on complex tidewater glacier dynamics.

To better constrain meltwater transport and ice viscosity in temperate glaciers, particularly in ice stream shear margins, we use a custom permeameter to study the untested model relationship between the permeability of temperate ice and its liquid water content. The permeability of lab-made ice of two mean grain diameters (1.8 and 4.2 mm) is measured, and water content is controlled with the ice salinity and measured calorimetrically. Fluorescein dye is added to through-flowing, chilled water to highlight flow pathways through the ice after experiments. As predicted by a simple model, permeability increases with approximately the square of the water content and by about three orders of magnitude across water contents of 0.1–4.4%. However, permeability values are less than those of the model by average factors of 2.6 and 4.1 for the finer and coarser ice, respectively. This discrepancy is likely due to tortuous, truncated or air-clogged veins. The order-of-magnitude agreement between measured and modeled values may indicate that reduced permeability from these factors is nearly compensated by preferential flow in oversized veins that are isolated or arborescent. Both kinds of preferred flow pathways are observed but the latter only in fine-grained ice at water contents > 2%.

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.

We investigate unusual discontinuous glacier motion on Thompson Glacier, Umingmat Nunaat, Arctic Canada, using synthetic aperture radar (SAR) images and ice-flow modeling. A novel intensity-rescaling scheme is developed to reduce errors in high-resolution speckle tracking, resulting in a ~25% improvement in accuracy. Interferometric SAR (InSAR) and speckle tracking using high resolution RADARSAT-2 data indicate velocity discontinuities of up to 1 cm d−1 across deep and longitudinally extensive supraglacial channels on Thompson Glacier. We use a cross-sectional finite-element ice-flow model to determine the conditions under which velocity discontinuities of the observed magnitude and signature are possible. The modeling suggests that discontinuous motion across (long and straight) supraglacial channels can occur without ice fracture and under a wide variety of glacier thermal structures, including in fully temperate glaciers. Despite the wide range of conditions conducive to discontinuous motion, the form we observe requires that the associated channels be deep, longitudinally extensive and located in regions of lateral shearing. We speculate that these combined conditions are rare except on polythermal glaciers, where drainage features such as moulins are comparatively scarce and lower deformation rates allow channels to incise consistently and persist over many years.

Bed topography is a critical parameter for determining the modern-day and future dynamics of ice sheets and their outlet glaciers. This is because the topography controls the state of stress for glaciers. At glacier termini, topography can influence the timing of terminus retreat by controlling access to warm ocean waters and/or by influencing the ability of a glacier terminus to retreat over bed bumps (moraines). Inland from the terminus, the topography can also influence where glacier retreat and thinning can stabilize. In part, this is because of knickpoints in bed topography created through glacial erosion that may influence the extent to which thinning can diffuse inland for an individual glacier and thus, the timing and magnitude of long-term mass loss. Here we provide a review of the current literature on these topics. While much of the reviewed literature assumes that topography is stable on relevant timescales to humans, new research suggests that topography may change much faster than previously thought and this further complicates our ability to project future outlet glacier change.

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.