scholarly journals Modelling dynamic ice-sheet boundaries and grounding line migration using the level set method

2020 ◽  
Vol 66 (259) ◽  
pp. 766-776
Author(s):  
M. Alamgir Hossain ◽  
Sam Pimentel ◽  
John M. Stockie
Keyword(s):  
Level Set Method ◽  
Level Set ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Numerical Approach ◽  
Ice Surface ◽  
Grounding Line ◽  
High Degree ◽  
Ice Water ◽  
Benchmark Solutions

AbstractComputing predictions of future sea level that include well-defined uncertainty bounds requires models that are capable of robustly simulating the evolution of ice sheets and glaciers. Ice flow behaviour is known to be sensitive to the location and geometry of dynamic ice boundaries such as the grounding line (GRL), terminus position and ice surface elevation, so that any such model should track these interfaces with a high degree of accuracy. To address this challenge, we implement a numerical approach that uses the level-set method (LSM) that accurately models the evolution of the ice–air and ice–water interface as well as capturing topological changes in ice-sheet geometry. This approach is evaluated by comparing simulations of grounded and marine-terminating ice sheets to various analytical and numerical benchmark solutions. A particular advantage of the LSM is its ability to explicitly track the moving margin and GRL while using a fixed grid finite-difference scheme. Our results demonstrate that the LSM is an accurate and robust approach for tracking the ice surface interface and terminus for advancing and retreating ice sheets, including the transient marine ice-sheet interface and GRL positions.

scholarly journals Attention Multi-Scale Network for Automatic Layer Extraction of Ice Radar Topological Sequences

2021 ◽  
Vol 13 (12) ◽  
pp. 2425
Author(s):  
Yiheng Cai ◽  
Dan Liu ◽  
Jin Xie ◽  
Jingxian Yang ◽  
Xiangbin Cui ◽  
...  
Keyword(s):  
Deep Learning ◽  
Global Climate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Sheet Thickness ◽  
Learning Methods ◽  
Convolutional Network ◽  
Multi Scale ◽  
Ice Surface ◽  
Layer Extraction

Analyzing the surface and bedrock locations in radar imagery enables the computation of ice sheet thickness, which is important for the study of ice sheets, their volume and how they may contribute to global climate change. However, the traditional handcrafted methods cannot quickly provide quantitative, objective and reliable extraction of information from radargrams. Most traditional handcrafted methods, designed to detect ice-surface and ice-bed layers from ice sheet radargrams, require complex human involvement and are difficult to apply to large datasets, while deep learning methods can obtain better results in a generalized way. In this study, an end-to-end multi-scale attention network (MsANet) is proposed to realize the estimation and reconstruction of layers in sequences of ice sheet radar tomographic images. First, we use an improved 3D convolutional network, C3D-M, whose first full connection layer is replaced by a convolution unit to better maintain the spatial relativity of ice layer features, as the backbone. Then, an adjustable multi-scale module uses different scale filters to learn scale information to enhance the feature extraction capabilities of the network. Finally, an attention module extended to 3D space removes a redundant bottleneck unit to better fuse and refine ice layer features. Radar sequential images collected by the Center of Remote Sensing of Ice Sheets in 2014 are used as training and testing data. Compared with state-of-the-art deep learning methods, the MsANet shows a 10% reduction (2.14 pixels) on the measurement of average mean absolute column-wise error for detecting the ice-surface and ice-bottom layers, runs faster and uses approximately 12 million fewer parameters.

scholarly journals Dynamical processes involved in the retreat of marine ice sheets

2001 ◽  
Vol 47 (157) ◽  
pp. 271-282 ◽  
Author(s):  
Richard C.A. Hindmarsh ◽  
E. Le Meur
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Ice Streams ◽  
Antarctic Ice Sheet ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
Neutral Equilibrium ◽  
Generally True

AbstractMarine ice sheets with mechanics described by the shallow-ice approximation by definition do not couple mechanically with the shelf. Such ice sheets are known to have neutral equilibria. We consider the implications of this for their dynamics and in particular for mechanisms which promote marine ice-sheet retreat. The removal of ice-shelf buttressing leading to enhanced flow in grounded ice is discounted as a significant influence on mechanical grounds. Sea-level rise leading to reduced effective pressures under ice streams is shown to be a feasible mechanism for producing postglacial West Antarctic ice-sheet retreat but is inconsistent with borehole evidence. Warming thins the ice sheet by reducing the average viscosity but does not lead to grounding-line retreat. Internal oscillations either specified or generated via a MacAyeal–Payne thermal mechanism promote migration. This is a noise-induced drift phenomenon stemming from the neutral equilibrium property of marine ice sheets. This migration occurs at quite slow rates, but these are sufficiently large to have possibly played a role in the dynamics of the West Antarctic ice sheet after the glacial maximum. Numerical experiments suggest that it is generally true that while significant changes in thickness can be caused by spatially uniform changes, spatial variability coupled with dynamical variability is needed to cause margin movement.

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 Modelling of a marine glacier and ice-sheet-ice-shelf transition zone based on asymptotic analysis

1996 ◽  
Vol 23 ◽  
pp. 59-67 ◽  
Author(s):  
Vladimir A. Chugunov ◽  
Alexander V. Wilchinsky
Keyword(s):  
Boundary Conditions ◽  
Transition Zone ◽  
Spatial Scales ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Stream Length ◽  
Glacier Surface ◽  
Ice Surface ◽  
Grounding Line ◽  
The Difference

All parts of a two-dimensional, isothermal, stationary marine glacier (grounded ice sheet, ice shelf and transition zone) with constant viscosity are analysed by perturbation methods. In so doing, all zones of different flow patterns can be considered separately. Correlations between spatial scales for all parts can be expressed in terms of the typical ice-surface slope distant from the ocean, which reflects exterior conditions of the glacier’s existence. In considering the ice-sheet–ice-shelf transition zone, a small parameter characterizing the difference between ice and water densities is used. Such an analysis allows us to find boundary conditions at the grounding line for the grounded ice mass. Glacier-surface profiles are determined by numerical methods. The grounding-line position found by using the boundary conditions derived in this paper differs from that obtained by using Thomas and Bentley’s (1978) boundary conditions by about 10% of the grounded ice-stream length.

scholarly journals Stochastic marine ice sheet variability

2018 ◽  
Vol 843 ◽  
pp. 748-777 ◽  
Author(s):  
T. E. Mulder ◽  
S. Baars ◽  
F. W. Wubs ◽  
H. A. Dijkstra
Keyword(s):  
Transition Probabilities ◽  
Accumulation Rate ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Field Measurements ◽  
Multiple Equilibrium ◽  
Short Time Scale ◽  
Two Dimensional ◽  
Grounding Line ◽  
Short Time

It is well known that deterministic two-dimensional marine ice sheets can only be stable if the grounding line is positioned at a sufficiently steep, downward sloping bedrock. When bedrock conditions favour instabilities, multiple stable ice sheet profiles may occur. Here, we employ continuation techniques to examine the sensitivity of a two-dimensional marine ice sheet to stochastic noise representing short time scale variability, either in the accumulation rate or in the sea level height. We find that in unique regimes, the position of the grounding line is most sensitive to noise in the accumulation rate and can explain excursions observed in field measurements. In the multiple equilibrium regime, there is a strong asymmetry in transition probabilities between the different ice sheet states, with a strong preference to switch to the branch with a steeper bedrock slope.

A Fast Semi-Implicit Level Set Method for Curvature Dependent Flows with an Application to Limit Cycles Extraction in Dynamical Systems

2015 ◽  
Vol 18 (1) ◽  
pp. 203-229 ◽  
Author(s):  
Guoqiao You ◽  
Shingyu Leung
Keyword(s):  
Dynamical Systems ◽  
Level Set Method ◽  
Level Set ◽  
Limit Cycles ◽  
Time Discretization ◽  
Numerical Approach ◽  
Initial Guess ◽  
Implicit Time ◽  
Time Step ◽  
Image Regularization

AbstractWe propose a new semi-implicit level set approach to a class of curvature dependent flows. The method generalizes a recent algorithm proposed for the motion by mean curvature where the interface is updated by solving the Rudin-Osher-Fatemi (ROF) model for image regularization. Our proposal is general enough so that one can easily extend and apply the method to other curvature dependent motions. Since the derivation is based on a semi-implicit time discretization, this suggests that the numerical scheme is stable even using a time-step significantly larger than that of the corresponding explicit method. As an interesting application of the numerical approach, we propose a new variational approach for extracting limit cycles in dynamical systems. The resulting algorithm can automatically detect multiple limit cycles staying inside the initial guess with no condition imposed on the number nor the location of the limit cycles. Further, we also propose in this work an Eulerian approach based on the level set method to test if the limit cycles are stable or unstable.

scholarly journals Marine ice-sheet profiles and stability under Coulomb basal conditions

2015 ◽  
Vol 61 (226) ◽  
pp. 205-215 ◽  
Author(s):  
Victor C. Tsai ◽  
Andrew L. Stewart ◽  
Andrew F. Thompson
Keyword(s):  
Power Law ◽  
Coulomb Friction ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Friction Behavior ◽  
West Antarctic Ice Sheet ◽  
West Antarctic ◽  
Grounding Line ◽  
Catastrophic Loss ◽  
Bed Slope

AbstractThe behavior of marine-terminating ice sheets, such as the West Antarctic ice sheet, is of interest due to the possibility of rapid grounding-line retreat and consequent catastrophic loss of ice. Critical to modeling this behavior is a choice of basal rheology, where the most popular approach is to relate the ice-sheet velocity to a power-law function of basal stress. Recent experiments, however, suggest that near-grounding line tills exhibit Coulomb friction behavior. Here we address how Coulomb conditions modify ice-sheet profiles and stability criteria. The basal rheology necessarily transitions to Coulomb friction near the grounding line, due to low effective stresses, leading to changes in ice-sheet properties within a narrow boundary layer. Ice-sheet profiles ‘taper off’ towards a flatter upper surface, compared with the power-law case, and basal stresses vanish at the grounding line, consistent with observations. In the Coulomb case, the grounding-line ice flux also depends more strongly on flotation ice thickness, which implies that ice sheets are more sensitive to climate perturbations. Furthermore, with Coulomb friction, the ice sheet grounds stably in shallower water than with a power-law rheology. This implies that smaller perturbations are required to push the grounding line into regions of negative bed slope, where it would become unstable. These results have important implications for ice-sheet stability in a warming climate.

scholarly journals The Dynamics of Marine Ice Sheets

1979 ◽  
Vol 24 (90) ◽  
pp. 167-177 ◽  
Author(s):  
Robert H. Thomas
Keyword(s):  
Sea Level ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Ice Streams ◽  
Ice Shelves ◽  
The North ◽  
West Antarctic ◽  
Grounding Line ◽  
Ice Sheet Dynamics

AbstractMarine ice sheets rest on land that, for the most part, is below sea-level. Ice that flows across the grounding line, where the ice sheet becomes afloat, either calves into icebergs or forms a floating ice shelf joined to the ice sheet. At the grounding line there is a transition from ice-sheet dynamics to ice-shelf dynamics, and the creep-thinning rate in this region is very sensitive to sea depth; rising sea-level causes increased thinning-rates and grounding-line retreat, falling sea-level has the reverse effect. If the bedrock slopes down towards the centre of the ice sheet there may be only two stable modes: a freely-floating ice shelf or a marine ice sheet that extends to the edge of the continental shelf. Once started, collapse of such an ice sheet to form an ice shelf may take place extremely rapidly. Ice shelves which form in embayments of a marine ice sheet, or which are partially grounded, have a stabilizing influence since ice flowing across the grounding line has to push the ice shelf past its sides. Retreat of the grounding line tends to enlarge the ice shelf, which ultimately may become large enough to prevent excessive outflow from the ice sheet so that a new equilibrium grounding line is established; removal of the ice shelf would allow retreat to continue. During the late-Wisconsin glacial maximum there may have been marine ice sheets in the northern hemisphere but the only current example is the West Antarctic ice sheet. This is buttressed by the Ross and Ronne Ice Shelves, and if climatic warming were to prohibit the existence of these ice shelves then the ice sheet would collapse. Field observations suggest that, at present, the ice sheet may be advancing into parts of the Ross Ice Shelf. Such advance, however, would not ensure the security of the ice sheet since ice streams that drain to the north appear to flow directly into the sea with little or no ice shelf to buttress them. If these ice streams do not flow over a sufficiently high bedrock sill then they provide the most likely avenues for ice-sheet retreat.

scholarly journals Mass balance of the Sør Rondane glacial system, East Antarctica

2015 ◽  
Vol 56 (70) ◽  
pp. 63-69 ◽  
Author(s):  
Denis Callens ◽  
Nicolas Thonnard ◽  
Jan T.M. Lenaerts ◽  
Jan M. Van Wessem ◽  
Willem Jan Van de Berg ◽  
...  
Keyword(s):  
Mass Balance ◽  
Drainage Basin ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Antarctic Ice Sheet ◽  
Outlet Glacier ◽  
Surface Mass ◽  
Mass Budget ◽  
Grounding Line ◽  
The Antarctic

AbstractMass changes of polar ice sheets have an important societal impact, because they affect global sea level. Estimating the current mass budget of ice sheets is equivalent to determining the balance between surface mass gain through precipitation and outflow across the grounding line. For the Antarctic ice sheet, grounding line outflow is governed by oceanic processes and outlet glacier dynamics. In this study, we compute the mass budget of major outlet glaciers in the eastern Dronning Maud Land sector of the Antarctic ice sheet using the input/output method. Input is given by recent surface accumulation estimates (SMB) of the whole drainage basin. The outflow at the grounding line is determined from the radar data of a recent airborne survey and satellite-based velocities using a flow model of combined plug flow and simple shear. This approach is an improvement on previous studies, as the ice thickness is measured, rather than being estimated from hydrostatic equilibrium. In line with the general thickening of the ice sheet over this sector, we estimate the regional mass balance in this area at 3.15 ± 8.23 Gt a−1 according to the most recent SMB model results.

scholarly journals The Dynamics of Marine Ice Sheets

1979 ◽  
Vol 24 (90) ◽  
pp. 167-177 ◽  
Author(s):  
Robert H. Thomas
Keyword(s):  
Sea Level ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Ice Streams ◽  
Ice Shelves ◽  
The North ◽  
West Antarctic ◽  
Grounding Line ◽  
Ice Sheet Dynamics

AbstractMarine ice sheets rest on land that, for the most part, is below sea-level. Ice that flows across the grounding line, where the ice sheet becomes afloat, either calves into icebergs or forms a floating ice shelf joined to the ice sheet. At the grounding line there is a transition from ice-sheet dynamics to ice-shelf dynamics, and the creep-thinning rate in this region is very sensitive to sea depth; rising sea-level causes increased thinning-rates and grounding-line retreat, falling sea-level has the reverse effect. If the bedrock slopes down towards the centre of the ice sheet there may be only two stable modes: a freely-floating ice shelf or a marine ice sheet that extends to the edge of the continental shelf. Once started, collapse of such an ice sheet to form an ice shelf may take place extremely rapidly. Ice shelves which form in embayments of a marine ice sheet, or which are partially grounded, have a stabilizing influence since ice flowing across the grounding line has to push the ice shelf past its sides. Retreat of the grounding line tends to enlarge the ice shelf, which ultimately may become large enough to prevent excessive outflow from the ice sheet so that a new equilibrium grounding line is established; removal of the ice shelf would allow retreat to continue. During the late-Wisconsin glacial maximum there may have been marine ice sheets in the northern hemisphere but the only current example is the West Antarctic ice sheet. This is buttressed by the Ross and Ronne Ice Shelves, and if climatic warming were to prohibit the existence of these ice shelves then the ice sheet would collapse. Field observations suggest that, at present, the ice sheet may be advancing into parts of the Ross Ice Shelf. Such advance, however, would not ensure the security of the ice sheet since ice streams that drain to the north appear to flow directly into the sea with little or no ice shelf to buttress them. If these ice streams do not flow over a sufficiently high bedrock sill then they provide the most likely avenues for ice-sheet retreat.

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