Gudmundur Hilmar Gudmundsson

Ice calving plays a significant role in ice sheet mass loss. Predictions of future ice sheet mass balance require accurate representations of the calving process in numerical ice models to determine rates of future global mean sea level rise. Whilst calving has recently begun to be implemented in numerical models there has not yet been a systematic investigation into how this implementation compares between different ice flow models. The Calving Model Intercomparison Project (CalvingMIP) has been established to address this question by providing a framework of experiments to investigate the accuracy of simulated calving rates and how simulated properties at the calving front evolve over time. Our initial focus has been on how calving is implemented in models, therefore focusing on calving algorithms, rather than on how much ice should be calved at a particular time via a calving law. Our results, from thirteen different numerical modelling groups, show that the majority of calving algorithms implemented are able to accurately implement a given calving rate with an ice front that evolves smoothly throughout the calving process, albeit with slightly more variation of results in a more complex domain. These results show that we can have confidence in the models capacity to accurately implement calving laws in the future.

When modelling ice flows there are several aspects which are poorly constrained by observations, in particular parameters related to ice rheology and basal sliding. In computational ice flow models, inversion methods are frequently used to estimate the spatial distribution of these hidden fields. These methods use surface measurement data in combination with a forward model of the ice dynamics that relate the hidden fields to the surface fields. In this study we approximate the forward model using first-order linear perturbation theory to gain insights into our ability to extract information about the ice viscosity at the same time as basal slipperiness, and to understand the theoretical limitations. We frame the inversion problem in terms of a Gaussian maximum a-posteriori estimation with explicitly stated priors for the hidden fields. We illustrate the inversion behaviour with perturbations applied to flow down a laterally confined channel, where both viscosity and slipperiness can play a significant role in the ice sheet dynamics. Our results indicate that it is possible to extract information about the viscosity field at the same time as estimating the basal slipperiness, with strong horizontal gradients in the surface velocity field essential for good viscosity retrieval. We recommend always inverting for basal slipperiness and viscosity together over grounded ice areas in ice-sheet models, and explicitly recognising prior knowledge of the hidden fields in the retrieval through either the inclusion of appropriate priors and regularisation.

The shallow-shelf approximation (SSA) is widely used to model the evolution of fast-flowing ice that is either floating or sliding rapidly over the bed, resulting in plug flow. However, so far there has been no rigorous, comparative study of the different numerical approaches to solve the SSA equations. We calculate the conditions for different numerical schemes to remain stable and accurate when solving the linear 1D SSA equations for a simple geometry. The comparison spans central difference and upwind schemes, explicit and semi-implicit multistep schemes, and explicit or implicit monolithic schemes. Also considered are schemes time stepping using the Θ-method, where the value of Θ is used to form a weighted combination of the forward and backward Euler methods. We find that monolithic schemes remain stable at all tested time steps for Θ ≥ 0.5 whilst multistep schemes become unstable at large time steps. Of the tested schemes the monolithic finite element scheme with Θ = 0.5 remains accurate for the largest range of time steps.

When modelling ice flows there are several aspects which are poorly constrained by observations, in particular parameters related to ice rheology and basal sliding. In computational ice flow models, inversion methods are frequently used to estimate the spatial distribution of these hidden fields. These methods use surface measurement data in combination with a forward model of the ice dynamics that relate the hidden fields to the surface fields. In this study we approximate the forward model using first-order linear perturbation theory to gain insights into our ability to extract information about the ice viscosity at the same time as basal slipperiness, and to understand the theoretical limitations. We frame the inversion problem in terms of a Gaussian maximum a-posteriori estimation with explicitly stated priors for the hidden fields. We illustrate the inversion behaviour with perturbations applied to flow down a laterally confined channel, where both viscosity and slipperiness can play a significant role in the ice sheet dynamics. Our results indicate that it is possible to extract information about the viscosity field at the same time as estimating the basal slipperiness, with strong horizontal gradients in the surface velocity field essential for good viscosity retrieval. We recommend always inverting for basal slipperiness and viscosity together over grounded ice areas in ice-sheet models, and explicitly recognising prior knowledge of the hidden fields in the retrieval through either the inclusion of appropriate priors and regularisation.

Ice calving plays a significant role in ice sheet mass loss. Predictions of future ice sheet mass balance require accurate representations of the calving process in numerical ice models to determine rates of future global mean sea level rise. Whilst calving has recently begun to have been implemented in numerical models there has not been a systematic investigation into how this implementation compares between different ice flow models. The Calving Model Intercomparison Project (CalvingMIP) has been established to address this question by providing a framework of experiments to investigate the accuracy of simulated calving rates and how simulated properties at the calving front evolve over time. Our initial focus has been on how calving is implemented in models, therefore focusing on calving algorithms, rather than on how much ice should be calved at a particular time (calving law). Our results, from thirteen different numerical modelling groups, show that the majority of calving algorithms implemented are able to accurately implement a given calving rate with an ice front that evolves smoothly throughout the calving process. These results show that we can have confidence in the models capacity to accurately implement calving laws in the future.

When modelling ice flows there are several aspects which are poorly constrained by observations, in particular parameters related to ice rheology and basal sliding. In computational ice flow models, inversion methods are frequently used to estimate the spatial distribution of these hidden fields. These methods use surface measurement data in combination with a forward model of the ice dynamics that relate the hidden fields to the surface fields. In this study we approximate the forward model using first-order linear perturbation theory to gain insights into our ability to extract information about the ice viscosity at the same time as basal slipperiness, and to understand the theoretical limitations. We frame the inversion problem in terms of a Gaussian maximum a-posteriori estimation with explicitly stated priors for the hidden fields. We illustrate the inversion behaviour with perturbations applied to flow down a laterally confined channel, where both viscosity and slipperiness can play a significant role in the ice sheet dynamics. Our results indicate that it is possible to extract information about the viscosity field at the same time as estimating the basal slipperiness, with strong horizontal gradients in the surface velocity field essential for good viscosity retrieval. We recommend always inverting for basal slipperiness and viscosity together over grounded ice areas in ice-sheet models, and explicitly recognising prior knowledge of the hidden fields in the retrieval through either the inclusion of appropriate priors and regularisation.

Ocean-driven ice shelf melting is a major contributor of present and future ice loss from the Antarctic Ice Sheet. In the Ice Sheet Model Intercomparison Project (ISMIP6) Antarctic 2300 projections, sea level rise varies widely, from -0.6 to 4.4 m, highlighting significant uncertainty. Here, we assess drivers of this spread, focussing on sub-shelf melting and dynamic ice loss as well as sectors that have the potential for large-scale, rapid ice loss: the Amundsen Sea, Filchner-Ronne, and Ross sectors, and the Aurora and Wilkes Subglacial Basins. We derive two sensitivity factors for each ISMIP6 simulation: a) a melt sensitivity factor, describing how simulated sub-shelf melt rates respond to ocean thermal forcing changes; and b) a dynamic ice loss sensitivity factor, describing how simulated dynamic ice loss (and hence sea level contribution) responds to cumulative sub-shelf melt changes. Melt sensitivities range from 1.5–21.3 ma⁻¹ K⁻¹, with no clear dependency on the melt parameterisation. Model simulations cluster into two groups based on calving strength. The dynamic ice loss sensitivities range from 0.1 to 2.6 (unitless), with larger variations in the Amundsen sector, and Aurora and Wilkes Subglacial Basins. These sensitivity factors are good predictors of short-term integrated melting and sea level rise, respectively, but are less robust on longer time scales. Our findings show that these factors explain much of the ensemble spread in projected ice loss to 2300. We recommend to further constrain these factors, and advocate for their use in model calibration and emulator design, with the ultimate aim of explaining uncertainties in future projections of sea level rise from Antarctica.

When modelling ice flows there are several aspects which are poorly constrained by observations, in particular parameters related to ice rheology and basal sliding. In computational ice flow models, inversion methods are frequently used to estimate the spatial distribution of these hidden fields. These methods use surface measurement data in combination with a forward model of the ice dynamics that relate the hidden fields to the surface fields. In this study we approximate the forward model using first-order linear perturbation theory to gain insights into our ability to extract information about the ice viscosity at the same time as basal slipperiness, and to understand the theoretical limitations. We frame the inversion problem in terms of a Gaussian maximum a-posteriori estimation with explicitly stated priors for the hidden fields. We illustrate the inversion behaviour with perturbations applied to flow down a laterally confined channel, where both viscosity and slipperiness can play a significant role in the ice sheet dynamics. Our results indicate that it is possible to extract information about the viscosity field at the same time as estimating the basal slipperiness, with strong horizontal gradients in the surface velocity field essential for good viscosity retrieval. We recommend always inverting for basal slipperiness and viscosity together over grounded ice areas in ice-sheet models, and explicitly recognising prior knowledge of the hidden fields in the retrieval through either the inclusion of appropriate priors and regularisation.

Future projections of ice loss from the Greenland ice sheet are subject to large and often poorly quantified uncertainties. These arise both from uncertainties in climate forcing projections and poorly constrained processes in ice sheet models. Ice-sheet model initialisation, in particular, is a major contributor to projection uncertainty. Here, we aim to calibrate a Greenland-wide ice sheet model configuration that replicates the recent trend (1996--2022) in observed changes in ice speed and thickness. First, we generate an ensemble of simulations using the ice-sheet model Úa, each forced with datasets of surface mass balance and ice front positions, and input parameter values sampled from prior probability distributions. This ensemble is then used to train a surrogate model, designed to emulate the temporal- and spatially integrated combined misfit between observed and modelled changes in ice speed and thickness. We then use this emulator for Bayesian inference to determine the posterior model parameter distributions needed to minimise the misfit between observed and modelled quantities of interest and ultimately best replicate the observed trend in Greenland ice sheet mass loss. By calibrating the model in such a way, we can reduce the uncertainties in forward-projections and have confidence in the predictive capabilities of our model.

The Wilkes Subglacial Basin (WSB) holds approximately 3-4 m sea-level equivalent ice volume (Rignot et al., 2019; Crotti et al., 2022), and is characterised by a reverse-sloping bed, making it vulnerable to marine ice sheet instability. However, the conditions and indeed the possibility of large retreat is still highly debated. Using the finite element ice-sheet model, Úa, we conduct a sensitivity analysis to determine the climate conditions for large scale retreat. We further explored uncertainties arising from poorly known physical mechanisms, particularly the sliding law. Our simulations are initialised using present-day ice dynamics reproduced through inversion methods. Transient simulations of 500 years are then conducted with different surface temperature forcing. In the control experiment, constant present-day thermal forcing is applied to the local quadratic parameterisation (Jourdain et al., 2020) for sub-ice-shelf melting, and surface mass balance is prescribed using constant RACMO model output (Noël et al., 2023). Increase of surface temperature proportionally increase precipitation and thermal forcing. A mesh convergence study with mesh sizes up to sub-kilometre scale is conducted to ensure our conclusions are numerically robust. We increase the surface temperature by up to 8 degrees and the ocean temperature by up to 40 degrees with a range of different sliding laws. The migration of the grounding line positions, total ice volume and volume above floatation are calculated in order to determine if and where large scale retreat has occurred.