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.

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.

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.

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.

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 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.

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.

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.

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 developed a novel laser melting sampler (LMS) for ice cores to measure the stable water isotope ratios (δ18O and δD) as temperature proxies at sub-centimeter depth resolutions. In this LMS system, a 2 mm diameter movable evacuation nozzle holds an optical fiber through which a laser beam irradiates the ice core. The movable nozzle intrudes into the ice core, the laser radiation meanwhile melts the ice cylindrically, and the meltwater is pumped away simultaneously through the same nozzle and transferred to a vial for analysis. To avoid isotopic fractionation of the ice through vaporization, the laser power is adjusted to ensure that the temperature of the meltwater is always kept well below its boiling point. A segment of a Dome Fuji shallow ice core (Antarctica), using the LMS, was then demonstrated to have been discretely sampled with a depth resolution as small as 3 mm: subsequent analysis of δ18O, δD, and deuterium excess (d) was consistent with results obtained by hand segmentation within measurement uncertainties. With system software to control sampling resolution, the LMS will enable us to identify temperature variations that may be detectable only at sub-centimeter resolutions in ice cores.

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.

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.

Ice records provide a qualitative rather than a quantitative indication of the trend of climate change. Using the bulk aerodynamic method and degree day model, this study quantified ice mass loss attributable to sublimation/evaporation (S/E) and meltwater on the basis of integrated observations (1960–2006) of glacier-related and atmospheric variables in the northeastern Tibetan Plateau. During 1961–2005, the average annual mass loss in the ice core was 95.33 ± 20.56 mm w.e. (minimum: 78.97 mm w.e. in 1967, maximum: 146.67 mm w.e. in 2001), while the average ratio of the revised annual ice accumulation was 21.2 ± 7.7% (minimum: 11.0% in 1992, maximum 44.8% in 2000). A quantitative formula expressing the relationship between S/E and air temperature at the monthly scale was established, which could be extended to estimation of S/E changes of other glaciers in other regions. The elevation effect on alpine precipitation determined using revised ice accumulation and instrumental data was found remarkable. This work established a method for quantitative assessment of the temporal variation in ice core mass loss, and advanced the reconstruction of long-term precipitation at high elevations. Importantly, the formula established for reconstruction of S/E from temperature time series data could be used in other regions.

We present the surface mass balance (SMB) dataset from Vostok Station's accumulation stake farms which provide the longest instrumental record of its kind obtained with a uniform technique in central Antarctica over the last 53 years. The snow build-up values at individual stakes demonstrate a strong random scatter related to the interaction of wind-driven snow with snow micro-relief. Because of this depositional noise, the signal-to-noise ratio (SNR) in individual SMB time series derived at single points (from stakes, snow pits or firn cores) is as low as 0.045. Averaging the data over the whole stake farm increases the SNR to 2.3 and thus allows us to investigate reliably the climatic variability of the SMB. Since 1970, the average snow accumulation rate at Vostok has been 22.5 ± 1.3 kg m−2 yr−1. Our data suggest an overall increase of the SMB during the observation period accompanied by a significant decadal variability. The main driver of this variability is local air temperature with an SMB temperature sensitivity of 2.4 ± 0.2 kg m−2 yr−1 K−1 (11 ± 2% K−1). A covariation between the Vostok SMB and the Southern Oscillation Index is also observed.

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.

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.

We present the first systematic inventory of surge-type glaciers for the whole of Greenland compiled from published datasets and multitemporal satellite images and digital elevation models. The inventory allows us to define the spatial and climatic distribution of surge-type glaciers and to analyse the timing of surges from 1985 to 2019. We identified 274 surge-type glaciers, an increase of 37% compared to previous work. Mapping surge-type glacier distribution by temperature and precipitation variables derived from ERA5-Land reanalysis data shows that the west and east clusters occur in well-defined climatic envelopes. Analysis of the timing of surge active phases during the periods ~1985 to 2000 (T1) and ~2000 to 2019 (T2) suggests that overall surge activity is similar in T1 and T2, but there appears to be a reduction in surging in the west cluster in T2. Our climate analysis shows a coincident increase in mean annual and mean winter air temperature between T1 and T2. We suggest that as glaciers thin under current warming, some surge-type glaciers in the west cluster may be being prevented from surging due to (1) their inability to build-up sufficient mass and (2) a switch from a polythermal to a largely cold-based thermal regime.

Glaciers in the Russian High Arctic have undergone accelerated mass loss due to atmospheric and oceanic warming in the Barents–Kara Sea region. Most studies have concentrated on the western Barents–Kara sector, despite evidence of accelerating mass loss as far east as Severnaya Zemlya. However, long-term trends in glacier change on Severnaya Zemlya are largely unknown and this record may be complicated by surge-type glaciers. Here, we present a long-term assessment of glacier change (1965–2021) on Severnaya Zemlya and a new inventory of surge-type glaciers using declassified spy-satellite photography (KH-7/9 Hexagon) and optical satellite imagery (ASTER, Sentinel-2A, Landsat-4/5 TM and 8 OLI). Glacier area reduced from 17 053 km2 in 1965 to 16 275 in 2021 (−5%; mean: −18%, max: −100%), with areal shrinkage most pronounced at land-terminating glaciers on southern Severnaya Zemlya, where there is a recent (post-2010s) increase in summer atmospheric temperatures. We find that surging may be more widespread than previously thought, with three glaciers classified confirmed as surge-type, eight as likely to have surged and nine as possible, comprising 11% of Severnaya Zemlya's 190 glaciers (37% by area). Under continued warming, we anticipate accelerated retreat and increased likelihood of surging as basal thermal regimes shift.

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.