Variational formulation of marine ice-sheet and subglacial-lake grounding-line dynamics

Stubblefield, A. G.; Spiegelman, Marc; Creyts, T. T.

doi:10.1017/jfm.2021.394

Cited by 13 publications

(40 citation statements)

References 82 publications

(168 reference statements)

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“…(2007) and Stubblefield et al. (2021). When computing the points along the steady sliding law in figure 4 with our method, the number of time steps required to converge to a steady state can become very large (of order 1000) in the highly cavitated stages along the downsloping region of the curve.…”

Section: Discussionmentioning

confidence: 96%

“…This is the approach used in Stubblefield et al. (2021). We find that what works best in combination with the advection equation is a mixed method with Lagrange multipliers that enforces an average-wise contact condition.…”

Section: Formulation and Approximation Of The Problem Of Subglacial C...mentioning

confidence: 99%

“…We find that this latter property of the numerical scheme enables us to evolve the surface of the viscous flow in a robust way. To the best of our knowledge, viscous contact problems have been solved previously as variational inequalities only in Stubblefield, Spiegelman & Creyts (2021), where a penalty method is used.…”

Section: Introductionmentioning

confidence: 99%

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Numerical approximation of viscous contact problems applied to glacial sliding

2022

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Viscous contact problems describe the time evolution of fluid flows in contact with a surface from which they can detach and reattach. These problems are of particular importance in glaciology, where they arise in the study of grounding lines and subglacial cavities. In this work, we propose a novel numerical method for solving viscous contact problems based on a mixed formulation with Lagrange multipliers of a variational inequality involving the Stokes equations. The advection equation for evolving the geometry of the domain occupied by the fluid is then solved via a specially-built upwinding scheme, leading to a robust and accurate algorithm for viscous contact problems. We first verify the method by comparing the numerical results to analytical results obtained by a linearised method. Then we use this numerical scheme to reconstruct friction laws for glacial sliding with cavitation. Finally, we compute the evolution of cavities from a steady state under oscillating water pressures. The results depend strongly on the location of the initial steady state along the friction law. In particular, we find that if the steady state is located on the downsloping or rate-weakening part of the friction law, then the cavity evolves towards the upsloping section, indicating that the downsloping part is unstable.

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Section: Discussionmentioning

confidence: 96%

Section: Formulation and Approximation Of The Problem Of Subglacial C...mentioning

confidence: 99%

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Numerical approximation of viscous contact problems applied to glacial sliding

2022

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“…Stress continuity implies that the normal stress equals the water pressure at the ice-water interface and that the shear stress vanishes there. In the formulation of Stubblefield et al (2021), outward migration of the subglacial lake shorelines is allowed when the water pressure exceeds the normal stress at the bed, analogous to grounding line migration at the ice-ocean interface (Durand et al, 2009;Favier et al, 2012). The subglacial lake water is assumed to have a hydrostatic pressure field (Stubblefield et al, 2021).…”

Section: Nonlinear Modelmentioning

confidence: 99%

“…The overlying ice is modeled as an isothermal, incompressible viscous fluid that deforms according to the Stokes equations with nonlinear viscosity following Glen's law (Cuffey & Paterson, 2010;Glen, 1955;Jouvet et al, 2008). The model formulation is described in detail in Stubblefield et al (2021) and Text S1.…”

Section: Nonlinear Modelmentioning

confidence: 99%

Surface Expression and Apparent Timing of Subglacial Lake Oscillations Controlled by Viscous Ice Flow

Stubblefield

Creyts

Kingslake

et al. 2021

Geophysical Research Letters

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Reconstructing subglacial lake activity with an altimetry-based inverse method

Stubblefield,

Meyer,

Siegfried

et al. 2023

J. Glaciol.

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Subglacial lake water-volume changes produce ice-elevation anomalies that provide clues about water flow beneath glaciers and ice sheets. Significant challenges remain in the quantitative interpretation of these elevation-change anomalies because the surface expression of subglacial lake activity depends on basal conditions, rate of water-volume change, and ice rheology. To address these challenges, we introduce an inverse method that reconstructs subglacial lake activity from altimetry data while accounting for the effects of viscous ice flow. We use a linearized approximation of a Stokes ice-flow model under the assumption that subglacial lake activity only induces small perturbations relative to a reference ice-flow state. We validate this assumption by accurately reconstructing lake activity from synthetic data that are produced with a fully nonlinear model. We then apply the method to estimate the water-volume changes of several active subglacial lakes in Antarctica by inverting data from NASA's Ice, Cloud, and land Elevation Satellite 2 (ICESat-2) laser altimetry mission. The results show that there can be substantial discrepancies (20% or more) between the inversion and traditional estimation methods due to the effects of viscous ice flow. The inverse method will help refine estimates of subglacial water transport and further constrain the role of subglacial hydrology in ice-sheet evolution.

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Variational formulation of marine ice-sheet and subglacial-lake grounding-line dynamics

Abstract: Abstract

Cited by 13 publications

References 82 publications

Numerical approximation of viscous contact problems applied to glacial sliding

Numerical approximation of viscous contact problems applied to glacial sliding

Surface Expression and Apparent Timing of Subglacial Lake Oscillations Controlled by Viscous Ice Flow

Reconstructing subglacial lake activity with an altimetry-based inverse method

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