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.

Sea-ice deformation is concentrated at linear kinematic features such as ridges and leads. Ridging and leads opening processes are highly related to sea-ice fracture. Different rheology models have been successfully applied in various scenarios. However, most of the approaches adopted are based on continuum mechanics that do not explicitly model fracture processes. There are emerging needs for a more physically informed modelling methods that explicitly address fracture at the kilometre scale. In pursuing this objective, in this paper we explored the potential of applying a promising mesh free numerical method, peridynamics (PD), in modelling ice floe (~km) fractures. PD offers a physically and mathematically consistent theory through which spontaneous emergence and propagation of cracks can be achieved. The integral nature of the governing equations in PD remains valid even if a crack appears. We numerically investigated in this paper the tensile fracture (e.g. lead opening) of an elastic heterogenous ice floe. The modelling results were compared with published numerical results obtained by another numerical method. The potentials and challenges of PD in this application are discussed and summarized.

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.

Classical sea-ice models in climate model resolution do not resolve the small-scale physics of sea ice. New methods to address this problem include modifications to established viscous-plastic (VP) rheology models, sub-gridscale parameterizations or new rheologies such as the Maxwell elasto-brittle (MEB) rheology. Here, we investigate differences in gridscale dynamics simulated by the VP and MEB models, their dependency on tunable model parameters and their response to added stochastic perturbations of material parameters in a new implementation in the Massachusetts Institute of Technology general circulation model. Idealized simulations are used to demonstrate that material parameters can be tuned so that both VP and MEB rheologies lead to similar cohesive stress states, arching behaviour and heterogeneity in the deformation fields. As expected, simulations with MEB rheology generally show more heterogeneity than the VP model as measured by the number of simulated linear kinematic features (LKFs). For both rheologies, the cohesion determines the emergence of LKFs. Introducing gridscale heterogeneity by random model parameter perturbation, however, leads to a larger increase of LKF numbers in the VP simulations than in the MEB simulations and similar heterogeneity between VP and MEB models.

Glacier and snow melt are the primary sources of water for streams, and rivers in upper Indus region of the western Himalaya. However, the magnitude of runoff from this glacierized basin is expected to vary with the available energy in the catchment. Here, we used a physically based energy balance model to estimate the surface energy and surface mass balance (SMB) of the upper Chandra Basin glaciers for 7 hydrological years from 2015 to 2022. A strong seasonality is observed, with net radiation being the dominant energy flux in the summer, while latent and sensible heat flux dominated in the winter. The estimated mean annual SMB of the upper Chandra Basin glaciers is −0.51 ± 0.28 m w.e. a−1, with a cumulative SMB of −3.54 m w.e during 7 years from 2015 to 2022. We find that the geographical factors like aspect, slope, size and elevation of the glacier contribute towards the spatial variability of SMB within the study region. The findings reveal that a 42% increase in precipitation is necessary to counteract the additional mass loss resulting from a 1°C increase in air temperature for the upper Chandra Basin glaciers.

The propagation of elastic-flexural–gravity waves through an ice shelf is modeled using full three-dimensional elastic models that are coupled with a treatment of under-shelf sea-water flux: (i) finite-difference model (Model 1), (ii) finite-volume model (Model 2) and (iii) depth-integrated finite-difference model (Model 3). The sea-water flow under the ice shelf is described by a wave equation involving the pressure (the sea-water flow is treated as a “potential flow”). Numerical experiments were undertaken for an ice shelf with ‘rolling’ surface morphology, which implies a periodic structure of the ice shelf. The propagation of ocean waves through an ice shelf with rolling surface morphology is accompanied by Bragg scattering (also called Floquet band insulation). The numerical experiments reveal that band gaps resulting from this scattering occur in the dispersion spectra in frequency bands that are consistent with the Bragg’s law. Band gaps render the medium opaque to wave, that is, essentially, the abatement of the incident ocean wave by ice shelf with rolling surface morphology is observed in the models. This abatement explains the ability of preserving of ice shelves like the Ward Hunt Ice Shelf, Ellesmere Island, Canadian Arctic, from the possible resonant-like destroying impact of ocean swell.

The two main large-scale features of Arctic sea-ice drift are the Beaufort Gyre and the Transpolar Drift Stream. They exhibit strong intraseasonal and interannual variability. Winter 2016/17 showed increased cyclone activity, leading to the collapse of the Beaufort Sea high and the reversal of the Beaufort Gyre. Winter 2020/21 displayed decreased cyclone activity and intense anticyclonic ice transport in the Beaufort Gyre. Here we show that the European Centre for Medium-Range Weather Forecasts’s (ECMWF) extended-range (46 days) retrospective forecasts were able to predict the ice motion during these cases. The initial contrasts in sea level pressure, surface winds and ice drift were well captured, and their temporal evolution—including the reversal of the usual drift direction—well reproduced by the forecasts initialized about a week before the event. Sea-ice thickness in the forecast exhibited initial errors even greater than 1 m that persisted throughout the forecast and negatively affected the ice speed forecast. Despite these shortcomings, the dynamic forecast outperformed the persistence and climatology forecast and represented the observed relation between surface winds and ice drift well. The benefit of dynamic forecasts is especially clear in cases that differ from climatology, like the one we focus on.

Passive microwave measurements of Arctic sea ice have been conducted over the last 50 years from space and during airborne, ship- and ground-based measurement campaigns. The different radiometric signatures of distinct surface types have led to satellite retrievals of, e.g., sea-ice concentration. In contrast, ground-based upward-viewing radiometers measure radiation emitted from the atmosphere and are used to retrieve atmospheric variables. Here, we present results from a ship-based radiometer setup with a mirror construction, which allows us to switch between atmospheric and surface measurements flexibly. This way, in summer 2022, surface observations in the Arctic marginal sea-ice zone could be performed from the research vessel Polarstern by two radiometers covering the frequency range from 22 to 243 GHz. At low frequencies, the brightness temperatures show clear signatures of different surface conditions. We estimate emissivities at 53∘ zenith angle from infrared-based skin temperatures. Predominantly vertically polarized 22–31 GHz emissivities are between 0.51 and 0.55 for open ocean and around 0.95 for sea ice. Predominantly horizontally polarized 243 GHz ocean emissivities are around 0.78 and ice surfaces exhibit a large variability from 0.67 to 0.82. Our results can improve the characterization of surface emissions in satellite retrieval algorithms.

Sea-ice floating in the Arctic ocean is a constantly moving, growing and melting layer. The seasonal cycle of sea-ice volume has an average amplitude of $10\,000\,\mathrm{km}^3$ or 9 trillion tonnes of sea ice. The role of dynamic redistribution of sea ice is observable during winter growth by the incorporation of satellite remote sensing of ice thickness, concentration and drift. Recent advances in the processing of CryoSat-2 radar altimetry data have allowed for the retrieval of summer sea-ice thickness. This allows for a full year of a purely remote sensing-derived ice volume budget analysis.

Here, we present the closed volume budget of Arctic sea ice over the period October 2010–May 2022 revealing the key contributions to summer melt and minimum sea-ice volume and extent. We show the importance of ice drift to the inter-annual variability in Arctic sea-ice volume and the regional distribution of sea ice. The estimates of specific areas of sea-ice growth and melt provide key information on sea-ice over-production, the excess volume of ice growth compared to melt. The statistical accuracy of each key region of the Arctic is presented, revealing the current accuracy of knowledge of Arctic sea-ice volume from observational sources.

The mass and heat balance of Arctic sea ice is affected by the deformation of level ice and the amount of ice stored in sea ice ridges and rubble fields. One important property of sea ice ridges is the macroporosity or void fraction. While macroporosity has been observed in field and laboratory studies, data are sparse and a concise theory of its evolution is lacking. In the present study, the hypothesis is investigated that the initial macroporosity of sea ice ridges is related to random loose packing. When laboratory results on the packing of ice blocks are corrected for boundary effects, good agreement with random loose packing predictions is obtained. The macroporosity then depends mainly on the length-to-thickness ratio of the ice blocks ϵb and it can be expected to fall in the range of $0.4 \lt \phi \lt 0.5$ for typical dimensions of ice blocks in sea ice ridges. In the field, such high macroporosity values are seldom observed., because thermodynamic adjustment, related to the increase in microporosity of submerged cold ice blocks, rapidly decreases the initial macroporosity by 0.1 to 0.15 for typical Arctic freezing conditions. Taking into account this effect, field observations are also consistent with random loose packing of ice blocks. The proposed macroporosity prediction can be useful for modeling the consolidation and property evolution of sea ice ridges and rubble fields and for improving thickness redistribution algorithms in sea ice models.

Observation of thin sections of the WAIS (West Antarctic Ice Sheet) Divide ice core in cross-polarized light reveals a wealth of microstructures and textural characteristics indicative of strain and recovery in an anisotropic crystalline substance undergoing high-temperature plastic deformation. The appearance of abundant subgrain domains—relatively strain-free regions inside crystals (grains) surrounded by walls of dislocations across which small structural orientation changes occur—is particularly noticeable in the depth range associated with the brittle ice (∼650–1300 m). Here we describe a subgrain texture, not previously reported in ice, that resembles chessboard-pattern subgrains in β-quartz. This chessboard texture at WAIS Divide is strongly associated with the presence of bubbles. We hypothesize that chessboard-subgrain development may affect grain-size evolution, the fracture of ice cores recovered from the brittle ice zone and perhaps grain-boundary sliding as well.

Calving is the process of ice loss through the breaking of ice from a glacier’s terminus. Ice-flow models describe calving in various ways, although no consensus exists on the optimal approach. This is critical as the modelled calving rate can strongly influence projections of mass loss from glaciers and ice sheets. As the sub-aerial cliff height at a glacier’s ice front can be considered an indicator of the terminus stress regime, we used a wealth of high-resolution remote-sensing datasets to perform a detailed investigation into the observed relationship between the terminus cliff height and calving rate of 15 tidewater glaciers around the Antarctic Peninsula. The overall long-term response of the assessed glaciers revealed a linearly increasing relationship between calving rate and sub-aerial terminus cliff height from which we derived a calving parameterisation intended for implementation in long-term modelling of tidewater glaciers in the Antarctic Peninsula. Further, other existing calving parameterisations which are based on the terminus ice geometry yielded a poor fit to the assessed observational data. With the availability of such high-resolution data, better validation and constraint of calving parameterisations are now possible, which could greatly improve confidence in the implementation of calving and reliability of outputs from modelling studies.

The Ice Sheet Model Intercomparison Project for CMIP6 (ISMIP6) resulted in many ice-sheet simulations from multiple ice-sheet models. To date, no model weighting studies have analyzed or quantified the model performance, possible duplication of the ISMIP6 ice-sheet models and the effect on mass loss projections. In this study, we adopt a model weighting scheme for the ISMIP6-Greenland that accounts for both model performance compared to observation and model similarity due to possible duplication. We choose ice velocity and thickness for the measurement of model performance, and we use all suitable variables to compute similarity indexes. We update the sea level rise contribution from ISMIP6-Greenland by the end of this century with the weights, and we find that, although the multi-model mean is not considerably shifted (mostly within $ \pm 1{\text{cm}}$), the model spreads are reduced by 10–30% after applying the model weights. The magnitude of reduction varies largely among experiments and types of model weights applied. In general, we find that the model weighting scheme is skillful in producing model weights that effectively and reasonably quantify the model performance and inter-dependency, which can potentially benefit the future phase of the Ice Sheet Model Intercomparison Project, i.e. ISMIP7.

The addition and refreezing of liquid water to Greenland’s accumulation area are increasingly important processes for assessing the ice sheet’s present and future mass balance, but uncertain initial conditions, complex infiltration physics and limited field data pose challenges. Satellite-based L-band radiometry offers a promising new tool for observing liquid water in the firn layer, although further validation is needed. This paper compares time series of liquid water amount (LWA) from three percolation zone sites generated by a localized point-model, a regional climate model, in situ measurement, and L-band radiometric retrievals. LWA integrates the interplay of liquid water generation and refreezing, which often occur simultaneously and repeatedly within firn layers on diurnal, episodic, and seasonal scales offering insights into methods for measuring and modeling meltwater processes. The four LWA records showed average discrepancies of up to 62% nRMSE, reflecting shortcomings inherent to each method. Better agreement between series occurred after excluding the regional climate model record, lowering nRMSE to 8–13%. The agreement between L-band radiometry and other LWA records inspires confidence in this observational tool for understanding firn meltwater processes and serving as a validation target for simulations of water processes in Greenland’s melting firn layer.

This study investigated surface energy fluxes of the Huayna-Potosí Glacier in Bolivia to validate existing empirical melt estimates, including degree-day models and enhanced temperature-index models. A multilayer energy balance model of the snowpack was employed to estimate melt energy and analyze its correlation with meteorological variables. The energy balance analysis revealed that melt energy peaked in October and November, the period corresponding to the progressive development toward the core wet season. Most of the net radiation was consumed by the conductive heat flux into the snowpack or glacier ice, contributing to surface temperature increases. The remaining energy was used for melt. An analysis of diurnal variation indicated that atmospheric longwave radiation suppresses melt during the dry season while driving melt during the wet season. Variables such as specific humidity and relative humidity, which are related to atmospheric longwave radiation, emerged as primary controlling factors after solar radiation in estimating melt based on meteorological variables. This study highlights that a combination of solar radiation and specific humidity outperforms existing empirical melt models that depend exclusively on temperature or a combination of temperature and solar radiation.

Updated estimates of 2024 ice thickness, the surface elevation losses in the last years and simulations of mass balance and evolution (using the Instructed Glacier Model) for the three largest Pyrenean glaciers strongly suggest that by 2034 the Pyrenees will be ice-free. If extreme summers like 2022 and 2023 recur, this could happen even earlier. We show that by 2030, 94% (from 0.22 to 0.01 km2) of the ice in Monte Perdido, 91% (from 0.22 to 0.05 km2) of the ice in Ossoue and 79% of the ice in Aneto (from 0.34 to 0.06 km2) will have melted under the RCP4.5 scenario; these numbers are 83%, 72% and 57% under a committed ice loss scenario, meaning that only 0.05, 0.12 and 0.12 km2 of ice will remain, respectively. In 2034, most likely they will have completely disappeared under the three considered scenarios (RCP 4.5, ‘committed ice loss’ and extreme 2022 year in a loop). The loss of these glaciers is a harbinger for what will happen in many other mountain regions.

Continuous monitoring of the mass balance of the Greenland ice sheet is crucial to assess its contribution to the rise of sea levels. The GRACE and GRACE-FO missions have provided monthly estimates of the Earth’s gravity field since 2002, which have been widely used to estimate monthly mass changes of ice sheets. However, there is an 11 month gap between the two missions. Here, we propose a data-driven approach that combines atmospheric variables from the ERA5 reanalysis with GRACE-derived mass anomalies from previous months to predict mass changes. Using an auto-regressive structure, the model is naturally predictive for shorter times without GRACE/-FO observations. The results show a high r2-score (> 0.73) between model predictions and GRACE/-FO observations. Validating the model’s ability to reproduce mass anomalies when observations are available builds confidence in estimates used to bridge the GRACE and GRACE/-FO gap. Although GRACE and GRACE-FO are treated equally by the model, we see a decrease in model performance for the period covered by GRACE-FO, indicating that they may not be as well-calibrated as previously assumed. Gap predictions align well with mass change estimates derived from other geodetic methods and remain within the uncertainty envelope of the GRACE-FO observations.