scholarly journals Existence and stability of steady-state solutions of the shallow-ice-sheet equation by an energy-minimization approach

2011 ◽  
Vol 57 (202) ◽  
pp. 345-354 ◽  
Author(s):  
Guillaume Jouvet ◽  
Jacques Rappaz ◽  
Ed Bueler ◽  
Heinz Blatter
Keyword(s):  
Shear Stress ◽  
Steady State ◽  
Mass Balance ◽  
Energy Minimization ◽  
Existence Of Solutions ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Existence And Stability ◽  
Steady State Solutions ◽  
Minimization Approach

AbstractThe existence of solutions of the non-sliding shallow-ice-sheet equation on a flat horizontal bed with a mass balance linearly depending on altitude is proven for fixed margins. Free-margin solutions for the same mass balance do not exist. Fixed-margin solutions show unbounded shear stress and nonzero mass flux at the margin. Steady-state solutions with realistic margins, vanishing ice flux and vanishing shear stress are found numerically for ice sheets with Weertman-type sliding.

The response of large ice sheets to climatic change

1992 ◽  
Vol 338 (1285) ◽  
pp. 235-242 ◽  
Keyword(s):  
Mass Balance ◽  
Sea Level ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Sea Level Change ◽  
Mixing Ratio ◽  
Ice Dynamics ◽  
Environmental Models ◽  
Level Change ◽  
The Antarctic

The prediction of short-term (100 year) changes in the mass balance of ice sheets and longer-term (1000 years) variations in their ice volumes is important for a range of climatic and environmental models. The Antarctic ice sheet contains between 24 M km 3 and 29 M km 3 of ice, equivalent to a eustatic sea level change of between 60m and 72m. The annual surface accumulation is estimated to be of the order of 2200 Gtonnes, equivalent to a sea level change of 6 mm a -1 . Analysis of the present-day accumulation regime of Antarctica indicates that about 25% ( ca. 500 Gt a -1 ) of snowfall occurs in the Antarctic Peninsula region with an area of only 6.8% of the continent. To date most models have focused upon solving predictive algorithms for the climate-sensitivity of the ice sheet, and assume: (i) surface mass balance is equivalent to accumulation (i.e. no melting, evaporation or deflation); (ii) percentage change in accumulation is proportional to change in saturation mixing ratio above the surface inversion layer; and (iii) there is a linear relation between mean annual surface air tem perature and saturation mixing ratio. For the A ntarctic Peninsula with mountainous terrain containing ice caps, outlet glaciers, valley glaciers and ice shelves, where there can be significant ablation at low levels and distinct climatic regimes, models of the climate response must be more complex. In addition, owing to the high accumulation and flow rates, even short- to medium -term predictions must take account of ice dynamics. Relationships are derived for the mass balance sensitivity and, using a model developed by Hindmarsh, the transient effects of ice dynamics are estimated. It is suggested that for a 2°C rise in mean annual surface tem perature over 40 years, ablation in the A ntarctic Peninsula region would contribute at least 1.0 mm to sea level rise, offsetting the fall of 0.5 mm contributed by increased accum ulation.

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.

Exploring the complex uncertainties in coupled climate-ice simulations of the Last Glacial Maximum

2021 ◽  
Author(s):  
Lauren Gregoire ◽  
Niall Gandy ◽  
Lachlan Astfalck ◽  
Robin Smith ◽  
Ruza Ivanovic ◽  
...  
Keyword(s):  
Mass Balance ◽  
Last Glacial Maximum ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Glacial Maximum ◽  
Sea Surface ◽  
Surface Mass ◽  
Last Glacial ◽  
The Last Glacial Maximum ◽  
The Last Glacial

<p>Simulating the co-evolution of climate and ice-sheets during the Quaternary is key to understanding some of the major abrupt changes in climate, ice and sea level. Indeed, events such as the Meltwater pulse 1a rapid sea level rise and Heinrich, Dansgaard–Oeschger and the 8.2 kyr climatic events all involve the interplay between ice sheets, the atmosphere and the ocean. Unfortunately, it is challenging to simulate the coupled Climate-Ice sheet system because small biases, errors or uncertainties in parts of the models are strongly amplified by the powerful interactions between the atmosphere and ice (e.g. ice-albedo and height-mass balance feedbacks). This leads to inaccurate or even unrealistic simulations of ice sheet extent and surface climate. To overcome this issue we need some methods to effectively explore the uncertainty in the complex Climate-Ice sheet system and reduce model biases. Here we present our approach to produce ensemble of coupled Climate-Ice sheet simulations of the Last Glacial maximum that explore the uncertainties in climate and ice sheet processes.</p><p>We use the FAMOUS-ICE earth system model, which comprises a coarse-resolution and fast general circulation model coupled to the Glimmer-CISM ice sheet model. We prescribe sea surface temperature and sea ice concentrations in order to control and reduce biases in polar climate, which strongly affect the surface mass balance and simulated extent of the northern hemisphere ice sheets. We develop and apply a method to reconstruct and sample a range of realistic sea surface temperature and sea-ice concentration spatio-temporal field. These are created by merging information from PMIP3/4 climate simulations and proxy-data for sea surface temperatures at the Last Glacial Maximum with Bayes linear analysis. We then use these to generate ensembles of FAMOUS-ice simulations of the Last Glacial maximum following the PMIP4 protocol, with the Greenland and North American ice sheets interactively simulated. In addition to exploring a range of sea surface conditions, we also vary key parameters that control the surface mass balance and flow of ice sheets. We thus produce ensembles of simulations that will later be used to emulate ice sheet surface mass balance.  </p>

scholarly journals The Effect of Longitudinal Stress on the Shear Stress at the Base of an Ice Sheet

1969 ◽  
Vol 8 (53) ◽  
pp. 207-213 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Shear Stress ◽  
Theoretical Basis ◽  
Ice Sheets ◽  
Ice Sheet ◽  
High Accuracy ◽  
Longitudinal Stress ◽  
Surface Slope ◽  
Two Dimensional Flow ◽  
Basal Shear ◽  
Longitudinal Strain Rate

Robin (1967) and Budd (1968, unpublished) have succeeded in connecting the variations in surface slope of an ice sheet with variations in the gradient of the longitudinal strain-rate. This paper tries to improve the theoretical basis of their work. By choice of a suitable coordinate system and suitable redefinition of the variables, Budd’s formula for the basal shear stress is derived with a minimum of restrictive assumptions. The resulting formula, containing the gradient of a longitudinal stress, is thought to be of high accuracy for the two-dimensional flow of cold ice sheets, and is valid for slopes of any magnitude.

scholarly journals Erosion by Continental Ice Sheets

1979 ◽  
Vol 23 (89) ◽  
pp. 401-402
Author(s):  
I. M. Whillans
Keyword(s):  
Mass Balance ◽  
Short Distance ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Present Theory ◽  
Frictional Heat ◽  
Break Up ◽  
Basal Melting ◽  
Continental Ice Sheets

Abstract Some of the problems with earlier theories for erosion and transport by ice sheets are discussed, and it is noted that those theories cannot simply account for the often-reported finding that most till is derived from bedrock only a few tens of kilometers up-glacier. Considerations of the mass balance of debris in transport lead to the conclusion that ice sheets are capable of transporting most debris only a short distance. The theory that the break-up of bedrock is mostly a preglacial process is developed. The advancing ice sheet collects the debris and then deposits it after a short travel. As the ice sheet first advances over the regolith, debris is frozen onto the base and is carried until basal melting due to geothermal and frictional heat causes lodgment till deposition. Most debris is deposited during the advance of the ice sheet and is carried only a short distance. A generally small amount of debris is carried at higher levels and is deposited during ice standstill and retreat as melt-out and ablation tills. The present theory makes many predictions, among them, that most till units are not traceable over long distances, that thick till sequences represent unstable glacier margins and not necessarily long periods of glacier occupation, and that lodgment tills are to be interpreted in terms of ice advances and ablation tills in terms of ice retreats. This paper is published in full in Journal of Geology, Vol. 86, No. 4, 1978, p. 516–24.

scholarly journals Ice-Sheet Erosion—A Result of Maximum Conditions?

1979 ◽  
Vol 23 (89) ◽  
pp. 402-404 ◽  
Author(s):  
D. E. Sugden
Keyword(s):  
Steady State ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Gradual Transition ◽  
Glacial Erosion ◽  
Mountain Glaciers ◽  
State Models ◽  
Ice Sheet Erosion ◽  
The Relationship ◽  
Sheet Erosion

Abstract Understanding the relationship between the morphology of former ice-sheet beds and glaciological processes is handicapped by the difficulty of establishing which stage of a cycle of ice-sheet growth and decay is responsible for most erosion. Discussions at this conference and in the literature display a variety of opinions, some favouring periods of ice-sheet build up, others periods of fluctuations, and still others steady-state maximum conditions. Here it is suggested that there is geomorphological evidence which points to the dominance of maximum conditions. Along the eastern margins of the Laurentide and Greenland ice sheets there is a sharp discontinuity between Alpine relief which stood above the ice-sheet surface at the maximum and plateau scenery which was covered by the ice sheet. Often the two types of relief are adjacent and yet separated by an altitudinal difference of only 100–200 m. The existence of an abrupt rather than gradual transition from one relief type to the other suggests that most glacial sculpture must have taken place while the ice sheet was at its maximum extent. In other geomorphological situations where high mountains were submerged by ice sheets, the major erosional landforms are frequently found to relate to ice sheets rather than to local mountain glaciers, again suggesting the dominance of erosion during full ice-sheet conditions. Finally, the identification of patterns of glacial erosion on an ice-sheet scale in North America and Greenland points to erosion when the ice sheets were fully expanded, rather than to the variable flow conditions associated with growth or decay. If ice-sheet erosion is accepted as being a result of maximum conditions, then it places certain constraints on glacial theory, for example the need to develop theories of glacial erosion which apply beneath ice thicknesses of several thousand metres. It also suggests that the use of steady-state models of ice sheets is likely to be a profitable way of relating glaciological processes to the morphology of former ice-sheet beds.

scholarly journals The Reconstruction of Former Ice Sheets and their Mass Balance Characteristics using a Non-Linearly Viscous Flow Model

1984 ◽  
Vol 30 (105) ◽  
pp. 140-152 ◽  
Author(s):  
G. S. Boulton ◽  
G. D. Smith ◽  
L. W. Morland
Keyword(s):  
Boundary Condition ◽  
Mass Balance ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Equilibrium Line Altitude ◽  
Isostatic Compensation ◽  
Geological Evidence ◽  
Wide Range ◽  
Terminal Zone ◽  
Subglacial Topography

AbstractA model of a non-linearly viscous ice sheet is used to investigate the influence of net mass-balance pattern, basal boundary condition, and subglacial topography on the size and shape of ice sheets. The aim is to enable geological evidence of the extent of former ice sheets to be used as indicators of palaeoclimate. A series of curves are presented showing the relationships between ice-sheet span, net mass balance, and equilibrium-line altitude (ELA) for zero and complete isostatic compensation. These are applicable to a very wide range of basal boundary conditions. The way in which they can be used to reconstruct net mass-balance gradients for former ice sheets is demonstrated. Changes in the basal boundary condition only have a strong influence on glacier span when they occur in the terminal zone. Ice-sheet expansion and contraction is not merely accompanied by changes in snow-line elevation, but also by changes in the net mass-balance gradient. The combinations of these required to cause ice-sheet expansion and contraction are analysed. A non-linearly viscous model for ice suggests that ice-sheet volume changes may not be a simple function of their change in areal extent.

scholarly journals Hydrodynamic Model Of Glaciers and Ice Sheets Interacted With Ocean

1990 ◽  
Vol 14 ◽  
pp. 347-347
Author(s):  
V.L. Mazo
Keyword(s):  
Shear Stress ◽  
Hydrodynamic Model ◽  
Evolution Equations ◽  
Three Dimensional ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Longitudinal Stress ◽  
First Order ◽  
Longwave Approximation ◽  
Different Parts

Tidewater glaciers and large ice sheets, e.g. the Antarctic ice sheet and a late-Würm Arctic ice sheet, are complex but single dynamic systems composed of terrestrial, marine and floating parts. Morphology and dynamics of the different parts are different. The terrestrial parts are convex and their dynamics are controlled by shear stress only (the longitudinal stress is zero); the floating parts are concave and their dynamics are controlled by longitudinal stress only (the shear stress is zero). To connect the different parts we should consider transitional zones where shear and longitudinal stresses are comparable.To describe glacier and ice-sheet dynamics, longwave approximation of the first order is used. In this approximation it is impossible to connect terrestrial and floating parts dynamically, only morphologically and kinematically. It means that the first-order longwave approximation is not sufficient.If the transitional zone between the terrestrial and floating parts is long in comparison to ice thickness (in hydrodynamics the term “weak” is used) we can do the next step in the longwave approximation to describe the single dynamical system consisting of the terrestrial and floating parts and the weak transitional zones (ice streams). It is a purely hydrodynamical approach to the problem without ad hoc hypothesis.The presented model is a non-stationary three-dimensional hydrodynamic model of glaciers and ice sheets interacted with ocean, involving the conditions of ice continuity and dynamic equilibrium, ice rheology, and boundary conditions on the free surface (dynamic and kinematic) and on the bed (ice freezing or sliding). Longwave approximation is used to reduce the three-dimensional model to a two-dimensional one. The latter consists of (1) evolution equations for grounded and floating parts and weak transitional zones; (2) boundary conditions on the fronts (e.g. the conditions of calving); (3) equations governing the junctions of the parts (the most important junction is the grounded line) with the conditions connecting the evolution equations.

Trends and projections in ice sheet mass balance

2020 ◽  
Author(s):  
Andrew Shepherd ◽  
Keyword(s):  
Mass Balance ◽  
Sea Level Rise ◽  
Sea Level ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Greenland Ice Sheet ◽  
Ice Dynamics ◽  
Surface Mass ◽  
Sea Levels ◽  
Global Sea Level

<p>In recent decades, the Antarctic and Greenland Ice Sheets have been major contributors to global sea-level rise and are expected to be so in the future. Although increases in glacier flow and surface melting have been driven by oceanic and atmospheric warming, the degree and trajectory of today’s imbalance remain uncertain. Here we compare and combine 26 individual satellite records of changes in polar ice sheet volume, flow and gravitational potential to produce a reconciled estimate of their mass balance. <strong>Since the early 1990’s, ice losses from Antarctica and Greenland have caused global sea-levels to rise by 18.4 millimetres, on average, and there has been a sixfold increase in the volume of ice loss over time. Of this total, 41 % (7.6 millimetres) originates from Antarctica and 59 % (10.8 millimetres) is from Greenland. In this presentation, we compare our reconciled estimates of Antarctic and Greenland ice sheet mass change to IPCC projection of sea level rise to assess the model skill in predicting changes in ice dynamics and surface mass balance.  </strong>Cumulative ice losses from both ice sheets have been close to the IPCC’s predicted rates for their high-end climate warming scenario, which forecast an additional 170 millimetres of global sea-level rise by 2100 when compared to their central estimate.</p>

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