scholarly journals Parameterization of basal friction near grounding lines in a one-dimensional ice sheet model

2014 ◽  
Vol 8 (4) ◽  
pp. 1239-1259 ◽  
Author(s):  
G. R. Leguy ◽  
X. S. Asay-Davis ◽  
W. H. Lipscomb
Keyword(s):  
Shear Stress ◽  
Transition Zone ◽  
Ice Sheet ◽  
Vertical Shear ◽  
Smooth Transition ◽  
Effective Pressure ◽  
Ice Shelf ◽  
One Dimensional ◽  
Basal Friction ◽  
Fixed Grid

Abstract. Ice sheets and ice shelves are linked by the transition zone, the region where flow dominated by vertical shear stress makes a transition to flow dominated by extensional stress. Adequate resolution of the transition zone is necessary for numerically accurate ice sheet–ice shelf simulations. The required resolution depends on how the basal physics is parameterized. We propose a~new, simple parameterization of the effective pressure near the grounding line, combined with an existing friction law linking effective pressure to basal stress and sliding, in a one-dimensional, fixed-grid, vertically integrated model. This parameterization represents connectivity between the basal hydrological system and the ocean in the transition zone. Our model produces a smooth transition between finite basal friction in the ice sheet and zero basal friction in the ice shelf. In a set of experiments based on the Marine Ice Sheet Model Intercomparison Project (MISMIP), we show that with a smoother basal shear stress, the model yields accurate steady-state results at a fixed-grid resolution of ~1 km.

scholarly journals Parameterization of basal hydrology near grounding lines in a one-dimensional ice sheet model

2014 ◽  
Vol 8 (1) ◽  
pp. 363-419
Author(s):  
G. R. Leguy ◽  
X. S. Asay-Davis ◽  
W. H. Lipscomb
Keyword(s):  
Transition Zone ◽  
Ice Sheet ◽  
Smooth Transition ◽  
Ice Shelf ◽  
Ice Shelves ◽  
One Dimensional ◽  
Basal Friction ◽  
Hydrological System ◽  
Intercomparison Project ◽  
Basal Shear

Abstract. Ice sheets and ice shelves are linked by the transition zone, the region where the grounded ice lifts off the bedrock and begins to float. Adequate resolution of the transition zone is necessary for numerically accurate ice sheet–ice shelf simulations. The required resolution depends on how the basal physics is parameterized. We propose a new, simple parameterization of the basal hydrology in a one-dimensional vertically integrated model. This parameterization accounts for connectivity between the basal hydrological system and the ocean in the transition zone. Our model produces a smooth transition between finite basal friction in the ice sheet and zero basal friction in the ice shelf. Through a set of experiments based on the Marine Ice Sheet Model Intercomparison Project (MISMIP), we show that a smoother basal shear stress, in addition to adding physical realism, significantly improves the numerical accuracy of our fixed-grid model, allowing for reliable grounding-line dynamics at resolutions ~1 km.

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 Is Vertical Shear in an Ice Shelf Negligible?

1979 ◽  
Vol 22 (87) ◽  
pp. 285-292 ◽  
Author(s):  
T. J. O. Sanderson ◽  
C. S. M. Doake
Keyword(s):  
Shear Stress ◽  
Vertical Shear ◽  
Shear Stresses ◽  
Ice Shelf ◽  
Vertical Column ◽  
Ice Shelves ◽  
Glacier Tongue ◽  
Amery Ice Shelf ◽  
Differential Movement ◽  
Ice Shell

AbstractVertical shear stress in ice shelves cannot be precisely zero, since the upper and lower surfaces are generally not parallel. By performing stress balance on a vertical column in an ice shelf we calculate what its magnitude must be. This is done for an unconfined glacier tongue and for a confined bay ice shelf; first, using the assumption of constant temperature and density with depth, and secondly, using realistic data and profiles for Erebus Glacier tongue and for the Amery ice shelf. Shear stresses increase almost linearly with depth and are proportional to surface slope. For Erebus Glacier tongue the shear stress is at most 5% of the magnitude of the direct stress deviators and its action through the ice shell should result in differential movement of 1.8 cm a−1 between the top and bottom of the ice shelf. For the Amery ice shelf, the shear stress is at most 0.4% of the magnitude of the direct stress deviators and this should lead to differential movement of 2.5 cm a−1 between the top and bottom of the ice shelf. Shear stresses are therefore generally negligible in comparison with direct stress deviators and can be ignored when considering the overall dynamics of ice shelves. Differential movement is unlikely to be detectable.

scholarly journals Ice-shelf damming in the glacial Arctic Ocean: dynamical regimes of a basin-covering kilometre-thick ice shelf

2017 ◽  
Vol 11 (4) ◽  
pp. 1745-1765 ◽  
Author(s):  
Johan Nilsson ◽  
Martin Jakobsson ◽  
Chris Borstad ◽  
Nina Kirchner ◽  
Göran Björk ◽  
...  
Keyword(s):  
Arctic Ocean ◽  
Ice Sheet ◽  
Lomonosov Ridge ◽  
Fram Strait ◽  
Ice Shelf ◽  
Interior Region ◽  
Central Arctic Ocean ◽  
One Dimensional ◽  
Grounding Line ◽  
The Mean

Abstract. Recent geological and geophysical data suggest that a 1 km thick ice shelf extended over the glacial Arctic Ocean during Marine Isotope Stage 6, about 140 000 years ago. Here, we theoretically analyse the development and equilibrium features of such an ice shelf, using scaling analyses and a one-dimensional ice-sheet–ice-shelf model. We find that the dynamically most consistent scenario is an ice shelf with a nearly uniform thickness that covers the entire Arctic Ocean. Further, the ice shelf has two regions with distinctly different dynamics: a vast interior region covering the central Arctic Ocean and an exit region towards the Fram Strait. In the interior region, which is effectively dammed by the Fram Strait constriction, there are strong back stresses and the mean ice-shelf thickness is controlled primarily by the horizontally integrated mass balance. A narrow transition zone is found near the continental grounding line, in which the ice-shelf thickness decreases offshore and approaches the mean basin thickness. If the surface accumulation and mass flow from the continental ice masses are sufficiently large, the ice-shelf thickness grows to the point where the ice shelf grounds on the Lomonosov Ridge. As this occurs, the back stress increases in the Amerasian Basin and the ice-shelf thickness becomes larger there than in the Eurasian Basin towards the Fram Strait. Using a one-dimensional ice-dynamic model, the stability of equilibrium ice-shelf configurations without and with grounding on the Lomonosov Ridge are examined. We find that the grounded ice-shelf configuration should be stable if the two Lomonosov Ridge grounding lines are located on the opposites sides of the ridge crest, implying that the downstream grounding line is located on a downward sloping bed. This result shares similarities with the classical result on marine ice-sheet stability of Weertman, but due to interactions between the Amerasian and Eurasian ice-shelf segments the mass flux at the downstream grounding line decreases rather than increases with ice thickness.

scholarly journals Resolution requirements for grounding-line modelling: sensitivity to basal drag and ice-shelf buttressing

2012 ◽  
Vol 53 (60) ◽  
pp. 97-105 ◽  
Author(s):  
Rupert M. Gladstone ◽  
Antony J. Payne ◽  
Stephen L. Cornford
Keyword(s):  
Ice Sheet ◽  
Horizontal Resolution ◽  
Channel Width ◽  
Ice Shelf ◽  
Fixed Grid ◽  
Grounding Line ◽  
Poor Convergence ◽  
Set Up ◽  
Line Positions ◽  
Resolution Requirements

AbstractSimulations of grounding-line migration in ice-sheet models using a fixed grid have been shown to exhibit poor convergence at achievable resolutions. We present a series of ‘shelfy-stream’ flowline model experiments using an idealized set-up. We assess the performance of a range of grounding-line parameterizations (GLPs) over a large input space by varying bedrock gradient, rate factor, basal drag coefficient and net accumulation. The relative performance of GLPs is similar to Gladstone and others (2010a) except at low basal drag, in which case the grounding-line errors are very small for all GLPs. We find that grounding-line errors are far more sensitive to basal drag than to the other inputs or to choice of GLP. We then quantify grounding-line errors as a function of resolution while varying basal drag and channel width (using a parameterization to represent buttressing). Reducing either basal drag or channel width reduces the errors associated with the grounding line. Our results suggest that a structured fixed-grid shelfy-stream ice-sheet model would need to run at a horizontal resolution of ~1–2km to accurately simulate grounding-line positions of marine ice-sheet outlet glaciers such as Pine Island Glacier, Antarctica.

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).

scholarly journals Scaling of instability timescales of Antarctic outlet glaciers based on one-dimensional similitude analysis

2019 ◽  
Vol 13 (6) ◽  
pp. 1621-1633 ◽  
Author(s):  
Anders Levermann ◽  
Johannes Feldmann
Keyword(s):  
Response Time ◽  
Dynamic Modeling ◽  
Ice Sheet ◽  
West Antarctica ◽  
Ice Shelf ◽  
One Dimensional ◽  
Physical Conditions ◽  
The One ◽  
The Antarctic ◽  
Made In

Abstract. Recent observations and ice-dynamic modeling suggest that a marine ice-sheet instability (MISI) might have been triggered in West Antarctica. The corresponding outlet glaciers, Pine Island Glacier (PIG) and Thwaites Glacier (TG), showed significant retreat during at least the last 2 decades. While other regions in Antarctica have the topographic predisposition for the same kind of instability, it is so far unclear how fast these instabilities would unfold if they were initiated. Here we employ the concept of similitude to estimate the characteristic timescales of several potentially MISI-prone outlet glaciers around the Antarctic coast. Our results suggest that TG and PIG have the fastest response time of all investigated outlets, with TG responding about 1.25 to 2 times as fast as PIG, while other outlets around Antarctica would be up to 10 times slower if destabilized. These results have to be viewed in light of the strong assumptions made in their derivation. These include the absence of ice-shelf buttressing, the one-dimensionality of the approach and the uncertainty of the available data. We argue however that the current topographic situation and the physical conditions of the MISI-prone outlet glaciers carry the information of their respective timescale and that this information can be partially extracted through a similitude analysis.

Ice-stream-ice-shelf transition: theoretical analysis of two-dimensional flow

2000 ◽  
Vol 30 ◽  
pp. 153-162 ◽  
Author(s):  
Alexander V. Wilchinsky ◽  
Vladimir A. Chugunov
Keyword(s):  
Shear Stress ◽  
Transition Zone ◽  
Stokes Equations ◽  
Stress Deviator ◽  
Two Dimensional ◽  
Ice Shelf ◽  
Full System ◽  
Ice Stream ◽  
Grounding Line ◽  
Two Dimensional Flow

AbstractTwo-dimensional steady isothermal flow of a marine ice stream is studied. Gases of different relations between shear stress and longitudinal deviatoric stress in the ice stream are considered. Analysis of the ice-stream-ice-shelf transition zone shows that even if the longitudinal stress deviator in the ice stream is much larger than the shear stress (as it is in the ice shelf), the ice-stream-ice-shelf transition zone if singular and the full system of Stokes equations must be solved in it. Scales of fields in the transition zone and the relation between the ice thickness and the horizontal mass flux at the grounding line are found.

scholarly journals A Simplified Three-Dimensional Ice-Sheet Model Including Ice Shelves

1990 ◽  
Vol 14 ◽  
pp. 17-19 ◽  
Author(s):  
W.J. Böhmer ◽  
K. Herterich
Keyword(s):  
Transition Zone ◽  
Three Dimensional ◽  
Ice Sheet ◽  
Coupled System ◽  
Horizontal Resolution ◽  
Ice Age ◽  
Ice Shelf ◽  
Ice Shelves ◽  
Grounding Line ◽  
The Antarctic

We present a simplified numerical three-dimensional ice-sheet/ice-shelf model with a coarse horizontal resolution (100 km), designed for simulations of ice-volume changes on ice-age time scales (100 000 years and longer). The ice-sheet part uses the shallow-ice approximation to determine the flow, and includes a three-dimensional temperature calculation. The ice shelf is described in a quasi-stationary way. Ice-shelf thickness depends only on the thicknesses at the grounding line and the distances to the grounding line. The effect of the transition zone between ice sheet and ice shelf (assuming a width ≪100 km) is parameterized in terms of the ice thicknesses defined on the coarse grid. The characteristics at the base of the transition zone formally enter through a friction coefficient μ. We performed a series of sensitivity experiments with the coupled system, by integrating over 10 000 model years, starting from the present (modelled) state of the Antarctic and forcing the model by currently-observed accumulation rates. The position of the grounding line of the ice-sheet/ice-shelf model is quite sensitive to the choice of the friction parameter μ (in the range 0.025 > μ > 0.01). With μ = 0.05, the grounding line was maintained at the currently-observed position in the model.

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