Quantitative results from regional climate models (RCMs) run over ice sheets are frequently used to make projections of surface melt, ice-shelf stability, and subsequently sea-level rise. However, modelled relevant mass fluxes need to be evaluated first before using future output data for projections. This study makes the case for a two-step framework when evaluating RCMs. Firstly, the reliability of the RCM when forced with reanalysis data must be assessed through comparison with historical observations. Secondly, the accuracy of using a non-observationally constrained Earth System Model as forcing must be assessed through comparison with the reanalysis forced run during the same historical period. Simulating surface melt in Antarctica with the RCM RACMO2.3p2 is given as an example. Applying this two-step procedure we show that RACMO2.3p2 respectively forced with ERA5 and CESM2 is robust for modelling contemporary and future surface melt in Antarctica. Building on this conclusion, we briefly discuss an application, i.e. three future SSP realizations of melt-over-accumulation across the Antarctic ice sheet until 2100 are presented, providing insights into the future sensitivity to meltwater ponding of major Antarctic ice shelves.

This study introduces a custom implementation of the Ensemble Kalman Filter (EnKF) for calibrating a three-dimensional glacier evolution model. The EnKF can assimilate observations as they become available and provides uncertainty measures for the initial state after calibration. We calibrate an elevation-dependent surface mass balance (SMB) model using elevation change observations and test the EnKF’s performance in a Twin Experiment by varying internal and external hyperparameters. The best-performing configuration is applied to the Rhône Glacier in a Real-World Experiment. Using satellite-based elevation change fields for calibration, the EnKF estimates an average equilibrium line altitude of $2920 \pm 37$ m for the period 2000–19. A comparison of the results with glaciological measurements demonstrates the capabilities of the EnKF to simultaneously calibrate multiple SMB parameters. With this proof of concept, we expect that our methodology is readily extendable to other map or point observations and their combination, as well as to other calibration parameters.

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.

Subglacial drainage models, often motivated by the relationship between hydrology and ice flow, sensitively depend on numerous unconstrained parameters. We explore using borehole water-pressure time series to calibrate the uncertain parameters of a popular subglacial drainage model, taking a Bayesian perspective to quantify the uncertainty in parameter estimates and in the calibrated model predictions. To reduce the computation time associated with Markov Chain Monte Carlo sampling, we construct a fast Gaussian process emulator to stand in for the subglacial drainage model. We first carry out a calibration experiment using synthetic observations consisting of model simulations with hidden parameter values as a demonstration of the method. Using real borehole water pressures measured in western Greenland, we find meaningful constraints on four of the eight model parameters and a factor-of-three reduction in uncertainty of the calibrated model predictions. These experiments illustrate Gaussian process-based Bayesian inference as a useful tool for calibration and uncertainty quantification of complex glaciological models using field data. However, significant differences between the calibrated model and the borehole data suggest that structural limitations of the model, rather than poorly constrained parameters or computational cost, remain the most important constraint on subglacial drainage modelling.

We present analyses of bubble number-density (BND) data from the South Pole Ice Core (SPC14) showing warming of ∼7.5°C from the Late Glacial (∼19.5 ka), then relatively stable temperatures during the Holocene (<0.5°C warming), in close agreement with results of independent paleothermometers. The BND data span from ∼160 m just below pore close-off, to ∼1200 m, where bubble loss by clathrate formation is significant. Measurements were made with standard bubble ‘thick’-section techniques and a new application of three-dimensional micro-computed tomography (CT) imagery; the nearly identical results recommend the faster, nondestructive micro-CT. The very high BND at South Pole, typically 800 and 900 bubbles cm−3, reflects the joint effects of the relatively low mean-annual temperature (−49°C) and high accumulation rate (∼7.5 cm w.e. a−1). High BND is physically linked to small grain sizes at pore close-off, which in turn helps explain the near-absence of brittle-ice behavior at the site, contributing to the high quality of the recovered core with implications for siting of future ice cores. The accumulation history, derived from δ15N-N2 firn-column thickness estimates, correlates with the temperature history but varies somewhat more than saturation vapor pressure, suggesting dynamic controls including upstream slope variability.

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.

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.

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.

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.

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.

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.