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: We present benchmark experiments to test the implementation of enthalpy and the corresponding boundary conditions in numerical ice sheet models. Since we impose several assumptions on the experiment design, analytical solutions can be formulated for the proposed numerical experiments. The first experiment tests the functionality of the boundary condition scheme and the basal melt rate calculation during transient simulations. The second experiment addresses the steady-state enthalpy profile and the resulting position of the cold–temperate transition surface (CTS). For both experiments we assume ice flow in a parallel-sided slab decoupled from the thermal regime. We compare simulation results achieved by three different ice flow-models with these analytical solutions. The models agree well to the analytical solutions, if the change in conductivity between cold and temperate ice is properly considered in the model. In particular, the enthalpy gradient on the cold side of the CTS goes to zero in the limit of vanishing temperate-ice conductivity, as required from the physical jump conditions at the CTS.

Description: Over the past 3 decades, inversions for ice sheet basal drag have become commonplace in glaciological modeling. Such inversions require regularization to prevent over-fitting and ensure that the structure they recover is a robust inference from the observations, confidence which is required if they are to be used to draw conclusions about processes and properties of the ice base. While L-curve analysis can be used to select the optimal regularization level, the treatment of L-curve analysis in glaciological inverse modeling has been highly variable. Building on the history of glaciological inverse modeling, we demonstrate general best practices for regularizing glaciological inverse problems, using a domain in the Filchner-Ronne catchment of Antarctica as our test bed. We show a step-by-step approach to cost function normalization and L-curve analysis. We explore the spatial and spectral characteristics of the solution as a function of regularization, and we test the sensitivity of L-curve analysis and regularization to model resolution, effective pressure, sliding nonlinearity, and the flow equation. We find that the optimal regularization level converges towards a finite non-zero limit in the continuous problem, associated with a best knowable basal drag field. Nonlinear sliding laws outperform linear sliding in our analysis, with both a lower total variance and a more sharply cornered L-curve. By contrast, geometry-based approximations for effective pressure degrade inversion performance when added to a sliding law, but an actual hydrology model may marginally improve performance in some cases. Our results with 3D inversions suggest that the additional model complexity may not be justified by the 2D nature of the surface velocity data. We conclude with recommendations for best practices in future glaciological inversions.

Description: The Antarctic Ice Sheet represents the largest source of uncertainty in future sea level rise projections, with a contribution to sea level by 2100 ranging from −5 to 43 cm of sea level equivalent under high carbon emission scenarios estimated by the recent Ice Sheet Model Intercomparison for CMIP6 (ISMIP6). ISMIP6 highlighted the different behaviors of the East and West Antarctic ice sheets, as well as the possible role of increased surface mass balance in offsetting the dynamic ice loss in response to changing oceanic conditions in ice shelf cavities. However, the detailed contribution of individual glaciers, as well as the partitioning of uncertainty associated with this ensemble, have not yet been investigated. Here, we analyze the ISMIP6 results for high carbon emission scenarios, focusing on key glaciers around the Antarctic Ice Sheet, and we quantify their projected dynamic mass loss, defined here as mass loss through increased ice discharge into the ocean in response to changing oceanic conditions. We highlight glaciers contributing the most to sea level rise, as well as their vulnerability to changes in oceanic conditions. We then investigate the different sources of uncertainty and their relative role in projections, for the entire continent and for key individual glaciers. We show that, in addition to Thwaites and Pine Island glaciers in West Antarctica, Totten and Moscow University glaciers in East Antarctica present comparable future dynamic mass loss and high sensitivity to ice shelf basal melt. The overall uncertainty in additional dynamic mass loss in response to changing oceanic conditions, compared to a scenario with constant oceanic conditions, is dominated by the choice of ice sheet model, accounting for 52 % of the total uncertainty of the Antarctic dynamic mass loss in 2100. Its relative role for the most dynamic glaciers varies between 14 % for MacAyeal and Whillans ice streams and 56 % for Pine Island Glacier at the end of the century. The uncertainty associated with the choice of climate model increases over time and reaches 13 % of the uncertainty by 2100 for the Antarctic Ice Sheet but varies between 4 % for Thwaites Glacier and 53 % for Whillans Ice Stream. The uncertainty associated with the ice–climate interaction, which captures different treatments of oceanic forcings such as the choice of melt parameterization, its calibration, and simulated ice shelf geometries, accounts for 22 % of the uncertainty at the ice sheet scale but reaches 36 % and 39 % for Institute Ice Stream and Thwaites Glacier, respectively, by 2100. Overall, this study helps inform future research by highlighting the sectors of the ice sheet most vulnerable to oceanic warming over the 21st century and by quantifying the main sources of uncertainty.