Description: 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.

Description: 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.

Description: The thermal state of an ice sheet is an important control on its past and future evolution. Some parts of the ice sheet may be polythermal, leading to discontinuous properties at the cold–temperate transition surface (CTS). These discontinuities require a careful treatment in ice sheet models (ISMs). Additionally, the highly anisotropic geometry of the 3D elements in ice sheet modelling poses a problem for stabilization approaches in advection-dominated problems. Here, we present extended enthalpy formulations within the finite-element Ice-Sheet and Sea-Level System model (ISSM) that show a better performance than earlier implementations. In a first polythermal-slab experiment, we found that the treatment of the discontinuous conductivities at the CTS with a geometric mean produces more accurate results compared to the arithmetic or harmonic mean. This improvement is particularly efficient when applied to coarse vertical resolutions. In a second ice dome experiment, we find that the numerical solution is sensitive to the choice of stabilization parameters in the well-established streamline upwind Petrov–Galerkin (SUPG) method. As standard literature values for the SUPG stabilization parameter do not account for the highly anisotropic geometry of the 3D elements in ice sheet modelling, we propose a novel anisotropic SUPG (ASUPG) formulation. This formulation circumvents the problem of high aspect ratio by treating the horizontal and vertical directions separately in the stabilization coefficients. The ASUPG method provides accurate results for the thermodynamic equation on geometries with very small aspect ratios like ice sheets.

Description: Basal motion of ice sheets depends in part on the roughness and material properties of the subglacial bed and the occurrence of water. To date, basal motion represents one of the largest uncertainties in ice-flow models. It is that component of the total flow velocity that can change most rapidly and can, therefore, facilitate rapid variations in dynamic behaviour. In this study, we investigate the subglacial properties of the East Antarctic Ice Sheet by statistically analysing the roughness of the bed topography, inferred from radio-echo sounding measurements. We analyse two sets of roughness parameters, one derived in the spatial and the other in the spectral domain, with two roughness parameters each. This enables us to compare the suitability of the four roughness parameters to classify the subglacial landscapes below the ice sheet. We further investigate the relationship of the roughness parameters with observed surface flow velocity and modelled basal temperatures of the ice sheet. We find that one of the roughness parameters, the Hurst exponent derived in the spatial domain, coincides with the thermal condition at the base of the ice sheet for slow flow velocities and varies with flow velocity.

Description: Abstract. Various observational estimates indicate growing mass loss at Antarctica's margins as well as heavier precipitation across the continent. Simulated future projections reveal that heavier precipitation, falling on Antarctica, may counteract amplified iceberg discharge and increased basal melting of floating ice shelves driven by a warming ocean. Here, we test how the ansatz (implementation in a mathematical framework) of the precipitation boundary condition shapes Antarctica's sea level contribution in an ensemble of ice sheet simulations. We test two precipitation conditions: we either apply the precipitation anomalies from CMIP5 models directly or scale the precipitation by the air temperature anomalies from the CMIP5 models. In the scaling approach, it is common to use a relative precipitation increment per degree warming as an invariant scaling constant. We use future climate projections from nine CMIP5 models, ranging from strong mitigation efforts to business-as-usual scenarios, to perform simulations from 1850 to 5000. We take advantage of individual climate projections by exploiting their full temporal and spatial structure. The CMIP5 projections beyond 2100 are prolonged with reiterated forcing that includes decadal variability; hence, our study may underestimate ice loss after 2100. In contrast to various former studies that apply an evolving temporal forcing that is spatially averaged across the entire Antarctic Ice Sheet, our simulations consider the spatial structure in the forcing stemming from various climate patterns. This fundamental difference reproduces regions of decreasing precipitation despite general warming. Regardless of the boundary and forcing conditions applied, our ensemble study suggests that some areas, such as the glaciers from the West Antarctic Ice Sheet draining into the Amundsen Sea, will lose ice in the future. In general, the simulated ice sheet thickness grows along the coast, where incoming storms deliver topographically controlled precipitation. In this region, the ice thickness differences are largest between the applied precipitation methods. On average, Antarctica shrinks for all future scenarios if the air temperature anomalies scale the precipitation. In contrast, Antarctica gains mass in our simulations if we apply the simulated precipitation anomalies directly. The analysis reveals that the mean scaling inferred from climate models is larger than the commonly used values deduced from ice cores; moreover, it varies spatially: the highest scaling is across the East Antarctic Ice Sheet, and the lowest scaling is around the Siple Coast, east of the Ross Ice Shelf. The discrepancies in response to both precipitation ansatzes illustrate the principal uncertainty in projections of Antarctica's sea level contribution.

Description: 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.