Ice Flow Model Research Articles

Concentrating Antarctic meteorites on blue ice fields—The Frontier Mountain meteorite trap

The collection of meteorites in Antarctica has greatly stimulated advancement in the field of meteoritics by providing the community with significant numbers of rare and unique meteorites types and by yielding large numbers of meteorites that sample older infall epochs (Grady et al., 1998). The majority of Antarctic meteorites are found on blue fields, where they are thought to be concentrated by wind and glacial drift (cf. Cassidy et al., 1992). The basic ice flow model describes the concentration of meteorites by the stagnation or slowing of as it moves against a barrier located in a zone with low snow accumulation. However, our limited knowledge of the details of the actual concentration mechanisms prevents establishing firm conclusions concerning the past meteorite flux from the Antarctic record (Zolensky, 1998). The terrestrial ages of Antarctic meteorites indicate that their concentration occurs on time scales of tens to hundreds of thousands of years (Nishiizumi et al., 1989). It is a challenge to measure a mechanism that operates so slowly, and since such time scales can span more than one glacial epoch one cannot assume that the snow accumulation rates, velocities and directions, etc. that are measured today are representative of those extant over the age of the trap. Testing the basic ice flow model therefore requires the careful measurement of meteorite locations, glacialogical flow data, thicknesses, bedrock and surface topology, ablation and snow accumulation rates, and mass transport by wind over an extended period of time in a location where these quantities can be interpreted in the context of past glacialogical history.

Isochrones and isotherms beneath migrating ice divides

AbstractWe use simple numerical and analytical models of ice flow and heat flow to characterize the shape of isochrones and isotherms beneath moving ice divides. Both nonlinear ice flow and reduced accumulation (wind scouring) at a divide can cause reduced downward flow in a region about one ice thickness wide under a divide. Greater downward velocities on the flanks cause isochrones and isotherms to become arched at depth. The magnitudes and shapes of these arches depend on the history of divide position. Arch amplitudes decrease by approximately e−1 for each increase in migration rate of 3–5 times the accumulation rate, the arches become asymmetric, with steeper leading edges and more gentle trailing edges, and the arch apex lags behind the divide. Isochrone and isotherm shapes can be used to infer past divide motions. In advection-dominated ice sheets, isochrone shapes record a longer history of divide position than do isotherm shapes. The opposite is true for diffusion-dominated ice sheets, in which a spatial array of ice-temperature measurements might extend the recorded history of divide position.

Depth–age and temperature prediction at Dome Fuji station, East Antarctica

AbstractThe geophysical metronome (Milankovitch components of the past surface temperature variations) and the isotope–temperature transfer function deduced from the borehole temperature profile at Vostok station, Antarctica, are applied to date the 2500 mdeep ice core from Dome Fuji station, Antarctica, and to reconstruct paleoclimatic conditions at the drilling site on the basis of the local δ18O isotope record. Special attention is paid to consistency of this depth–age relation with the mass-balance reconstruction and predictions of ice-flow modeling. the present-day ice mass-balance rate at Dome Fuji is estimated as 3.2 cm a–1. the ice age at the borehole bottom (590m above the bedrock) is around 335 ± 4.5 kyr and may reach 2000 kyr at about 3000 mdepth.The difference in the ice-sheet surface temperatures between Holocene optimum and Last Glacial Maximum is found to be 17.8˚C at the temporal isotope/temperature slope, about 30% lower than the modern geographical estimates. A good agreement between modeled and measured (preliminary data) borehole temperatures is obtained at the geothermal flux 0.059 Wm–2 and ice-fusion temperature (–2˚C) at the ice–rock interface with minimum (zero) melt rates.

Transient glacier response with a higher-order numerical ice-flow model

AbstractIn this paper, a higher-order numerical flowline model is presented which is numerically stable and fast and can cope with very small horizontal grid sizes (<10 m). The model is compared with the results from Blatter and others (1998) on Haut Glacier d’Arolla, Switzerland, and with the European Ice-Sheet Modelling Initiative benchmarks (Huybrechts and others, 1996). Results demonstrate that the significant difference between calculated basal-drag and driving-stress profiles in a fixed geometry disappears when the glacier profile is allowed to react to the surface mass-balance conditions and reaches a steady state. Dynamic experiments show that the mass transfer in higher-order models occurs at a different speed in the accumulation and ablation areas and that the front position is more sensitive to migration compared to the shallow-ice approximation.

Lateral boundary conditions for a local anisotropic ice-flow model

AbstractA local two-dimensional flow model which accounts for the anisotropic behaviour of polar ice and the evolution of its strain-induced anisotropy is briefly reviewed. Due to its complexity, it is not yet possible to use this model to simulate the flow of a whole ice sheet, and its potential applications are presently restricted to limited spatial domains around existing drilling sites. In order to calculate the local flow of ice, boundary conditions must be applied on the lateral edges of the studied domain. Since these limits correspond to fictitious sections of the ice sheet, the type of boundary condition to adopt is not obvious. In the present paper, different kinds of boundary conditions of the Dirichlet type, applied at the lateral boundary of an idealized ice sheet of simplified geometry, are discussed. This will serve as a first step towards the coupling of the local flow model with a global ice-sheet flow model.

Parallel numerical modelling of the Antarctic Ice Sheet

The Antarctic Ice Sheet comprises the West Antarctic Ice Sheet and the much larger East Antarctic Ice Sheet. Fast flowing ice streams and outlet glaciers are important dynamic components of the ice sheet system, and a grid resolution of at least 20 km is required to identify many of these areas. Previous fine resolution numerical models have focussed on ice flow in West Antarctica or on fine resolution modelling of subsections of the ice sheet, since the size of East Antarctica has generally precluded studies of the whole ice sheet at a resolution adequate to identify complex flow features. The equations describing ice flow are highly non-linear, making this a computationally intensive problem. We use a staggered grid for calculation of ice diffusivity to overcome numerical instability, and a sparse packing scheme to take account of the irregular boundary of Antarctica. We have developed an efficient parallel temperature-dependent ice flow model of the entire grounded portion of the Antarctic Ice Sheet at a resolution of 20 km. The model was primarily written to run on a commodity cluster of workstations, and performance results for this and other systems are presented. Ice flow patterns at steady state compare well with recently published balance velocity calculations.

Reconstruction of the paleoaccumulation rate of central Greenland during the last 75 kyr using the cosmogenic radionuclides 36Cl and 10Be and geomagnetic field intensity data

The accumulation rate is one of the most fundamental climate parameters to be derived from ice cores. In addition to its climatic importance, the accumulation rate provides a crucial constraint on depth–age scales where annual layer counting is not possible. So far, there is no consistent picture of the accumulation rate for the last ice age in central Greenland. Therefore, we have derived the accumulation rate for the time interval of about 3–75 kyr BP by applying a method based on the cosmogenic radionuclides 36Cl and 10Be in the Summit ice cores and on geomagnetic field data. The main difference between our approach and the methods applied previously is that the accumulation rate based on 36Cl and 10Be does not depend on an ice flow model estimating the original thickness of annual layers. Our new reconstruction agrees well with the accumulation rate published by Johnsen et al. [Tellus 47B (1995) 624–629] until 60 kyr BP and differs significantly from that of Cuffey and Clow [J. Geophys. Res. 102 (1997) 26383–26393].

A tentative chronology for the EPICA Dome Concordia Ice Core

A tentative age scale (EDC1) for the last 45 kyr is established for the new 788‐m EPICA Dome C ice core using a simple ice flow model. The age of volcanic eruptions, the end of the Younger Dryas event, and the estimated depth and age of elevated 10Be, about 41 kyr ago were used to calibrate the model parameters. The uncertainty of EDC1 is estimated to ±10 yr for 0 to 700 yr BP, up to ±200 yr back to 10 kyr BP, and up to ±2 kyr back to 41 kyr BP. The age of the air in the bubbles is calculated with a firn densification model. In the Holocene the air is about 2000 yr younger than the ice and about 5500 yr during the last glacial maximum.

Modelling ice flow in various Glacier zones

A simplified model of plane isothermal steady ice flow in the land-based part, the shelf and the ice-sheet-ice-shelf transition zone of a glacier which interacts with the sea is constructed using Glen's flow law and perturbation methods. Boundary conditions on the joining line are obtained for the land-based part of the glacier. The dynamics of the ice-divide domain of the glacier is analysed for the case of axially symmetric, steady, isothermal ice flow.

Short-term volume changes of the Greenland ice sheet in response to doubled CO2 conditions

This paper focuses on the rôle of accumulation and cloudiness changes in the response of the Greenland ice sheet to global warming. Changes in accumulation or cloudiness were often neglected, or coupled to temperature changes. We used model output on temperature, precipitation and cloudiness from a GCM (ECHAM4 T106). The GCM output was used to drive the Greenland model that exists of a vertically averaged ice flow model, coupled to a 1D surface energy balance model that calculates the ablation. Variables are temperature, accumulation and cloudiness. Sensitivity experiments with this model show that changes in accumulation are very important for the ice sheet mass balance, whereas cloudiness is of secondary importance. If the Greenland model is forced by the GCM output, the Greenland model is found to contribute 70% less to sea level rise after 70 years than is indicated by the results presented in the IPCC report. This large discrepancy is mainly due to the fact that the enhanced ablation is strongly compensated by increased accumulation. Comparing the result obtained here with changes in mass balance derived directly from the same general circulation model, indicates a 20% larger contribution to sea level. This increase is due to changes in ice flow, and a different method for the ablation calculation.

Glacier–volcano interactions deduced by SAR interferometry

AbstractGlacier-surface displacements produced by geothermal and volcanic activity beneath Vatnajökull ice cap in Iceland are described by field surveys of the surface topography combined with interferograms acquired from repeat-pass synthetic aperture radar images. A simple ice-flow model serves well to confirm the basic interpretation of the observations. The observations cover the period October 1996–January 1999 and comprise: (a) the ice-flow field during the infilling of the depressions created by the subglacial Gjálp eruption of October 1996, (b) the extent and displacement of the floating ice cover of the subglacier lakes of Grímsvötn and the Skaftá cauldrons, (c) surface displacements above the subglacier pathways of the jökulhlaups from the Gjálp eruption site and the Grímsvötn lake, (d) detection of areas of increased basal sliding due to lubrication by water, and (e) detection of spots of temporal displacement that may be related to altering subglacial volcanic activity. At the depression created by the Gjálp eruption, the maximum surface displacement rate away from the radar decreased from 27 cm d−1to 2 cm d−1over the period January 1997–January 1999. The observed vertical displacement of the ice cover of Grímsvötn changed from an uplift rate of 50 cm d−1to sinking of 48 cm d−1, and for Skaftá cauldrons from 2 cm d to 25 cm d−1.

Implications of till deformation on glacier dynamics

AbstractThe dynamics of glacier motion are governed to a large extent by the properties of the basal interface. In this paper we address the interaction of a glacier with a layer of till at its bed in an attempt to test whether our physical understanding of till is sufficient to explain general features of the observed flow field and changes in geometry of Black Rapids Glacier, Alaska, U.S.A. We also investigate whether or not a till layer has a clear surface-observable signature in the dynamics of the glacier. Towards this end we use a finite-element ice-flow model with a Coulomb failure criterion within the basal till layer. We find that simple “till physics” can be used to describe decadal, seasonal and short-term (hours to days) velocity variations, and possibly uplift events. Mechanisms for each of these variations involve an increase in the extent of till at failure, a transfer of shear stress across the bed, and a consequent increase in ice deformation. “Effective shape factors” are calculated that permit a simple incorporation of this boundary condition into glacier response models. Our analyses, however, have not resulted in the identification of a clear and unique signature of a till layer in the surface dynamics of a glacier.

The elevation history of ice streams and the spatial accumulation pattern along the Siple Coast of West Antarctica inferred from ground-based radar data from three inter-ice-stream ridges

AbstractMeasurements of the surface and internal layer geometry from ice-penetrating radar and global positioning system surveys on three inter-ice-stream ridges in West Antarctica (Siple Dome, ridge DE and ridge BC) are examined with ice-flow models to infer (1) the history of the divide position at each site and (2) the spatial pattern of accumulation across the ridges. We find that the divide position is most steady at Siple Dome, somewhat steady at ridge DE and highly variable at ridge BC. Data from Siple Dome and ridge DE show evidence for steady northward motion of the ice divide for the past few thousand years. The layers beneath ridge BC suggest a 5 km northward shift of the divide position within the past several hundred years. Assuming the divide shifts are all due to changing elevation of the bounding ice streams, we infer the relative elevation history for segments of Ice Streams B–E. The northward displacement of the divide for all ridges implies a progressive relative thinning of the ice streams from E to B, with most dramatic recent thinning (100 m in <103 years) of Ice Stream B relative to Ice Stream C. Analysis of the internal layer pattern across the ridges indicates a south–north accumulation gradient with higher accumulation rates on the northern flanks of the ridges in all three cases. The inferred accumulation distribution is nearly uniform on the northern flanks, decreases sharply within a few ice thicknesses across the divides, and then decreases gradually farther to the south. The north/south decrease is strongest for ridge DE and weakest for ridge BC. This spatial pattern and the reduction in gradient strength with distance from the Amundsen Sea is consistent with the hypothesis that storms from the Amundsen Sea carry moisture first south then west over West Antarctica and deposit more snow on the windward side of ridges due to orographic lifting. This pattern has been stable for at least the past several thousand years.

On the characteristics of cosmogenic in situ 14C in some GISP2 Holocene and late glacial ice samples

In previous studies, we have shown that information on ice accumulation processes is recorded by the in situ production of 14C, from nuclear interactions of cosmic rays with oxygen in ice (Lal et al., 1997). In this report, we discuss a study of a number of Holocene and several glacial ice samples from the GISP2 core whose accumulation rates are known and which should be little affected by uncertainties in ice flow models (Cuffey et al., 1997), to determine trapping efficiencies of in situ 14C. We present new results along with discussion of the earlier results of Lal et al. (1997), which include results on partitioning of in situ 14C among the CO and CO 2 phases through time in ice. The usefulness of the in situ 14C data to measurements of ice accumulation rates and ages are discussed.

Age vs depth of glacial ice at South Pole

Knowledge of age as a function of depth in glacial ice is important for both glaciology and paleoclimatology. For sites near a ridge or dome, an ice flow model together with information on accumulation rate provides a first approximation. If the accumulation rate is high enough, annual layering of isotopes and dust measured in a solid core can provide a precise age vs depth relationship. For South Pole, the flow geometry is not simple and no deep core exists. Nevertheless, by remotely sensing peaks in scattering and absorption of light from pulsed sources buried at depths down to 2200 m, we have been able to determine age vs depth for ages up to 65,000 years. Analysis of radar isochrons by Siegert and Hodgkins provides a rough extension of the age vs depth model to ∼165,000 years near bedrock.

Glacier mass-balance determination by remote sensing and high-resolution modelling

AbstractAn indirect methodology for determining the distribution of mass balance at high spatial resolution using remote sensing and ice-flow modelling is presented. The method, based on the mass-continuity equation, requires two datasets collected over the desired monitoring interval: (i) the spatial pattern of glacier surface-elevation change, and (ii) the mass-flux divergence field. At Haut Glacier d’Arolla, Valais, Switzerland, the mass-balance distribution between September 1992 and September 1993 is calculated at 20 m resolution from the difference between the pattern of surface-elevation change derived from analytical photogrammetry and the mass-flux divergence field determined from three-dimensional, numerical flow modelling constrained by surface-velocity measurements. The resultant pattern of mass balance is almost totally negative, showing a strong dependence on elevation, but with large localized departures. The computed distribution of mass balance compares well (R2 = 0.91) with mass-balance measurements made at stakes installed along the glacier centre line over the same period. Despite the highly optimized nature of the flow-modelling effort employed in this study, the good agreement indicates the potential this method has as a strategy for deriving high spatial and temporal-resolution estimates of mass balance.

Tributaries to West Antarctic ice streams: characteristics deduced from numerical modelling of ice flow

AbstractA network of relatively fast-flowing tributaries in the catchment basins of the West Antarctic ice streams transport ice from the inland reservoir to the heads of the ice streams. Branches of the network follow valleys in basal topography but not all valleys contain tributaries. We investigate the circumstances favoring tributary flow upstream of Ice Streams D and E, using a combination of observation and numerical modelling. No consistent pattern emerges. The transition from tributary to ice-stream flow occurs smoothly along the main tributary feeding into the onset of Ice Stream D, with ice thickness being relatively more important upstream, and sliding being relatively more important downstream. Elsewhere, the downstream pattern of flow is more complicated, with local increases and decreases in the contribution of sliding to ice speed. Those changes may be due to variations in basal water storage, subglacial geologic properties or a combination of the two.

Modelling glacier response to measured mass-balance forcing

AbstractMeasurements of summer and winter mass balances have been carried out over the past 53 years on Storglaciären, northern Sweden. Repeated surveys of the glacier have resulted in several maps of surface topography as well as a map of the bed topography A new time-dependent ice flow model allows us to compare the observed surface evolution of the glacier with that computed by the model using measured mass-balance maps as input. The computed volume change compares well with the measured change: the model replicates the distribution of surface elevation to within ±10 m over 30 years of integration. On the model side, these deviations can be attributed to the low-resolution discretization of the model domain as well as to the limited accuracy of the ice rheology and omitted basal sliding. On the other hand, the uncertainties of the topography and mass-balance maps match the model uncertainties. In this sense, the experiments are a validation of both model and observations.

Elevation of ice-stream margin scars after stagnation

AbstractThe evolution of an inter-ice-stream ridge flanked by stagnated ice streams is simulated using a finite-difference, continuity ice-flow model. The model tracks the elevation of small-scale topographic undulations on the ice surface (“scars”) which form at ice-stream margins, and shows that after ice-stream stagnation these surface features are lifted onto the flanks of the evolving ridge before they are carried downslope by ice flow. The model is applied to the stagnant ice streams bounding Siple Dome, West Antarctica: “Siple Ice Stream” (SIS) on the northeast flank near Ice Stream D, and the “Duckfoot” area (DF) on the south flank near Ice Stream C. The volume-adjustment time-scale corresponding to the evolution of Siple Dome and these stagnant ice-stream areas is 1500–2000 years. The present geometry and elevation of the scar features, in addition to measurements of the present mass flux across the ridge, are used to estimate stagnation ages for SIS and DF. These measurements suggest that both SIS and DF stagnated 200–500 years ago.

Photogrammetric reconstruction of glacier mass balance using a kinematic ice-flow model: a 20 year time series on Grubengletscher, Swiss Alps

AbstractThe kinematic boundary condition at the glacier surface can be used to provide glacier mass balance at individual points if changes in surface elevation, horizontal and vertical surface velocities and surface slope are known. Vertical ice velocity can in turn be estimated from basal slope, basal ice velocity and surface strain. This relation is applied to reconstruct a 20 year mass-balance curve of Grubengletscher, Swiss Alps, largely using repeated aerial photogrammetry, with only a minimum of fieldwork For individual years the mass-balance distribution on the glacier tongue was modelled with an accuracy of about ±0.9 m a"1. Ice-mechanical assumptions and errors in glacier bed geometry markedly affect discrete mass-balance patterns but are largely eliminated in the calculation of year-to-year mass-balance changes The resulting 1973–92 curve for the Grubengletscher tongue shows reasonable consistency with meteorological data and other glaciologically derived mass-balance series. Large changes in measured ice speed on the glacier tongue (±50%) significantly governed the long-term variability of ice thickness over the observational period.