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Abstract Basal melting of ice shelves is a major source of mass loss from the Antarctic Ice Sheet. In situ measurements of ice shelf basal melt rates are sparse, while the more extensive estimates from satellite altimetry require precise information about firn density and characteristics of near‐surface layers. We describe a novel method for estimating multidecadal basal melt rates using airborne ice penetrating radar data acquired during a 3‐year survey of the Ross Ice Shelf. These data revealed an ice column with distinct upper and lower units whose thicknesses change as ice flows from the grounding line toward the ice front. We interpret the lower unit as continental meteoric ice that has flowed across the grounding line and the upper unit as ice formed from snowfall onto the relatively flat ice shelf. We used the ice thickness difference and strain‐induced thickness change of the lower unit between the survey lines, combined with ice velocities, to derive basal melt rates averaged over one to six decades. Our results are similar to satellite laser altimetry estimates for the period 2003–2009, suggesting that the Ross Ice Shelf melt rates have been fairly stable for several decades. We identify five sites of elevated basal melt rates, in the range 0.5–2 m a⁻¹, near the ice shelf front. These hot spots indicate pathways into the sub‐ice‐shelf ocean cavity for warm seawater, likely a combination of summer‐warmed Antarctic Surface Water and modified Circumpolar Deep Water, and are potential areas of ice shelf weakening if the ocean warms. 

Surface meltwater reaching the base of the Greenland Ice Sheet transits through drainage networks, modulating the flow of the ice sheet. Dye and gas-tracing studies conducted in the western margin sector of the ice sheet have directly observed drainage efficiency to evolve seasonally along the drainage pathway. However, the local evolution of drainage systems further inland, where ice thicknesses exceed 1000 m, remains largely unknown. Here, we infer drainage system transmissivity based on surface uplift relaxation following rapid lake drainage events. Combining field observations of five lake drainage events with a mathematical model and laboratory experiments, we show that the surface uplift decreases exponentially with time, as the water in the blister formed beneath the drained lake permeates through the subglacial drainage system. This deflation obeys a universal relaxation law with a timescale that reveals hydraulic transmissivity and indicates a two-order-of- magnitude increase in subglacial transmissivity (from 0.8 ± 0.3 mm3 to 215 ± 90.2 mm3) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input. 

Grounding lines exist where land-based glacial ice flows on to a body of water. Accurately modelling grounding-line migration at the ice–ocean interface is essential for estimating future ice-sheet mass change. On the interior of ice sheets, the shores of subglacial lakes are also grounding lines. Grounding-line positions are sensitive to water volume changes such as sea-level rise or subglacial-lake drainage. Here, we introduce numerical methods for simulating grounding-line dynamics in the marine ice sheet and subglacial-lake settings. Variational inequalities arise from contact conditions that relate normal stress, water pressure and velocity at the base. Existence and uniqueness of solutions to these problems are established using a minimisation argument. A penalty method is used to replace the variational inequalities with variational equations that are solved using a finite-element method. We illustrate the grounding-line response to tidal cycles in the marine ice-sheet problem and filling–draining cycles in the subglacial-lake problem. We introduce two computational benchmarks where the known lake volume change is used to measure the accuracy of the numerical method. 

Mountain glaciers and ice sheets often host marginal and subglacial lakes that are hydraulically connected through subglacial drainage systems. These lakes exhibit complex dynamics that have been the subject of models for decades. Here we introduce and analyze a model for the evolution of glacial lakes connected by subglacial channels. Subglacial channel equations are supplied with effective pressure boundary conditions that are determined by a simple lake model. While the model can describe an arbitrary number of lakes, we solve it numerically with a finite element method for the case of two connected lakes. We examine the effect of relative lake size and spacing on the oscillations. Complex oscillations in the downstream lake are driven by discharge out of the upstream lake. These include multi-peaked and anti-phase filling–draining events. Similar filling–draining cycles have been observed on the Kennicott Glacier in Alaska and at the confluence of the Whillans and Mercer ice streams in West Antarctica. We further construct a simplified ordinary differential equation model that displays the same qualitative behavior as the full, spatially-dependent model. We analyze this model using dynamical systems theory to explain the appearance of filling–draining cycles as the meltwater supply varies. 

The East Antarctic Ice Sheet contains a wealth of information that can be extracted from its internal architecture such as distribution of age, past flow features, and surface and basal properties. Airborne radar surveys can sample this stratigraphic archive across broad areas. Here, we identify and trace key horizons across several radar surveys to obtain the stratigraphic information. We transfer the age–depth scales from ice cores to intersecting radar data. We then propagate these age scales across the ice sheet using the high fidelity continuity of the radar horizons. In Dronning Maud Land, including Dome Fuji, we mapped isochrones with ages of 38 and 74 ka. In the central region of East Antarctica around Dome Concordia, Vostok and Dome Argus, we use isochrone ages of 38, 48, 90 and 161 ka. Taking together both regions, we provide isochrone depths traced along a combined profile length of more than 40 000 km and discuss uncertainties of the obtained stratigraphy, as well as factors important to consider for further expansion. This data set is the most extensive distribution of internal horizons in East Antarctica to date. The isochrone depths presented in this study are available on PANGAEA (https://doi.org/10.1594/PANGAEA.895528; Winter et al., 2018).