[1] A new three-dimensional thermomechanically coupled ice sheet model is developed. Contrary to the majority of three-dimensional ice sheet models (shallow ice approximation), higher-order stress gradients (longitudinal and transverse) are accounted for in the force balance equations. The horizontal velocity field is determined from the force balance equations in their ''derivative form'' (elliptical equation) using the method presented by Pattyn [2000, 2002a]. The model is solved on a regular grid in the horizontal and an irregular grid in the vertical and is numerically stable. Basic experiments include the European Ice Sheet Modeling Initiative (EISMINT) benchmarks for largescale ice sheet models and a comparison with the Saito-Blatter ice sheet model including higher-order stress gradients [Saito et al., 2003]. Detailed calculations of ice flow over three-dimensional bedrock perturbations showed the validity of the higher-order solution. The model is capable of simulating the evolution of an ice stream within the ice sheet and shows important aspects of observed ice stream features, such as the surface flattening and the importance of side drag. The simulation of the ice flow over a subglacial lake results in a flattening of the surface, a local velocity increase over the lake, and a deviation of the ice flow from the main flow direction, features which are also observed at Lake Vostok, Antarctica.INDEX TERMS: 1827 Hydrology: Glaciology (1863); 1863 Hydrology: Snow and ice (1827); 3230 Mathematical Geophysics: Numerical solutions; KEYWORDS: higher-order, ice sheet model, thermomechanical, ice stream, subglacial lake Citation: Pattyn, F., A new three-dimensional higher-order thermomechanical ice sheet model: Basic sensitivity, ice stream development, and ice flow across subglacial lakes,

Abstract. We present the results of the first ice sheet model intercomparison project for higher-order and full-Stokes ice sheet models. These models are compared and verified in a series of six experiments of which one has an analytical solution obtained from a perturbation analysis. The experiments are applied to both 2-D and 3-D geometries; five experiments are steady-state diagnostic, and one has a time-dependent prognostic solution. All participating models give results that are in close agreement. A clear distinction can be made between higher-order models and those that solve the full system of equations. The full-Stokes models show a much smaller spread, hence are in better agreement with one another and with the analytical solution.

Abstract. Ice flow models of the Antarctic ice sheet are commonly used to simulate its future evolution in response to different climate scenarios and assess the mass loss that would contribute to future sea level rise. However, there is currently no consensus on estimates of the future mass balance of the ice sheet, primarily because of differences in the representation of physical processes, forcings employed and initial states of ice sheet models. This study presents results from ice flow model simulations from 13 international groups focusing on the evolution of the Antarctic ice sheet during the period 2015–2100 as part of the Ice Sheet Model Intercomparison for CMIP6 (ISMIP6). They are forced with outputs from a subset of models from the Coupled Model Intercomparison Project Phase 5 (CMIP5), representative of the spread in climate model results. Simulations of the Antarctic ice sheet contribution to sea level rise in response to increased warming during this period varies between −7.8 and 30.0 cm of sea level equivalent (SLE) under Representative Concentration Pathway (RCP) 8.5 scenario forcing. These numbers are relative to a control experiment with constant climate conditions and should therefore be added to the mass loss contribution under climate conditions similar to present-day conditions over the same period. The simulated evolution of the West Antarctic ice sheet varies widely among models, with an overall mass loss, up to 18.0 cm SLE, in response to changes in oceanic conditions. East Antarctica mass change varies between −6.1 and 8.3 cm SLE in the simulations, with a significant increase in surface mass balance outweighing the increased ice discharge under most RCP 8.5 scenario forcings. The inclusion of ice shelf collapse, here assumed to be caused by large amounts of liquid water ponding at the surface of ice shelves, yields an additional simulated mass loss of 28 mm compared to simulations without ice shelf collapse. The largest sources of uncertainty come from the climate forcing, the ocean-induced melt rates, the calibration of these melt rates based on oceanic conditions taken outside of ice shelf cavities and the ice sheet dynamic response to these oceanic changes. Results under RCP 2.6 scenario based on two CMIP5 climate models show an additional mass loss of 0 and 3 cm of SLE on average compared to simulations done under present-day conditions for the two CMIP5 forcings used and display limited mass gain in East Antarctica.

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Abstract. 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 of Antarctica's future contribution to global sea level rise that arises from large uncertainty in the oceanic forcing and the associated ice shelf melting. Ice shelf melting is considered to be a major if not the largest perturbation of the ice sheet's flow into the ocean. However, by computing only the sea level contribution in response to ice shelf melting, our study is neglecting a number of processes such as surface-mass-balance-related contributions. In assuming linear response theory, we are able to capture complex temporal responses of the ice sheets, but we neglect any self-dampening or self-amplifying processes. This is particularly relevant in situations in which an instability is dominating the ice loss. The 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 ocean 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 CMIP5 climate model sensitivities), uncertainty in the oceanic transport to the Southern Ocean (obtained from the time-delayed and scaled oceanic subsurface warming in CMIP5 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 of the ice loss due to basal ice shelf melting is 10.2 mm, with a likely range between 5.2 and 21.3 mm. For the same period the Antarctic ice sheet lost mass equivalent to 7.4 mm of global sea level rise, with a standard deviation of 3.7 mm (Shepherd et al., 2018) including all processes, especially surface-mass-balance changes. For the unabated warming path, Representative Concentration Pathway 8.5 (RCP8.5), we obtain a median contribution of the Antarctic ice sheet to global mean sea level rise from basal ice shelf melting within the 21st century of 17 cm, with a likely range (66th percentile around the mean) between 9 and 36 cm and a very likely range (90th percentile around the mean) between 6 and 58 cm. For the RCP2.6 warming path, which will keep the global mean temperature below 2 ∘C of global warming and is thus consistent with the Paris Climate Agreement, the procedure yields a median of 13 cm of global mean sea level contribution. The likely range for the RCP2.6 scenario is between 7 and 24 cm, and the very likely range is between 4 and 37 cm. The structural uncertainties in the method do not allow for 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 RCP8.5 scenario. The maximum within the 21st century of the median value is 4 cm per decade, with a likely range between 2 and 9 cm per decade and a very likely range between 1 and 14 cm per decade.