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.
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Modeling oscillations in connected glacial lakes
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.
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- Award ID(s):
- 1643970
- NSF-PAR ID:
- 10144205
- Date Published:
- Journal Name:
- Journal of Glaciology
- Volume:
- 65
- Issue:
- 253
- ISSN:
- 1727-5652
- Page Range / eLocation ID:
- 745-758
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract Lakes set in arctic permafrost landscapes can be susceptible to rapid drainage and downstream flood generation. Of many thousands of lakes in northern Alaska, hundreds have been identified as having high drainage potential directly to river systems and 18 such drainage events have been documented since 1955. In 2018 we began monitoring a large lake with high drainage potential as part of a long‐term hydrological observation network designed to evaluate impacts of land use and climate change. In early June 2022, surface water was observed flowing over a 30‐m wide bluff, with active headward erosion of ice‐rich permafrost soils apparent by late June. This overflow point breached rapidly in early July, draining almost the entire lake within 12 h and generating a 191 m3/s flood to a downstream creek. Water level and turbidity sensors and time‐lapse cameras captured this rapid lake‐drainage event at high resolution. A wind‐driven surface seiche and warming waters following ice‐out helped trigger the initial thermomechanical breach. We estimate at least 600 MT of lake sediment was eroded, mobilized, and transported downstream. A flood wave peaking at 42 m3/s arrived 14 h after the initial breach at a river gauge 9‐km downstream. Comparing this event with three other quantified arctic lake‐drainage floods suggests that lake surface area coupled with drainage gradient height can predict outburst flood magnitude. Using this relationship we estimated future flood hazards from the 146 lakes in the Arctic Coastal Plain of northern Alaska (ACP) with high drainage potential, of which 20% are expected to generate outburst floods exceeding 100 m3/s to downstream rivers. This fortunate and detailed drainage‐event observation adds to a growing body of research on the impact of lakes on arctic hydrology, hazard forecasting in a region with an increasing human footprint, and broader processes of landscape evolution in arctic lowlands.
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null (Ed.)Abstract 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 $${\rm{m}}{{\rm{m}}}^{3}$$ m m 3 to 215 ± 90.2 $${\rm{m}}{{\rm{m}}}^{3}$$ m m 3 ) as the melt season progresses, suggesting significant changes in basal hydrology beneath the lakes driven by seasonal meltwater input.more » « less
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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.more » « less
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Abstract Subglacial lakes require a thawed bed either now or in the past; thus, their presence and stability have implications for current and past basal conditions, ice dynamics, and climate. Here, we present the most extensive geophysical exploration to date of a subglacial lake near the geographic South Pole, including radar‐imaged stratigraphy, surface velocities, and englacial vertical velocities. We use a 1.5‐dimensional temperature model, optimized with our geophysical data set and nearby temperature measurements, to estimate past basal‐melt rates. The ice geometry, reflected bed‐echo power, surface and vertical velocities, and temperature model indicate that the ice‐bed interface is regionally thawed, contradicting prior studies. Together with an earlier active‐source seismic study, which showed a 32‐m deep lake underlain by 150 m of sediment, our results suggest that the lake has been thermodynamically stable through at least the last 120,000 years and possibly much longer, making it a promising prospective site for sediment coring.
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://doi.org/10.1017/
