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Earlier large-scale Greenland ice sheet sea-level projections (e.g., those run during the ice2sea and SeaRISE initiatives) have shown that ice sheet initial conditions have a large effect on the projections and give rise to important uncertainties. The goal of the initMIP-Greenland intercomparison exercise is to compare, evaluate and improve the initialisation techniques used in the ice sheet modelling community and to estimate the associated uncertainties in modelled mass changes. initMIP-Greenland is the first in a series of ice sheet model intercomparison activities within ISMIP6 (the Ice Sheet Model Intercomparison Project for CMIP6), which is the primary activity within the Coupled Model Intercomparison Project - phase 6 (CMIP6) focusing on the ice sheets. Two experiments for the large-scale Greenland ice sheet have been designed to allow intercomparison between participating models of 1) the initial present-day state of the ice sheet and 2) the response in two idealised forward experiments. The forward experiments serve to evaluate the initialisation in terms of model drift (forward run without additional forcing) and in response to a large perturbation (prescribed surface mass balance anomaly), and should not be interpreted as sea-level projections. We present and discuss results that highlight the diversity of data sets, boundary conditions and initialisation techniques used in the community to generate initial states of the Greenland ice sheet. We find good agreement across the ensemble for the dynamic response to surface mass balance changes in areas where the simulated ice sheets overlap, but differences arising from the initial size of the ice sheet. The model drift in the control experiment is reduced for models that participated in earlier intercomparison exercises.

The Wordie Ice Shelf-Fleming Glacier system in the southern Antarctic Peninsula has experienced a long-term retreat and disintegration of its ice shelf in the past 50 years. Increases in the glacier velocity and dynamic thinning have been observed over the past two decades, especially after 2008 when only a small ice shelf remained at the Fleming Glacier front. It is important to know whether the substantial further speed-up and greater surface draw-down of the glacier since 2008 is a direct response to ocean forcing, or driven by feedbacks within the grounded marine-based glacier system, or both. Recent observational studies have suggested the 2008-2015 velocity change was due to the ungrounding of the Fleming Glacier front. To explore the mechanisms underlying the recent changes, we use a full-Stokes ice sheet model to simulate the basal shear stress distribution of the Fleming system in 2008 and 2015. This study is part of the first high resolution modelling campaign of this system. Comparison of inversions for basal shear stresses for 2008 and 2015 suggests the migration of the grounding line ĝ1/4 9 km upstream by 2015 from the 2008 ice front/grounding line positions, which virtually coincided with the 1996 grounding line position. This migration is consistent with the change in floating area deduced from the calculated height above buoyancy in 2015. The retrograde submarine bed underneath the lowest part of the Fleming Glacier may have promoted retreat of the grounding line. Grounding line retreat may also be enhanced by a feedback mechanism upstream of the grounding line by which increased basal lubrication due to increasing frictional heating enhances sliding and thinning. Improved knowledge of bed topography near the grounding line and further transient simulations with oceanic forcing are required to accurately predict the future movement of the Fleming Glacier system grounding line and better understand its ice dynamics and future contribution to sea level..

Many glaciers in the Antarctic Peninsula are now rapidly losing mass. Understanding of the dynamics of these fast-flowing glaciers, and their potential future behaviour, can be improved through ice sheet modelling studies. Inverse methods are commonly used in ice sheet models to infer the spatial distribution of a basal friction coefficient, which has a large effect on the basal velocity and ice deformation. Here we use the full-Stokes Elmer/Ice model to simulate the Wordie Ice Shelf-Fleming Glacier system in the southern Antarctic Peninsula. With an inverse method, we infer the pattern of the basal friction coefficient from surface velocities observed in 2008. We propose a multi-cycle spin-up scheme to reduce the influence of the assumed initial englacial temperature field on the final inversion. This is particularly important for glaciers like the Fleming Glacier, which have areas of strongly temperature-dependent deformational flow in the fast-flowing regions. Sensitivity tests using various bed elevation datasets, ice front positions and boundary conditions demonstrate the importance of high-accuracy ice thickness/bed geometry data and precise location of the ice front boundary..

While a lot of attention has been given to the numerical implementation of grounding lines and basal friction in the grounding zone, little has been done about the impact of the numerical treatment of ocean-induced basal melting in this region. Several strategies are currently being employed in the ice sheet modeling community, and the resulting grounding line dynamics may differ strongly, which ultimately adds significant uncertainty to the projected contribution of marine ice sheets to sea level rise. We investigate here several implementations of basal melt parameterization on partially floating elements in a finite-element framework, based on the Marine Ice Sheet-Ocean Model Intercomparison Project (MISOMIP) setup: (1) melt applied only to entirely floating elements, (2) melt applied over all elements that are crossed by the grounding line, and (3) melt integrated partially over the floating portion of a finite element using two different sub-element integration methods. All methods converge towards the same state when the mesh resolution is fine enough. However, (2) and (3) will systematically overestimate the rate of grounding line retreat in coarser resolutions, while (1) converges faster to the solution in most cases. The differences between sub-element parameterizations are exacerbated for experiments with high melting rates in the vicinity of the grounding line and for a Weertman sliding law. As most real-world simulations use horizontal mesh resolutions of several hundreds of meters at best, and high melt rates are generally present close to the grounding lines, we recommend not using (3) to avoid overestimating the rate of grounding line retreat and to carefully assess the impact of mesh resolution and sub-element melt parameterizations on all simulation results.

Antarctica and Greenland hold enough ice to raise sea level by more than 65 m if both ice sheets were to melt completely. Predicting future ice sheet mass balance depends on our ability to model these ice sheets, which is limited by our current understanding of several key physical processes, such as iceberg calving. Large-scale ice flow models either ignore this process or represent it crudely. To model fractured zones, an important component of many calving models, continuum damage mechanics as well as linear fracture mechanics are commonly used. However, these methods have a large number of uncertainties when applied across the entire Antarctic continent because the models were typically tuned to match processes seen on particular ice shelves. Here we present an alternative, statistics-based method to model the most probable zones of the location of fractures and demonstrate our approach on all main ice shelf regions in Antarctica, including the Antarctic Peninsula. We can predict the location of observed fractures with an average success rate of 84 % for grounded ice and 61 % for floating ice and a mean overestimation error rate of 26 % and 20 %, respectively. We found that Antarctic ice shelves can be classified into groups based on the factors that control fracture location.

Estimating the future evolution of the Antarctic Ice Sheet (AIS) is critical for improving future sea level rise (SLR) projections. Numerical ice sheet models are invaluable tools for bounding Antarctic vulnerability; yet, few continental-scale projections of century-scale AIS SLR contribution exist, and those that do vary by up to an order of magnitude. This is partly because model projections of future sea level are inherently uncertain and depend largely on the model's boundary conditions and climate forcing, which themselves are unknown due to the uncertainty in the projections of future anthropogenic emissions and subsequent climate response. Here, we aim to improve the understanding of how uncertainties in model forcing and boundary conditions affect ice sheet model simulations. With use of sampling techniques embedded within the Ice Sheet System Model (ISSM) framework, we assess how uncertainties in snow accumulation, ocean-induced melting, ice viscosity, basal friction, bedrock elevation, and the presence of ice shelves impact continental-scale 100-year model simulations of AIS future sea level contribution. Overall, we find that AIS sea level contribution is strongly affected by grounding line retreat, which is driven by the magnitude of ice shelf basal melt rates and by variations in bedrock topography. In addition, we find that over 1.2 m of AIS global mean sea level contribution over the next century is achievable, but not likely, as it is tenable only in response to unrealistically large melt rates and continental ice shelf collapse. Regionally, we find that under our most extreme 100-year warming experiment generalized for the entire ice sheet, the Amundsen Sea sector is the most significant source of model uncertainty (1032 mm 6σ spread) and the region with the largest potential for future sea level contribution (297 mm). In contrast, under a more plausible forcing informed regionally by literature and model sensitivity studies, the Ronne basin has a greater potential for local increases in ice shelf basal melt rates. As a result, under this more likely realization, where warm waters reach the continental shelf under the Ronne ice shelf, it is the Ronne basin, particularly the Evans and Rutford ice streams, that are the greatest contributors to potential SLR (161 mm) and to simulation uncertainty (420 mm 6spread).

Thwaites Glacier (TG), West Antarctica, has been losing mass and retreating rapidly in the past few decades. Here, we present a study of its calving dynamics combining a two-dimensional flow-band full-Stokes (FS) model of its viscous flow with linear elastic fracture mechanics (LEFM) theory to model crevasse propagation and ice fracturing. We compare the results with those obtained with the higher-order (HO) and the shallow-shelf approximation (SSA) models coupled with LEFM. We find that FS/LEFM produces surface and bottom crevasses that are consistent with the distribution of depth and width of surface and bottom crevasses observed by NASA's Operation IceBridge radar depth sounder and laser altimeter, whereas HO/LEFM and SSA/LEFM do not generate crevasses that are consistent with observations. We attribute the difference to the nonhydrostatic condition of ice near the grounding line, which facilitates crevasse formation and is accounted for by the FS model but not by the HO or SSA models. We find that calving is enhanced when pre-existing surface crevasses are present, when the ice shelf is shortened or when the ice shelf front is undercut. The role of undercutting depends on the timescale of calving events. It is more prominent for glaciers with rapid calving rates than for glaciers with slow calving rates. Glaciers extending into a shorter ice shelf are more vulnerable to calving than glaciers developing a long ice shelf, especially as the ice front retreats close to the grounding line region, which leads to a positive feedback to calving events. We conclude that the FS/LEFM combination yields substantial improvements in capturing the stress field near the grounding line of a glacier for constraining crevasse formation and iceberg calving.

Knowledge of the ice thickness distribution of glaciers and ice caps is an important prerequisite for many glaciological and hydrological investigations. A wealth of approaches has recently been presented for inferring ice thickness from characteristics of the surface. With the Ice Thickness Models Intercomparison eXperiment (ITMIX) we performed the first coordinated assessment quantifying individual model performance. A set of 17 different models showed that individual ice thickness estimates can differ considerably - locally by a spread comparable to the observed thickness. Averaging the results of multiple models, however, significantly improved the results: on average over the 21 considered test cases, comparison against direct ice thickness measurements revealed deviations on the order of 10 ± 24% of the mean ice thickness (1σ estimate). Models relying on multiple data sets - such as surface ice velocity fields, surface mass balance, or rates of ice thickness change - showed high sensitivity to input data quality. Together with the requirement of being able to handle large regions in an automated fashion, the capacity of better accounting for uncertainties in the input data will be a key for an improved next generation of ice thickness estimation approaches.

Understanding of long-term dynamics of glaciers and ice caps is vital to assess their recent and future changes, yet few long-term reconstructions using ice flow models exist. Here we present simulations of the maritime Hardangerjøkulen ice cap in Norway from the mid-Holocene through the Little Ice Age (LIA) to the present day, using a numerical ice flow model combined with glacier and climate reconstructions. In our simulation, under a linear climate forcing, we find that Hardangerjøkulen grows from ice-free conditions in the mid-Holocene to its maximum extent during the LIA in a nonlinear, spatially asynchronous fashion. During its fastest stage of growth (2300-1300 BP), the ice cap triples its volume in less than 1000 years. The modeled ice cap extent and outlet glacier length changes from the LIA until today agree well with available observations. Volume and area for Hardangerjøkulen and several of its outlet glaciers vary out-of-phase for several centuries during the Holocene. This volume-area disequilibrium varies in time and from one outlet glacier to the next, illustrating that linear relations between ice extent, volume and glacier proxy records, as generally used in paleoclimatic reconstructions, have only limited validity. We also show that the present-day ice cap is highly sensitive to surface mass balance changes and that the effect of the ice cap hypsometry on the mass balance- altitude feedback is essential to this sensitivity. A mass balance shift by +0.5m w.e. relative to the mass balance from the last decades almost doubles ice volume, while a decrease of 0.2 mw.e. or more induces a strong mass balance-altitude feedback and makes Hardangerjøkulen disappear entirely. Furthermore, once disappeared, an additional +0.1m w.e. relative to the present mass balance is needed to regrow the ice cap to its present-day extent. We expect that other ice caps with comparable geometry in, for example, Norway, Iceland, Patagonia and peripheral Greenland may behave similarly, making them particularly vulnerable to climate change.

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Calving is a major mechanism of ice discharge of the Antarctic and Greenland ice sheets, and a change in calving front position affects the entire stress regime of marine terminating glaciers. The representation of calving front dynamics in a 2-D or 3-D ice sheet model remains non-trivial. Here, we present the theoretical and technical framework for a level-set method, an implicit boundary tracking scheme, which we implement into the Ice Sheet System Model (ISSM). This scheme allows us to study the dynamic response of a drainage basin to user-defined calving rates. We apply the method to Jakobshavn Isbræ, a major marine terminating outlet glacier of the West Greenland Ice Sheet. The model robustly reproduces the high sensitivity of the glacier to calving, and we find that enhanced calving triggers significant acceleration of the ice stream. Upstream acceleration is sustained through a combination of mechanisms. However, both lateral stress and ice influx stabilize the ice stream. This study provides new insights into the ongoing changes occurring at Jakobshavn Isbræ and emphasizes that the incorporation of moving boundaries and dynamic lateral effects, not captured in flow-line models, is key for realistic model projections of sea level rise on centennial timescales.

The Arctic sea ice cover has changed drastically over the last decades. Associated with these changes is a shift in dynamical regime seen by an increase of extreme fracturing events and an acceleration of sea ice drift. The highly non-linear dynamical response of sea ice to external forcing makes modelling these changes and the future evolution of Arctic sea ice a challenge for current models. It is, however, increasingly important that this challenge be better met, both because of the important role of sea ice in the climate system and because of the steady increase of industrial operations in the Arctic. In this paper we present a new dynamical/thermodynamical sea ice model called neXtSIM that is designed to address this challenge. neXtSIM is a continuous and fully Lagrangian model, whose momentum equation is discretised with the finite-element method. In this model, sea ice physics are driven by the combination of two core components: a model for sea ice dynamics built on a mechanical framework using an elasto-brittle rheology, and a model for sea ice thermodynamics providing damage healing for the mechanical framework. The evaluation of the model performance for the Arctic is presented for the period September 2007 to October 2008 and shows that observed multi-scale statistical properties of sea ice drift and deformation are well captured as well as the seasonal cycles of ice volume, area, and extent. These results show that neXtSIM is an appropriate tool for simulating sea ice over a wide range of spatial and temporal scales.