A user-friendly anisotropic flow law for ice-sheet modeling

AbstractFor accurate ice-sheet flow modelling, the anisotropic behaviour of ice must be taken fully into account. However, physically based micro-macro (μ-M) models for the behaviour of an anisotropic ice polycrystal are too complex to be implemented easily in large-scale ice-sheet flow models. An easy and efficient method to remedy this is presented. Polar ice is assumed to behave as a linearly viscous orthotropic material whose general flow law (GOLF) depends on six parameters, and its orthotropic fabric is described by an ‘orientation distribution function’ (ODF) depending on two parameters. A method to pass from the ODF to a discrete description of the fabric, and vice versa, is presented. Considering any available μ-M model, the parameters of the GOLF that fit the response obtained by running this μ-M model are calculated for any set of ODF parameters. It is thus possible to tabulate the GOLF over a grid in the space of the ODF parameters. This step is performed once and for all. Ice-sheet flow models need the general form of the GOLF to be implemented in the available code (once), then, during each individual run, to retrieve the GOLF parameters from the table by interpolation. As an application example, the GOLF is tabulated using three different μ-M models and used to derive the rheological properties of ice along the Greenland Icecore Project (GRIP) ice core.

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Precise altimetric topography in ice-sheet flow studies

Annals of Glaciology ◽

10.1017/s0260305500012830 ◽

1993 ◽

Vol 17 ◽

pp. 195-200 ◽

Cited By ~ 9

Author(s):

F. Remy ◽

J.F. Minster

Keyword(s):

Activation Energy ◽

Flow Direction ◽

Ice Sheet ◽

Rheological Parameters ◽

Least Squares Regression ◽

Sheet Flow ◽

Ice Flow ◽

Flow Models ◽

Altimetric Data ◽

Basal Shear

The precision of radar altimetry above an ice sheet can improve glaciological studies such as mass balance surveys or ice-sheet flow models, the first by comparing altimetric data at different times (see this issue), the second by testing or constraining models with data. This paper is a first step towards the latter. From a precise topography deduced by inversion of altimetric data (Remy and others, 1989), we calculate ice-flow direction, balance velocity and basal shear stress. The rheological parameters involved in the relation linking velocity, stress and temperature are then derived by least-squares regression. Ice flow is well represented by setting the Glen parameter,nto 1 ± 0.25 and the activation energy as 70 ± 10 kJ mol−1.

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Issues with fracturing ice during an ice drilling project in Greenland (EastGRIP)

10.5194/egusphere-egu2020-21768 ◽

2020 ◽

Author(s):

Ilka Weikusat ◽

David Wallis ◽

Steven Franke ◽

Nicolas Stoll ◽

Julien Westhoff ◽

...

Keyword(s):

Grain Size ◽

Standard Procedure ◽

Ice Core ◽

Ice Sheet ◽

Ice Cores ◽

Orientation Distribution ◽

Geothermal Heat ◽

Ice Dynamics ◽

The Core ◽

Pulling Forces

Drilling an ice core through an ice sheet (typically 2000 to 3000 m thick) is a technical challenge that nonetheless generates valuable and unique information on palaeo-climate and ice dynamics. As technically the drilling cannot be done in one run, the core has to be fractured approximately every 3 m to retrieve core sections from the bore hole. This fracture process is initiated by breaking the core with core-catchers which also clamp the engaged core in the drill head while the whole drill is then pulled up with the winch motor.&#160;This standard procedure is known to become difficult and requires extremely high pulling forces (Wilhelms et al. 2007), in the very deep part of the drill procedure, close to the bedrock of the ice sheet, especially when the ice material becomes warm (approximately -2&#176;C) due to the geothermal heat released from the bedrock. Recently, during the EastGRIP (East Greenland Ice coring Project) drilling we observed a similar issue with breaking off cored sections only with extremely high pulling forces, but started from approximately 1800 m of depth, where the temperature is still very cold (approximately -20&#176;C). This has not been observed at other ice drilling sites. As dependencies of fracture behaviour on crystal orientation and grain size are known (Schulson & Duval 2009) for ice, we thus examined the microstructure in the ice samples close to and at the core breaks.&#160;First preliminary results suggest that these so far unexperienced difficulties are due to the profoundly different c-axes orientation distribution (CPO) in the EastGRIP ice core. In contrast to other deep ice cores which have been drilled on ice domes or ice divides, EastGRIP is located in an ice stream. This location means that the deformation geometry (kinematics) is completely different, resulting in a different CPO (girdle pattern instead of single maximum pattern). Evidence regarding additional grain-size dependence will hopefully help to refine the fracturing procedure, which is possible due to a rather strong grain size layering observed in natural ice formed by snow precipitation.&#160;---------------------Wilhelms, F.; Sheldon, S. G.; Hamann, I. & Kipfstuhl, S. Implications for and findings from deep ice core drillings - An example: The ultimate tensile strength of ice at high strain rates.&#160;Physics and Chemistry of Ice (The proceedings of the International Conference on the Physics and Chemistry of Ice held at Bremerhaven, Germany on 23-28 July 2006), 2007, 635-639Schulson, E. M. & Duval, P. Creep and Fracture of Ice. Cambridge University Press, 2009, 401

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Greenland accumulation and its connection to the large-scale atmospheric circulation in ERA-Interim and paleo-climate simulations

Climate of the Past Discussions ◽

10.5194/cpd-9-3825-2013 ◽

2013 ◽

Vol 9 (4) ◽

pp. 3825-3870

Author(s):

N. Merz ◽

C. C. Raible ◽

H. Fischer ◽

V. Varma ◽

M. Prange ◽

...

Keyword(s):

Atmospheric Circulation ◽

Large Scale ◽

Ice Core ◽

Ice Sheet ◽

Greenland Ice Sheet ◽

Circulation Pattern ◽

Local Flow ◽

Large Scale Circulation ◽

Circulation Patterns ◽

Local Accumulation

Abstract. Accumulation and aerosol chemistry records from Greenland ice cores offer the potential to reconstruct variability in Northern Hemisphere atmospheric circulation over the last millennia. However, an important prerequisite for a reconstruction is the stable relationship between local accumulation at the ice core site with the respective circulation pattern throughout the reconstruction period. We address this stability issue by using a comprehensive climate model and performing time-slice simulations for the present, the pre-industrial, the early Holocene and the last glacial maximum (LGM). The relationships between accumulation, precipitation and atmospheric circulation are investigated on on various time-scales. The analysis shows that the relationship between local accumulation on the Greenland ice sheet and the large-scale circulation undergoes a significant seasonal cycle. As the weights of the individual seasons change, annual mean accumulation variability is not necessarily related to the same atmospheric circulation patterns during the different climate states. Within a season, local Greenland accumulation variability is indeed linked to a consistent circulation pattern, which is observed for all studied climate periods, even for the LGM, however these circulation patterns are specific for different regions on the Greenland ice sheet. The simulated impact of orbital forcing and changes in the ice-sheet topography on accumulation exhibits strong spatial variability emphasizing that accumulation records from different ice core sites cannot be expected to look alike since they include a distinct local signature. Accumulation changes between different climate periods are dominated by changes in the amount of snowfall and are driven by both thermodynamic and dynamic factors. The thermodynamic impact determines the strength of the hydrological cycle, and warmer temperatures are generally accompanied by an increase in Greenland precipitation. Dynamical drivers of accumulation changes are the large-scale circulation and the local orography having a distinct influence on the local flow characteristic and hence the amount of precipitation deposited in any Greenland region.

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Retrieving the paleoclimatic signal from the deeper part of the EPICA Dome C ice core

The Cryosphere ◽

10.5194/tc-9-1633-2015 ◽

2015 ◽

Vol 9 (4) ◽

pp. 1633-1648 ◽

Cited By ~ 15

Author(s):

J.-L. Tison ◽

M. de Angelis ◽

G. Littot ◽

E. Wolff ◽

H. Fischer ◽

...

Keyword(s):

High Resolution ◽

Large Scale ◽

Ice Core ◽

Ice Sheet ◽

Remote Sensing Data ◽

Ice Cores ◽

Air Content ◽

Confining Effect ◽

Chemical Profiles ◽

Subglacial Topography

Abstract. An important share of paleoclimatic information is buried within the lowermost layers of deep ice cores. Because improving our records further back in time is one of the main challenges in the near future, it is essential to judge how deep these records remain unaltered, since the proximity of the bedrock is likely to interfere both with the recorded temporal sequence and the ice properties. In this paper, we present a multiparametric study (δD-δ18Oice, δ18Oatm, total air content, CO2, CH4, N2O, dust, high-resolution chemistry, ice texture) of the bottom 60 m of the EPICA (European Project for Ice Coring in Antarctica) Dome C ice core from central Antarctica. These bottom layers were subdivided into two distinct facies: the lower 12 m showing visible solid inclusions (basal dispersed ice facies) and the upper 48 m, which we will refer to as the "basal clean ice facies". Some of the data are consistent with a pristine paleoclimatic signal, others show clear anomalies. It is demonstrated that neither large-scale bottom refreezing of subglacial water, nor mixing (be it internal or with a local basal end term from a previous/initial ice sheet configuration) can explain the observed bottom-ice properties. We focus on the high-resolution chemical profiles and on the available remote sensing data on the subglacial topography of the site to propose a mechanism by which relative stretching of the bottom-ice sheet layers is made possible, due to the progressively confining effect of subglacial valley sides. This stress field change, combined with bottom-ice temperature close to the pressure melting point, induces accelerated migration recrystallization, which results in spatial chemical sorting of the impurities, depending on their state (dissolved vs. solid) and if they are involved or not in salt formation. This chemical sorting effect is responsible for the progressive build-up of the visible solid aggregates that therefore mainly originate "from within", and not from incorporation processes of debris from the ice sheet's substrate. We further discuss how the proposed mechanism is compatible with the other ice properties described. We conclude that the paleoclimatic signal is only marginally affected in terms of global ice properties at the bottom of EPICA Dome C, but that the timescale was considerably distorted by mechanical stretching of MIS20 due to the increasing influence of the subglacial topography, a process that might have started well above the bottom ice. A clear paleoclimatic signal can therefore not be inferred from the deeper part of the EPICA Dome C ice core. Our work suggests that the existence of a flat monotonic ice–bedrock interface, extending for several times the ice thickness, would be a crucial factor in choosing a future "oldest ice" drilling location in Antarctica.

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Deriving a Physically-Based Calving Rate Law for Marine Ice-Cliff Instability

10.5194/egusphere-egu2020-15790 ◽

2020 ◽

Author(s):

Anna Crawford ◽

Joe Todd ◽

Doug Benn ◽

Jan Åström ◽

Thomas Zwinger

Keyword(s):

Viscous Flow ◽

Sea Level Rise ◽

Sea Level ◽

Large Scale ◽

Ice Sheet ◽

Rate Law ◽

Grounding Line ◽

Physically Based ◽

Calving Rate ◽

Global Sea Level

Rapid grounding line retreat at marine-terminating glaciers could expose ice cliffs with heights greater than those on observational record. However, the finite strength of ice places a limit on the height of subareal cliffs. It is proposed that marine ice-cliff instability (MICI) will begin once a stable height threshold is exceeded. If a glacier is situated over a retrograde slope, as is the case for Thwaites Glacier and much of the West Antarctic Ice Sheet, MICI can be expected to accelerate as retreat progresses and increasingly tall and unstable ice cliffs are formed. This is consequential for global sea level rise, yet large uncertainties remain in the prediction of MICI retreat rates. We investigate MICI by pairing the full Stokes continuum model Elmer/Ice and the Helsinki Discrete Element Model (HiDEM). Viscous flow, simulated in Elmer/Ice, is found to be a necessary pre-condition for MICI collapse. Forward advance and bulging lead to ice-front instability and pervasive crevassing in HiDEM. This culminates in full-thickness calving events. We do not observe calving at ice faces prior to viscous deformation. HiDEM simulations that implement viscous flow (HiDEM-ve) also show forward advance and waterline bulging, similar to the Elmer/Ice simulations. However, the importance of granular shear is highlighted by pronounced shear bands and patterns of surface lowering in HiDEM-ve output. These results emphasize the importance and complexity of viscous and brittle process interaction during MICI.A simulation matrix of grounded termini shows that calving frequency and magnitude increase with the thickness of the calving front. The time required for viscous flow to recreate unstable conditions is influenced by thickness as well as ice temperature and basal friction. Simulations of buoyant termini are seen to calve through basal-crevassing and block-rotation, as opposed to incising surface-crevasses. Lastly, we observe that buttressing m&#233;lange can suppress retreat rate if a sufficient resistive force is delivered to the calving front. A physically-based law for MICI retreat rate is derived from our simulation matrix; this calving rate law can be incorporated into large-scale ice sheet models to constrain projections of Antarctic retreat and associated global sea level rise. Our results will also be used to investigate the future retreat of Thwaites Glacier, which is vulnerable to MICI due to a retreating grounding line, fragile floating ice shelf, and precarious positioning above an overdeepening basin.

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Representation of basal melting at the grounding line in ice flow models

The Cryosphere ◽

10.5194/tc-12-3085-2018 ◽

2018 ◽

Vol 12 (10) ◽

pp. 3085-3096 ◽

Cited By ~ 22

Author(s):

Hélène Seroussi ◽

Mathieu Morlighem

Keyword(s):

Finite Element ◽

Ice Sheet ◽

Ocean Model ◽

Flow Models ◽

Grounding Line ◽

Ice Sheet Modeling ◽

Mesh Resolution ◽

Intercomparison Project ◽

Basal Melting ◽

The Impact

Abstract. While a lot of attention has been given to the numerical implementation of grounding lines and basal friction in the grounding zone, little has been done about the impact of the numerical treatment of ocean-induced basal melting in this region. Several strategies are currently being employed in the ice sheet modeling community, and the resulting grounding line dynamics may differ strongly, which ultimately adds significant uncertainty to the projected contribution of marine ice sheets to sea level rise. We investigate here several implementations of basal melt parameterization on partially floating elements in a finite-element framework, based on the Marine Ice Sheet–Ocean Model Intercomparison Project (MISOMIP) setup: (1) melt applied only to entirely floating elements, (2) melt applied over all elements that are crossed by the grounding line, and (3) melt integrated partially over the floating portion of a finite element using two different sub-element integration methods. All methods converge towards the same state when the mesh resolution is fine enough. However, (2) and (3) will systematically overestimate the rate of grounding line retreat in coarser resolutions, while (1) converges faster to the solution in most cases. The differences between sub-element parameterizations are exacerbated for experiments with high melting rates in the vicinity of the grounding line and for a Weertman sliding law. As most real-world simulations use horizontal mesh resolutions of several hundreds of meters at best, and high melt rates are generally present close to the grounding lines, we recommend not using (3) to avoid overestimating the rate of grounding line retreat and to carefully assess the impact of mesh resolution and sub-element melt parameterizations on all simulation results.

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A Map-plane Finite-element Model: Three Modeling Experiments

Journal of Glaciology ◽

10.3189/002214389793701464 ◽

1989 ◽

Vol 35 (119) ◽

pp. 48-52 ◽

Cited By ~ 51

Author(s):

James L. Fastook ◽

Judith E.. Chapman

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Ice Sheet ◽

Time Dependent ◽

Element Formulation ◽

Initial Surface ◽

The Finite Element Method ◽

Sheet Flow ◽

Flow Law ◽

Element Method

AbstractPreliminary results are presented on a solution of the two-dimensional time-dependent continuity equation for mass conservation governing ice-sheet dynamics. The equation is solved using a column-averaged velocity to define the horizontal flux in a finite-element formulation. This yields a map-plane model where flow directions, velocities, and surface elevations are defined by bedrock topography, the accumulation/ablation pattern, and in the time-dependent case by the initial surface configuration. This alleviates the flow-band model limitation that the direction of flow be defined and fixed over the course of the modeling experiment. The ability of the finite-element method to accept elements of different dimensions allows detail to be finely modeled in regions of steep gradients, such as ice streams, while relatively uniform areas, such as areas of sheet flow, can be economically accommodated with much larger elements. Other advantages of the finite-element method include the ability to modify the sliding and/or flow-law relationships without materially affecting the method of solution.Modeling experiments described include a steady-state reconstruction showing flow around a three-dimensional obstacle, as well as a time-dependent simulation demonstrating the response of an ice sheet to a localized decoupling of the bed. The latter experiment simulates the initiation and development of an ice stream in a region originally dominated by sheet flow. Finally, a simulation of the effects of a changing mass-balance pattern, such as might be anticipated from the expected carbon dioxide warming, is described. Potential applications for such a model are also discussed.SYMBOLS USEDa(x,y) Accumulation/ablation rate.A Flow-law parameter.B Sliding-law parameter.CijC Global capacitance matrix.f Fraction of the bed melted.Fij,F Global load vector.g Acceleration of gravity.hj,h Ice-surface elevation.H Ice thickness.k(x,y) Constitutive equation constant of proportionality.kij Global stiffness matrix.m Sliding-law exponent.n Flow-law exponent.ρ Density of ice.σ(x,y) Ice flux.t Time.U Column-average ice velocity.UF Column-average deformation (flow) velocity.US Sliding velocity.v Variational trial function.x,y Map-plane coordinates.

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Vostok (Antarctica) ice-core time-scale from datings of different origins

Annals of Glaciology ◽

10.3189/172756404781814023 ◽

2004 ◽

Vol 39 ◽

pp. 283-292 ◽

Cited By ~ 18

Author(s):

Andrey N. Salamatin ◽

Elena A. Tsyganova ◽

Vladimir Ya. Lipenkov ◽

Jean Robert Petit

Keyword(s):

Time Scale ◽

Accumulation Rate ◽

Ice Core ◽

Ice Sheet ◽

Monte Carlo Sampling ◽

Age Dating ◽

Ice Age ◽

Sheet Flow ◽

Glacier Ice ◽

Different Origins

AbstractThree different approaches to ice-core age dating are employed to develop a depth–age relationship at Vostok, Antarctica: (1) correlating the ice-core isotope record to the geophysical metronome (Milankovich surface temperature cycles) inferred from the borehole temperature profile, (2) importing a known chronology from another (Devils Hole, Nevada, USA) paleoclimatic signal, and (3) direct ice-sheet flow modeling. Inverse Monte Carlo sampling is used to constrain the accumulation-rate reconstruction and ice-flow simulations in order to find the best-fit glaciological time-scale matched with the two other chronologies. The general uncertainty of the different age estimates varies from 2 to 6 kyr on average and reaches 6–15 kyr at maximum. Whatever the causes of this discrepancy might be, they are thought to be of different origins, and the age errors are assumed statistically independent. Thus, the average time-scale for the Vostok ice core down to 3350m depth is deduced consistent with all three dating procedures within the standard deviation limits of ±3.6 kyr, and its accuracy is estimated as 2.2 kyr on average. The constrained ice-sheet flow model allows, at least theoretically, extrapolation of the ice age–depth curve further to the boundary with the accreted lake ice where (at 3530m depth) the glacier-ice age may reach ∼2000 kyr.

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Recumbent folding of divide arches in response to unsteady ice-divide migration

Journal of Glaciology ◽

10.3189/172756505781829412 ◽

2005 ◽

Vol 51 (173) ◽

pp. 201-209 ◽

Cited By ~ 11

Author(s):

H. Paul Jacobson ◽

Edwin D. Waddington

Keyword(s):

Ice Core ◽

Ice Sheet ◽

Sheet Flow ◽

Ice Streams ◽

Shearing Flow ◽

Wide Range ◽

Core Site

AbstractArches in stratigraphic layers directly under a flow divide (Raymond bumps) are predicted by models of steady ice-sheet flow, and have been observed in several ice domes. Here, we model the evolution of these layers when a formerly stationary divide migrates rapidly to a new position, then again becomes stationary, leaving the arched layers in a flank position. As they are then carried downstream with the flow, these abandoned arches can develop into recumbent folds. These folds can occur over a wide range of divide migration speeds. The shearing flow that produces these recumbent folds also distributes the folded layers over a wide distance downstream from the original divide location. If the divide offset is abrupt, ‘pre-cores’, or material lines comprising core-relative isochrones, can be used to quickly identify portions of an abandoned Raymond bump that would be overturned at any future ice-core site downstream. If, as appears to be the case in Greenland, the divide is never stable long enough to produce a mature arch, folds of this type would not occur. The most likely place to find such folds might be the flank of an ice ridge bounded by unsteady ice streams.

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Ice-fabrics study in the upper 1500 m of the Dome C (East Antarctica) deep ice core

Annals of Glaciology ◽

10.3189/172756403781816031 ◽

2003 ◽

Vol 37 ◽

pp. 97-104 ◽

Cited By ~ 29

Author(s):

Yun Wang ◽

Sepp Kipfstuhl ◽

Nobuhiko Azuma ◽

Thorsteinn Thorsteinsson ◽

Heinz Miller

Keyword(s):

Ice Core ◽

Ice Sheet ◽

Ice Cores ◽

Orientation Distribution ◽

East Antarctica ◽

Statistical Parameters ◽

Axis Orientation ◽

Orientation Data ◽

Thin Sections ◽

Ice Fabrics

AbstractA study of c-axis orientations in the upper 1500m of the Dome C (East Antarctica) deep ice core has been carried out using an automatic ice-fabric analyzer (AIFA). Twenty-nine vertical and a few horizontal thin sections from different depths in the core have been analyzed. Several statistical parameters describing fabric strength and fabric shapes have been calculated from the c-axis orientation data. The fabric diagrams display a near-random c-axis orientation distribution in the uppermost parts of the ice sheet. A tendency of c-axis rotation towards a broad single-maximum fabric is observed in the lowest part of the studied interval. The fabric development at Dome C thus appears typical for ice-sheet summit and dome sites. The fabric development at Dome C is compared with the fabric evolution in the Dome F and GRIP ice cores, and data on crystal size obtained with image-analysis techniques are presented. Studies of misorientation angles between the c axes of neighbouring crystals reveal little evidence for polygonization, but microscopic observations show that sub-grain boundaries are present in half of the grains at any depth.

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