the effect of the subglacial water pressure on the sliding velocity of a glacier in an idealized numerical model in order to interpret observed short term variations of the sliding velocity of a glacier the effect of a variable subglacial water pressure on the sliding velocity has been studied using an idealized numerical model in particular the transient stages of growing or shrinking water filled cavities at the ice bedrock interface were analysed it was found that the sliding velocity was larger when cavities were growing than when they had reached the steady state size for a given water pressure the smallest sliding velocities occurred while cavities were shrinking when cavitation is substantial a small drop of water pressure below the steady state value e g by 0 5 bar can temporarily cause backward sliding a limiting water pressure at which sliding becomes unstable is derived the consequences of more realistic assumptions than those of the model are discussed

weertman lliboutry and the development of sliding theory this paper reviews the seminal contributions and tussles of weertman and lliboutry to the theory of glacier sliding in the 1950s and 1960s and summarizes later developments up to the present day the sliding law solid ice in the form of glaciers and ice sheets flows on long timescales due to solid state creep processes and the resulting rheology is usually described in terms of a generalized newtonian fluid most commonly this takes the form of glen s law although other variants are possible the formulation of a viscous glacier flow in this way leads to an elliptic partial differential equation for the flow velocity which requires the posing of boundary data at both the upper free surface and the base or bed of the glacier mostly viscous liquids are thought to obey a no slip boundary condition at a solid boundary on the intuitive notion that the fluid molecules effectively adhere to the boundary but there is no intrinsic reason why this should be so and indeed the veracity of the condition was a subject of controversy in the 19th century goldstein 1938 a generalization called the navier slip condition allows a nonzero slip velocity proportional to stress and it is thought that such a condition is necessary to alleviate an unphysical singularity discontinuous velocity which would otherwise occur in the motion of a contact line where a two fluid interface intersects a wall dussan and davis 1974 it has long been understood that glaciers also slip at the bed and the resulting boundary condition for the flow which relates basal velocity u to basal stress has come to be known as the sliding law and it is the efforts that have been put into its determination that form the subject of this paper an issue which needs immediate clarification is what is meant by the basal stress the quantityrefers to the shear stress in the ice near the bed on the scale of the ice depth di but far from the bed on the scale l of the bed roughness in the language of matched asymptotic expansions the basal shear stress is the limiting value at the bed of the outer solution in an asymptotic expansion in the small parameter l di 1 1

calving processes and the dynamics of calving glaciers abstract calving of icebergs is an important component of mass loss from the polar ice sheets and glaciers in many parts of the world calving rates can increase dramatically in response to increases in velocity and or retreat of the glacier margin with important implications for sea level change despite their importance calving and related dynamic processes are poorly represented in the current generation of ice sheet models this is largely because understanding the calving problem involves several other long standing problems in glaciology combined with the difficulties and dangers of field data collection in this paper we systematically review different aspects of the calving problem and outline a new framework for representing calving processes in ice sheet models we define a hierarchy of calving processes to distinguish those that exert a fundamental control on the position of the ice margin from more localised processes responsible for individual calving events the first order control on calving is the strain rate arising from spatial variations in velocity particularly sliding speed which determines the location and depth of surface crevasses superimposed on this first order process are second order processes that can further erode the ice margin these include fracture propagation in response to local stress imbalances in the immediate vicinity of the glacier front undercutting of the glacier terminus by melting at or below the waterline and bending at the junction between grounded and buoyant parts of an ice tongue calving of projecting submerged ice feet can be regarded as a third order process because it is paced by first or second order calving above the waterline first order calving can be represented in glacier models using a calving criterion based on crevasse depth which is a function of longitudinal strain rate modelling changes in terminus position and calving rates thus reduces to the problem of determining the ice geometry and velocity distribution realistic solutions to the problem of modelling ice flow therefore depend critically on an appropriate choice of sliding law models that assume that basal velocities are controlled by basal drag can replicate much of the observed behaviour of calving glaciers with grounded termini but an important limitation is that they cannot be used to model floating glacier termini or ice shelves alternative sliding laws that parameterise drag from the glacier margins provide more flexible and robust ways of representing calving in ice sheet models such models can explain a remarkable range of observed phenomena within a simple unifying framework including downglacier increases in velocity and strain rates where basal and or lateral drag diminishes flow acceleration in response to thinning through time the tendency for glaciers to stabilise at pinning points in relatively shallow water or fjord narrowings the constraints on ice shelf stability and the contrasts in calving rates between tidewater and freshwater calving glaciers many unresolved issues remain however including the role played by the removal of backstress in the acceleration of retreating calving glaciers and the controls on melting at and below the waterline

coupled ice till deformation near subglacial channels and cavities previous models of ice till deformation near subglacial channels or cavities neglect the fact that the motions of the two materials are coupled and thus the interface between ice and till may not remain stationary here we analyze in succession two models which address the effect of such coupling via specification of appropriate continuity conditions for stress and velocity across the interface the modelled scenario is that of a shallow channel cavity with its long axis parallel to the principal ice flow direction overlying actively deforming till sediments by applying asymptotic techniques we investigate how the pattern and velocity of the creep flow depend generally on the ratio between the ice and till viscosities and on the deforming till thickness a more sophisticated non linear rheology for till sediments is then introduced it reveals that the two way interaction between water percolation and deformation in the till will enhance the localization of sediment flow near the channel margins the length scale over which transition of effective stress in the till takes place from its relatively high far field value to the low channel value is found to depend critically on a dimensionless permeability parameter a in any case coupled deformation causes sediment and ice flow towards the channel subsidence of the ice till interface just outside the channel and extension of the area over which the ice is in contact with till apart from having direct implications for subglacial sediment transport these results indicate that coupled deformation can contribute significantly to the spatial evolution of stress distribution under a glacier and thus its incorporation into future sliding and drainage theories for a soft bed should be considered essential

modifications to the theory of intraglacial waterways for the case of subglacial ones on defend l idee que dans les glaciers de montagne temperes les voies d eau sont sous glaciaires pour un conduit noye sous glaciaire il faut introduire deux processus importants l accroissement de la deformation plastique sur les cotes amont des bosses et la chaleur apportee par l eau des sources qui en hiver rend compte de la plus grande partie du debit la theorie explique pourquoi rothlisberger 1972 dut adopter une valeur non realiste pour le parametre rheologique de la glace elle conduit a la conclusion que dans les zones non surcreusees la plus grande partie de l annee les conduits sous glaciaires doivent rester non noyes et a la pression atmospherique cas des surcreusements l incidence de ce nouveau modele sur la theorie du glissement des glaciers

the importance of pressurized subglacial water in separation and sliding at the glacier bed l effet de l eau sous glaciaire sous pression sur le processus de glissement est examine a partir d un parametre appele indice de decollement du lit qui exprime les contraintes perpendiculaires au lit et la pression d eau les donnees proviennent de trois glaciers de formes differentes une loi puissance du type de weertman avec un exposant voisin de 3 modifiee pour tenir compte de l effet de la pression des eaux sous glaciaires apparait comme etant la meilleure

rapid glacier sliding reverse ice motion and subglacial water pressure during an autumn rainstorm measurements of basal water pressure from 15 boreholes located at both local tens of meters and regional kilometers length scales were used to elucidate the pressure sliding relationship during an autumn rapid motion event on bench glacier alaska usa the 8 day event had two distinct phases each with a ten fold speed up with respect to winter velocity the water pressure in all 15 boreholes varied synchronously during the speed up the first phase of rapid sliding began after a peak in basal water pressure and continued while the pressure was elevated and stable or decreasing the second phase of rapid sliding occurred when the basal water pressure was low but increasing and terminated before the pressure peaked pressure and velocity do not appear unrelated but the pressure sliding relationship was not consistently linked to increasing decreasing or a critical water pressure the pressure variations and sliding accelerations are a response to a warm rainstorm although equally large input events occurred in weeks prior with no apparent response drainage system evolution therefore appears to play a key role in both the acceleration and the pressure velocity relationship basal cavity dynamics are likely responsible for three episodes of reverse up valley motion observed after enhanced sliding

flow thermal structure and subglacial conditions of a surge type glacier temperature measurements in a subpolar surge type glacier reveal a distinctive thermal structure associated with the boundary between the ice reservoir and receiving areas in the receiving area the glacier is cold based but bottom temperature has increased as much as 0 5 c between 1981 and 1982 and the basal heat flux is roughly 10 times the expected geothermal flux water percolation through permeable subglacial material is the probable energy source deformation of the substrate could destroy this drainage system and trigger a surge

extent and dynamics of the scandinavian ice sheet during oxygen isotope stage 3 65 000 25 000 yr b p the climate of the middle weichselian glaciation marine oxygen isotope stage 3 ois 3 a relatively mild period compared to the glacial maxima of ois 4 and ois 2 consisted of long warm interstades punctuated by brief cold excursions that grew colder and more frequent with time the ois 4 ice sheet is generally thought to have persisted throughout ois 3 but evidence from dated ois 3 interstadial deposits suggests that it was swiftly reduced to small remnants which only briefly expanded and retreated only 30 000 years ago the deteriorating climate initiated a sustained ice advance leading toward the final glacial maximum of ois 2 dynamic ice sheet models support the existence of a prolonged ice free interval during ois 3 induced perhaps by low precipitation due to extensive sea ice cover offshore

sliding with cavity formation we present a model for the determination of a sliding law in the presence of sub glacial cavitation this law determines the basal stress at a clean ice bedrock interf ace in terms of the velocity and effective pressure the method is based on an exact solut ion of the nye kamb linearly viscous sliding problem with cavities and uses ideas of lliboutry 979 to construct via re norma lization methods an approximate law for gene ral bedrock form we show that for a bedrock whose spectrum has a power law behaviour one obtains a sliding law which gives the basal shear stress proportional to a power of the velocity and to a power of the effective pressure the effect of subgl acial cavitation on the drainage system is exam ined using recent ideas of kamb for sufficiently high velocities drainage through a r6thlisberger tunnel system is unstable and drai nage takes place through the linked system of cavities this leads to a reduction of the effective pressure and by taking account of this one can rewrite the sliding law in terms of st ress and velocity only this sliding law can be multi v alued and it is suggested that this unde rlies the dynamic phenomenon of surges

hydraulics of subglacial cavities modele theorique du comportement a l etat stationnaire des cavites remplies d eau et interconnectees sur le lit du glacier

rapid advance of two mountain glaciers in response to mine related debris loading 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

on the role of mechanical energy in maintaining subglacial water conduits at atmospheric pressure recent theo retical studies of glacier hydrology have assumed that subglacial conduits are completely filled with water under steady state conditions this however is not necessarily the case where discharges are larger than a few tens of liters per second and the down glacier slope of the bed is more than a few degrees the potential energy released by water descending this slope may be capable of melting the walls of a subglacial conduit many times faster than the conduit can close by plastic flow of the ice as a result the pressure in such tunnels may normally be atmospheric or possibly even at the triple point pressure if there is no open connection to the glacier surface simple calcu lations suggest that such pressures in subglacial conduits may be more common than herclofore anticipated the positions of such open conduits may be unstable to small per turbations in discharge or ice veloci ty this is because the mechanical energy available in excess of that needed to balance closure can instead offset the gene ral flow of the ice cond ui ts can thus trend diago nally across the direction of ice aow if an increase in the angle which such a conduit makes with the ice flow direction also results in an increase in slope of he conduit more mechanical energy will become available resulting in a positive feedback process subglacial channels at atmospheric pressure may inauence the origin and morphology of certain glacial landforms such as eskers and plastically molded features resume sur le role de l inergie newtonnienne dam le maintien du riseau aquiflrl sous glaciaire cl la pression almosph irique de recentes etudes theoriques d hydrologie glaciaire ont suppose que le reseau sous glaci aire clait corn pletement rempli d eau en condition d cquil ibre stable ceci neanmoins n est pas necess airement le cas lorsque les debits sonl superieurs a quelques dizaines de litres par seconde et que la pente du lit du glacier est superieure a quelques degres i energie potentielle mise en oeuvre par i eau descendant celle pente peut ire capable de fondre les parois d un chenal sous glaciaire beaucoup plus vite que le chenal ne peut se refermer par le auage plastique de la glace il en resuhe que la pression dans de tels chenaux peut nor rnalement etre atrnospherique

spatially distributed runoff at the grounding line of a large greenlandic tidewater glacier inferred from plume modelling understanding the drivers of recent change at greenlandic tidewater glaciers is of great importance if we are to predict how these glaciers will respond to climatic warming a poorly constrained component of tidewater glacier processes is the near terminus subglacial hydrology here we present a novel method for constraining near terminus subglacial hydrology with application to marine terminating kangiata nunata sermia in south west greenland by simulating proglacial plume dynamics using buoyant plume theory and a general circulation model we assess the critical subglacial discharge if delivered through a single compact channel required to generate a plume that reaches the fjord surface we then compare catchment runoff to a time series of plume visibility acquired from a time lapse camera we identify extended periods throughout the 2009 melt season where catchment runoff significantly exceeds the discharge required for a plume to reach the fjord surface yet we observe no plume we attribute these observations to spatial spreading of runoff across the grounding line persistent distributed drainage near the terminus would lead to more spatially homogeneous submarine melting and may promote more rapid basal sliding during warmer summers potentially providing a mechanism independent of ocean forcing for increases in atmospheric temperature to drive tidewater glacier acceleration

experimental determination of a double valued drag relationship for glacier sliding the contribution of glaciers to sea level rise and their effects on landscape evolution depend on the poorly known relationship between sliding speed and drag at the ice bed interface results from experiments with a new rotary laboratory device demonstrate empirically for the first time a double valued drag relationship like that suggested by some sliding theories steady drag on a rigid sinusoidal bed increases peaks and declines at progressively higher sliding speeds due to growth of cavities in the lee sides of bed undulations drag decreases with increased sliding speed if cavities extend beyond the inflection points of up glacier facing surfaces so that adverse bed slopes in contact with ice diminish with further cavity growth these results indicate that shear tractions on glacier beds can potentially decrease due to increases in sliding speed driven by weather or climate variability promoting even more rapid glacier motion by requiring greater strain rates to produce resistive stresses although a double valued drag relationship has not yet been demonstrated for the complicated geometries of real glacier beds both its potential major implications and the characteristically convex stoss surfaces of bumps on real glacier beds provide stimulus for exploring the effects of this relationship in ice sheet models

a theoretical treatment of the sliding of glaciers in the absence of cavitation a model is proposed for the description of glacier sliding which includes the nonlinearity of the flow law for ice the model describes coupled flow problems in the basal ice and a thin water film together with a temperature problem in the underlying bedrock to determine the sliding law relating basal velocity to basal stress the sliding theory should be formulated as a boundary layer to the larger scale bulk ice flow dimensional analysis indicates that the regelative component of ice velocity may be neglected provided roughness is absent at the smallest wavelengths and then the ice flow effectively uncouples from the other problems in this case with the crucial but unrealistic assumption that the flow law for temperate ice is independent of the moisture content there exist complementary variational principles that describe the functional form of the sliding law and give bounds on the magnitude of the 9roughness9 coefficient these principles are valid for nonlinear stress strain rate relations and for non vanishing bedrock corrugation and indicate how the basal velocity is determined by two parameters that together describe the degree of roughness of the bed specific estimates are then given finally the main weakness in the model as a predictor of quantitatively accurate results is pointed out that is that the variation of moisture within the basal layer and the resultant effect on the flow law are neglected a valid description of this phenomenon does not yet appear to be available

combined measurements of subglacial water pressure and surface velocity of findelengletscher switzerland conclusions about drainage system and sliding mechanism interpretation des mesures de pression dans les forages et des vitesses superficielles la comparaison avec les modeles suggere que l on a neglige le frottement du aux debris dans les modeles et qu il n existe jamais de chenaux cylindriques rectilignes

global dynamics of a temperate valley glacier mer de glace and past velocities deduced from forbes bands transverse profiles and velocities which have been measured on the ablation zone of mer de glace more or less continuously since 1891 contradict the weertman nye theory of glacier kinematic waves faint broad waves which undoubtedly result from fluctuations in the balance travel down the glacier faster than this theory predicts this theory having first been completed by taking changes in width with time and with distance down the glacier into account on the other hand velocity fluctuations are synchronous and more or less the same over the entire length studied 6 km these discrepancies result from bottom friction being of the solid type i e independent of sliding velocity friction should also be almost insensitive to discharge in subglacial waterways since in the steady state energy for keeping them open not entirely flooded and at atmospheric pressure is superabundant the sliding velocities at all cross profiles are thus controlled by some areas where the body of the glacier suffers strong deformation because the valley shape is far from cylindrical one such controlling zone exists on mer de glace owing to the existence of a subglacial transverse shoulder a new perturbation equation and a new rough expression for wave velocity are given intervals between forbes bands were plotted on seven aerial surveys between 1939 and 1979 progressive tilting of the slices of blue dusty ice from the position from which these dark bands proceed and progressive lowering of their exposed edge must be taken into account this analysis confirms the validity of our simple model for velocity fluctuations and allows us to estimate the entire series since the year 1888

finite element modeling of subglacial cavities and related friction law 1 sliding velocity and basal drag are strongly influenced by changes in subglacial water pressure or subglacial water storage associated with opening and closing of water cavities in the lee of bedrock obstacles to better understand this influence finite element simulations of ice flowing past bedrock obstacles with cavity formation are carried out for different synthetic periodic bedrock shapes in the numerical model the cavity roof is treated as an unknown free surface and is part of the solution as an improvement over earlier studies the cases of nonlinear ice rheology and infinite bedrock slopes are treated our results show that the relationship between basal drag and sliding velocity the friction law can be easily extended from linear to nonlinear ice rheology and is bounded even for bedrocks with locally infinite slopes combining our results with earlier works by others a phenomenological friction law is proposed that includes three independent parameters that depend only on the bedrock geometry this formulation yields an upper bound of the basal drag for finite sliding velocity and a decrease in the basal drag at low effective pressure or high velocity this law should dramatically alter results of models of temperate glaciers and should also have important repercussions on models of glacier surges and fast glacier flows

basal hydraulic system of a west antarctic ice stream constraints from borehole observations pressure and tracer measurements in boreholes drilled to the bottom of ice stream b west antarctica are used to obtain information about the basal water conduit system in which high water pressures are developed these high pressures presumably make possible the rapid movement of the ice stream pressure in the system is indicated by the borehole water level once connection to the conduit system is made on initial connection here also called breakthrough to the basal water system the water level drops in a few minutes to an initial depth in the range 96 117 m below the surface these water levels are near but mostly somewhat deeper than the flotation level of about 100m depth water level at which basal water pressure and ice overburden pressure are equal which is calculated from depth density profiles and is measured in one borehole the conduit system can be modelled as a continuous or somewhat discontinuous gap between ice and bed the thickness of the gap has to be about 2 mm to account for the water level drop on breakthrough and about 4 mm to fit the results of a salt tracer experiment indicating downstream transport at a speed of 7 5 mm s 1 the above gap conduit model is however ruled out by the way a pressure pulse injected into the basal water system at breakthrough propagates outward from the injection hole and also by the large hole to hole variation in measured basal pressure which if present in a gap conduit system with 2 or 4 mm would result in unacceptably large local water fluxes an alternative model that avoids the e objections called the gap opening model involves opening a gap as injection proceeds starting with a thin film the injection of water under pressure lifts the ice mass a round the borehole creating a gap 3 or 4 mm wide at the ice bed interface evaluated quantitatively the gap opening model accounts for the volume of water that the basal watery system accepts on breakthrough which obviates the gap conduit model in order to transport basal meltwater from upstream it is then necessary for the complete hydraulic model to contain also a network of relatively large conduits of which the most promising type is the canal conduit proposed theoretically by walder and fowler 1994 flat low conduits incised into the till 0 1 m deep and perhaps 1 m wide with a flat ice roof the basal water pressure data suggest that the canals are spaced 50 300 m apart much closer than r tunnel would be the deepest observed water level 117 m i the most likely to reflect the actual water pressure in the canals corresponding to a basal effective pressure of 1 6 bar in this interpretation the shallower water levels are affected by loss of hydraulic head in the narrow passageway s that connect along the bed from borehole to canal s once a borehole has frozen up and any passageways connecting with canals have become closed a pressure sensor in contact with the unfrozen till that underlies the ice will measure the pore pressure in the till given enough time for pressure equilibration this pressure varies considerably with time over the equivalent water level range from 100 to 113 m basal pressure sensors 500 m apart report uncorrelated variations whereas sensors in boreholes 25 m apart report mostly but not entirely well correlated variations of unknown origin in part of the record remarkable anticorrelated variations are interspersed with positively correlated one and there are rare abrupt excursions to extreme water levels as deep as 125m and as shallow as 74 m a diurnal pressure fluctuation intermittently observed may possibly be caused by the ocean tide in the ross sea the lack of any observed variation in ice stream motion when large percentagewise variations in basal effective pressure were occurring according to our data suggests that the observed pressure variations are sufficiently local and so randomly variable from place to place that they are averaged out in the process by which the basal motion of the ice stream is determined by an integration over a large area of the bed

cavities and the effective pressure between abrading clasts and the bedrock the mechanical configuration of cavities associated with clasts is discussed and how this affects the water pressure underneath the clast the range of permissible water pressure is determined by flow parallel to the bed rather than by flow towards the bed the actual pressure is controlled by hydraulic connections to areas away from the clast the degree of cavitation provides an additional degree of freedom which adjusts to ensure that horizontal and vertical forces respect the coulomb friction condition

experiments on the dynamics and sedimentary products of glacier slip abstract experimental work in glacial geomorphology is focused almost entirely on processes in the thin shear zone at the beds of sliding glaciers where ice at its pressure melting temperature moves over either rigid rock or deformable till experiments with rotary shear devices illuminate constitutive behavior there central to the dynamics of fast moving glaciers and provide a foundation for interpreting the sedimentary record of glacier slip and associated sediment transport results from experiments designed to study ice sliding over a rigid wavy bed shear deformation of till and plowing of clasts across the surface of a till bed point to a common conclusion drag at the bed can decrease with increasing slip velocity thereby concentrating driving stress elsewhere and promoting rapid glacier flow this rate weakening behavior at glacier beds is in contrast to the viscous slip resistance assumed in ice sheet models and most efforts to determine distributions of basal drag from glacier surface velocities ring shear experiments in which various basal tills and more idealized materials are sheared to high strains provide quantitative insight into grain size evolution mixing at contacts between basal tills microstructure development particle fabric development and development of anisotropy of magnetic susceptibility preferred orientations of principal magnetic susceptibilities provide the most dependable and complete description of till shear patterns when applied to basal tills of the geologic record magnetic till fabrics measured along thick till sections and calibrated experimentally indicate that deformation of the bed by two lobes of the laurentide ice sheet was shallow

frictional strength of fault gouge in taiwan chelungpu fault obtained from tcdp hole b abstract three fault zones fzb1136 fzb1194 and fzb1243 are found in core samples in hole b borehole penetrating through the chelungpu fault central taiwan that activated at the 1999 taiwan chi chi earthquake each fault zone is composed of a black gouge zone bgz and a gray gouge zone ggz surrounded by a fault breccia zone bz and or fracture damaged zone fz we conducted tri axial friction experiments on samples collected from subzones of the above three fault zones under the 1 km depth ambient condition with axial shortening rates of 0 1 to 10 m s to investigate frictional strength and its velocity dependence we found that the coefficient of friction is 0 3 for the bgz at fzb1136 1136bgz which is lower than those at other fault zones this result indicates that fault slip at the chi chi earthquake occurred at the 1136bgz the estimated frictional strength profile across fzb1136 was that the frictional strength was the lowest the coefficient of friction was 0 3 for the bgz and increased up to 0 5 for undeformed host rock with increasing distance from the bgz presence of the intermediate frictional strength zone consisting of the ggz and the bz suggests a development of off fault damage zone where deformation occurred not only in the bgz but also in the intermediate zone this feature should be important to estimate total fracture energy released during earthquakes we also suggest that coefficients of friction and the velocity dependences of the samples are closely related to localization of shear deformation and clay content respectively

the sliding velocity over a sinusoidal bed at high water pressure under idealized conditions when pressurized water has access to all low pressure areas at the glacier bed a sliding instability exists at a critical pressure p c well below the overburden pressure p 0 the critical pressure is given by p c p 0 l 2 a where l is the wavelength and a is the amplitude of a sinusoidal bedrock and is the basal shear stress when the subglacial water pressure p w approaches this critical value the area of ice bed contact l becomes very small and the pressure on the contact area becomes very large this pressur is calculated from a force balance and the corresponding rate of compression is obtained using glen s flow law for ice on the assumption that compression in the vicinity of the contact area occurs over a distance of the order of the size of this area l a deformational velocity is estimated the resultant slidin velocity sho the expected instability at the critical water pressure the dependency on other parameters such as wavelength l and roughness a l w as found to be the same as for sliding w ithout bed separation

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

basal conditions and glacier motion during the winter spring transition worthington glacier alaska u s a observations of the motion and basal conditions of worthington glacier alaska u s a during late winter and spring melt seasons revealed no evidence of relationship between water pressure and sliding velocity measurements included borehole water levels used as a proxy for basal water pressure surface velocity englacial deformation sliding velocity and time lapse videography of subglacial water flow and bed characteristics the boreholes were spaced 10 15 m apart six were instrumented in 1997 and five in 1998 in late winter the water pressure field showed spatially synchronous fluctuations with a diurnal cycle the glacier s motion was relatively slow and non cyclic in spring the motion was characterized by rapid diurnally varying sliding the basal water pressure displayed no diurnal signal but showed high magnitude fluctuations and often strong gradients between holes this transition in character of the basal water pressure field may represent a seasonal evolution of the drainage system from linked cavities to a network of isolated patches and conduits these changes occurred as the glacier was undergoing a seasonal velocity peak the apparent lack of correlation between sliding velocity and water pressure suggests that local scale water pressure does not directly control sliding during late winter or early in the melt season

a general theory of glacier surges we present the first general theory of glacier surging that includes both temperate and polythermal glacier surges based on coupled mass and enthalpy budgets enthalpy in the form of thermal energy and water is gained at the glacier bed from geothermal heating plus frictional heating expenditure of potential energy as a consequence of ice flow enthalpy losses occur by conduction and loss of meltwater from the system because enthalpy directly impacts flow speeds mass and enthalpy budgets must simultaneously balance if a glacier is to maintain a steady flow if not glaciers undergo out of phase mass and enthalpy cycles manifest as quiescent and surge phases we illustrate the theory using a lumped element model which parameterizes key thermodynamic and hydrological processes including surface to bed drainage and distributed and channelized drainage systems model output exhibits many of the observed characteristics of polythermal and temperate glacier surges including the association of surging behaviour with particular combinations of climate precipitation temperature geometry length slope and bed properties hydraulic conductivity enthalpy balance theory explains a broad spectrum of observed surging behaviour in a single framework and offers an answer to the wider question of why the majority of glaciers do not surge

a theory of ice sheet surges a simplified model of a two dimensional ice sheet is described it includes basal ice sliding dependent on the basal water pressure which itself is described by a simple theory of basal drainage we show that this simple but sophisticated model predicts surges of the ice mass in realistic circumstances and we describe these surges by solving the problem numerically we also are able to describe some parts of the surge analytically the numerical solution of the model is a delicate matter and highlights pitfalls to be avoided if more complicated models are to be solved successfully

a multicomponent coupled model of glacier hydrology 2 application to trapridge glacier yukon canada 1 a new glaciohydraulic model is tailored to trapridge glacier yukon canada where long term measurements of subglacial water pressure provide parameter constraints and a platform for model evaluation using digital elevation models and meteorological data as input we investigate hydrology on diurnal and seasonal timescales quantitative comparisons of simulated and observed pressure records allow us to select a reference model objectively from which we gain first insights into the gross spatial characteristics of the drainage system equilibrium simulations highlight target areas for water storage and potential sticky spots both of which have established relevance to glacier dynamics seasonal simulations capture the key signatures of spring and autumn transitions and corroborate our understanding of the processes involved successfully modeled features of the spring transition include increased hydraulic coupling between the surface and bed with time temporary augmentation of subglacial storage and rapid subglacial transitions from a hydraulically unconnected to connected state autumn transitions are characterized by deterioration of the basal drainage network drawdown of subglacial storage reservoirs and heightened sensitivity to precipitation and surface refreezing finally we draw attention to the important role of groundwater transport in cold glacial environments where permafrost can impede drainage from the ice margin

a renormalization group approach to the stick slip behavior of faults we treat a fault as an array of asperities with a prescribed statistical distribution of strengths when an asperity fails the stress on the failed asperity is transferred to one or more adjacent asperities for a linear array the stress is transferred to a single adjacent asperity and for a two dimensional array to three adjacent asperities using a renormalization group rg method we investigate the properties of a scale invariant hierarchical model for the stochastic growth of fault breaks through induced failure by stress transfer an extrapolation to arbitrarily large scales shows the existence of a critical applied stress at which the solutions bifurcate at stresses less than the critical stress virtually no asperities fail on a large scale and the fault is locked above the critical stress asperity failure cascades away from the nucleus of failure we interpret this catastrophic failure as an earthquake and it corresponds to the transition from stick to slip behavior on the fault thus the stick slip behavior of most faults can be attributed to the distribution of asperities on the fault we propose our stochastic mechanism as an alternative to the traditional hypotheses for the stick slip behavior of faults a major advantage of our approach is the inclusion of scale invariance thus the observed frequency magnitude relation for seismicity is a natural consequence of our basic hypothesis

glacier surge mechanism 1982 1983 surge of variegated glacier alaska the hundredfold speedup in glacier motion in a surge of the kind the kind that took place in variegated glacier in 1982 1983 is caused by the buildup of high water pressure in the basal passageway system which is made possible by a fundamental and pervasive change in the geometry and water transport characteristics of this system the behavior of the glacier in surge has many remarkable features which can provide clues to a detailed theory of the surging process the surge mechanism is akin to a proposed mechanism of overthrust faulting

water flow through temperate glaciers understanding water movement through a glacier is fundamental to several critical issues in glaci ology including glacier dynamics glacier induced floods and the prediction of runoff from glacierized drainage basins to this end we have synthesized a conceptual model of water movement through a temper ate glacier from the surface to the outlet stream pro cesses that regulate the rate and distribution of water input at the glacier surface and that regulate water movement from the surface to the bed play important but commonly neglected roles in glacier hydrology where a glacier is covered by a layer of porous perme able firn the accumulation zone the flux of water to the glacier interior varies slowly because the firn tempo rarily stores water and thereby smooths out variations in the supply rate in the firn free ablation zone in con trast the flux of water into the glacier depends directly on the rate of surface melt or rainfall and therefore varies greatly in time water moves from the surface to the bed through an upward branching arborescent net work consisting of both steeply inclined conduits formed by the enlargement of intergranular veins and gently inclined conduits spawned by water flow along the bottoms of near surface fractures crevasses engla cial drainage conduits deliver water to the glacier bed at a limited number of points probably a long distance downglacier of where water enters the glacier englacial conduits supplied from the accumulation zone are quasi steady state features that convey the slowly varying water flux delivered via the firn their size adjusts so that they are usually full of water and flow is pressurized in contrast water flow in englacial conduits supplied from the ablation area is pressurized only near times of peak daily flow or during rainstorms flow is otherwise in an open channel configuration the subglacial drainage system typically consists of several elements that are distinct both morphologically and hydrologically an up glacier branching arborescent network of channels in cised into the basal ice conveys water rapidly much of the water flux to the bed probably enters directly into the arborescent channel network which covers only a small fraction of the glacier bed more extensive spatially is a nonarborescent network which commonly includes cav ities gaps between the glacier sole and bed channels incised into the bed and a layer of permeable sediment the nonarborescent network conveys water slowly and is usually poorly connected to the arborescent system the arborescent channel network largely collapses during winter but reforms in the spring as the first flush of meltwater to the bed destabilizes the cavities within the nonarborescent network the volume of water stored by a glacier varies diurnally and seasonally small temper ate alpine glaciers seem to attain a maximum seasonal water storage of 200 mm of water averaged over the area of the glacier bed with daily fluctuations of as much as 20 30 mm the likely storage capacity of subglacial cavities is insufficient to account for estimated stored water volumes so most water storage may actually occur englacially stored water may also be released abruptly and catastrophically in the form of outburst floods

hydraulic run away a mechanism for thermally regulated surges of ice sheets by using a simple parameterized model of thermomechanically coupled flow in cold ice sheets together with a physically based sliding law which includes a description of basal drainage we show that relationships between ice flux and ice thickness can realistically be multi valued and hence that hydraulically induced surges can occur we term this mechanism hydraulic run away as it relies on the positive feed back between sliding velocity and basal melt production for this feed back to operate it is essential that water pressure increases with water storage this is consistent with various recent ideas concerning drainage under ice sheets be it through a system of canals a distributed film or a subglacial aquifer for confined flows such as valley glaciers e g trapridge glacier or topographically constrained ice streams e g hudson strait in the laurentide ice sheet which are underlain by sufficiently deformable sediment we can expect thermally regulated surges to occur while in a laterally unconfined drainage basin such as that which flows into the ross ice shelf we might expect ice streams to develop

drainage through subglacial water sheets 1 subglacial drainage plays an important role in controlling coupling between glacial ice and underlying bed here we study the flow of water in thin macroporous sheets between ice and bed previous work shows that small perturbations in depth of a nearly parallel sided water film grow unstably because these areas have enhanced viscous dissipation that leads to enhanced melting of an ice roof we argue that in the presence of bed protrusions bridging a water sheet downward motion of the ice roof can stabilize this sheet stability results when the rate of roof closure increases faster with water depth than the rate of viscous dissipation we therefore modify existing theory to include protrusions that partially support the overlying glacier differences in the pressure on protrusions relative to water pressure drive roof closure the mechanisms of both regelation and creep normal to the bed close the overlying ice roof and decrease the ice bed gap in order to account for multiple protrusion sizes along the bed for instance resulting from an assortment of various sized sediment grains we incorporate a method of partitioning overburden pressure among different protrusion size classes and the water sheet partitioning is dependent on the amount of ice protrusion contact and therefore water depth this method allows prediction of roof closure rates we then investigate stable steady sheet configurations for reasonable parameter choices and find that these steady states can occur for modest water depths at very low effective pressures as is appropriate for ice streams moreover we find that multiple steady sheet thicknesses exist raising the possibility of switches between low and high hydraulic conductivity regimes for the subglacial water system

links between proglacial stream suspended sediment dynamics glacier hydrology and glacier motion at midtdalsbreen norway two hourly suspended sediment concentration variations observed during the summer of 1987 in the proglacial stream draining midtdalsbreen norway are modelled using multiple regression and time series techniques suspended sediment fluctuations are influenced by stream discharge variations diurnal hysteresis effects medium term sediment supply and transport variations and the recent suspended sediment concentration history of the stream they do not appear to be influenced by seasonal exhaustion or rainfall variations possible reasons for this are discussed large positive residuals from the fitted models are major pulses of suspended sediment unrelated to discharge variations these sediment flushes correlate with periods of enhanced glacier motion they cannot be explained by enhanced sediment production by subglacial erosion but are probably due to the tapping of subglacially stored sediment during sudden changes in the hydraulics and or configuration of the subglacial hydrological system seasonal changes in the lag between glacier motion peaks and suspended sediment flushes suggest that the subglacial hydrological system evolves over the summer from a distributed to a more channelized configuration

sedimentary and structural evolution of a relict subglacial to subaerial drainage system and its hydrogeological implications an example from anglesey north wales uk subglacial drainage systems exert a major control on basal sliding rates and glacier dynamics however comparatively few studies have examined the sedimentary record of subglacial drainage this is due to the paucity of modern analogues the limited recognition and preservation of upper flow regime deposits within the geological record and the difficulty of distinguishing subglacial meltwater deposits from other meltwater sediments e g glacier outburst flood deposits within this study the sedimentological and structural evolution of a subglacial to subaerial ice marginal proglacial drainage system is examined particular emphasis is placed upon the genetic development and preservation of upper flow regime bedforms and specifically recognising them within a subglacial meltwater context facies are attributed to subglacial meltwater activity and record sedimentation within a confined but progressively enlargening subglacial channel system produced under dune to upper flow regime conditions bedforms include rare large scale sinusoidal bedding with syn depositional deformation produced by current induced traction and shearing within the channel margins subglacial sedimentation culminated with the abrupt change to a more ephemeral drainage regime indicating channel abandonment or a seasonal drainage regime retreat of the ice margin led to the establishment of subaerial drainage with phases of sheet flow punctuated by channel incision and anastomosing channel development under diurnal ablation related seasonal discharge the presence of extensive hydrofracture networks demonstrate that proglacial groundwater levels fluctuated markedly and this may have influenced later overriding of the site by an ice stream

sedimentation in a drumlin lee side subglacial wave cavity northwest ireland abstract lee side stratification sequences in a late pleistocene drumlin in northwest ireland are used to assess sedimentation patterns in subglacial wave cavities formed on the lee sides of drumlins three major subglacial cavity sub environments are identified 1 high energy divergent trough like closed conduit characterised by channel fill pebbly sand facies 2 low energy closed conduit characterised by alternating sand silts 3 trough margin dominated by stratified diamicts facies arrangements suggest two major transient states reflecting variations in subglacial meltwater flux the active phase showed meltwater flow directed across the drumlin apex suggesting complete uncoupling from the glacier bed supercavitation as flow velocities waned pebbly sand facies were deposited by in situ freezing of within conduit sediment admixtures the later quiescent phase was characterised by meltwater flow directed transverse to ice flow cavity shrinkage and concomitant deposition of subglacial sheetwash and cohesive sediment flows along cavity margins cavity closure resulted in complete coupling at the ice substrate interface with localised glaciotectonic loading on underlying lee side stratification sequences and concomitant till deposition these late stage sedimentation events at shinnan hill produced a very complex polygene endform which cannot be simply attributed to one formative process more realistically they reflect the influence of a rather complex and very dynamic subglacial system subject to complex spatial and temporal variations in subglacial erosion deposition and meltwater flux at the time of drumlinisation

meltwater intensive glacial retreat in polar environments and investigation of associated sediments example from pine island bay west antarctica abstract modern pine island and thwaites glaciers which both drain into pine island bay are among the fastest changing portions of the cryosphere and the least stable ice streams in antarctica here we show that the uppermost sediment unit in pine island bay was deposited from a meltwater plume a plumite during the late stages of ice sheet retreat 7 8 6 k cal yr bp and argue that this deposit records episodes of meltwater intensive sedimentation the plumite is a hydraulically sorted glacially sourced draping deposit that overlies proximal glacimarine sediments and thickens towards the modern grounding line the uppermost sediment unit is interpreted as a product of non steady state processes in which low background sedimentation in large bedrock carved basins alternates with episodic purging of sediment laden water from these basins the inner part of pine island bay contains several basins that are linked by channels with a storage capacity on the order of 70 km 3 of stagnant water and significant sediment storage capacity purging of these basins is caused by changes in hydraulic potential and glacial reorganization the sediment mobilized by these processes is found here to total 120 km 3 this study demonstrates that episodes of meltwater intensive sedimentation in pine island bay occurred at least three times in the holocene the most recent episode coincides with rapid retreat of the grounding line in historical time and has an order of magnitude greater flux relative to the entire unit we note that the final phase of ice stream retreat in marguerite bay was marked by a similar sedimentary event and suggest that the modern thwaites glacier is poised for an analogous meltwater intensive phase of retreat