Marine ice sheet stability

2012 ◽  
Vol 698 ◽  
pp. 62-72 ◽  
Author(s):  
Christian Schoof
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Multiple Equilibria ◽  
Moving Boundary ◽  
Ice Sheets ◽  
Mass Gain ◽  
Ice Thickness ◽  
Grounding Line ◽  
Type Boundary ◽  
The Stability

AbstractWe examine the stability of two-dimensional marine ice sheets in steady state. The dynamics of marine ice sheets is described by a viscous thin-film model with two Stefan-type boundary conditions at the moving boundary or ‘grounding line’ that marks the transition from grounded to floating ice. One of these boundary conditions constrains ice thickness to be at a local critical value for flotation, which depends on depth to bedrock at the grounding line. The other condition sets ice flux as a function of ice thickness at the grounding line. Depending on the shape of the bedrock, multiple equilibria may be possible. Using a linear stability analysis, we confirm a long-standing heuristic argument that asserts that the stability of these equilibria is determined by a simple mass balance consideration. If an advance in the grounding line away from its steady-state position leads to a net mass gain, the steady state is unstable, and stable otherwise. This also confirms that grounding lines can only be stable in positions where bedrock slopes downwards sufficiently steeply.

scholarly journals Suppression of marine ice sheet instability

2018 ◽  
Vol 857 ◽  
pp. 648-680 ◽  
Author(s):  
Samuel S. Pegler
Keyword(s):  
Steady State ◽  
Rapid Assessment ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Stable Steady State ◽  
Ice Shelf ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
The Stability

A long-standing open question in glaciology concerns the propensity for ice sheets that lie predominantly submerged in the ocean (marine ice sheets) to destabilise under buoyancy. This paper addresses the processes by which a buoyancy-driven mechanism for the retreat and ultimate collapse of such ice sheets – the marine ice sheet instability – is suppressed by lateral stresses acting on its floating component (the ice shelf). The key results are to demonstrate the transition between a mode of stable (easily reversible) retreat along a stable steady-state branch created by ice-shelf buttressing to tipped (almost irreversible) retreat across a critical parametric threshold. The conditions for triggering tipped retreat can be controlled by the calving position and other properties of the ice-shelf profile and can be largely independent of basal stress, in contrast to principles established from studies of unbuttressed grounding-line dynamics. The stability and recovery conditions introduced by lateral stresses are analysed by developing a method of constructing grounding-line stability (bifurcation) diagrams, which provide a rapid assessment of the steady-state positions, their natures and the conditions for secondary grounding, giving clear visualisations of global stabilisation conditions. A further result is to reveal the possibility of a third structural component of a marine ice sheet that lies intermediate to the fully grounded and floating components. The region forms an extended grounding area in which the ice sheet lies very close to flotation, and there is no clearly distinguished grounding line. The formation of this region generates an upsurge in buttressing that provides the most feasible mechanism for reversal of a tipped grounding line. The results of this paper provide conceptual insight into the phenomena controlling the stability of the West Antarctic Ice Sheet, the collapse of which has the potential to dominate future contributions to global sea-level rise.

scholarly journals Ice-shelf buttressing and the stability of marine ice sheets

2012 ◽  
Vol 6 (5) ◽  
pp. 3937-3962 ◽  
Author(s):  
G. H. Gudmundsson
Keyword(s):  
Ice Sheets ◽  
Theoretical Work ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Recent Theoretical Work ◽  
Grounding Line ◽  
Monotonically Increasing Function ◽  
The Stability ◽  
Line Positions ◽  
Increasing Function

Abstract. Ice-shelf buttressing and the stability of marine-type ice sheets is investigated numerically. Buttressing effects are analysed for a situation where a stable grounding line is located on a bed sloping upwards in the direction of flow. Such grounding-line positions are known to be unconditionally unstable in the absence of transverse flow variations. It is shown that ice-shelf buttressing effects are responsible for restoring stability. Ice flux at the grounding line is, in general, not a monotonically increasing function of ice thickness. This, at first sight possibly somewhat counterintuitive result, is found to be fully consistent with recent theoretical work.

scholarly journals Marine ice-sheet dynamics. Part 1. The case of rapid sliding

2007 ◽  
Vol 573 ◽  
pp. 27-55 ◽  
Author(s):  
CHRISTIAN SCHOOF
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Ice Shelves ◽  
Sea Floor ◽  
Stefan Problems ◽  
Grounding Line ◽  
Ice Sheet Dynamics ◽  
The Stability

Marine ice sheets are continental ice masses resting on bedrock below sea level. Their dynamics are similar to those of land-based ice sheets except that they must couple with the surrounding floating ice shelves at the grounding line, where the ice reaches a critical flotation thickness. In order to predict the evolution of the grounding line as a free boundary, two boundary conditions are required for the diffusion equation describing the evolution of the grounded-ice thickness. By analogy with Stefan problems, one of these conditions imposes a prescribed ice thickness at the grounding line and arises from the fact that the ice becomes afloat. The other condition must be determined by coupling the ice sheet to the surrounding ice shelves. Here we employ matched asymptotic expansions to study the transition from ice-sheet to ice-shelf flow for the case of rapidly sliding ice sheets. Our principal results are that the ice flux at the grounding line in a two-dimensional ice sheet is an increasing function of the depth of the sea floor there, and that ice thicknesses at the grounding line must be small compared with ice thicknesses inland. These results indicate that marine ice sheets have a discrete set of steady surface profiles (if they have any at all) and that the stability of these steady profiles depends on the slope of the sea floor at the grounding line.

scholarly journals Upper and lower limits on the stability of calving glaciers from the yield strength envelope of ice

2011 ◽  
Vol 468 (2140) ◽  
pp. 913-931 ◽  
Author(s):  
J. N. Bassis ◽  
C. C. Walker
Keyword(s):  
Yield Strength ◽  
Water Depth ◽  
Shear Failure ◽  
Ice Sheets ◽  
Direct Consequence ◽  
Ice Thickness ◽  
Tightly Coupled ◽  
The Stability ◽  
Induced Changes ◽  
Lower Limits

Observations indicate that substantial changes in the dynamics of marine-terminating ice sheets and glaciers are tightly coupled to calving-induced changes in the terminus position. However, the calving process itself remains poorly understood and is not well parametrized in current numerical ice sheet models. In this study, we address this uncertainty by deriving plausible upper and lower limits for the maximum stable ice thickness at the calving face of marine-terminating glaciers, using two complementary models. The first model assumes that a combination of tensile and shear failure can render the ice cliff near the terminus unstable and/or enable pre-existing crevasses to intersect. A direct consequence of this model is that thick glaciers must terminate in deep water to stabilize the calving front, yielding a predicted maximum ice cliff height that increases with increasing water depth, consistent with observations culled from glaciers in West Greenland, Antarctica, Svalbard and Alaska. The second model considers an analogous lower limit derived by assuming that the ice is already fractured and fractures are lubricated by pore pressure. In this model, a floating ice tongue can only form when the ice entering the terminus region is relatively intact with few pre-existing, deeply penetrating crevasses.

scholarly journals Boundary layer models for calving marine outlet glaciers

2017 ◽  
Vol 11 (5) ◽  
pp. 2283-2303 ◽  
Author(s):  
Christian Schoof ◽  
Andrew D. Davis ◽  
Tiberiu V. Popa
Keyword(s):  
Boundary Layer ◽  
Ice Sheets ◽  
Ice Thickness ◽  
Ice Shelf ◽  
Bedrock Channel ◽  
Extensional Stress ◽  
Grounding Line ◽  
Direct Numerical Solution ◽  
Glacier Ice ◽  
Side Walls

Abstract. We consider the flow of marine-terminating outlet glaciers that are laterally confined in a channel of prescribed width. In that case, the drag exerted by the channel side walls on a floating ice shelf can reduce extensional stress at the grounding line. If ice flux through the grounding line increases with both ice thickness and extensional stress, then a longer shelf can reduce ice flux by decreasing extensional stress. Consequently, calving has an effect on flux through the grounding line by regulating the length of the shelf. In the absence of a shelf, it plays a similar role by controlling the above-flotation height of the calving cliff. Using two calving laws, one due to Nick et al. (2010) based on a model for crevasse propagation due to hydrofracture and the other simply asserting that calving occurs where the glacier ice becomes afloat, we pose and analyse a flowline model for a marine-terminating glacier by two methods: direct numerical solution and matched asymptotic expansions. The latter leads to a boundary layer formulation that predicts flux through the grounding line as a function of depth to bedrock, channel width, basal drag coefficient, and a calving parameter. By contrast with unbuttressed marine ice sheets, we find that flux can decrease with increasing depth to bedrock at the grounding line, reversing the usual stability criterion for steady grounding line location. Stable steady states can then have grounding lines located on retrograde slopes. We show how this anomalous behaviour relates to the strength of lateral versus basal drag on the grounded portion of the glacier and to the specifics of the calving law used.

scholarly journals Hydrostatic grounding line parameterization in ice sheet models

2014 ◽  
Vol 8 (3) ◽  
pp. 3335-3365
Author(s):  
H. Seroussi ◽  
M. Morlighem ◽  
E. Larour ◽  
E. Rignot ◽  
A. Khazendar
Keyword(s):  
Steady State ◽  
High Spatial Resolution ◽  
Numerical Models ◽  
Ice Sheets ◽  
Line Position ◽  
Balance Equations ◽  
Grounding Line ◽  
Mesh Resolution ◽  
Averaged Model ◽  
Line Positions

Abstract. Modeling of grounding line migration is essential to simulate accurately the behavior of marine ice sheets and investigate their stability. Here, we assess the sensitivity of numerical models to the parameterization of the grounding line position. We run the MISMIP3D benchmark experiments using a two-dimensional shelfy-stream approximation (SSA) model with different mesh resolutions and different sub-element parameterizations of grounding line position. Results show that different grounding line parameterizations lead to different steady state grounding line positions as well as different retreat/advance rates. Our simulations explain why some vertically depth-averaged model simulations exhibited behaviors similar to full-Stokes models in the MISMIP3D benchmark, while the vast majority of simulations based on SSA showed results deviating significantly from full-Stokes results. The results reveal that differences between simulations performed with and without sub-element parameterization are as large as those performed with different approximations of the stress balance equations and that the reversibility test can be passed at much lower resolutions than the steady-state grounding line position. We conclude that fixed grid models that do not employ such a parameterization should be avoided, as they do not provide accurate estimates of grounding line dynamics, even at high spatial resolution. For models that include sub-element grounding line parameterization, a mesh resolution lower than 2 km should be employed.

Memory-type boundary control of a laminated Timoshenko beam

2020 ◽  
Vol 25 (8) ◽  
pp. 1568-1588 ◽  
Author(s):  
Baowei Feng ◽  
Abdelaziz Soufyane
Keyword(s):  
Boundary Conditions ◽  
Timoshenko Beam ◽  
Stability Result ◽  
Kernel Functions ◽  
The Other ◽  
Interfacial Slip ◽  
Small Thickness ◽  
Memory Type ◽  
Type Boundary ◽  
The Stability

In this paper, we consider a laminated Timoshenko beam with boundary conditions of a memory type. This structure is given by two identical uniform layers, one on top of the other, taking into account that an adhesive of small thickness bonds the two surfaces and produces an interfacial slip. Under the assumptions of wider classes of kernel functions, we establish an optimal explicit energy decay result. The stability result is more general than previous works and hence improves earlier results in the literature.

scholarly journals Third type boundary conditions for steady state ambipolar diffusion equation

2016 ◽  
Vol 158 ◽  
pp. 012102 ◽  
Author(s):  
V S Zheltukhin ◽  
S I Solov'ev ◽  
P S Solov'ev ◽  
V Yu Chebakova ◽  
A M Sidorov
Keyword(s):  
Steady State ◽  
Diffusion Equation ◽  
Boundary Conditions ◽  
Ambipolar Diffusion ◽  
Type Boundary

scholarly journals An exact solution for a steady, flowline marine ice sheet

2014 ◽  
Vol 60 (224) ◽  
pp. 1117-1125 ◽  
Author(s):  
Ed Bueler
Keyword(s):  
Exact Solution ◽  
Numerical Models ◽  
Plug Flow ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Thickness ◽  
Longitudinal Stress ◽  
Surface Mass ◽  
Continuity Equations ◽  
Grounding Line

AbstractG. Böðvarsson’s 1955 plug-flow solution for an Icelandic glacier problem is shown to be an exact solution to the steady form of the simultaneous stress-balance and mass-continuity equations widely used in numerical models of marine ice sheets. The solution, which has parabolic ice thickness and constant vertically integrated longitudinal stress, solves the steady shallow-shelf approximation with linear sliding on a flat bed. It has an elevation-dependent surface mass-balance rate and, in the interpretation given here, a contrived location-dependent ice hardness distribution. By connecting Böðvarsson’s solution to the Van der Veen (1983) solution for floating ice, we construct an exact solution to the ‘rapid-sliding’ marine ice-sheet problem, continuously across the grounding line. We exploit this exact solution to examine the accuracy of two numerical methods, one grid-free and the other based on a fixed, equally spaced grid.

scholarly journals Ice-shelf buttressing and the stability of marine ice sheets

2013 ◽  
Vol 7 (2) ◽  
pp. 647-655 ◽  
Author(s):  
G. H. Gudmundsson
Keyword(s):  
Ice Sheets ◽  
Theoretical Work ◽  
Ice Shelf ◽  
Recent Theoretical Work ◽  
Grounding Line ◽  
Bed Slope ◽  
The Stability ◽  
Stability Regime ◽  
Line Positions ◽  
Increasing Function

Abstract. Ice-shelf buttressing and the stability of marine-type ice sheets are investigated numerically. Buttressing effects are analysed for a situation where a stable grounding line is located on a bed sloping upwards in the direction of flow. Such grounding-line positions are known to be unconditionally unstable in the absence of transverse flow variations. It is shown that ice-shelf buttressing can restore stability under these conditions. Ice flux at the grounding line is, in general, not a monotonically increasing function of ice thickness. This, possibly at first somewhat counterintuitive result, is found to be fully consistent with recent theoretical work. Grounding lines on retrograde slopes are conditionally stable, and the stability regime is a non-trivial function of bed and ice-shelf geometry. The stability of grounding lines cannot be assessed from considerations of local bed slope only.

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