a vertically integrated treatment of ice stream and ice shelf thermodynamics the extremely small vertical shear in ice stream and ice shelf flow simplifies the equations which govern their thermodynamic evolution complemented by the widely used shallow shelf approximation used to simplify the ice flow momentum balance a vertically integrated formulation of heat transfer presented here reduces the dimensionality of the thermodynamic problem from three to two plan view dimensions and thus significantly reduces the computational cost of treating ice stream and ice shelf thermodynamics in models for realistic conditions errors in ice stiffness parameter ice thickness and speed caused by the vertically integrated treatment of heat transfer are less than 5 of magnitudes of these values compared to the standard three dimensional thermomechanical computations in addition for the specific case of ice shelves with strong bottom melting the governing equation describing evolution of the vertically integrated ice stiffness parameter is derived which further reduces computational cost the presented error analysis and formulations of ice stream and ice shelf thermodynamics in terms of the vertically integrated temperature allow the thermodynamic effects on ice deformation to be easily incorporated into studies that traditionally disregard them

rheology of till beneath storglaciaren sweden in order to study in situ the rheology of a deforming subglacial till various instruments were emplaced in till beneath storglaciaren sweden boreholes were used to gain access to the till beneath about 100 m of ice tiltmeters provided an estimate of the shear strain rate in the till two other instruments yielded measures of till strength in addition water pressures were recorded in boreholes and in the till a computer controlled distance meter provided an effectively continuous record of the surface velocity and data from frequent surveys of a stake network were used to estimate the mean basal drag based on a force balance calculation tilt rates varied directly with effective pressure so decreases in water pressure apparently increased the coupling between the glacier and the bed surface speed was either out of phase with tilt or varied independently of tilt thus increases in speed were apparently a consequence either of longitudinal coupling or of reduced coupling between the glacier and the bed they were not a result of till deformation till strength varied directly with effective pressure which is consistent with it being a mohr coulomb or frictional material the devices measuring till strength are presumed to have been pulled through the till at a speed that varied in phase with the surface speed but till strength did not vary systematically with surface speed this implies that the residual strength of the till is insensitive to strain rate thus the appropriate constitutive equation for till rheology may be of the form e e k where k is a constant this is consistent with experimental data reported in the geotechnical literature

shear margins in glaciers and ice sheets analytical and numerical techniques are used to examine the flow response of a sloped slab of power law fluid power n subjected to basal boundary conditions that vary spatially across the flow direction as for example near an ice stream margin with planar basal topography the primary assumption is that basal shear stress is proportional to the basal speed time a spatially variable slip resistance the ratio of mean basal speed to the speed originating from shearing through the thickness denoted as r gives a measure of how slippery the bed is the principal conclusion is that a localized disturbance in slip resistance affects the basal stress and speed in a zone spread over a greater width of the flow in units of ice thickness h the spatial scale of spreading is proportional to a single dimensionless number r n r n 1 1 n 1 derived from n and r the consequence for a shear zone above a sharp jump in slip resistance is that the shearing is spread out over a boundary layer with a width proportional to r n for an ice stream caused by a band of low slip resistance with a half width of wh the margins influence velocity and stress in the central part of the band depending on r n in comparison to w three regimes can be identified which for n 3 are quantified as follows low r defined as r 3 1w for which the boundary layers from both sides bridge across the full flow width and the driving stress in the center is supported almost entirely by side drag intermediate r for which the driving stress in the center is supported by a combination of basal and side drag shear zones that are narrower than predicted on the basis of this theory r 3 would require localized softening of the ice to explain the concentration of deformation at a shorter scale

a variational approach to ice stream flow ice sheets are susceptible to the formation of ice streams or narrow bands of fast flowing ice whose high velocities are caused by rapid sliding at the contact between ice and the underlying bed based on recent geophysical work which has shown that the sliding motion of ice streams may be described by a coulomb friction law we investigate how the location of ice streams depends on the geometry of an ice sheet and on the mechanical properties of the underlying bed more generally this problem is relevant to the flow of thin films with coulomb or solid friction laws applied at their base by analogy with friction problems in elasticity we construct a variational formulation for the free boundary between ice streams where bed failure occurs and the surrounding ice ridges where there is little or no sliding this variational problem takes the form of a non coercive variational inequality and we show that solutions exist provided a force and moment balance condition is satisfied in that case solutions are also unique except under certain specialized circumstances which are unlikely to arise for a real ice sheet further we show how the variational formulation of the ice flow problem can be exploited to calculate numerical solutions and to simulate the effect of changing ice geometry and bed friction on the location and velocities of streaming flow lastly we study the effect of ice shelf buttressing on the flow of ice streams whose spatial extent is determined by the yield stress distribution of the bed in line with previous studies of ice shelf buttressing we find that the removal of an ice shelf can cause an ice stream feeding the ice shelf to speed up considerably which underlines the important role ice shelves may play in controlling the dynamics of marine ice sheets

model experiments on the evolution and stability of ice streams this is the publisher s version also available electronically from http www igsoc org annals 23

seismic measurements reveal a saturated porous layer beneath an active antarctic ice stream seismic reflection studies recently conducted on ice stream b part of the marine ice sheet of west antarctica show a metres thick layer immediately beneath the ice in which both compressional p and shear s wave speeds are very low these low wave speeds imply that the material in the layer is highly porous and is saturated with water at a high pore pressure from this and from arguments presented in an accompanying paper1 to the effect that the layer would be too weak to support the shear stress exerted by the overlying ice we conclude that the layer is deforming and that the ice stream probably moves principally by such deformation

a new approach to inferring basal drag and ice rheology in ice streams with applications to west antarctic ice streams drag at the bed and along the lateral margins are the primary forces resisting flow in outlet glaciers simultaneously inferring these parame ters is challenging since basal drag and ice viscosity are coupled in the momen tum balance which governs ice flow here we test the ability of adjoint based inverse methods to infer the slipperiness coefficient in a power law sliding law and the flow rate parameter in the constitutive relation we modify existing inversions by including surface strain rates into the regularization of the in version using synthetic data generated with physically motivated variations in basal drag and ice rheology we show that this allows for more accurate in ferences we apply this method to bindschadler and macayeal ice streams in west antarctica our results show relatively soft ice in the shear margins and spatially varying basal drag with an increase in drag with distance upstream of the grounding line punctuated by localized areas of relatively high drag we interpret the former to reflect a combination of heating through viscous dissipation and changes in the crystalline structure these results suggest that adjoint based inverse methods can provide inferences of basal drag and ice rheology when the regularization is informed by strain rates

ring shear studies of till deformation coulomb plastic behavior and distributed strain in glacier beds a ring shear device was used to study the factors that control the ultimate steady strength of till at high shear strains tests at a steady strain rate and at different stresses normal to the shearing direction yielded ultimate friction angles of 26 3 and 18 6 for tills containing 4 and 30 clay sized particles respectively other tests at steady normal stresses and variable shear strain rates indicated a tendency for both tills to weaken slightly with increasing strain rate this weakening may be due to small increases in till porosity these results provide no evidence of viscous behavior and suggest that a coulomb plastic idealization is reasonable for till deformation however viscous behavior has often been suggested on the basis of distributed shear strain observed in subglacial till we hypothesize that deformation may become distributed in till that is deformed cyclically in response to fluctuations in basal water pressure during a deformation event transient dilation ofdiscrete shear zones should cause a reduction in internal pore water pressure that should strengthen these zones relative to the surrounding till a process called dilatant hardening consequent changes in shear zone position when integrated over time may yield the observed distributed strain

transmission of stress between an ice stream and interstream ridge measurements of strain rate are used to describe the stress distribution at the lateral margin of an active west antarctic ice stream the goal is to describe the way in which drag at the sides operates to control the motion of this ice stream the problem is inherently complex but with some approximations a mainly analytic solution is obtained allowing for spatially varying ice strength shows that the shear strain rate decreases over a larger distance from the ice stream than for ice of uniform strength the simplest explanation using the results of field measurements is that the upper 40 of the ice stream is able to support lateral stress for the slow moving interstream ridge rather more of the thickness is strong the lateral shear stress from the ice stream is transferred to a basal zone about 3 km wide where basal drag reaches 60 kpa this basal zone controls the speed of the ice stream

physical conditions at the base of a fast moving antarctic ice stream boreholes drilled to the bottom of ice stream b in the west antarctic ice sheet reveal that the base of the ice stream is at the melting point and the basal water pressure is within about 1 6 bars of the ice overburden pressure these conditions allow the rapid ice streaming motion to occur by basal sliding or by shear deformation of unconsolidated sediments that underlie the ice in a layer at least 2 meters thick the mechanics of ice streaming plays a role in the response of the ice sheet to climatic change

variability along the atlantic water pathway in the forced norwegian earth system model the growing attention on mechanisms that can provide predictability on interannual to decadal time scales makes it necessary to identify how well climate models represent such mechanisms in this study we use a high 0 25 horizontal grid and a medium 1 resolution version of a forced global ocean sea ice model utilising the norwegian earth system model to assess the impact of increased ocean resolution our target is the simulation of temperature and salinity anomalies along the pathway of warm atlantic water in the subpolar north atlantic and the nordic seas although the high resolution version has larger biases in general at the ocean surface the poleward propagation of thermohaline anomalies is better resolved in this version i e the time for an anomaly to travel northward is more similar to observation based estimates the extent of these anomalies can be rather large in both model versions as also seen in observations e g stretching from scotland to northern norway the easternmost branch into the nordic and barents seas carrying warm atlantic water is also improved by higher resolution both in terms of mean heat transport and variability in thermohaline properties a more detailed assessment of the link between the north atlantic ocean circulation and the thermohaline anomalies at the entrance of the nordic seas reveals that the high resolution is more consistent with mechanisms that are previously published this suggests better dynamics and variability in the subpolar region and the nordic seas in the high resolution compared to the medium resolution this is most likely due a better representation of the mean circulation in the studied region when using higher resolution as the poleward propagation of ocean heat anomalies is considered to be a key source of climate predictability we recommend that similar methodology presented herein should be performed on coupled climate models that are used for climate prediction

bedform signature of a west antarctic palaeo ice stream reveals a multi temporal record of flow and substrate control abstract the presence of a complex bedform arrangement on the sea floor of the continental shelf in the western amundsen sea embayment west antarctica indicates a multi temporal record of flow related to the activity of one or more ice streams in the past mapping and division of the bedforms into distinct landform assemblages reveals their time transgressive history which implies that bedforms can neither be considered part of a single downflow continuum nor a direct proxy for palaeo ice velocity as suggested previously a main control on the bedform imprint is the geology of the shelf which is divided broadly between rough bedrock on the inner shelf and smooth dipping sedimentary strata on the middle to outer shelf inner shelf bedform variability is well preserved revealing information about local complex basal ice conditions meltwater flow and ice dynamics over time these details which are not apparent at the scale of regional morphological studies indicate that past ice streams flowed across the entire shelf at times and often had onset zones that lay within the interior of the antarctic ice sheet today in contrast highly elongated subglacial bedforms on sedimentary strata of the middle to outer shelf represent a timeslice snapshot of the last activity of ice stream flow and may be a truer representation of fast palaeo ice flow in these locations a revised model for ice streams on the shelf captures complicated multi temporal bedform patterns associated with an antarctic palaeo ice stream for the first time and confirms a strong substrate control on a major ice stream system that drained the west antarctic ice sheet during the late quaternary

interaction and variability of ice streams under a triple valued sliding law and non newtonian rheology 1 ice streams are regions of fast flowing glacier ice that transport a significant portion of the total ice flux from present ice sheets the flow pattern of ice streams can vary both temporally and spatially in particular ice streams can become stagnant and change their path we study the dynamics of ice streams using an idealized model of an isothermal and power law viscous ice flow that includes horizontal lateral shear stresses the basal sliding law is assumed to be triple valued we investigate the spatiotemporal patterns formed because of the flow over a flat bed fed from an upstream mass source the ice flows from the mass source region through one or two gaps in a prescribed upstream topographic ridge which restricts the flow leading to the formation of one or two ice streams we find a relation between the parameters of the ice rheology and the width of the ice stream shear margins and show how these parameters can affect the minimum width of an ice stream we also find that complex asymmetric spatiotemporal patterns can result from the interaction of two ice streams sharing a common mass source the rich spatiotemporal variability is found to mostly be a result of the triple valued sliding law but non newtonian effects are found to play a significant role in setting a more realistic shear margin width and allowing for relevant time scales of the variability

reactivation of kamb ice stream tributaries triggers century scale reorganization of siple coast ice flow in west antarctica ongoing centennial scale flow variability within the ross ice streams of west antarctica suggests that the present day positive mass balance in this region may reverse in the future here we use a three dimensional ice sheet model to simulate ice flow in this region over 250 years the flow responds to changing basal properties as a subglacial till layer interacts with water transported in an active subglacial hydrological system we show that a persistent weak bed beneath the tributaries of the dormant kamb ice stream is a source of internal ice flow instability which reorganizes all ice streams in this region leading to a reduced positive mass balance within decades and a net loss of ice within two centuries this hitherto unaccounted for flow variability could raise sea level by 5 mm this century furthermore better constraints on future sea level change from this region will require improved estimates of geothermal heat flux and subglacial water transport

shallow shelf approximation as a sliding law in a thermomechanically coupled ice sheet model 1 the shallow shelf approximation a balance of membrane stresses for ice flow is an effective sliding law for ice sheet modeling our use of it as a sliding law becomes a standard model for ice stream flow when the sliding velocity is large 100 m a 1 and faster following schoof 2006a we describe the basal resistance as plastic till for which the yield stress is given by a mohr coulomb formula pore water pressure is related to basal melt rate the velocity field used in the mass continuity and conservation of energy equations is an average of velocities from the shallow shelf approximation and the nonsliding shallow ice approximation using this scheme our model has realistic time dependent ice streams which exhibit the range of surface velocities seen in actual ice streams we demonstrate the model at high spatial resolution 5 km grid over multiple millenia using its implementation in the parallel ice sheet model numerical experiments show that the entire scheme is stable with respect to many parameter changes some experiments reveal significant ice stream variability in a hypothetical steady climate with characteristic cycles on the order of 1000 years we believe this is the first practical whole ice sheet model with a unified treatment of vertical shear stresses and membrane stresses it is capable of high resolution thermomechanically coupled multimillenia simulations of ice sheets containing ice streams

effects of ice deformation on rothlisberger channels and implications for transitions in subglacial hydrology along the base of glaciers and ice sheets the sliding of ice over till depends critically on water drainage in locations where drainage occurs through rothlisberger channels the effective pres sure along the base of the ice increases and can lead to a strengthening of the bed which reduces glacier sliding the formation of rothlisberger channels depends on two competing effects 1 melting from tur bulent dissipation opens the channel walls and 2 creep flow driven by the weight of the overlying ice closes the channels radially inward variation in downstream ice velocity along the channel axis re ferred to as an antiplane shear strain rate decreases the effective viscosity the softening of the ice increases creep closure velocities in this way even a modest addition of antiplane shear can double the size of the rothlisberger channels for a fixed water pressure or allow channels of a fixed radius to operate at lower effective pressure potentially decreasing the strength of the surrounding bed furthermore we show that rothlisberger channels can be deformed away from a circular cross section under applied antiplane shear these results can have broad impacts on sliding velocities and po tentially affect the total ice flux out of glaciers and ice streams

spontaneous generation of pure ice streams via flow instability role of longitudinal shear stresses and subglacial till 1 a significant portion of the ice discharge in ice sheets is drained through ice streams with subglacial sediment till acting as a lubricant the known importance of horizontal friction in shear margins to ice stream dynamics suggests a critical role of longitudinal stresses the effects of subglacial till and longitudinal stresses on the stability of an ice sheet flow are studied by linear stability analysis of an idealized ice till model in two horizontal dimensions a power law viscous constitutive relation is used explicitly including longitudinal shear stresses the till which has compressible viscous rheology affects the ice flow through bottom friction we examine the possibility that pure ice streams develop via a spontaneous instability of ice flow we demonstrate that this model can be made intrinsically unstable for a seemingly relevant range of parameters and that the wavelengths and growth rates that correspond to the most unstable modes are in rough agreement with observed pure ice streams instabilities occur owing to basal friction and meltwater production at the ice till interface the most unstable wavelength arise because of selective dissipation of both short and long perturbation scales longitudinal stress gradients stabilize short transverse wavelengths while nye diffusion stabilizes long transverse wavelengths the selection of an intermediate unstable wavelength occurs however only for certain parameter and perturbation structure choices these results do not change qualitatively for a newtonian ice flow law indicating no significant role to shear thinning although this may very well be due to the restrictive assumptions of the model and analysis

the role of lateral drag in the dynamics of ice stream b antarctica the partitioning of resistive force between the bed and sides of ice stream b antarctica is obtained for three large areas that have been measured using repeat aerial photogrammetry problems associated with data errors and local variations in ice strength and velocity are reduced by considering the areally averaged budget of forces for each photo block results indicate that the bed under ice stream b must be very weak and unable to provide muche resistance mechanical control on this ice stream emanates almost entirely from the lateral margins

pressure dependent viscosity and interfacial instability in coupled ice sediment flow we study an interfacial instability in the coupled flow of ice and subglacial sediment both modelled as viscous media unlike other interfacial instabilities in coupled viscous flows at zero reynolds number the mechanism considered here does not rely on buoyancy or the effect of an upper free surface but on the pressure dependence of the sediment viscosity specifically the instability relies on sediment rheology being such that when sediment flows in simple shear sediment flux increases with compressive normal stress at the ice sediment interface when the velocity of the interface is kept constant when ice moves over a shallow bump in the interface it generates a higher compressive stress on the bump s upstream side than in its lee if in addition the effective sediment viscosity is low compared with that of ice interfacial velocity remains approximately constant and this then implies that more sediment flows into the bump than out of it causing it to grow modelling ice as a newtonian material we show that this mechanism works for a wide range of sediment rheologies including the highly nonlinear shear thinning ones typically thought most appropriate for the description of nearly plastic sediment the instabilities predicted are essentially two dimensional with infinite transverse wavelength and a nonlinear model shows that growth is unbounded until cavitation occurs in the lee of evolving bumps on the interface the instability mechanism does not seem to predict the formation of common glacial landforms but may explain the formation of water filled cavities on deformable glacier beds

deformation induced melting in the margins of the west antarctic ice streams flow of glacial ice in the west antarctic ice sheet localizes in narrow bands of fast flowing ice streams bordered by ridges of nearly stagnant ice but our understanding of the physical processes that generate this morphology is incomplete here we study the thermal and mechanical properties of ice stream margins where flow transitions from rapid to stagnant over a few kilometers our goal is to explore under which conditions the intense shear deformation in the margin may lead to deformation induced melting we propose a 2 d model that represents a cross section through the ice stream margin perpendicular to the downstream flow direction we limit temperature to the melting point to estimate melt rates based on latent heat using rheology parameters as constrained by laboratory data and observations we conclude that a zone of temperate ice is likely to form in active shear margins

temperate ice in the shear margins of the antarctic ice sheet controlling processes and preliminary locations abstract the flux of grounded ice from the antarctic ice sheet ais primarily occurs through narrow fast flowing outlet glaciers and ice streams shearing generates heat in the lateral glacier margins where there is a transition from fast flow to near stagnant ice or rock this heat warms the ice and can form zones of water saturated porous ice at the melting temperature known as temperate ice here we derive a one dimensional thermomechanical model to infer which ais shear margins may contain temperate ice our model provides expressions for the critical shear strain rate at which a zone of temperate ice initiates and the thickness of the temperate zone both of these quantities are described by two nondimensional numbers the brinkman and peclet numbers that are functions of observable parameters such as shear strain rate surface temperature surface accumulation rate and ice thickness the development of temperate zones is incited by shear strain rates brinkman number and suppressed by the advection of cold ice from the surface peclet number which scales with surface accumulation rate we also include a parametrization for lateral advection which can suppress the formation of temperate ice applying recent observations and outputs from a regional climate model we show that many active glacier shear margins could contain temperate ice the spatial distribution and thickness of temperate zones are controlled largely by shear strain rates and surface accumulation rates

basal mechanics of ice stream b west antarctica 2 undrained plastic bed model based on the results of our studies of the physical conditions beneath ice stream b we formulate a new analytical ice stream model the undrained plastic bed model henceforth the upb model mathematically the upb model is represented by a non linear system of four coupled equations which express the relationships among ice sliding velocity till strength water storage in till and basal melt rate we examine this system of equations for conditions of ice stream stability over short timescales that permit holding ice stream geometry constant less than hundreds of years temporal variability is introduced into the upb model only by the direct dependence of till void ratio changes e t on the basal melting rate m r since till strength b e and ice stream velocity u b b change as long as till void ratio varies the first condition for ice stream stability is that of constant till water storage 0 the second condition for ice stream stability arises from the feedback between ice stream velocity till strength and the basal melting rate which depends on shear heating m r u b b this is the weak till condition which requires that in a steady state till strength is a small fraction of the gravitational driving stress b n 1 1 d the salient feature of the upb model is its ability to produce two thermo mechanically controlled equilibrium states one with a strong bed and slow ice velocities ice sheet mode and one with a weak bed and fast ice velocities ice stream mode this bimodality of basal conditions is consistent with the available observations of subglacial conditions beneath slow and fast moving ice in west antarctica basal conditions that do not correspond to these two steady states may occur transiently during switches between the two stable modes the upb model demonstrates that ice streams may be prone to thermally triggered instabilities during which small perturbations in the basal thermal energy balance grow leading to generation or elimination of the basal conditions which cause ice streaming

stress balances of ice streams in a vertically integrated higher order formulation one challenge in improving our understanding of ice stream dynamics is to develop models of the spatial and temporal transition from ice sheet to ice stream flow we address this with a new vertically integrated higher order formulation for ice sheet dynamics that captures the leading order physics of low aspect ratio viscous fluid flow regardless of the amount of slip at the bed the theory introduces a parameter which approximates the ratio of the basal stress to the shear stress scale providing a measure of the relative importance of sliding and internal deformation our model is able to simultaneously describe the dynamics of both a slow moving sheet and rapidly flowing ice streams to test the formulation we apply a triple valued sliding law as the basal boundary condition and obtain numerical solutions that can be compared with previous work we investigate the sensitivity of flow regimes and shear margin width to parameter variation deriving a scaling for the latter we also consider a double valued sliding law which enforces a constant low basal stress beneath the ice stream comparisons of the resultant stress fields illustrate the different stress balances that can maintain

rheological nonlinearity and flow instability in the deforming bed mechanism of ice stream motion contrary to what has recently been assumed in modeling the proposed deforming bed mechanism for the rapid motion of antarctic ice streams the rheology of water saturated till is probably highly nonlinear according to information from soil mechanics and preliminary experiments on till from the base of ice stream b the equivalent flow law exponent n is probably as high as 100 and the nonlinearities of the shear stress and effective pressure dependences are closely linked the high nonlinearity has important consequences for the deforming bed mechanism a flow system operating by this mechanism can be unstable as a result of feedback from the generation of basal water by shear heating of basal till the short term feedback effect is analyzed for a perturbation in a model ice stream in which the basal meltwater is transported through a distributed system of narrow gap conduits at the ice till interface although the analysis is approximate and some of the system parameters are poorly known the results suggest that the deforming bed mechanism is unstable for n 20 the apparent lack of such an instability in the currently active ice streams implies that their motion is controlled not by the deforming bed mechanism but by some other as yet unidentified mechanism

massive destabilization of an arctic ice cap abstract ice caps that are mostly frozen at the bedrock ice interface are thought to be stable and respond slowly to changes in climate we use remote sensing to measure velocity and thickness changes that occur when the margin of the largely cold based vavilov ice cap in the russian high arctic advances over weak marine sediments we show that cold based to polythermal glacier systems with no previous history of surging may evolve with unexpected and unprecedented speed when their basal boundary conditions change resulting in very large dynamic ice mass losses an increase in annual mass loss by a factor of 100 over a few years we question the future long term stability of cold and polythermal polar ice caps many of which terminate in marine waters as the climate becomes warmer and wetter in the polar regions

energy balance of ice streams analysis of the cross flow transmission of force from the central parts of a well lubricated ice stream to its margins shows that there is a corresponding shift in the lateral location of motion induced heat generation the rate of basal heat generation in the center can be substantially smaller than the local rate of potential energy loss given by driving stress times the speed of downslope motion the basal heating is a maximum for an intermediate level of lubrication for which speed is about 40 of the speed over a frictionless bed and base stress is about 25 of the driving stress stable and unstable balances between meltwater production and drainage on the bed are identified a stable steady state with a speed less more than that giving maximum heat generation is termed drainage production limited since an increase in speed would lead to increased decreased basal melting and must need not be balanced by increased drainage it is shown that gradual evolution of the basal water drainage system and the factors affecting basal melting can cause discontinuous jumps between fast and slow moving states a simplified analysis applied to six cross sections of west antarctic ice streams b d e and rutford ice stream shows them to be diverse in the level of support from the sides and corresponding shift of mechanical heating sideward from their central parts the cross sections of ice stream b near upstream b may be production limited because of especially high lubrication and related support from the sides cross sections in the upper part of ice stream d ice stream e and rutford ice stream are in a drainage limited condition substantial reduction of basal heat generation by side drag in most cases and expected high heat flow into the basal ice associated with low thickness in some cases tends to favor basal freezing nevertheless all of the examined cross sections except one are expected to experience basal melting with a modest geothermal heat flux density of 60 mw m or less in some cases the lower part of ice stream b is an exception where the analysis indicates that geothermal flux density must exceed 80 100 mw m to maintain melting if this high geothermal flux is not present then the base of the lower part of ice stream b may be freezing which would suggest continued deceleration of this part of ice stream b

thermally driven migration of ice stream shear margins ice stream shear margins are the lateral boundaries of narrow fast flowing bands of ice within an ice sheet we develop a theory for the migration of shear margins over time driven by viscous dissipation of heat within the ice focusing on widening of the ice stream the location of the margin is modelled as a transition from a cold to a temperate ice sheet bed and simultaneously as the transition from no slip to free slip at the same location the temperature field in the ice is affected by intense shear heating as well as by the migration velocity of the margin i e by the widening rate of the ice stream if migration is too fast there is little time for the ice to warm up and the margin remains cold causing the bed to freeze this suppresses widening conversely if the migration speed is too slow the ice in the margin warms up causing the bed on the far side of the cold temperate transition to reach the melting point and migration to speed up using a wiener hopf method we show that for a given far field shear stress geothermal heat flux and ice geometry there is a single migration velocity that balances the two effects and permits widening at a steady rate this velocity increases with the far field lateral shear stress imposed by the ice stream which controls shear heating in the margin our results also indicate that i a region of temperate ice must form in the margin and that ii lateral advection of ice may play a significant role in controlling migration speeds

basal mechanics of ice stream b west antarctica 1 till mechanics data from laboratory geotechnical tests on till recovered from beneath ice stream b west antarctica at the upstream b camp hereinafter the upb till show that failure strength of this till is strongly dependent on effective stress but is practically independent of strain and strain rate these data support use of a coulomb plastic rheology in modeling of ice stream behavior and subglacial till deformation our testing program combined triaxial ring shear and confined uniaxial tests to investigate till strength and compressibility results show that the upb till follows closely coulomb s equation in which shear strength is a linear function of normal effective stress apparent cohesion near zero and internal friction angle equal to 24 till compressibility is best described by a logarithmic function that relates void ratio to normal effective stress in general the behavior of the upb till is consistent with other experimental evidence regarding mechanical behavior of granular materials based on our laboratory results we formulate the compressible coulomb plastic till model in which there are three interrelated primary state variables shear strength void ratio and normal effective stress this model is used in the second part of our study to simulate response of subglacial till to realistic effective stress forcings these simulations demonstrate that the model is capable of reproducing fundamental aspects of subglacial till kinematics 1 occurrence of tilt rate oscillations and negative tilt rates in tiltmeter records and 2 distributed till deformation to depths of 0 1 1 0 m beneath the ice base our laboratory and modeling results substantiate application of the compressible coulomb plastic model in simulations of the motion of ice stream b over its weak till bed

shear heating and weakening of the margins of west antarctic ice streams ice streams are fast flowing bands of ice separated from stagnant ridges by shear margins the mechanisms controlling the location of the margins remain unclear we use published ice deformation data and a simple one dimensional thermal model to show that west antarctic ice stream margins have temperate ice over a substantial fraction of their thickness a condition that may control their width the model predicts a triple valued relation between the thickness averaged lateral shear stress and the lateral shear strain rate observed strain rates at the margins imply that they support slightly less lateral shear stress than adjacent ice within the stream this requires enhanced basal resistance near the margin we suggest in agreement with the limited observations the presence of a channelized drainage system at the margin that reduces the pore fluid pressure at the ice till interface thus increasing the shear stress acting on the yielding coulomb plastic bed

basal sliding of ice stream b west antarctica a tethered stake apparatus is used to measure basal sliding in a borehole on ice stream b west antarctica about 300 km upstream east from its grounding line near the head of the ross ice shelf a metal stake emplaced at the top of a layer of unfrozen till underlying the ice is connected by a tether line to a metering unit that measures the tether line as it is pulled out from the borehole by the stake as a result of basal sliding the measured sliding motion includes any actual slip across the ice till interface and may include in addition a possible contribution from shear deformation of till within about 3 cm of the interface this 3 cm figure follows from a qualitative model of the movements of the stake in the course of the experiment based on features of the record of apparent sliding alternative but less likely models would increase the figure from 3 cm to 10 cm or 25 cm in any case it is small compared to the seismically inferred till thickness of 9 m measured apparent sliding averages 69 of the total motion of 1 2 m d 1 over 26 days of observation if a 3 5 day period of slow apparent sliding 8 of the total motion is included in the average the occurrence of the slow period raises the possibility that the sliding motion switches back and forth between c 80 and c 8 of the total motion on a time scale of a few days however it is likely that the period of slow apparent sliding represents instead a period when the stake got caught on the ice sole if the slow period is therefore omitted the indicated average basal sliding rate is 83 of the total motion in either case basal sliding predominates as the cause of the rapid ice stream motion in the last 2 days of observation the average apparent sliding rate reached 1 17 m d 1 essentially 100 of the motion of the ice stream if till deformation contributes significantly to the ice stream motion the contribution is concentrated in a shear zone 3 cm to possibly 25 cm thick at the top of the 9 m thick till layer these observations if applicable to the west antarctic ice sheet in general pose complications in modeling the rapid ice streaming motion

the marginal shear stress of ice stream b west antarctica to ascertain whether the velocity of ice stream b west antarctica may be controlled by the stress in its marginal shear zones the snake and the dragon we undertook a determination of the marginal shear stress in the dragon near camp up b by using ice itself as a stress meter the observed marginal shear strain rate of 0 14 a 1 is used to calculate the marginal shear stress from the flow law of ice determined by creep tests on ice cores from a depth of 300 m in the dragon obtained by using a hot water ice coring drill the test specimen orientation relative to the stress axes in the tests is chosen on the basis of c axis fabrics so that the test applies horizontal shear across vertical planes parallel to the margin the resulting marginal shear stress is 2 2 0 3 10 5 pa this implies that 63 100 of the ice stream s support against gravitational loading comes from the margins and only 37 0 from the base so that the margins play an important role in controlling the ice stream motion the marginal shear stress value is twice that given by the ice stream model of echelmeyer and others 1994 and the corresponding strain rate enhancement factors differ greatly e 1 2 vs 10 12 5 this large discrepancy could be explained by recrystallization of the ice during or shortly after coring estimates of the expected recrystallization time scale bracket the 1 h time scale of coring and leave the likelihood of recrystallization uncertain however the observed two maximum fabric type is not what is expected for annealing recrystallization from the sharp single maximum fabric that would be expected in situ at the high shear strains involved 20 experimental data from wilson 1982 suggest that if the core did recrystallize the prior fabric was a two maximum fabric not substantially different from the observed one which implies that the measured flow law and derived marginal shear stress are applicable to the in situ situation these issues need to be resolved by further work to obtain a more definitive observational assessment of the marginal shear stress

recent changes in glacier velocities and thinning at novaya zemlya abstract ice loss from the glaciers of novaya zemlya nvz is the dominant contributor to sea level for the russian arctic here we present maps of glacier elevation change rates dh dt and velocities at novaya zemlya that reveal evidence of the impact of both calving flux and surface melt on ice mass loss dh dt are calculated by applying a weighted linear regression to stacked digital elevation models dems from a 1952 map and dems created from stereo pairs of worldview images acquired between 2012 and 2014 the 60 year average mass change rate is 0 23 0 04 m w e yr 1 the recent short term 2012 2013 2014 average mass change rate is 0 40 0 09 m w e yr 1 we apply the same weighted linear regression to stacked worldview dems and icesat elevations from 2003 to 2009 as well as stacked worldview dems and aster dems from 2000 to 2013 the dh dt from both datasets confirm that thinning has been more rapid than the 60 year average since 2000 average mass loss has accelerated at the lower elevations of land terminating glaciers suggesting that recent near surface warming and increased melt have led to greater thinning marine terminating glaciers along the barents sea coast have substantially higher thinning rates near their termini in recent years than adjacent land terminating glaciers suggesting that calving flux is an important contributor to overall ice mass loss in the region flow velocities are generated by feature tracking on optical and radar image pairs marine terminating glaciers along the barents sea coast have the highest frontal velocities of any glaciers on nvz our surface velocity measurements constrain the calving flux at the two fastest retreating glaciers inostrantseva ino and vil kitskogo vis which are both on the barents sea coast we find that the calving flux is high enough to drive frontal thinning and retreat at those two glaciers summer terminus speeds at inostrantseva glacier have accelerated from a 2006 maximum of 3 m day 1 to a 2012 maximum of 9 to 10 m day 1 and the front has retreated by more than 3 km between 2006 06 27 and 2013 08 17

a boundary layer model for ice stream margins the majority of antarctic ice is discharged via long and narrow fast flowing ice streams at ice stream margins the rapid transition from the vertical shearing flow in the ice ridges surrounding the stream to a rapidly sliding plug flow in the stream itself leads to high stress concentrations and a velocity field whose form is non trivial to determine in this paper we develop a boundary layer theory for this narrow region separating a lubrication type ice ridge flow and a membrane type ice stream flow this allows us to derive jump conditions for the outer models describing ridge and stream self consistently much of our focus is however on determining the velocity and shear heating fields in the margin itself ice stream margins have been observed to change position over time with potentially significant implications for ice stream discharge our boundary layer model allows us to extend previous work that has determined rates of margin migration from a balance between shear heating in the margin and the cooling effect of margin migration into the colder ice of the surrounding ice ridge solving for the transverse velocity field in the margin allows us to include the effect of advection due to lateral inflow of ice from the ridge on margin migration and we demonstrate that this reduces the rate of margin migration as previously speculated

on the mechanics of ice stream shear margins we investigate the mechanics of ice stream shear margins based on the assumption that the underlying bed behaves plastically sliding is assumed to occur if a prescribed locally defined yield stress is attained while no sliding is assumed possible if basal shear stress is lower than the yield stress mathematically the ice flow problem takes the form of a contact problem in which the zones of sliding are part of the solution and cannot be prescribed arbitrarily simplistic assumptions about the location of till failure or about mechanical conditions at the bed predict stress singularities at the margins which lead to corresponding singularities in the basal melt rate the ice flow problem is solved using a complex variable method and an associated quasi static thermal problem is also solved using a green s function high stress concentrations which coincide with high rates of strain heating are found on the ice stream side of the margins where basal melting is also greatest our results further indicate that a temperate zone may form over time above the bed in the margins these findings differ from earlier studies based on dif ferent sliding laws suggesting a high sensitivity of margin behaviour to basal conditions

coupling between a glacier and a soft bed i a relation between effective pressure and local shear stress determined from till elasticity to predict the distribution of motion beneath glaciers on soft beds the strength of the coupling between the ice and the bed and its variation with effective pressure must be known a record of shear strain acquired with a tiltmeter emplaced in till beneath storglaciaren sweden indicates that fluctuations in water pressure cause variations in the local shear stress on the bed and that the bed deforms elastically in response to these variations to estimate the shear stress from the elastic component of the total shear strain the shear modulus of the till was measured in relaxation tests conducted in the laboratory with a ring shear device after accounting for the elastic compliance of the device these tests yielded shear moduli of about 1000 and 1800 kpa at confining pressures of 85 and 280 kpa respectively these values are comparable to those of other granular materials undergoing recoverable shear strains of the same magnitude the local shear stress on the till calculated by applying the measured shear moduli to the tilt record scales with p e 1 7 where p e is the effective pressure this relation implies that as p e decreases at the ice till interface shear stresses on the till are reduced and concentrated elsewhere on the bed perhaps where the till is absent or the glacier is frozen to the bed when compared with the strength of the till determined from ring shear tests this relation also accounts for the lack of permanent deformation at depth in the bed during periods of low p e and indicates that most basal motion was by sliding or ploughing

processes controlling the downstream evolution of ice rheology in glacier shear margins case study on rutford ice stream west antarctica ice rheology governs how glaciers flow and respond to environmental change the rheology of glacier ice evolves in response to a variety of mechanisms including damage heating melting and the development of crystalline fabric the relative contributions of these rheological mechanisms are not well understood using remotely sensed data and physical models we decouple the influence of each of the aforementioned mechanisms along the margins of rutford ice stream a laterally confined outlet glacier in west antarctica we show that fabric is an important control on ice rheology in the shear margins with an inferred softening effect consistent with a single maximum fabric fabric evolves to steady state near the onset of streaming flow and ice progressively softens downstream almost exclusively due to shear heating the rate of heating is sensitive to local shear strain rates which respond to local changes in bed topography as ice is squeezed through the basal trough the impact of shear heating on the downstream evolution of ice rheology in a laterally confined glacier suggests that the thermoviscous feedback wherein faster ice flow leads to higher rates of shear heating further softening the ice is a fundamental control on glacier dynamics

variational methods for glacier flow over plastic till we investigate the mechanics of ice streams and glaciers flowing over a bed consisting of coulomb plastic subglacial sediment or more generally of channel flows with coulomb or solid friction laws at the boundary sliding is assumed to occur if shear stress at the glacier bed attains a prescribed locally defined yield stress while no sliding is assumed possible below that yield stress importantly the location of regions of slip and no slip at the bed is not known a priori but forms part of the solution by analogy with friction problems in elasticity we derive a weak formulation as a semi coercive variational inequality which admits a unique solution provided a solvability condition ensuring force balance is satisfied the variational formulation is then exploited to calculate numerical solutions and we investigate the effect of variations in subglacial water pressure ice thickness and surface slope on the discharge of a valley glacier with a plastic bed significant differences are found between the behaviour of wide and narrow as well as steep and shallow angled glaciers and our results further indicate the need to develop models capable of accounting for longitudinal stresses

thermal effects on the location of ice stream margins west antarctic ice streams move rapidly over beds that are thawed by heat generated by the motion intervening zones of slow moving ice are probably freezing at their bases where heat generation is absent heat is also generated in the shear zone between the slow and fast moving ice through modeling of coupled heat and mass flow we show that the position of the boundary between freezing and melting at the bed is unstable for an otherwise morphologically uniform bed above a threshold speed in the ice stream heat generation in the shear zone allows melting beneath the slow ice and possible widening of the stream below this threshold heat generation at the edge of the thawed zone is insufficient to maintain melting leading to freezing and narrowing of the stream the threshold speed appears to be a function of the temperature at the base of slow ice relative to the melting point and is also highly sensitive to the inflow of colder ice from the slow zone for environmental conditions typical of west antarctica the threshold speed is about 100 m yr 1 in the absence of inflow and increases to typical ice stream speeds 500 m yr 1 for inflow speeds of a few meters per year thus the ice streams can be in a delicate thermal balance with the potential of melting outward or freezing inward rapidly moving ice streams could expand unless blocked by bed properties that would prevent fast motion even when there is melting at the bed

lateral shear moraines and lateral marginal moraines of palaeo ice streams abstract an understanding of the nature of sedimentation at ice stream lateral margins is important in reconstructing the dynamics of former ice sheets and modelling the mechanisms by which sediment is transported beneath contemporary ice streams theories of the formation of ice stream lateral moraines islms have hitherto been based on a relatively limited number of terrestrial and marine examples here an inventory of islms is compiled from available studies together with independent analysis of seismic reflection and bathymetric datasets the locations and dimensions of 70 islms alongside a synthesis of their key architectural and geomorphic characteristics are presented two different types of islms are identified type 1 islms are up to 3 5 km wide and 60 m thick they maintain a constant width thickness and cross sectional shape along their length type 1 islms are interpreted and referred to as ice stream lateral shear moraines that form subglacially in the shear zone between ice streams and slower flowing regions of an ice sheet in contrast type 2 islms are up to 50 km wide and 300 m thick they are only identified close to the shelf break in the marine environment type 2 islms exhibit an increase in width and thickness along their length and their distal slopes become steeper in a seaward direction they contain internal dipping reflections that indicate sediment progradation away from the former ice stream type 2 islms are interpreted and referred to as ice stream lateral marginal moraines that were formed at the lateral boundary between ice streams and seafloor terrain that was free of grounded ice we suggest that using bathymetric images and acoustic profiles it is possible to differentiate between ice stream lateral shear moraines and lateral marginal moraines in the geological record this distinction is important for understanding the mechanisms of sediment transfer beneath ice streams and for making inferences about the conditions that existed beyond the lateral ice stream margin at the time of lateral moraine formation slow moving ice beyond lateral shear moraines and ocean water rather than ice beyond lateral marginal moraines

bed radar reflectivity across the north margin of whillans ice stream west antarctica and implications for margin processes surface based ice penetrating radar profiles were made across the active north margin the snake of the upper part of whillans ice stream formerly ice stream b branch b2 west antarctica at three locations low frequency about 2 mhz and the ground deployment of the radar allowed penetration through the near surface zone of fracturing to detect internal layering and bed reflection characteristics on continuous profiles spanning from the slow moving ice of engelhardt ridge well into the chaotic zone of the shear margin internal layers were tracked beneath the chaotic zone where they are warped but remain continuous the energy returned from internal layers showed no systematic changes associated with the transition from the undisturbed surface of the slow moving ice into the fractured surface of the shear margin thus indicating little effect from the surface crevasses on the penetration of the radar signal based on this calibration of the near surface effects and corrections for path length spreading and attenuation we examine the spatial variation of bed reflectivity low bed reflectivity found under engelhardt ridge extends under the chaotic zone of the margin into fast moving ice we argue that the fast motion in a band along the margin is mediated by processes other than deformation of thick dilated till that is the source of lubrication allowing fast motion in the interior of the ice stream

measurement of temperature in a margin of ice stream b antarctica implications for margin migration and lateral drag ice temperature was measured in and around the chaotically crevassed south margin of ice stream b antarctica from 1992 to 1994 the temperatures at 30 m depth in the chaotic zone are about 12 k lower than in the adjacent uncrevassed ice due to the ponding of cold winter air at depths greater than 150 m there is clear evidence of internal heating of the ice due to the large shear deformation rate in the marginal zone analysis of the depth of cooling below the crevasses and of the internal heating gives two pieces of information first over the last half century the lateral shear stress averaged 2 0 x 10 5 pa in the top third of the margin and second the margin moved outward at an average rate of 7 3 m a these values do not involve any assumptions about the flow law of ice the uncertainties are roughly 20 the value of lateral shear stress indicates that the most of the drag on the ice stream is along its sides

rapid ice flow rearrangement induced by subglacial drainage in west antarctica ice streams are corridors of rapid ice flow draining the ice sheets they can exhibit astonishing spatial variability on annual to centennial time scales we propose that changes in the subglacial drainage of meltwater could induce these sudden rearrangements of ice streams we develop a two dimensional thermomechanical model representing an ice stream cross section and couple it to a plastically deforming bed with spatially variable meltwater influx we find that where ice flows over deformable sediments and lacks significant topographic control the efficiency of subglacial water drainage exerts direct control on the velocity location and width of ice streams this implies that meltwater percolation at the meter scale could have a significant effect on the short term variability in ice loss from a continental scale ice sheet we verify our model against previous analytical results and validate it against surface observations from the siple coast of west antarctica

steady flow of a viscous ice stream across a no slip free slip transition at the bed an exact analytic description of the steady downhill flow of a viscous ice stream across a no slip to free slip transition in basal boundary condition suggests ways in which such transitions might be detected by observations of ice stream surface properties we find that the best expression of this transition is in the free surface profile which dips over the point of transition and becomes horizontal far downstream

formation mechanisms for ice stream lateral shear margin moraines the lateral shear margins of palaeo ice stream beds are occasionally marked by large curvilinear moraines but little work has addressed how they might form in this paper we review the characteristics of lateral shear margin moraines and present two quantitative models for their formation i differential erosion rates related to lateral variations in the stream velocity and ii lateral incursion from inter stream ridges after the thinner stream retreats where the shear margin moraine is consequently just a terminal moraine of the inter stream ridge other possible mechanisms of formation are addressed qualitatively both of our quantitative theories are in principle feasible but the incursion model is less plausible and inconsistent with observations the differential erosion model can predict moraines tens of metres thick and several kilometres wide which can be formed in a thousand years the width of the moraine depends on the competition between a term that varies across the ice stream because it is dependent on ice velocity and that always causes erosion and a term related to the local accumulation rate which causes erosion if is positive and deposition if negative these terms combine to create the possibility of deposition at the shear margins of ice streams in ablation areas the width of the moraine has a tendency to increase with the width of the stream the conditions that permit shear margin moraines to form are quite constrained too much ablation and deposition occurs everywhere rather than just near the lateral margins of the ice streams too little ablation and there is erosion everywhere this is consistent with the infrequent observations of lateral shear margin moraines

marine ice sheet dynamics part 1 the case of rapid sliding marine ice sheets are continental ice masses resting on bedrock below sea level their dynamics are similar to those of land based ice sheets except that they must couple with the surrounding floating ice shelves at the grounding line where the ice reaches a critical flotation thickness in order to predict the evolution of the grounding line as a free boundary two boundary conditions are required for the diffusion equation describing the evolution of the grounded ice thickness by analogy with stefan problems one of these conditions imposes a prescribed ice thickness at the grounding line and arises from the fact that the ice becomes afloat the other condition must be determined by coupling the ice sheet to the surrounding ice shelves here we employ matched asymptotic expansions to study the transition from ice sheet to ice shelf flow for the case of rapidly sliding ice sheets our principal results are that the ice flux at the grounding line in a two dimensional ice sheet is an increasing function of the depth of the sea floor there and that ice thicknesses at the grounding line must be small compared with ice thicknesses inland these results indicate that marine ice sheets have a discrete set of steady surface profiles if they have any at all and that the stability of these steady profiles depends on the slope of the sea floor at the grounding line