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Microseismicity, induced by the sliding of a glacier over its bed, can be used to characterize frictional properties of the ice‐bed interface, which are a key parameter controlling ice stream flow. We use naturally occurring seismicity to monitor spatiotemporally varying bed properties at Rutford Ice Stream, West Antarctica. We locate 230000 micro‐earthquakes with local magnitudes from –2.0 to –0.3 using 90 days of recordings from a 35‐station seismic network located ∼40 km upstream of the grounding line. Events exclusively occur near the ice‐bed interface and indicate predominantly flow‐parallel stick‐slip. They mostly lie within a region of interpreted stiff till and along the likely stiffer part of mega‐scale glacial landforms. Within these regions, micro‐earthquakes occur in spatially (

In times of warming in polar regions, the prediction of ice sheet discharge is of utmost importance to society, because of its impact on sea level rise. In simulations the flow rate of ice is usually implemented as proportional to the differential stress to the power of the exponent n=3. This exponent influences the softness of the modeled ice, as higher values would produce faster flow under equal stress. We show that the stress exponent, which best fits the observed state of the Greenland Ice Sheet, equals n=4. Our results, which are not dependent on a possible basal sliding component of flow, indicate that most of the interior northern ice sheet is currently frozen to bedrock, except for the large ice streams and marginal ice. Ice in the polar ice sheets flows towards the oceans under its own weight. Knowing how fast the ice flows is of crucial importance to predict future sea level rise. The flow has two components: (1) internal shearing flow of ice and (2) basal motion, which is sliding along the base of ice sheets, especially when the ice melts at this base. To determine the first component we need to know how "soft" the ice is. By considering the flow velocities at the surface of the northern Greenland Ice Sheet and calculating the stresses that cause the flow, we determined that the ice is effectively softer than is usually assumed. Previous studies indicated that the base of the ice is thawed in large parts (up to about 50%) of the Greenland Ice Sheet. Our study shows that that is probably overestimated, because these studies assumed ice to be harder than it actually is. Our new assessment reduces the area with basal motion and thus melting to about 6-13% in the Greenland study area.

Quarrying of bedrock is a primary agent of subglacial erosion. Although the mechanical theory behind the process has been studied for decades, it has proven difficult to formulate the governing principles so that large-scale landscape evolution models can be used to integrate erosion over time. The existing mechanical theory thus stands largely untested in its ability to explain post-glacial topography. In this study we relate the physics of quarrying to long-term landscape evolution with a multi-scale approach that connects meter-scale cavities to kilometer-scale glacial landscapes. By averaging the quarrying rate across many small-scale bedrock steps, we quantify how regional trends in basal sliding speed, effective pressure, and bed slope affect the rate of erosion. A sensitivity test indicates that a power-law formulated in terms of these three variables provides an acceptable basis for quantifying regional-scale rates of quarrying. Our results highlight the strong influence of effective pressure, which intensifies quarrying by increasing the volume of the bed that is stressed by the ice and thereby the probability of rock failure. The resulting pressure dependency points to subglacial hydrology as a primary factor for influencing rates of quarrying and hence for shaping the bedrock topography under warm-based glaciers. When applied in a landscape evolution model, the erosion law for quarrying produces recognizable large-scale glacial landforms: U-shaped valleys, hanging valleys and overdeepenings. The landforms produced are very similar to those predicted by more standard sliding-based erosion laws, but overall quarrying is more focused in valleys, and less effective at higher elevations.

Accurate dynamical models of the Antarctic ice sheet with carefully specified initial conditions and well-calibrated rheological parameters are needed to forecast global sea level. By adapting an inverse method previously used in electric impedance tomography, we infer present-day flow speeds within the ice sheet. This inversion uses satellite observations of surface velocity, snow accumulation rate, and rate of change of surface elevation to estimate the basal drag coefficient and an ice stiffness parameter that influences viscosity. We represent interior ice motion using a vertically integrated approximation to incompressible Stokes flow. This model represents vertical shearing within the ice and membrane stresses caused by horizontal stretching and shearing. Combining observations and model, we recover marked geographical variations in the basal drag coefficient. Relative changes in basal shear stress are smaller. No simple sliding law adequately represents basal shear stress as a function of sliding speed. Low basal shear stress predominates in central East Antarctica, where thick insulating ice allows liquid water at the base to lubricate sliding. Higher shear stress occurs in coastal East Antarctica, where a frozen bed is more likely. Examining Thwaites glacier in more detail shows that the slowest sliding often coincides with elevated basal topography. Differences between our results and a similar adjoint-based inversion suggest that inversion or regularization methods can influence recovered parameters for slow sliding and finer scales; on broader scales we recover a similar pattern of low basal drag underneath major ice streams and extensive regions in East Antarctica that move by basal sliding.

Rapid glacier advance is known to occur by a range of mechanisms. However, although large-scale debris loading has been proposed as a process for causing rapid terminus advance, it has rarely been observed. We use satellite remote sensing data to observe accelerated glacier terminus advance in response to massive supraglacial loading on two glaciers in Kyrgyzstan. Over a 15 year period, mining activity has led to the dumping of spoil of up to 180 m thick on large parts of these valley glaciers. We find that the termini of these glaciers advance by 1.2 and 3.2 km, respectively, at a rate of up to 350 m yr−1. Our analysis suggests that although enhanced basal sliding could be an important process, massive supraglacial loads have also caused enhanced internal ice deformation that would account for most, or all, of the glacier terminus advance. In addition, narrowing of the glacier valley and mining and dumping of ice alter the mass balance and flow regime of the glaciers. Although the scale of supraglacial loading is massive, this full-scale experiment provides insight into glacier flow acceleration response where small valley glaciers are impacted by very large volumes of landslide debris.

Critical-state wedges, ice glaciers, and salt sheets have many geometric and mechanical similarities. Each has a tapering geometry and moves along a basal detachment. Their motions result from the combined effects of internal deformation and basal sliding. Wedge deformation and geometry, basal conditions, and overpressure (pore fluid pressure less hydrostatic pore fluid pressure) development within the substrate interact with each other in this mechanically coupled system. However, the nature of this interaction is poorly understood. In order to investigate this coupled system, we have developed two-dimensional poromechanical finite-element models with porous fluid flow in sediments. We have simulated the advance of a salt sheet wedge across poroelastic sediments in this study. We emphasize that our results have applications beyond salt wedges to both critical-state wedges and ice glaciers. Overpressure develops within the substrate over time during the advance of the wedge. The magnitude of the overpressure influences the wedge geometry and the wedge advance rate. Lower overpressure results in a thicker and steeper wedge geometry, and a slower advance rate, while higher overpressure favors a thinner, wider, and more flattened wedge geometry and a faster advance rate. This study provides key insights into the links between wedge geometry, basal shear stress, and overpressure in substrates.

We have detected over 150,000 small (M 3000 m) on the glacier-covered edifice and occur primarily in weeklong to monthlong swarms composed of simultaneous distinct families of events. Each family contains up to thousands of earthquakes repeating at regular intervals as often as every few minutes. Mixed polarity first motions, a linear relationship between recurrence interval and event size, and strong correlation between swarm activity and snowfall suggest the source is stick-slip basal sliding of glaciers. The sudden added weight of snow during winter storms triggers a temporary change from smooth aseismic sliding to seismic stick-slip sliding in locations where basal conditions are favorable to frictional instability. Coda wave interferometry shows that source locations migrate over time at glacial speeds, starting out fast and slowing down over time, indicating a sudden increase in sliding velocity triggers the transition to stick-slip sliding. We propose a hypothesis that this increase is caused by the redistribution of basal fluids rather than direct loading because of a 1–2 day lag between snow loading and earthquake activity. This behavior is specific to winter months because it requires the inefficient drainage of a distributed subglacial drainage system. Identification of the source of these frequent signals offers a view of basal glacier processes, discriminates against alarming volcanic noises, documents short-term effects of weather on the cryosphere, and has implications for repeating earthquakes, in general.

On most glaciers and ice sheet outlets the majority of motion is due to basal slip, a combination of basal sliding and bed deformation. The importance of basal water in controlling sliding is well established, with increased sliding generally related to high basal water pressure, but the details of the interactions between the ice and water systems has not received much study when there is coupling between the systems. Here we use coupled subglacial hydrology and ice dynamics models within the Community Ice Sheet Model to investigate feedbacks between the ice and water systems. The dominant feedback we find is negative: sliding over bedrock bumps opens additional cavity space, which lowers water pressure and, in turn, sliding. We also find two small positive feedbacks: basal melt increases through frictional heat during sliding, which raises water pressure, and strain softening of basal ice during localized speedup causes cavities to close more quickly and maintain higher water pressures. Our coupled modeling demonstrates that a sustained input of surface water to a distributed drainage system can lead to a speedup event that decays even in the absence of channelization, due to increased capacity of the system through opening of cavities, which is enhanced through the sliding-opening feedback. We find that the negative feedback resulting from sliding-opening is robust across a wide range of parameter values. However, our modeling also argues that subglacial channelization is required to terminate speedup events over timescales that are commensurate with observations of late summer slowdown on mountain glaciers.

Basal friction beneath ice sheets remains poorly characterized and yet is a fundamental control on ice mechanics. Here we use a complete map of surface velocity of the Antarctic Ice Sheet to infer the basal friction over the entire continent by combining these observations with a three-dimensional, thermomechanical, higher-order ice sheet numerical model from the Ice Sheet System Model open source software. We demonstrate that inverse methods can be readily applied at the continental scale with appropriate selections of cost function and of scheme of regularization, at a spatial resolution as high as 3 km along the coastline. We compare the convergence of two descent algorithms with the exact and incomplete adjoints to show that the incomplete adjoint is an excellent approximation. The results reveal that the driving stress is almost entirely balanced by the basal shear stress over 80% of the ice sheet. The basal friction coefficient, which relates basal friction to basal velocity, is, however, significantly heterogeneous: it is low on fast moving ice and high near topographic divides. Areas with low values extend far out into the interior, along glacier and ice stream tributaries, almost to the flanks of topographic divides, suggesting that basal sliding is widespread beneath the Antarctic Ice Sheet. ©2013. American Geophysical Union. All Rights Reserved.

[1] The distribution of cold and temperate ice within glaciers and ice sheets affects processes relevant to englacial and basal hydrology, sliding, and material rheology. Thermal regimes, in turn, are shaped by glacier and ice sheet dynamics, as well as environmental setting. We investigate the thermal structures of two small (

[1] Wintertime satellite-derived ice surface velocities, from 2001 through 2007, suggest an increase in ice velocity in the wet snow zone of Southwest Greenland. We present a thermomechanical model to evaluate the influence of surface meltwater runoff on englacial temperatures, via cryo-hydrologic warming (CHW), as a possible mechanism to explain this velocity increase at Sermeq Avannarleq. The model incorporates CHW through a previously published dual-column parameterization. We compare model simulations with (i) CHW active over the entire ice thickness (“base case CHW”), (ii) CHW active only in the surface 80 m of the ice sheet (“surface CHW”), and (iii) “no CHW” to represent a traditional thermomechanical model. The horizontal extent of CHW is prescribed based on equilibrium line altitude position and thus incorporates the upstream expansion of the ablation zone over the past decade. The base case CHW simulations reproduce the observed increase in inland ice velocity between 2001 and 2007 reasonably well. The no CHW and surface CHW simulations significantly underestimate observed ice surface velocities in both epochs. The higher ice velocities in the base case CHW simulations are attributable to both decreased basal ice viscosities associated with increased basal ice temperatures and an increase in the extent of basal sliding permitted by temperate bed conditions. Only the temperate bed extent predicted by the base case CHW simulation is consistent with independent observations of basal sliding. Based on our sensitivity analysis of CHW, we evaluate alternative explanations for an increase in inland ice velocity and suggest CHW is the most plausible mechanism.

[1] Saturated crevasses occur in local depressions within the shear margins of Jakobshavn Isbrae at inflections in the ice stream's flow direction. Spatio-temporal variability of seven distinctive saturated crevasse groups was examined during the 2007 melt season. The area of saturated crevasses reached its maximum extent, ~1.8 km2, in early July, and remained largely constant until early August. Filling rates are correlated with regional melt production, while drainage rates are highly correlated with areal extent. Estimates on potential drainage volume from the largest crevasse system are ~9.23 × 10−3 km3 ± 2.15 × 10−8 km3 and ~ 4.92 × 10−2 km3 ± 3.58 × 10−8 km3, respectively, over a 16 day interval and are more than required for a distributed basal hydrologic system across this area to temporarily flood bedrock obstacles believed to control basal sliding. Future drainage events, likely extending farther inland with warming, could result in enhanced lateral mass discharge into the ice stream, with implications for the dynamic evolution of the entire basin.

[1] New laboratory experiments exploring likely subglacial conditions reveal controls on the transition between stable sliding and stick-slip motion of debris-laden ice over rock, with implications for glacier behavior. Friction between a rock substrate and clasts in ice generates heat, which melts nearby ice to produce lubricating water. An increase in sliding speed or an increase in entrained debris raises heat generation and thus meltwater production. Unstable sliding is favored by low initial lubrication followed by rapid meltwater production in response to a velocity increase. Low initial lubrication can result from cold or drained conditions, whereas rapid increase in meltwater generation results from strong frictional heating caused by high sliding velocity or high debris loads. Strengthening of the interface (healing) during “stick” intervals between slip events occurs primarily through meltwater refreezing. When healing and unstable sliding are taken together, the experiments reported here suggest that stick-slip behavior is common from motion of debris-laden glacier ice over bedrock.

New data sets of bed and surface elevation have been combined with balance velocities, bed topography, and radar reflectivity to investigate the relationship between ice flow and bed conditions. It has been found that the bed topography affects the local driving stresses and initiates the onset of streaming flow in specific areas where there are large undulations. This onset region only appears significantly inland in three areas: the northeast Greenland ice stream, Kangerdlugssuaq Gletscher, and a region in the southwest associated with abnormally low driving stresses and an apparently unnamed but active glacier. Bed reflectance values below the northeast ice stream suggest that basal melting could be occurring along its length, and it seems likely therefore that the enhanced flow observed inland from the onset of streaming may be due, in part, to basal sliding.

A seismic reflection profile, perpendicular to the ice flow direction has been acquired on Rutford Ice Stream, Antarctica. An interpretation of both the amplitude and phase of the seismic reflections from the ice-bed interface has been made to investigate the properties of the sub-ice material. The interpretation assumes that acoustic impedance can be used to imply subglacial sediment porosity. Multiple reflections from the ice-bed interface on a number of seismic wide-angle lines allowed a calibration of the reflection coefficient at the bed. This enabled the acoustic impedance of the bed material to be calculated from the seismic reflection data. Mean acoustic impedance in the different sections of the bed ranges from 2.70×106 kg m−2 s−1 to 4.31×106 kg m−2 s−1. Almost three quarters of the ice stream bed at this site appears to be saturated, deforming sediments. The rest of the bed is probably also saturated sediments, but they are not deforming to any significant degree. Ice flow could include a combination of subglacial deformation and basal sliding. Localized regions which support disproportionately high amounts of basal shear stress may also occur. From the seismic data, it is not possible to apportion relative amounts of restraint to these different processes. There does not appear to be any correlation between the different sections identified on the ice stream bed with either satellite images or nearby surface velocity data. A feature which is interpreted as a subglacial drumlin is seen on the seismic section.

The end of the Little Ice Age (LIA) in Svalbard (76–81°N), a climate-sensitive region at the northern extreme of strong poleward heat transfer, was marked by an abrupt increase in mean annual air temperature of up to 5°C around 1920. Glacier mass balance has been consistently negative since this time, and large cumulative net losses of mass have occurred at most glaciers. Energy-balance modelling confirms the sensitivity of Svalbard glaciers to climate change, predicting a negative shift in net mass balance of up to 0.8 m a−1 (water equivalent) per degree temperature rise. This climate-related shift in glacier mass balance has reduced the intensity of glacier surge activity in Svalbard. One glacier, known to have surged since the end of the LIA, has since failed to accumulate the mass required to re-initiate the surge cycle, and is also now cold at its base and incapable of rapid flow by basal sliding. Three overviews of the total number of actively-surging glaciers in Svalbard between 1936–90 show a decrease from 18 to 5. This is significant compared with the expected numbers of surges based on LIA conditions. Post-LIA climate change in Svalbard has therefore affected not only glacier extent, but also ice dynamics. This is trend will probably continue given CO2-induced climate-warming.

This paper investigates the thermodynamic consequences of introducing basal sliding into a two-dimensional ice sheet model. The coupling of ice sheet form, flow field, and temperature evolution gives rise to limit cycles in the basal thermal regime of the ice sheet. Typical periods are 4000 to 5000 years and up to 45% of the ice sheet length can be affected. The limit cycles are caused by the switching on and off of sliding as basal ice reaches the pressure melting point. An analysis of the various heat fluxes at the ice sheet base stresses the roles of vertical diffusion and the heat generated by internal deformation and sliding in controlling the period and extent of the cycles. Limit cycles are found to persist in the face of various climatic (snow accumulation rate and air temperature) parameterizations, as well as for different basal sliding parameterizations. The type of oscillation change produced by varying accumulation rate is particularly interesting. Several distinct patterns of behavior are observed. For low accumulation rate ice sheets, a period of 6000–7000 years is dominant; for medium accumulation rate ice sheets, the 3000 to 4000 year period is dominant; while for larger accumulation rates, the oscillations become highly irregular with long (>10,000 years) periods.

[1] During more intense melt years, supraglacial lakes on the Greenland Ice Sheet are found to fill more rapidly and to drain earlier in the melt season. They also develop at higher latitudes and elevations. Since the rapid drainage of lakes has been shown to enhance basal sliding and since the lake volume can play an important role in determining if and when it drains, understanding and modeling the processes which control lake filling rates forms a key development in successfully modeling the possible impacts of lake drainage events on ice motion. We have developed a surface water routing and lake filling model and applied it to a 100 km2area of the Paakitsoq region, west Greenland. The model takes the time series of calculated runoff (melt minus refreezing) over the area and calculates flow paths and water velocities over the snow-/ice-covered surface, routing the water into topographic depressions which can fill to form lakes. Runoff is calculated from a distributed, surface energy-balance model coupled to a subsurface model, which calculates changes in temperature, density and water content in the snow, firn and upper ice layers, and hence refreezing and therefore net runoff. The model is calibrated against field measurements of a filling lake in our study area during June 2011 and can be used to calculate the filling rate of the instrumented lake with a high degree of accuracy. The filling rate of the instrumented/modeled lake depends on melt and routing from the immediate lake catchment and from overflowing lakes in upstream catchments.

[1] Increases in surface melt rates along the Greenland ice sheet margin have accelerated meltwater production, resulting in supraglacial lakes that can drain rapidly and enhance basal sliding. In this study, supraglacial lakes in western Greenland are mapped from multitemporal Landsat panchromatic imagery during the 2007 melt season. The analysis models lake spatial structure and establishes sequencing of drainage from 6 June through 9 August 2007. Results indicate high spatial clustering at lower elevations (between ∼100 and 700 m), with minimum lake-to-lake distances of ∼100–500 m and lake sizes

[1] We compare high-resolution 1985 and 2009 imagery to assess changes in crevasse extent in the Sermeq Avannarleq ablation zone, West Greenland. The area occupied by crevasses >2 m wide significantly increased (13 ± 4%) over the 24-year period. This increase consists of an expansion of existing crevasse fields, and is accompanied by widespread changes in crevasse orientation (up to 45°). We suggest that a combination of ice sheet thinning and steepening are responsible for the increase in crevasse extent. We examine the potential impact of this change on the hydrology of the ice sheet. We provide a first-order demonstration that moulin-type drainage is more efficient in transferring meltwater fluctuations to the subglacial system than crevasse-type drainage. As enhanced basal sliding is associated with meltwater “pulses”, an increase in crevasse extent can therefore be expected to result in a net decrease in basal sliding sensitivity. An increase in crevasse extent may also accelerate cryo-hydrologic warming and enhance surface ablation.

[1] The basal sliding surfaces in large rockslides are often composed of several surfaces and possess a complex geometry. The exact morphology and location in three dimensions of the sliding surface remains generally unknown, in spite of extensive field and subsurface investigations, such as those at the Aknes rockslide (western Norway). This knowledge is crucial for volume estimations, failure mechanisms, and numerical slope stability modeling. This paper focuses on the geomorphologic characterization of the basal sliding surface of a postglacial rockslide scar in the vicinity of Aknes. This scar displays a stepped basal sliding surface formed by dip slopes of the gneiss foliation linked together by steeply dipping fractures. A detailed characterization of the rockslide scar by means of high-resolution digital elevation models permits statistical parameters of dip angle, spacing, persistence, and roughness of foliation surfaces and step fractures to be obtained. The characteristics are used for stochastic simulations of stepped basal sliding surfaces at the Aknes rockslide. These findings are compared with previous models based on geophysical investigations. This study discusses the investigation of rockslide scars and rock outcrops for a better understanding of potential rockslides. This work identifies possible basal sliding surface locations, which is a valuable input for volume estimates, design and location of monitoring instrumentation, and numerical slope stability modeling.

[1] The rugged topography of mountain ranges represents a special challenge to computational ice sheet models simulating past or present glaciations. In mountainous regions, the topography steers glaciers through relatively narrow and steep valleys, and as a consequence hereof, the flow rate of alpine-style glaciers varies significantly at length scales comparable to that of the topography. Localized flow rate undulations generate longitudinal and transverse stress gradients within the ice, which, in turn, are of known importance to the flow itself, whether by internal deformation of the ice or by basal sliding, and to the interaction with topography through glacial erosion. Standard models capable of simulating mountain range–scale glaciations build on the so-called shallow ice approximation, which, among other parameters, neglects the longitudinal and transverse stress gradients, and therefore fails to capture the full effects of the rugged topography and related feedbacks between erosion by glacial sliding and the extent and style of glaciation. Here we present and test a new depth-integrated model framework which, on the one hand, takes into account the “higher-order” effects related to steep and rugged bed topography while it still, on the other hand, provides the computational efficiency needed for three-dimensional simulations of glaciation and landscape evolution in response to, for example, long-term climate variations. The model framework (integrated second-order shallow ice approximation (iSOSIA)) is based on depth integration of the second-order shallow ice approximation. Although depth integration is not guaranteed to maintain so-called second-order accuracy, the results of computational benchmark experiments show that iSOSIA, in spite of its efficient depth-integrated structure, performs well in situations with steep and rapidly undulating bed topography.

Received 21 September 2009; revised 3 November 2009; accepted 30 November 2009; published 30 December 2009. [1] To better understand mechanisms of ice-sheet decay, we investigate the surface mass balance of the Laurentide Ice Sheet (LIS) during the early Holocene, a period of known rapid LIS retreat. We use a surface energy-mass balance model (EMBM) driven with conditions derived from an equilibrium atmosphere-ocean general circulation model 9 kilo-years ago simulation. Our EMBM indicates a net LIS surface mass balance of 0.67 ± 0.13 m yr 1 , with losses primarily due to enhanced boreal summer insolation and warmer summers. This rate of loss compared to LIS volume reconstructions suggests that surface ablation accounted for 74 ± 22% of the LIS mass loss with the remaining loss likely driven by dynamics resulting in basal sliding and calving. Thus surface melting likely played a governing role in the retreat and disappearance of this ice sheet. Citation: Carlson, A. E., F. S. Anslow, E. A. Obbink, A. N. LeGrande, D. J. Ullman, and J. M. Licciardi (2009), Surface-melt driven Laurentide Ice Sheet retreat during the early Holocene, Geophys. Res. Lett., 36, L24502, doi:10.1029/ 2009GL040948.

[1] Radar layer geometry in divide areas is strongly influenced by the operation of the Raymond effect, which causes upwarping of the layers as a consequence of the nonlinear rheology of ice. The detailed geometry of these layers is known to store a record of change in the cryosphere, of local thinning, and of the age of formation of the divide and has been surmised to provide information about lateral motion of divides. Such lateral motion can be caused by changes in flanking ice streams, and the divide area thereby contains a record of ice stream dynamics. It has also been suggested that a large perturbation of divide position will obliterate the cumulative effects of the operation of the Raymond mechanism, leading to the disappearance of Raymond bumps. Since the Raymond effect has a strong influence on the age-depth relation in ice cores, knowledge of whether its operation is localized (leading to strong bump formation) or distributed is crucial in the interpretation of ice cores. The detailed evolution of ice divide radar layer geometry remains poorly understood. Employing a full thermomechanically coupled transient model, we qualitatively explore the effect of divide migration on radar layer geometry. Certain qualitative features emerge which can be used to infer history of cryosphere change, in particular, in areas distant from the usual sites of geological dating. There remains uncertainty about the influence of sliding on the operation of the Raymond effect. Under certain conditions, the existence of sliding can damp or eliminate the operation of the Raymond effect. If this is generally true, then dating of ice divides may simply be a date for the freezing of the divide bottom. We show that sliding does not necessarily eliminate the formation of bumps. Dates of divide formation are likely to be dates for the location of the ridge at a particular spot. Raymond bump evolution is weakened by flow along the ridge. We explore quantitatively the strength of this effect, using a scaling analysis to show that the weakening can efficiently be described by one parameter, the ratio of along-ridge slope to a measure of the across-divide curvature.

[1] Spatially coincident radar and seismic data collected two weeks apart on Rutford Ice Stream were analyzed to investigate the mechanical and hydrological characteristics of the ice-bed interface. Seismic data allow the differentiation of bed deformation from basal sliding. In radar data, sliding regions are characterised by highly variable permittivity values. We suggest these regions are characterized by small water bodies, possibly a cavity system. In contrast, deforming regions are characterised by consistent, low permittivity, which suggests intimate ice-sediment contact without a distinct interface. However, in deforming regions we identified three bright radar features similar to 50 m wide, consistent in lateral location over distances of 5-10 km up and downstream, and comprised of water less than similar to 0.2 m deep. We interpret these as part of a water evacuation system, most likely canals. Our results emphasise the great potential of radar and seismic techniques in combination to infer basal conditions beneath ice streams.

[1] Ten passive seismic recording stations were deployed in a 9 km by 6 km array on Rutford Ice Stream, West Antarctica, to detect microearthquakes from the ice stream bed. The array covered an area where a varying distribution of basal sedimentary conditions had been identified from seismic reflection surveys and interpreted as areas of both basal sliding and subglacial sediment deformation. The passive seismic experiment was designed to give an independent confirmation of this interpretation, as basal sliding is believed to be associated with the release of more acoustic energy than a deforming bed. The results show that this is the case, basal sliding producing six times more events. This confirms that the spatial pattern of basal conditions does indeed reflect the distribution of different ice flow mechanisms. It also shows that microearthquake monitoring can be a valuable new technique for mapping ice stream basal conditions over wide areas.

Since glacier beds are mostly inaccessible, numerical inversion of the surface velocity field provides a valuable method for calculating the basal shear stress and sliding velocity. However, previous theoretical studies (limited either to planar slabs or linear ice rheology) have suggested small errors in surface velocity measurements lead to large uncertainties in calculated basal sliding. Here a numerical ice flow model and Monte Carlo simulation are used to calculate the sliding velocity and basal shear stress and their associated uncertainties from field measurements of surface velocity along a two-dimensional long section of Glacier de Tsanfleuron, Switzerland. The model does not require the restrictive assumption of a sliding law since both sliding and basal shear stress are calculated independently and can include a spatially variable rate factor in the flow law for ice. Results indicate that sliding contributes between 45 and 84% of the surface velocity and that calculated sliding velocities are strongly dependent on ice rheology. Amplification of surface velocity errors is generally smaller than theoretical estimates and is a power law function of the horizontal grid spacing in the ice flow model.

[1] Transmission of basal variability to a glacier surface is investigated using analytical models for a linearly viscous medium. The three-dimensional transient response of the surface to both bedrock undulations and spatial variations in basal slipperiness for perturbations of arbitrary wavelengths is determined using perturbation methods. Both information transfer toward the surface and lateral transmission of horizontal stresses are strongly affected by the slip ratio, that is, the ratio of basal sliding to deformational velocity. For any mean bedrock slope, and above a minimum value of slip ratio, the amplitude transfer of bedrock undulations toward the surface has a local maximum at undulation span corresponding to about 3–8 times the mean ice thickness. The transmission of basal variability to a glacier surface increases quite significantly with increasing slip ratio. This explains why the surfaces of fast flowing ice streams are more undulating than the slower moving bordering areas. At slip ratios higher than about 100, the flow of glaciers and ice sheets becomes nonlocal in the sense that surface velocities and buildup and propagation of surface undulations cannot be calculated accurately on the basis of local thickness and slope. Using linearized long-wave theories at these slip ratios, instead of the more accurate arbitrary wavelength theory, gives estimates of decay times that are an order-of-magnitude too small and phase velocities several times too large. The problem of the propagation and decay of small-amplitude surface undulations on glaciers in three dimensions is solved. Small-amplitude surface waves on glaciers are strongly diffusive and dispersive. Redistribution of mass on ice sheets and glaciers is a diffusion process, and it is misleading, albeit not mathematically incorrect, to describe the reaction of glaciers to surface perturbations in terms of a wave propagation.

[1] Community Earth System Model Land Ice Working Group Meeting; Boulder, Colorado, 13 January 2011; Recent observations indicate that mass loss from glaciers and ice sheets (“land ice”) is increasing. The drivers of these changes are not well understood, and modeling the land ice response to them remains challenging. As a result, the Intergovernmental Panel on Climate Change explicitly avoided speculating on 21st-century sea level rise from ice dynamical processes in its fourth assessment report. The mismatch between observations of land ice change and model skill at mimicking those changes is behind recent efforts to develop next-generation land ice models. Necessary improvements to existing models include improved dynamics, coupling to climate models, and better representations of important boundary conditions and physical processes. Basal sliding, the primary control on the rate of land ice delivery to the oceans, is one such boundary condition that is largely controlled by land ice hydrology.

Ice thickness, computed within the fjord region of Byrd Glacier on the assumptions that Byrd Glacier is in mass-balance equilibrium and that ice velocity is entirely due to basal sliding, are on average 400 m less than measured ice thicknesses along a radio-echo profile. We consider four explanations for these differences: (1) active glacier ice is separated from a zone of stagnant ice near the base of the glacier by a shear zone at depth; (2) basal melting rates are some 8 m/yr; (3) internal shear occurs with no basal sliding in much of the region above the grounding zone; or (4) internal creep and basal sliding contribute to the flow velocity in varying proportions above the grounding zone. Large gradients of surface strain rate seem to invalidate the first explanation. Computed values of basal shear stress (140 to 200 kPa) provide insufficient factional heat to melt the ice demanded by the second explanation. Both the third and fourth explanations were examined by making simplifying assumptions that prevented a truly quantitative evaluation of their merit. Nevertheless, there is no escaping the qualitative conclusion that internal shear contributes strongly to surface velocities measured on Byrd Glacier, as is postulated in both these explanations.

A finite element model is used to calculate temperature and velocity along a two-dimensional glacier flow line. The model incorporates automatic element mesh generation, interpolation from point input data to all boundary nodes, comprehensive output graphics, linkage between velocity and temperature under one control program to allow iteration between the two, and time stepping in discrete units. The model results are tested against analytical solutions (for ice temperatures and velocities in simple situations) and field data (ice thickness, velocity, temperature, and mass balance). Sensitivity analyses were conducted with respect to model resolution, changed time step interval, geothermal temperature gradient, and bedrock topography. Limitations and strengths of applying finite element techniques to the modeling of glaciers are discussed. Some problems are encountered with the technique and methods of computation (e.g., limitation of mesh size, discretizing of a continuous body, equation approximation). Others arise from an inability to handle complex ice conditions (e.g., basal sliding and non sliding/sliding transition, cavitation, basal water). The inadequacy of glaciological data sets to provide sufficiently accurate and numerous boundary conditions and input values is a further major problem. Nevertheless, finite element methods hold considerable promise for modeling studies of cold, creep-dominated ice masses where there are marked gradients in temperature and velocity. These conditions are least well handled by conventional numerical techniques.

A numerical model of ice sheet flow is developed, and preliminary results are described. This model includes vertical resolution of temperature, stress, and strain rate which represents a considerable improvement over previous vertically averaged ice sheet models. The model follows the flow of ice along a flow line within an ice sheet drainage basin. Longitudinal stresses and basal sliding are included. Basal sliding is dependent on the base shear stress and a specified distribution of basal water pressure. The numerical methods used to solve the coupled set of stress and velocity equations for the static and time-evolutionary cases are discussed. A steady state profile simulating an ice stream is calculated for a particular set of input parameters, and changes in the profile are examined for different choices of parameters. Preliminary studies of response behavior are completed using a simplified ice sheet geometry with a fixed terminus or grounding line. The results of these studies illustrate ice sheet thinning in response to a lowered sea level or to a reduction in the extent of ice rises (or pinning points) within ice shelves.

Some iceberg-calving outlet glaciers flow continuously at speeds normally associated with surging glaciers arid exhibit dramatic instability scenarios related to those suggested for marine ice sheets. No temperate tidewater glaciers are known to have floating termini, but many polar and subpolar tidewater glaciers do. The fast flow of temperate calving glaciers is almost entirely due to basal sliding and appears to be a function of the effective pressure on the bed, which may approach zero, and the longitudinal back stress on the terminus. The terminus boundary condition (the calving relation) is imperfectly known yet is vital to the dynamics of these glaciers. Calving relations for grounded tidewater glaciers have been suggested on empirical grounds but have not been rigorously tested; the calving relations for floating termini are virtually unknown. This, together with the imperfect understanding of basal sliding, inhibits confidence in our understanding of the stability of these glaciers. Columbia Glacier (Alaska) is an instructive example because observations have been made on the major changes in its geometry, calving rate, and dynamics that have occurred in less than 10 years. The calving flux has increased more rapidly than the glacier flux, causing thinning and retreat; as a result, the ice velocity has increased markedly. The short-term velocity changes relate to changes in back pressure (ice recession, tidal changes) and the flux of water injected to the bed. These results have relevance to the mechanisms of basal sliding, glacier surges, and the stability of marine ice streams.