scholarly journals Dynamically coupling Full Stokes and Shallow Shelf Approximation for marine ice sheet flow using Elmer/Ice (v8.3)

2018 ◽  
Author(s):  
Eef C. H. van Dongen ◽  
Nina Kirchner ◽  
Martin B. van Gijzen ◽  
Roderik S. W. van de Wal ◽  
Thomas Zwinger ◽  
...  
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Computation Time ◽  
Ice Shelf ◽  
Rapid Convergence ◽  
Matrix Assembly ◽  
Ice Flow ◽  
Current Implementation ◽  
Grounding Line ◽  
Near Future

Abstract. Ice flow forced by gravity is governed by the Full Stokes (FS) equations, which are computationally expensive to solve due to their non-linearity introduced by the rheology. Therefore, approximations to the FS equations are used, especially when modelling an ice sheet complex (ice sheet, ice shelf and/or ice stream) on the order of 1000 years or longer. The Shallow Ice Approximation (SIA) and Shallow Shelf Approximation (SSA) are commonly used but are accurate only in certain parts of an ice sheet. Here, we report on a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS-SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5 % for diagnostic and below 5 % for prognostic runs. Results for grounding line dynamics obtained with the FS-SSA coupling are similar to results obtained from a FS model in an experiment with a periodical temperature forcing over 3000 years inducing grounding line advance and retreat. The rapid convergence of the FS-SSA coupling shows a large potential in reducing computation time, such that modelling an ice sheet complex for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced significantly, i.e. by 32 %, when the coupling is applied to a 3D ice shelf. In the future, the FS-SSA coupling can be extended to include a SIA-FS coupling of ISCAL (Ice Sheet Coupled Approximation Level)-type.

scholarly journals Dynamically coupling full Stokes and shallow shelf approximation for marine ice sheet flow using Elmer/Ice (v8.3)

2018 ◽  
Vol 11 (11) ◽  
pp. 4563-4576 ◽  
Author(s):  
Eef C. H. van Dongen ◽  
Nina Kirchner ◽  
Martin B. van Gijzen ◽  
Roderik S. W. van de Wal ◽  
Thomas Zwinger ◽  
...  
Keyword(s):  
Ice Sheets ◽  
Ice Sheet ◽  
Computation Time ◽  
Ice Shelf ◽  
Rapid Convergence ◽  
Matrix Assembly ◽  
Ice Flow ◽  
Current Implementation ◽  
Grounding Line ◽  
Near Future

Abstract. Ice flow forced by gravity is governed by the full Stokes (FS) equations, which are computationally expensive to solve due to the nonlinearity introduced by the rheology. Therefore, approximations to the FS equations are commonly used, especially when modeling a marine ice sheet (ice sheet, ice shelf, and/or ice stream) for 103 years or longer. The shallow ice approximation (SIA) and shallow shelf approximation (SSA) are commonly used but are accurate only for certain parts of an ice sheet. Here, we report a novel way of iteratively coupling FS and SSA that has been implemented in Elmer/Ice and applied to conceptual marine ice sheets. The FS–SSA coupling appears to be very accurate; the relative error in velocity compared to FS is below 0.5 % for diagnostic runs and below 5 % for prognostic runs. Results for grounding line dynamics obtained with the FS–SSA coupling are similar to those obtained from an FS model in an experiment with a periodical temperature forcing over 3000 years that induces grounding line advance and retreat. The rapid convergence of the FS–SSA coupling shows a large potential for reducing computation time, such that modeling a marine ice sheet for thousands of years should become feasible in the near future. Despite inefficient matrix assembly in the current implementation, computation time is reduced by 32 %, when the coupling is applied to a 3-D ice shelf.

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 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 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 Dynamics of laterally confined marine ice sheets

2016 ◽  
Vol 790 ◽  
Author(s):  
Katarzyna N. Kowal ◽  
Samuel S. Pegler ◽  
M. Grae Worster
Keyword(s):  
Transition Region ◽  
Gravity Current ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Vertical Shear ◽  
Shear Stresses ◽  
Horizontal Shear ◽  
Ice Shelf ◽  
Slip Boundary ◽  
Grounding Line

We present an experimental and theoretical study of the dynamics of laterally confined marine ice sheets in the natural limit in which the long, narrow channel into which they flow is wider than the depth of the ice. A marine ice sheet comprises a grounded ice sheet in contact with bedrock that floats away from the bedrock at a ‘grounding line’ to form a floating ice shelf. We model the grounded ice sheet as a viscous gravity current resisted dominantly by vertical shear stresses owing to the no-slip boundary condition applied at the bedrock. We model the ice shelf as a floating viscous current resisted dominantly by horizontal shear stresses owing to no-slip boundary conditions applied at the sidewalls of the channel. The two shear-dominated regions are coupled by jump conditions relating force and fluid flux across a short transition region downstream of the grounding line. We find that the influence of the stresses within the transition region becomes negligible at long times and we model the transition region as a singular interface across which the ice thickness and mass flux can be discontinuous. The confined shelf buttresses the sheet, causing the grounding line to advance more than it would otherwise. In the case that the sheet flows on a base of uniform slope, we find asymptotically that the grounding line advances indefinitely as $t^{1/3}$, where $t$ is time. This contrasts with the two-dimensional counterpart, for which the shelf provides no buttressing and the grounding line reaches a steady state (Robison, J. Fluid Mech., vol. 648, 2010, pp. 363–380).

Response of a Marine Ice Sheet to Changes at the Grounding Line

1985 ◽  
Vol 24 (3) ◽  
pp. 257-267 ◽  
Author(s):  
C. J. Van der Veen
Keyword(s):  
Ice Sheet ◽  
Ice Shelf ◽  
West Antarctic Ice Sheet ◽  
Ice Shelves ◽  
West Antarctic ◽  
Grounding Line ◽  
Measured Profile ◽  
The Stability ◽  
Near Future ◽  
Basic Experiments

A numerical model was designed to study the stability of a marine ice sheet, and used to do some basic experiments. The ice-shelf/ice-sheet interaction enters through the flow law in which the longitudinal stress is also taken into account. Instead of applying the model to some (measured) profile and showing that this is unstable (as is common practice in other studies), an attempt is made to simulate a whole cycle of growth and retreat of a marine ice sheet, although none of the model sheets is particularly sensitive to changes in environmental conditions. The question as to what might happen to the West Antarctic Ice Sheet in the near future when a climatic warming can be expecied as a result of the CO2 effect, seems to be open for discussion again. From the results presented in this paper one can infer that a collapse, caused by increased melting on the ice shelves, is not very likely.

scholarly journals Dynamic influence of pinning points on marine ice-sheet stability: a numerical study in Dronning Maud Land, East Antarctica

2016 ◽  
Author(s):  
Lionel Favier ◽  
Frank Pattyn ◽  
Sophie Berger ◽  
Reinhard Drews
Keyword(s):  
Data Assimilation ◽  
Sea Level ◽  
Ice Sheets ◽  
Ice Sheet ◽  
East Antarctica ◽  
Ice Shelf ◽  
Ice Dynamics ◽  
Ice Shelves ◽  
Grounding Line ◽  
Dronning Maud Land

Abstract. The East Antarctic ice sheet is likely more stable than its West Antarctic counterpart, because its bed is largely lying above sea level. However, the ice sheet in Dronning Maud Land, East Antarctica, contains marine sectors that are in contact with the ocean through overdeepened marine basins interspersed by (more stable) grounded ice promontories and ice rises, pinning and stabilising the ice shelves. In this paper, we use the ice-sheet model BISICLES to investigate the effect of sub-ice shelf melting, using a series of scenarios compliant with current values, on the ice-dynamic stability of the outlet glaciers between the Lazarev and Roi Baudouin ice shelves over the next millennia. Overall, the sub-ice shelf melting substantially impacts the sea level contribution. Locally, we predict a short-term rapid grounding-line retreat of the overdeepened outlet glacier Hansenbreen, which further induces the collapse of the bordering ice promontories into ice rises. Furthermore, our analysis demonstrates that the onset of the marine ice-sheet retreat and subsequent promontory collapse is controlled by small pinning points within the ice shelves, mostly uncharted in pan-Antarctic datasets. Pinning points have a twofold impact on marine ice sheets. They decrease the ice discharge by buttressing effect, and play a crucial role in initialising marine ice sheets through data assimilation, leading to errors in ice-shelf rheology when omitted. Our results show that unpinning has a small effect on the total amount of sea level rise but locally affects the timing of grounding-line migration, advancing the collapse of a promontory by hundreds of years. On the other hand, omitting the same pinning point in data assimilation decreases the sea level contribution by 10 % and delays the promontory collapse by almost a millennium. This very subtle influence of pinning points on ice dynamics acts on kilometre scale and calls for a better knowledge of the Antarctic margins that will improve sea-level predictions.

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 A smoothed-particle hydrodynamics model for ice-sheet and ice-shelf dynamics

2012 ◽  
Vol 58 (208) ◽  
pp. 216-222 ◽  
Author(s):  
Wenxiao Pan ◽  
Alexandre M. Tartakovsky ◽  
Joe J. Monaghan
Keyword(s):  
Newtonian Fluid ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Ice Shelf ◽  
Grounding Line ◽  
Particle Hydrodynamics ◽  
Sph Model ◽  
Smoothed Particle ◽  
Shelf Dynamics ◽  
Large Material

AbstractMathematical modeling of ice sheets is complicated by the nonlinearity of the governing equations and boundary conditions. Standard grid-based methods require complex front-tracking techniques and have a limited capability to handle large material deformations and abrupt changes in bottom topography. Consequently, numerical methods are usually restricted to shallow ice-sheet and ice-shelf approximations. We propose a new smoothed-particle hydrodynamics (SPH) model for coupled ice-sheet and ice-shelf dynamics. SPH, a fully Lagrangian particle method, is highly scalable and its Lagrangian nature and meshless discretization are well suited to the simulation of free surface flows, large material deformation and material fragmentation. In this paper, we use the SPH model to study ice-sheet/ice-shelf behavior, and the dynamics of the grounding line. The steady-state position of the grounding line obtained from SPH simulations is in good agreement with laboratory observations for a wide range of simulated bedrock slopes and density ratios, similar to those of ice and sea water. The numerical accuracy of the SPH algorithm is verified by simulating the plane-shear flow of two immiscible fluids and the propagation of a highly viscous blob of fluid along a horizontal surface. In the experiment, the ice was represented with a viscous Newtonian fluid. For consistency, in the described SPH model the ice is also modeled as a viscous Newtonian fluid. Typically, ice sheets are modeled as a non-Newtonian fluid, accounting for the changes in the mechanical properties of the ice. Implementation of a non-Newtonian rheology in the SPH model is the subject of our ongoing research.

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