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Inaccurate representations of iceberg calving from ice shelves are a large source of uncertainty in mass-loss projections from the Antarctic ice sheet. Here, we address this limitation by implementing and testing a continuum damage-mechanics model in a continental scale ice-sheet model. The damage-mechanics formulation, based on a linear stability analysis and subsequent long-wavelength approximation of crevasses that evolve in a viscous medium, links damage evolution to climate forcing and the large-scale stresses within an ice shelf. We incorporate this model into the BISICLES ice-sheet model and test it by applying it to idealized (1) ice tongues, for which we present analytical solutions and (2) buttressed ice-shelf geometries. Our simulations show that the model reproduces the large disparity in lengths of ice shelves with geometries and melt rates broadly similar to those of four Antarctic ice shelves: Erebus Glacier Tongue (length ~ 13 km), the unembayed portion of Drygalski Ice Tongue (~ 65 km), the Amery Ice Shelf (~ 350 km) and the Ross Ice Shelf (~ 500 km). These results demonstrate that our simple continuum model holds promise for constraining realistic ice-shelf extents in large-scale ice-sheet models in a computationally tractable manner.

The sea level contribution of the Antarctic ice sheet constitutes a large uncertainty in future sea level projections. Here we apply a linear response theory approach to 16 state-of-the-art ice sheet models to estimate the Antarctic ice sheet contribution from basal ice shelf melting within the 21st century. The purpose of this computation is to estimate the uncertainty that arises from large uncertainty in the external forcing that future warming may exert onto the ice sheet. While ice shelf melting is considered to be a major if not the largest perturbation of the ice sheet's flow into the ocean, the approach is neglecting a number of processes such as surface mass balance related contributions and mechanisms. In assuming linear response theory, we are able to capture complex temporal responses of the ice sheets, but we neglect any dampening or self-amplifying processes. This is particularly relevant in situations where an instability is dominating the ice loss. Results obtained here are thus relevant in particular wherever the ice loss is dominated by the forcing as opposed to an internal instability, for example in strong warming scenarios. In order to allow for comparison the methodology was chosen to be exactly the same as in an earlier study (Levermann et al., 2014), but with 16 instead of 5 ice sheet models. We include uncertainty in the atmospheric warming response to carbon emissions (full range of CMIP-5 climate model sensitivities), uncertainty in the oceanic transport to the Southern Ocean (obtained from the time-delayed and scaled oceanic subsurface warming in CMIP-5 models in relation to the global mean surface warming) and the observed range of responses of basal ice shelf melting to oceanic warming outside the ice shelf cavity. This uncertainty in basal ice shelf melting is then convoluted with the linear response functions of each of the 16 ice sheet models to obtain the ice flow response to the individual global warming path. The model median for the observational period from 1992 to 2017 is 9.6 mm with a likely range between 5.2 mm and 20.3 mm compared to the observed sea-level contribution from Antarctica of 7.4 mm with a standard deviation of 3.7 mm (Shepherd et al., 2018). For the so-called business-as-usual warming path, RCP-8.5, we obtain a median contribution of the Antarctic ice sheet to global mean sea-level rise within the 21st century of 17 cm with a likely range (66-percentile around the mean) between 9 cm and 36 cm and a very likely range (90-percentile around the mean) between 6 cm and 59 cm. For the RCP-2.6 warming path which will keep the global mean temperature below two degrees of global warming and is thus consistent with the Paris Climate Agreement yields a median of 13 cm of global mean sea-level contribution. The likely range for the RCP-2.6 scenario is between 7 cm and 25 cm and the very likely range is between 5 cm and 39 cm. The structural uncertainties in the method do not allow an interpretation of any higher uncertainty percentiles. We provide projections for the five Antarctic regions and for each model and each scenario, separately. The rate of sea level contribution is highest under the RCP-8.5 scenario. The maximum within the 21st century of the median value is 4 cm per decade with a likely range between 2 cm/dec and 8 cm/dec and a very likely range between 1 cm/dec and 13 cm/dec.

We introduce MPAS-Albany Land Ice (MALI), a new, variable resolution land ice model that uses unstructured Voronoi grids on a plane or sphere. MALI is built using the Model for Prediction Across Scales (MPAS) framework for developing variable resolution Earth System Model components and the Albany multi-physics code base for solution of coupled systems of partial-differential equations, which itself makes use of Trilinos solver libraries. MALI includes a three-dimensional, first-order momentum balance solver ("Blatter-Pattyn") by linking to the Albany-LI ice sheet velocity solver, as well as an explicit shallow ice velocity solver. Evolution of ice geometry and tracers is handled through an explicit first-order horizontal advection scheme with vertical remapping. Evolution of ice temperature is treated using operator splitting of vertical diffusion and horizontal advection and can be configured to use either a temperature or enthalpy formulation. MALI includes a mass-conserving subglacial hydrology model that supports distributed and/or channelized drainage and can optionally be coupled to ice dynamics. Options for calving include "eigencalving", which assumes calving rate is proportional to extensional strain rates. MALI is evaluated against commonly used exact solutions and community benchmark experiments and shows the expected accuracy. We report first results for the MISMIP3d benchmark experiments for a Blatter-Pattyn type model and show that results fall in-between those of models using Stokes flow and L1L2 approximations. We use the model to simulate a semi-realistic Antarctic Ice Sheet problem for 1100 years at 20 km resolution. MALI is the glacier component of the Energy Exascale Earth System Model (E3SM) version 1, and we describe current and planned coupling to other components.