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.

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

Over half of the recent mass loss from the Greenland ice sheet, and its associated contribution to global sea level rise, can be attributed to increased surface meltwater runoff, with the remainder a result of dynamical processes such as calving and ice discharge. It is therefore important to quantify the distribution of melting on the ice sheet if we are to adequately understand past ice sheet change and make predictions for the future. In this article, we present a novel semi-empirical approach for characterising ice sheet surface conditions using high-resolution synthetic aperture radar (SAR) backscatter data from the Sentinel-1 satellite. We apply a state-space model to nine sites within North-East Greenland to identify changes in SAR backscatter, and we attribute these to different surface types with reference to optical satellite imagery and meteorological data. A set of decision-making rules for labelling ice sheet melting states are determined based on this analysis and subsequently applied to previously unseen sites. We show that our method performs well in (1) recognising some of the ice sheet surface types such as snow and dark ice and (2) determining whether the surface is melting or not melting. Sentinel-1 SAR data are of high spatial resolution; thus, in developing a method to identify the state of the surface from these data, we improve our capability to understand the variation of ice sheet melting across time and space.

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.

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.

Ground penetrating radar (GPR) has been extensively used in glaciology to infer glacier's ice thickness, liquid water content, water drainage pathways, and other properties. The interpretation of such GPR data is not always straightforward and for temperate glaciers, the signal is often affected by strong scattering and attenuation. It has often been suggested that such effects originate from englacial water inclusions, since water and ice have a large contrast in their di-electric permittivity. To investigate such effects quantitatively, we perform an extensive numerical modeling study of GPR signals. By exploring how different liquid water contents (LWC) and water-inclusions size affect the GPR signal, we show that their effects are much larger than the potential presence of a wet snowpack or a heterogeneous distribution of ice permittivity. In particularly, we show that the presence of such water inclusions is a necessary and sufficient condition for reproducing the typical characteristics of GPR data acquired in the field. Further, we find that for 25 MHz GPR antennas, a bulk LWC $\gtrsim$ 0.2%, associated with decimeters-scale water inclusions already limits bedrock detectability for ice thicknesses $\gtrsim 100$ m. Since these values are typical for Alpine glaciers, they clarify why the quality of GPR data is often poor in such environments.

We describe the annual pattern of frontal ablation driven by submarine melting mechanisms at the Hansbreen terminus: these are reflected in the intensity and spatial distribution of calving events. Analysis of time-lapse images of the Hansbreen front in conjunction with oceanographic and meteorological data shows that calving intensity is driven primarily by seawater temperature. Regression analysis also highlights the importance of air temperature, which we take to be a proxy for surface ablation and subglacial discharge. This, combined with seasonal changes in ice cliff tortuosity and the increasing significance of wave motion outside the ablation season, enabled us to determine seasonal changes in the mechanisms of ice cliff undercutting by submarine melting. While submarine melting controlled by estuarine circulation primarily drives frontal ablation in summer, wave-driven melting at the waterline is more important outside the ablation season. During winter, ice cliff undercutting by melting is suspended by low seawater temperature, negligible subglacial water discharge and sea-ice cover. The most intense frontal ablation, recorded in summer, was related to higher sea temperature and vigorous estuarine circulation.

Active subglacial lakes provide a rare glimpse of the subglacial environment and hydrological processes at play. Several studies contributed to establishing active subglacial lake inventories and document lake drainage and connection, but few focused on the period between lake drainage when the melt production and transport contribute to the refilling of these lakes. In this study, we employ high-resolution CryoSat-2 altimetry data from 2010 to 2021 to compile an inventory of recharging lakes across Antarctica. We extract recharge rates from these lakes, which serve as a lower limit on subglacial melt production. These recharge rates are compared against predictions obtained by routing modelled subglacial meltwater at the ice-sheet's base. Our findings indicate that modelled recharge rates are consistent with observations in all but one of the investigated lakes, providing a lower bound on geothermal heat fluxes. Lake Cook E2 displays recharge rates far exceeding predictions, indicating that processes are taking place that are currently unaccounted for. Considering recharge in hydrologically connected lake networks instead of individually provides a stricter constraint on melt production. Recharge rates extracted from the Thwaites Lake system suggest that subglacial melt production has been underestimated.

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.

We recently reported on the radio-frequency attenuation length of cold polar ice at Summit Station, Greenland, based on bi-static radar measurements of radio-frequency bedrock echo strengths taken during the summer of 2021. Those data also allow studies of (a) the relative contributions of coherent (such as discrete internal conducting layers with sub-centimeter transverse scale) vs incoherent (e.g. bulk volumetric) scattering, (b) the magnitude of internal layer reflection coefficients, (c) limits on signal propagation velocity asymmetries (‘birefringence’) and (d) limits on signal dispersion in-ice over a bandwidth of ~100 MHz. We find that (1) attenuation lengths approach 1 km in our band, (2) after averaging 10 000 echo triggers, reflected signals observable over the thermal floor (to depths of ~1500 m) are consistent with being entirely coherent, (3) internal layer reflectivities are ≈–60$\to$–70 dB, (4) birefringent effects for vertically propagating signals are smaller by an order of magnitude relative to South Pole and (5) within our experimental limits, glacial ice is non-dispersive over the frequency band relevant for neutrino detection experiments.

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.

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.

The hypothesis that ice-sheet evolution is only controlled by the long-term non-Newtonian viscous behavior of ice has been challenged by observations indicating that effects like brittle failure, stick-slip sliding, tides and wave action may affect ice-sheet evolution on sub-daily timescales. Over these timescales, the quasi-static-creep approximation is no longer appropriate and elastic effects become important. Simulating elastic effects in ice-sheet models over relevant timescales, however, remains challenging. Here, we show that by including a visco-elastic rheology and reintroducing the oft neglected acceleration term back into the ice-sheet stress balance, we can create a visco-elastic system where the velocity is locally determined and information propagates at the elastic wave speed. Crucially, the elastic wave speed can be treated like an adjustable parameter and set to any value to reproduce a range of phenomena, provided the wave speed is large compared to the viscous velocity. We illustrate the system using three examples. The first two examples demonstrate that the system converges to the steady-state viscous and elastic limits. The third example examines ice-shelf rifting and iceberg calving. This final example hints at the utility of the visco-elastic formulation in treating both long-term evolution and short-term environmental effects.

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.

We present a method for tracking radio-tagged pebbles and cobbles through subglacial meltwater channels under shallow temperate glaciers. Natural particles tagged with active radio transmitters were injected directly into a large subglacial channel 300 m up-glacier from the terminus of the Glacier d'Otemma, Switzerland. A roving antenna was developed to localise tagged particles planimetrically in subglacial and proglacial channel reaches (350 and 150 m long, respectively) using a probabilistic technique, delivering records of the change in particle location and transport distance over time with uncertainty. The roving antenna had a ±5−15 m planimetric precision, a 75% particle localisation rate and operated at a maximum ice depth of 47 m. Additionally, stationary supraglacial and proglacial antennas continuously monitored the passage of tagged particles through consecutive reaches of the channel, constraining the timing of particle transport events. The proglacial antenna system had a 98.1% detection rate and was operational to 0.89 m water depth during testing. Roving and stationary antenna records were combined to create a transport distance model for each particle, which may be used in conjunction with hydraulic data to investigate the kinematics of particle motion. When applied at scale in future studies, this method may be used to reveal the mechanisms and timescales of coarse sediment export from Alpine glaciers.

Ice-crystal fabric can induce mechanical anisotropy that significantly affects flow, but ice-flow models generally do not include fabric development or its effect upon flow. Here, we incorporate a new spectral expansion of fabric, and more complete description of its evolution, into the ice-flow model Elmer/Ice. This approach allows us to model the effect of both lattice rotation and migration recrystallization on large-scale ice flow. The fabric evolution is coupled to flow using an unapproximated non-linear orthotropic rheology that better describes deformation when the stress and fabric states are misaligned. These improvements are most relevant for simulating dynamically interesting areas, where recrystallization can be important, tuning data are scarce and rapid flow can lead to misalignment between stress and fabric. We validate the model by comparing simulated fabric to ice-core and phase-sensitive radar measurements on a transect across Dome C, East Antarctica. With appropriately tuned rates for recrystallization, the model is able to reproduce observations of fabric. However, these tuned rates differ from those previously derived from laboratory experiments, suggesting a need to better understand how recrystallization acts differently in the laboratory compared to natural settings.

Stable water isotope records of six firn cores retrieved from two adjacent plateaus on the northern Antarctic Peninsula between 2014 and 2016 are presented and investigated for their connections with firn-core glacio-chemical data, meteorological records and modelling results. Average annual accumulation rates of 2500 kg m−2 a−1 largely reduce the modification of isotopic signals in the snowpack by post-depositional processes, allowing excellent signal preservation in space and time. Comparison of firn-core and ECHAM6-wiso modelled δ18O and d-excess records reveals a large agreement on annual and sub-annual scales, suggesting firn-core stable water isotopes to be representative of specific synoptic situations. The six firn cores exhibit highly similar isotopic patterns in the overlapping period (2013), which seem to be related to temporal changes in moisture sources rather than local near-surface air temperatures. Backward trajectories calculated with the HYSPLIT model suggest that prominent δ18O minima in 2013 associated with elevated sea salt concentrations are related to long-range moisture transport dominated by westerly winds during positive SAM phases. In contrast, a broad δ18O maximum in the same year accompanied by increased concentrations of black carbon and mineral dust corresponds to the advection of more locally derived moisture with northerly flow components (South America) when the SAM is negative.

A major consideration for maritime activity in the Southern Hemisphere is the northern limit of icebergs, or the Southern Ocean Limit Of Known Ice (SOLOKI). This analysis of historical reports of icebergs during Southern Hemisphere voyages from 1687 to 1933 provides a basis for examination of their geographical and chronological occurrence during ~250 years. The analyses use tabulated data from 742 voyages and other reports from many sources, some including first-person descriptions. While these data are dependent on icebergs being reported by mariners, as well as the variable frequency of voyages, they demonstrate distinct periods of exceptional frequency of icebergs occurring in certain localities, particularly the far South Atlantic. Based upon historical records the evidence suggests unprecedented numbers of icebergs were present in southern shipping channels in the 1890s. When these historical observations are combined with modern iceberg drift trajectories, their possible origin can be elucidated. Owing to the numbers of icebergs seen and their geographical spread, our results suggest that this was possibly the largest near-synchronous calvings in the last 300 years, and the northernmost extent of the SOLOKI.

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.

We present seismic measurements of the firn column at Korff Ice Rise, West Antarctica, including measurements of compressional-wave velocity and attenuation. We describe a modified spectral-ratio method of measuring the seismic quality factor (Q) based on analysis of diving waves, which, combined with a stochastic method of error propagation, enables us to characterise the attenuative structure of firn in greater detail than has previously been possible. Q increases from 56 ± 23 in the uppermost 12 m to 570 ± 450 between 55 and 77 m depth. We corroborate our method with consistent measurements obtained via primary reflection, multiple, source ghost, and critically refracted waves. Using the primary reflection and its ghost, we find Q = 53 ± 20 in the uppermost 20 m of firn. From the critical refraction, we find Q = 640 ± 400 at 90 m depth. Our method aids the understanding of the seismic structure of firn and benefits characterisation of deeper glaciological targets, providing an alternative means of correcting seismic reflection amplitudes in cases where conventional methods of Q correction may be impossible.