subglacial processes

11 Mar 2005 22:21 AR AR233-EA33-08.tex XMLPublishSM(2004/02/24) P1: JRX10.1146/annurev.earth.33.092203.122621

Annu. Rev. Earth Planet. Sci. 2005. 33:247–76doi: 10.1146/annurev.earth.33.092203.122621

Copyright c© 2005 by Annual Reviews. All rights reservedFirst published online as a Review in Advance on January 7, 2005

SUBGLACIAL PROCESSES

Garry K.C. ClarkeDepartment of Earth and Ocean Sciences, University of British Columbia,Vancouver,British Columbia V6T 1Z4, Canada; email: [email protected]

Key Words subglacial hydrology, subglacial mechanics, sliding, sedimentdeformation, glacial landforms

■ Abstract Processes operating beneath glaciers can have a greater influence onflow dynamics than those operating within them. The variety and complexity of theseprocesses, which involve interactions among ice, water, and geological solids, resistefforts to establish simple truths and can lead to surprising outcomes. Thermal condi-tions at the ice-bed interface (melting or nonmelting) and the mechanical propertiesof the glacier substrate (soft or hard) determine which processes can be activated. Thewarm-soft case supports the greatest variety of processes and is the most important forfast-flow dynamics and for the mobilization of subglacial sediment. Process interac-tions can lead to oscillations and spatio-temporal switching behavior in glaciers andice sheets as well as to the generation of subglacial landforms.

1. INTRODUCTION

Glaciers are rich in phenomena. The stage on which their most significant pro-cesses act is hidden from the eye and barely three-dimensional, extending a fewmeters above and below the contact between glacier ice and a geological substrateof bedrock and sediment. Whether the ice-bed contact is melting or frozen andwhether the substrate is deformable or undeformable dictates which processesare activated and which are suppressed. In glaciological shorthand, one refers toglaciers as warm- or cold-bedded and hard- or soft-bedded. In this review, glaciersin the warm-soft class receive the greatest emphasis because these admit the great-est variety of processes and manifest the most complex behavior.

Subglacial processes are important because they determine the large-scale be-havior of glaciers and ice sheets, yet understanding the connections betweenpoint-scale processes and macro-scale products remains a serious knowledgegap. Interactions among processes underlie the most puzzling material and be-havioral products, including the largely unexplained mechanisms of subglaciallandform genesis and incompletely understood switches in the flow behavior ofglaciers and ice sheets. Figure 1 (see color insert), showing the arterial characterof West Antarctic ice streams, presents a striking illustration of the transforma-tion of point-scale processes to mega-scale products. The sharply defined margins,

0084-6597/05/0519-0247$20.00 247

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11 Mar 2005 22:21 AR AR233-EA33-08.tex XMLPublishSM(2004/02/24) P1: JRX

248 CLARKE

separating fast- and slow-flowing ice, suggest the operation of a spatial switch thatcontrols fast motion processes.

2. OBSERVATIONAL BASIS

The challenge of inferring processes from products is a long-standing problemof the geological sciences. The advent of new, formerly impossible, scientific ap-proaches has had a salient influence on glaciology and glacial geology. These newapproaches include (a) high-technology Earth imaging, (b) recovery of sedimentsamples from boreholes to the base of glaciers and sheets, (c) development ofsubglacial sensors to observe the operation of processes at the ice-bed contact, (d)establishment of subglacial laboratories, and (e) application of geotechnical labo-ratory methods to determine the mechanical properties of subglacial sediments.

Advances in our ability to image deglaciated subaerial and submarine surfacesfrom space and from oceanographic vessels have reignited interest in long-standingquestions concerning how subglacial landforms are generated. The spectacularsubmarine bedforms (Figure 2) imaged on the continental shelf off the west coast

Figure 2 Streamlined subglacial bedforms imaged in Marguerite Bay, AntarcticPeninsula. These are interpreted as being the geomorphic imprint of a paleo-ice stream(O Cofaigh et al. 2002). (a) Short irregular drumlins and crudely streamlined forms.(b) Meltwater channels in bedrock. (c) Streamlined bedforms. (d) Drumlins and lin-eations formed in sediment and bedrock. (e) Megascale lineations formed in sediment.Copyright by American Geophysical Union (2002).

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SUBGLACIAL PROCESSES 249

of the Antarctic Peninsula (O Cofaigh et al. 2002) provide a leading example.These bedforms have been convincingly interpreted as the geomorphic imprint ofa paleo-ice stream, and one marvels at the sense that individual features are theexpression of powerful organizing principles connected, in an unknown manner,to processes that controlled the former ice stream.

Surprising success has been achieved in recovering continuous sediment coresfrom beneath West Antarctic ice streams. Using a piston corer, cores as long as3.1 m were recovered from beneath Whillans, Kamb, and Bindschadler ice streams,1

and these were subjected to detailed soil mechanical testing (Engelhardt et al. 1990,Kamb 2001). A more direct sampling approach, using a commercial wireline drillrig, was followed to obtain sediment from beneath Black Rapids Glacier, Alaska(Truffer et al. 1999); in this case, the recovery of subglacial sediment was generallypoor.

Borehole instrumentation presents an alternative to borehole sampling, anda range of imaginative devices has been developed for monitoring changes inthe subglacial water system and underlying sediment. Sensors to measure thepressure, turbidity, and electrical conductivity of subglacial water are now usedto examine the temporal and spatial variability of the subglacial water system(Stone et al. 1993, Stone & Clarke 1996). Devices for measuring the sliding rateof glaciers (Blake et al. 1994) and of ice streams (Engelhardt & Kamb 1998)have also been developed. Both involve the placing of an anchor in subglacialsediment and measuring the length of a line as it pays out from a spool fixedin the borehole (Figure 3c). Instruments for measuring the strength of subglacialsediment (Figure 3c) include the dragometer (Iverson et al. 1994), which measuresthe tension on a cable as it tows a cylindrical “fish” through subglacial sediment;the ploughmeter (Fischer & Clarke 1994), which measures the bending moment ona steel rod that penetrates the glacier substrate; and the torvane, a vane-shear devicefor in situ soil testing adapted for subglacial use (Kamb 2001). Subglacial sedimentdeformation has been measured using electrolytic or solid-state tilt cells installed inthe substrate (Figure 3c) (Blake et al. 1992), but it is challenging to insert the cells togreat depth while maintaining an electrical connection to them, a problem that hasrecently been solved using autonomous sensors and data telemetry (Harrison et al.2004).

Hydroelectric developments in France and Norway have established two sub-glacial observatories that allow glaciologists to directly study the complex inter-actions between a glacier and its substrate. The Svartisen Subglacial Laboratory(e.g., Jansson et al. 1996) is situated beneath the 200-m-thick ice of Engebreen,Norway, and the bed is accessed through vertical and horizontal shafts radiatingfrom a tunnel in the subglacial bedrock (Figure 3d). The Svartisen Laboratory isbeing used to conduct a variety of ingenious and informative experiments (e.g.,Cohen et al. 2000, Iverson et al. 2003).

1In 2003, the U.S. Advisory Committee for Antarctic Names renamed the West Antarcticice streams A, B, C, D, E, and F as Mercer, Whillans, Kamb, Bindschadler, MacAyeal, andEchelmeyer, respectively.

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250 CLARKE

Figure 3 Approaches to measuring subglacial phenomena. (a) Laboratory triaxialcell. (b) Ring shear laboratory device. Inset: Sediment sample holder. (c) In situ instru-ments [from left to right: dragometer (A), slidometer (B), ploughmeter (C), tilt cells(D)]. (d) Subglacial laboratory beneath Engabreen, Norway.

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Although subglacial measurements most faithfully reproduce the subglacialenvironment, the conditions of this environment are usually beyond control anddifficult to infer. For this reason laboratory measurements on the physical prop-erties of subglacial sediment are especially informative, although it is commonlynecessary to eliminate the coarse sediment fraction from the samples. Thus therecan be a concern that laboratory studies do not replicate the natural setting andthat the samples have been disturbed by the sampling process. Most laboratorystudies have been aimed at measuring the consolidation properties and rheologyof glacial sediments. Standard devices for geotechnical characterization of soilsare the oedometer (Lambe & Whitman 1969, p. 118), triaxial cell (Figure 3a), andring shear apparatus (Iverson et al. 1997) (Figure 3b).

3. ELEMENTS

The constitutive properties and physical processes of water, ice, bedrock, and sedi-ment form the elements of any discussion of subglacial processes. These elementsinteract to form “compounds” that are discussed in a subsequent section.

3.1. Water

Beneath warm-based glaciers, free water can exist at the ice-bed contact and in-terstitially in subglacial sediment. The pressure pw of subglacial water is an inde-pendent variable that can vary temporally and spatially in a complicated mannerthat is determined by the balance between influx and outflux of water, the geome-try of the subglacial water system, the physical properties of the glacier substrate,thermodynamic conditions near the ice-bed interface, and ice overburden pressure.Water pressure can exert a decisive influence on ice flow dynamics, controllingboth the degree of frictional interaction between a glacier and its bed and, in thecase of soft-bedded glaciers, the strength of the subglacial sediment.

Glaciers are buoyantly supported by the pressure of subglacial water, and themagnitude of this support is indicated by comparing the water pressure to the iceoverburden pressure pi = ρigHi, where ρi is the density of ice, g is the gravityacceleration, and Hi is ice thickness. The flotation ratio f = pw/pi and the effectivepressure pe = pi − pw are two common measures of the importance of buoyancy.One of the most significant discoveries concerning the dynamics of glaciers andice sheets was the finding that water pressure beneath fast-flowing West Antarcticice streams is very close to the ice flotation pressure. For example, at site 88-1on Whillans Ice Stream, where ice thickness is Hi = 1035 m, it was found thatf = 0.997 and pe = 30 kPa (Engelhardt & Kamb 1997, Kamb 2001). The factthat active West Antarctic ice streams are virtually afloat on their subglacial waterremoves much of the mystery concerning their fast (∼1 km year−1) flow. Of thetwo buoyancy indicators, effective pressure proves to be the more useful conceptbecause it appears explicitly in equations that are used to describe the sliding rateof glaciers and the strength of subglacial sediment. The fact that these important

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252 CLARKE

characteristics are controlled by effective pressure has important consequences forglaciological research: Laboratory experiments and measurements beneath thinvalley glaciers, if conducted at appropriate values of pe, are immediately relevantto the same processes operating beneath thick ice sheets.

Glaciers underlain by permeable bedrock or unlithified sediment can containpore water in the void space between solids. Thus far, water pressure has beendenoted pw, but it is occasionally necessary to distinguish between the waterpressure pp in subglacial pore space and the water pressure pB at the ice-bedcontact. If subglacial sediment has low permeability and pB fluctuates diurnallyor seasonally, these pressures can differ substantially.

The production and fate of subglacial water are controlled by a combination ofprocesses that operate at the ice-bed interface and within the geological substrate.Water flow is driven by gradients in the fluid potential

φw = pw + ρwgz, (1)

where ρw is the density of water and z is the elevation above some datum; for waterat the ice-bed contact, z corresponds to the bed elevation ZB. In many cases thewater pressure approximates the ice overburden pressure so that pw = pi, and thisleads to the interesting result that ∇φw = ρig∇ZS + (ρw − ρi)∇ZB, where ∇ isthe gradient operator and ZS is the ice surface elevation. Because ρi = 900 kg m−3

and ρw = 1000 kg m−3, the first term is roughly an order of magnitude greaterthan the second term, so that, for the most part, the flow of subglacial water isdriven by the topography of the upper glacier surface and only weakly influencedby bed topography. The condition for ponding of water is ∇φw = 0 or, as a scalarexpression, dφw/ds = 0, where s is an along-path distance coordinate. Makingthe appropriate substitutions, the ponding threshold condition can be expressedas a relationship between surface and bed slopes dZB/ds = −10 dZS/ds, i.e., anadverse bed slope at least 10 times that of the surface slope is required for ponding.

Expressions for water transport depend on hydraulic geometry, with standardpossibilities summarized in the following expressions:

qw = − KH

ρwg∇φw aquifer (m s−1) (2)

qAw = − KA Hw

ρwg∇φw sheet-like (m2 s−1) (3)

Qw =

−π R4

8µw

∂φw

∂slaminar

pipe-like (m3 s−1)(8RH

fRρw

) 12(

−∂φw

∂s

) 12

Sw turbulent

(4)

where KH is the hydraulic conductivity (m s−1) of the aquifer, KA is the hydraulicconductivity of a water sheet, Hw is the sheet thickness, R is the radius of acircular conduit, µw the viscosity of water, RH is the hydraulic radius of a conduit

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(cross-sectional area divided by wetted perimeter), fR is the dimensionless Darcy-Weisbach wall friction parameter, and Sw is the cross-sectional area of the waterconduit. Pipe-like conduit geometries are associated with interface conduits thatare incised upward into ice (Rothlisberger channels), downward into bedrock (Nyechannels), downward into sediment (canals), or upward into ice and downward intosediment (Ng 2000a,b). Beneath glaciers and ice sheets several different drainagegeometries can coexist. Together, these can be viewed as a water circuit (Clarke1996), analogous to an electrical circuit, or as an interacting distributed system(Flowers & Clarke 2002). The general topic of glacial drainage systems has beenreviewed by Hubbard & Nienow (1997) and Fountain & Walder (1998).

The equation for water balance in a sheet-like water system of thickness Hw is

∂ Hw

∂t+ ∇ · qA

w = 1

ρwL

(qg − qi + vBτB − qA

w · ∇φw), (5)

where, collectively, the right-hand-side terms correspond to the volume rate ofwater production per unit area of the ice-bed contact (m s−1) and the individualterms correspond, respectively, to the input geothermal heat flux qg from beneaththe water sheet, the heat flux qi escaping to the overlying glacier, the frictionalenergy production from glacier sliding (vB is the sliding rate and τB the basal shearstress), and the rate of potential energy released by the subglacial water flow itself.

3.2. Ice

The thermal and mechanical properties of ice help to establish the character ofsubglacial interactions. Although ice is the essential prerequisite for all glaciers,its properties and processes are not necessarily the dominant influences on flowbehavior.

3.2.1. MELTING, REGELATION, AND PREMELTING Several important subglacial pro-cesses are tied to the fact that, among common materials, water is unusual in havinga solid phase that is less dense than its liquid phase. Because both the liquid andsolid phases of water are important in the subglacial environment, a close look atthe melting point relationship is warranted. For equilibrium between pure waterand ice phases at pressure p0 and temperature T0, the Gibb’s free energy per unitmass of the two phases must be equal; thus, gw(p0, T0) = gi(p0, T0). If pressureis changed but equilibrium is maintained then gw(pw, Tw) = gi(pi, Ti), so that forsmall changes gα(pα, Tα) = gα(p0, T0) + (pα − p0)να − (Tα − T0)sα , where α

denotes the phase, Tα is the temperature, sα is the entropy per unit mass, pα isthe pressure, and να = 1/ρα is the specific volume of phase α. Taking Tw = Ti

and sw − si = L/T0, where L = 333.5 kJ kg−1 is the latent heat of melting, butallowing the possibility that pw �= pi, the Gibbs equilibrium condition leads to ageneralized form of the Clapeyron equation:

Tm = T0

[1 − (pw − p0)

L

(1

ρi− 1

ρw

)−

(pi − pw

ρiL

)]. (6)

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254 CLARKE

The above expression is more general than what we require at this point and canbe simplified by assuming pi = pw = p so that the final term vanishes and thepressure dependence of melting temperature can be summarized by an expres-sion of the form Tm(p) = T0 − CT(p − p0), where CT = T0(ρw − ρi)/ρwρiL =0.0742 K MPa−1 is referred to as the Clapeyron slope or pressure melting coeffi-cient. (Note that to obtain this value of CT it is necessary to substitute values of ρw

and ρi appropriate to pure phases of water and ice and not rough-and-ready values,such as ρi = 900 kg m−3 used for calculating quantities such as ice overburdenpressure.) The melting temperature is also affected by dissolved air because thesaturation concentration of air is pressure dependent; for air-saturated water thenet effect is to modify the Clapeyron slope to CT = 0.098 K MPa−1. Rothlisberger& Lang (1987) advocate the former value and argue that the requirement of air-saturation is unlikely to apply subglacially. Finally, dissolved solute and the cur-vature of the ice-water phase boundary can affect melting temperature.

The fact that the ice melting temperature decreases with increasing pressureunderlies the glaciologically important process of regelation. If ice at temperatureT is in thermodynamic equilibrium at its melting temperature then T = Tm;if pressure is increased, the melting temperature is reduced so that, in effect,T > Tm and to restore equilibrium ice must melt. As melting proceeds, the icetemperature drops until a new equilibrium is established. A vivid example of theregelation process is provided by the classroom experiment of drawing a thinmetal piano wire through a block of ice. Melting occurs on the leading face ofthe wire and the same pressure gradient that sets the conditions for melting andfreezing drives meltwater from the upstream face to the downstream face whereit freezes. The ice block remains intact and there is no net heat source and no netmeltwater production. Analogous processes can operate subglacially and allow iceto pass small-scale asperities in the glacier bed, either transversely, contributingto the sliding motion of a glacier, or vertically, allowing ice to infiltrate subglacialgranular sediments.

Next we examine the consequences of reinstating the final term of Equation 6,which admits the possibility that at equilibrium the water pressure and ice pressurecan differ; discarding the term that is responsible for the pressure melting effect,one obtains

pi − pw = ρiLT0 − Tm

T0. (7)

The significant implication of the above expression is that if, at thermodynamicequilibrium, there is a pressure difference between the liquid and solid phases, theequilibrium melting temperature Tm is decreased relative to the expected “bulk”melting temperature T0. In cases of glaciological interest, the differential pres-sure can be written pi − pw = γiw κ + pT(d), where γiw is the surface tension(N m−1), κ is the curvature (m−1) of the ice-water phase boundary, and pT(d) isa “disjoining pressure” associated with intermolecular repulsion between ice andsediment grains. The curvature can be approximated as κ = 2/Rc, where Rc is the

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Figure 4 Migration of pore water to a freezing front. The scale of intergranularpore throats is 2Rp and the radius of curvature of the ice–water contact is Rc. Inset:Intermolecular forces acting across the thin water film separating ice from soil grainsgive rise to a force of repulsion between the ice and soil, which can be representedby the pressure pT. The decrease in separation distance that accompanies freezing ofinterstitial water is opposed by the increased strength of the repulsion force that acts todrive the surfaces apart and, in doing so, draws water toward the freezing front. AfterRempel et al. (2004).

radius of curvature of the ice-water contact (Figure 4) and is taken to be positiveif the center of curvature lies within the solid phase. The phenomenon known aspremelting (e.g., Dash et al. 1995) is associated with the existence of a disjoiningpressure between ice and other substances. For example, at a contact surface be-tween ice and a mineral grain there is a strong intermolecular force of repulsionbetween the two materials. The strength of this repulsion is reduced if the materialsare separated by a film of water having thickness d, and the resulting disjoiningpressure is an inverse function of the film thickness, for example, pT = A/d3.Consistent with Equation 7, a minimum energy configuration is achieved when athin film of water exists at the boundary surfaces of ice grains—even if the degreeof supercooling T = T0 − Tm exceeds 10 K. Volumetrically, the water fractionis negligible except when T becomes small.

3.2.2. STRESS AND RHEOLOGY Glaciological interest is focused on the ice-bed con-tact at which the ice overburden pressure is pi, the basal shear stress is τB, andthe driving stress established by the flow geometry is τD = ρigHi sin θS (whereθS is the surface slope and the glacier is approximated by an inclined slab). Thecommon and simplest assumption is that τB = τD, but this is not a general truth.Note that although stress and strain rate are second-order tensors, I shall consideronly scalar terms and henceforth take τ to denote shear stress and ε to denote strainrate.

The most widely used flow law for glacier ice is the Glen power law:

ε = B exp[−(E + pV )/RT ]τ n, (8)

where B is a material parameter, E is the creep activation energy, p is pressure, Vis the creep activation volume, R is the universal gas constant, and T is the absolute

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256 CLARKE

temperature. In most glaciological work the pV term is dropped and the flow lawexponent is taken as n = 3. Recent experiments have led to the proposal of a morecomplicated flow law (Goldsby & Kohlstedt 2001) that recognizes the simulta-neous operation of four distinct creep mechanisms, two of which involve grainboundary sliding (GBS). Individually, each of the mechanisms can be describedby a flow law of the form

ε = Bτ n

dqexp

(− E + pV

RT

), (9)

where d is the grain diameter of ice crystals and q is the grain size exponent.Collectively, these separate creep contributions lead to the flow law

ε = εdiff +(

1

εbasal+ 1

εgbs

)−1

+ εdisl. (10)

The curious form of the term in parentheses arises because the two GBS processesoperate in parallel, whereas the remaining creep processes operate in series. Theindividual contributions to the total creep rate ε are diffusion creep (n = 1, q = 2or 3), basal slip-accommodated GBS (n = 2.4, q = 1), GBS-accommodated basalslip (n = 1.8, q = 1.4), and dislocation creep (n = 4.0, q = 1). Goldsby & Kohlstedt(2001) are blunt in their assessment of the limitations of the Glen law, asserting thatthe “superplastic regime is very important for the description of the flow of glaciersand ice sheets for which differential stresses are typically <0.1 MPa, values smallerthan those explored in Glen’s experiments. The Glen law underestimates the creeprate of ice at glaciologically important stresses.”

3.3. Bedrock and Lithified Sediment

There is general agreement that the main processes enabling sliding are (a) rege-lation, (b) enhanced creep around bedrock asperities, and (c) cavitation in thelee-side of bed obstacles. The importance of the individual processes depends onthe characteristic size δ and spacing λ of bed roughness asperities, where the ratior = δ/λ represents a dimensionless bed roughness parameter. Neglecting cavi-tation, the separate contributions of regelation and enhanced creep to the overallsliding rate can be written as vr = (CT K/ρiLδ)(τB/r2) and ve = B ′δ(τB/r2)n ,where B ′ is proportional to the Glen flow law coefficient in Equation 8 and n is theflow law exponent. Noting that the regelation process is most effective when δ issmall and the enhanced creep process is most effective when δ is large, the slidingrate that results when the two processes operate together is taken to be that whenvr = ve. The critical value of obstacle size at which the equality holds is givenby δ∗ = [(1/B ′)(CT K/ρiL)]

12 τ

(1−n)/2B rn−1 and the associated sliding velocity is

vB ∼ (τ12

B /r )n+1. Estimates of the controlling obstacle size suggest δ∗ ≈ 0.5 m.The foregoing sketch of the sliding mechanism is nearly 50 years old and

can be revisited by referring to classic contributions by Weertman (1952) andLliboutry (1958). Subsequent work on sliding theory has had a mathematical or

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computational focus. Topics that have received attention include (a) improvementof the representation of bed roughness by introducing a one- or two-dimensionalspectral representation of roughness (but at the expense of replacing the nonlinearflow law by a linear viscous law) and (b) exploring the dependence of cavitationand sliding rate on effective pressure (usually by adopting a linear viscous law andneglecting the regelation process). A recent and potentially significant theoreticalresult suggests that bed topography having a length scale comparable to the icethickness can produce a multivalued sliding velocity (Schoof 2004).

Irrespective of problems with sliding theory, glaciologists require a slidinglaw to summarize field observations and to apply as a subglacial boundary con-dition in numerical ice dynamics models. A law of the form vB = Ap−b

e , withb = 0.40, can be fit to field observations at Storglaciaren, Sweden, and at Fin-delengletscher, Switzerland (Jansson 1995); for computational modeling, laws ofthe form vB = Aτ a

B p−be (where a and b are positive constants) have found favor

because they combine features of both the theoretical and observational slidinglaw. It is important to recognize that at the base of glaciers, both τB and pe canfluctuate markedly at spatial scales that are far less than the ice thickness Hi soit is necessary to distinguish between global and local sliding laws. Observationsin boreholes yield information about local sliding laws, whereas numerical icedynamics models require global laws.

3.4. Unlithified Sediment

Subglacial sediments tend to be poorly sorted, spanning a wide range of grain sizes.The term boulder clay, once synonymous with till, reflects this point. Size distribu-tions have been measured for till samples from the forefield of Trapridge Glacier,Canada (Clarke 1987); and for subglacial sediment samples from Storglaciaren,Sweden (Hooke & Iverson 1995); Engabreen, Norway (Hooke & Iverson 1995);and Whillans Ice Stream, West Antarctica (Tulaczyk et al. 1998). All show an evendistribution over a wide span of sizes, consistent with a fractal size distributionand a fractal dimension in the range 2.84–2.96 (Hooke & Iverson 1995).

The porosity n is an important property of granular materials, and the con-stituents that occupy the intergranular pore space of subglacial sediments can exerta strong influence on glacier flow mechanics. Pore space can be occupied by liquidwater, ice, and vapor having fractional volumes nw, ni, and nv respectively; the vol-ume fraction of pore space that is occupied by nongaseous substances is termed thesaturation S. For water-saturated sediment the volume fraction of water is nw = n,whereas for a partially water-saturated sediment nw = Swn, where Sw denotes thewater saturation; similarly for ice ni = Sin and for vapor nv = (1 − Sw − Si)n.

3.4.1. RHEOLOGY The flow law for subglacial sediment has been one of the mostcontested topics in glaciology. Expressed in the form of a power law ε = Aτ n

(where A is a coefficient that might vary with effective pressure and other factors),the endmember possibilities are n = 1 (linear viscous) and n = ∞ (perfectly

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258 CLARKE

plastic). The weakly nonlinear sediment flow laws proposed by Boulton &Hindmarsh (1987) have fallen from favor because of methodological concerns,and there is a developing consensus that the correct flow law for subglacial sedi-ment is Coulomb-plastic.

Our most secure knowledge of the sediment flow law is based on laboratorymeasurements, mainly using direct shear cells (e.g., Lambe & Whitman 1969,p. 120), triaxial cells (Figure 3a), and ring shear devices (Figure 3b). Depending onwhether water volume is kept constant or allowed to vary, such tests are describedas undrained or drained (see Figure 6 for examples). Laboratory examination ofsubglacial samples from West Antarctic ice streams (Kamb 1990, 2001; Tulaczyket al. 2000a) and from Storglaciaren, Sweden (Iverson et al. 1998), together withnear-surface samples of tills deposited near the southern margin of the LaurentideIce Sheet (Iverson et al. 1998), are consistent with a Coulomb-plastic deformationlaw that can be summarized as follows:

τu = c + pe tan ϕ (11)

ε

ε0=

(τu

τ0

)n

, (12)

where τu is the ultimate shear strength; c is the cohesive strength; ϕ is the frictionangle; and ε0, τ0, and n are constants. For perfect plasticity n is infinite.

When sediment is deformed, for example, in a ring shear device, its failurestrength τf and porosity change as deformation proceeds. Ultimately, a final “criti-cal” state is attained at which the porosity and failure strength reach steady valuesnu and τu. As indicated by Equation 11, there is a linear relationship between ulti-mate strength and effective pressure. Impressive confirmation of this relationshipis evidenced in Figure 5a, which presents results from three different till samples.Note that the intercept, which corresponds to the cohesive strength c, is small and,if neglected, leads to the result that τu/pe = tan ϕ is constant if ϕ is constant.Next we consider an inverted form of Equation 12, τu/τ0 = (ε/ε0)1/n , in light ofthe experimental results summarized in Figure 5b; these show that the ultimatestrength does not appear to vary as strain rate increases. For ε1/n to be constant, nmust be infinite, i.e., the material is perfectly plastic; in soil mechanical parlancethe material is described as Coulomb-plastic.

The startling and significant implication of these experimental studies is thatthe ultimate strength of subglacial sediment can be very low, in many cases lessthan the driving stress τD calculated from the ice thickness and surface slope. For aglacier underlain by a failing substrate, the basal stress is τB = τu; thus for overallstability the driving stress must be partially balanced by other stresses such asthose acting at ice stream margins (e.g., Whillans & van der Veen 1997, Raymondet al. 2001) and at “sticky spots” on the glacier bed (e.g., MacAyeal et al. 1995).

The critical state, achieved when τf = τu, plays a significant role in soil me-chanics (e.g., Schofield & Wroth 1968) and in discussions of the mechanics ofsoft-bedded glaciers and ice streams (e.g., Clarke 1987, Tulaczyk et al. 2000a). An

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Figure 5 Results of ring-shear measurements of the deformation properties of threetill samples. (a) Ultimate strength versus effective pressure. The cohesion c and frictionangle ϕ are indicated for each till. (b) Ratio of ultimate strength to effective pressureversus shearing rate. After Iverson et al. (1998) with additional results for the DesMoines Lobe till provided by N. Iverson (personal communication). Reprinted fromthe Journal of Glaciology with permission of the International Glaciological Society.

important feature of the critical state is that the sediment strength τf and porosityn, independent physical properties of the soil, become functionally dependent sothat nu(pe) and τu(pe), thereby reducing the number of degrees of freedom in thesystem. In the critical state, soil behavior is actually simplified.

3.4.2. CONSOLIDATION AND SWELLING When a porous soil is compressed, its po-rosity decreases. For water-saturated soils this response is complicated by the factthat both the soil matrix and pore water are virtually incompressible. Thus to reduceporosity it is necessary to expel water from the intergranular pore space. The cou-pled process by which porosity is reduced is termed consolidation and depends onthe hydraulic conductivity KH of the soil as well as the presence of a sink to receivethe expelled water. Unlike ideal elastic solids, soils preserve a memory of theirloading history, and for this reason soil compression is a profoundly irreversibleprocess; a decompressed soil will not recover its precompression porosity. (Inthe soil mechanics literature the decompression process is termed swelling.) The

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260 CLARKE

consolidation and swelling characteristics of soils are summarized by the equations

e ={

e0 − Cc log10(pe/pe0) swelling

e0 − Cs log10(pe/pe0) consolidation(13)

(e.g., Clarke 1987, Tulaczyk et al. 2000a), where e = n/(1 − n) is the void ratio,e0 is the initial void ratio, Cc is the consolidation index, Cs the swelling index, andpe0 is a reference value of effective pressure; typically Cs ≈ 0.2Cc.

The differing responses to compression and decompression explain why soilshave a memory of their loading history and why, in a repeated cycle of loadingand unloading, soils can progressively decrease their porosity. The memory ofpast loading, termed preconsolidation or overconsolidation and here denoted poc,is evidenced by the degree to which a soil is more compressed than it should beunder its present stress environment. Preconsolidation indicates past high values ofeffective pressure rather than past high values of overburden pressure; thus past icethickness cannot be inferred from the overconsolidation of contemporary surface-exposed sediments, although it may be possible to infer past subglacial hydrologicconditions (Boulton & Dobbie 1993, Piotrowski & Krauss 1997, Tulaczyk et al.2001, Christoffersen & Tulaczyk 2003a).

Figure 6 shows, schematically, the results of hypothetical compression andswelling tests performed using a triaxial cell. The limiting cases of the naturalsetting are mirrored in the laboratory by tests that are characterized as “undrained”(Figure 6a–c) or “drained” (Figure 6d–f ). In drained tests the sample is allowedto exchange water with an external reservoir so that the mass of water within thesample cell changes as the experiment proceeds. Pore pressure pp is kept constantas the load (which corresponds to pi) is varied; effective pressure pe = pi − pp

varies because pi varies. For undrained tests the water volume is kept constantso the pore water pressure must increase as the load increases. Not surprisingly,the measured soil compressibility differs in the two experiments, with drainedsoils consolidating more readily than undrained ones. Even in the presence of awater sink, fine-grained soils, which tend to have low permeability, resist consol-idation, whereas coarse-grained soils consolidate more readily. A different kindof undrained experiment (not illustrated) might be conducted by keeping the loadconstant and actively adding or removing pore water from the cell using a wa-ter pump. In this case the pore pressure pp is varied rather than the load; if porewater is extracted during the experiment, the effective pressure pe will increaseand, by Equation 11, the strength of the sediment is increased. In the absence ofsubglacial pumps, basal freeze-on provides a possible mechanism for extractingpore water from fine-grained subglacial sediments and for promoting subglacialtill consolidation (Christoffersen & Tulaczyk 2003a,b); it has been suggested thata freeze-on consolidation process could explain the shutdown of fast-flowing icestreams (Bougamont & Tulaczyk 2003).

Of special interest is the critical state when the effective pressure controls boththe sediment strength (Equation 11) and void ratio. Equation 13 gives relationships

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Figure 6 Consolidation and swelling testing of a water-saturated sedimentusing a triaxial cell. (a)–(c) Undrained. (d)–( f ) Drained.

between void ratio and effective pressure, but these apply for a nonfailing material.For sediments from the base of Whillans Ice Stream, Tulaczyk et al. (2000b)found that a relationship of the form τu = a exp(−be) yielded a good fit to theirexperimental data. Taken with Equation 11, the two expressions link e, τu, and pe

in a failing subglacial till and reduce the number of degrees of freedom from two(any two of e, τu, pe) to one. To distill these results: At low effective pressures afailing sediment will have low strength and high porosity; as effective pressure isincreased the strength will increase and the porosity decrease.

3.4.3. DILATANCY The concept of dilatancy has been experienced by anyone whohas hastily repacked a carefully packed suitcase: rearrangement of the contentsincreases the volume. Although dilatancy is a shared property of granular materials,irrespective of whether they are wet or dry, the situation of greatest interest iswhen the intergranular pore space is saturated with an incompressible fluid suchas water. A simple kitchen experiment involving a balloon filled with water andsand (Orowan 1966) provides a powerful illustration of the effects of dilatancy onsediment strength.

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262 CLARKE

Figure 7 Dilatancy of water-saturated granular sedimentsubjected to shearing. (a)–(b) Undrained tests. (c)–(d)Drained tests.

Essential features of dilatancy operating under drained and undrained conditionsare summarized schematically in Figure 7. For the undrained test, the flow ofwater is prevented and the increase in pore volume must be accommodated by avolumetric expansion of the pore fluid. However, water is nearly incompressible soa dilatant increase in pore volume produces a large drop in pore pressure, possiblyto negative values, and thus an increase in the yield strength τu. For the drained test,water is free to flow into the shear cell, and once pressure equilibration has occurred,the saturated sediment is in a looser packing and weaker than it was before sheardeformation commenced. Depending on the rate of dilatation, permeability of thesubstrate, and availability of water, both the drained and undrained idealizationsare relevant to the subglacial setting, and complicated soil responses can result(Moore & Iverson 2002). The mean of measured porosity for sediments underlyingactive Whillans and Bindschadler ice streams in West Antarctica lies in the range0.40 ≤ n ≤ 0.48 (Kamb 2001); such high values imply that these sediments aredilated.

Dilatancy has another significant consequence for subglacial sediments. Be-cause soils compress more readily than they decompress, there is a strong ten-dency for soils to reduce their pore volume when they are subjected to cycles ofloading and unloading. Dilatancy is the only subglacial mechanical process thatcan greatly increase porosity and, in doing so, erase the memory of loading historythat is encoded in the overconsolidation poc of the sediment.

3.4.4. EVOLUTION OF TEXTURE AND FABRIC Deformation of subglacial sedimentgives rise to intergranular interactions that can produce time-evolving granulom-etry through processes of intergranular sliding (leading to abrasion) and fracture(grain crushing or comminution). Effective pressure determines the magnitudeof the intergranular stresses, and the partitioning between sliding and fracture

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processes is influenced by the grain size distribution of the sediment, with thefracture process being most effective when grains of comparable size make con-tact. This consideration applies at every size scale and explains the tendency ofsubglacial sediments to develop a self-similar size distribution that minimizes thenumber of equal-sized grains in any size class. Iverson et al. (1996) have exam-ined grain-size evolution in the laboratory using a ring-shear device to deform awater-saturated mudstone at an effective pressure of 84 kPa, comparable to that forWhillans Ice Stream, and demonstrated that as shear strain increased, the fractaldimension evolved toward a limiting value around 2.85.

Clast fabric has been used by glacial geologists to infer the degree of subglacialdeformation experienced by glacial deposits, with the underlying premise thatfabric strength decreases with increasing cumulative strain. Hooyer & Iverson(2000) have tested this hypothesis using a ring shear device with natural andsynthetic tills and found that the effect of shearing was to strengthen the clastfabric rather than weaken it. Furthermore, the clast orientation was establishedvery rapidly, at a cumulative strain of less than 2, and ceased to evolve substantiallyas the cumulative strain increased to 50. Experiments of this type are essential inhelping field geologists distinguish fact from folklore.

4. COUPLING AND FEEDBACK

The length scales relevant to subglacial processes span a surprisingly large range,and the most obvious scale, ice thickness, provides a poor yardstick for discussingthe scales of spatial interaction. Beneath valley glaciers, subglacial water pressurecan fluctuate strongly over length scales of ∼1−10 m (Murray & Clarke 1995),yet ocean tides of ±1 m amplitude at the grounding lines of West Antarctic icestreams produce effects far upstream from the grounding line, indicating a lengthscale of ∼100 km (Anandakrishnan & Alley 1997, Anandakrishnan et al. 2003,Bindschadler et al. 2003). As for timescales, the stereotype of glaciers as slowsystems with sluggish responses is challenged on many fronts. Timescales basedon mass balance range from ∼102–104 years for glaciers and ice sheets, whereasthose for many subglacial processes lie in the range 10−6–100 year.

4.1. Thermomechanical and Thermohydraulic Processes

The flow law of ice is temperature dependent (Equation 8) and glacial flow producesstrain heating � = 2B exp(−E/RT )τ ε ( W m−3) so there is a positive feedbackbetween the flow rate and strain heating. For a glacier sliding over its bed, thevolumetrically distributed heat source � is concentrated at the ice-bed contact,and the resulting frictional heating can be represented by an equivalent frictionalheat flux qB = vBτB as in Equation 5.

Thermally controlled processes such as glaciohydraulic supercooling, rege-lation infiltration, and frost heave are thought to be important for entraining

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264 CLARKE

subglacial sediment (Alley et al., 1997). The processes are complementary in thesense that they require differing conditions to function effectively. Glaciohydraulicsupercooling has the important feature that it can operate without the necessity ofexporting heat from the ice-bed contact, but it requires special geometric precon-ditions before it can operate at all. Whether glaciohydraulic supercooling can bea vigorous process is less clear, because if supercooling is extreme there shouldbe a strong tendency for the drainage pathway to freeze shut, effectively shuttingdown the process. Regelation infiltration operates most effectively if the ice-bedcontact is warm and the grain size of subglacial sediment is not too fine, whereasfrost heave processes require a frozen ice-bed contact.

4.1.1. GLACIOHYDRAULIC SUPERCOOLING The freezing temperature of water ispressure dependent (Equation 6) and the flow of water is driven by the fluid poten-tial gradient (Equation 1), which also depends on pressure. If the water pressurechanges along the flow path then so also must the freezing temperature. Becausethe freezing temperature of water decreases with pressure, ascending water willbecome supercooled relative to surrounding ice that is at the melting temperature;the process is termed glaciohydraulic supercooling (Alley et al. 1998, Lawson et al.1998).

To maintain water at the melting temperature when it is flowing in a conduit,energy must be supplied at the rate Pp = −ρwcwCT Qw dpw/ds (where cw isthe specific heat capacity of water and Pp has dimensions of W m−1). The rateof potential energy release (per unit length) associated with the flowing wateris Pφ = −Qwdφw/ds. The sign of the difference P = Pφ − Pp determineswhether supercooling occurs. From Equation 1, with the assumptions that thedrainage path is at the ice-bed contact and the water pressure is approximated bythe ice overburden pressure, the threshold condition can be expressed as a criticalbed slope:

dZB

ds= − (1 − ρwcwCT)ρi

ρw − (1 − ρwcwCT)ρi

dZS

ds. (14)

With cw = 4220 J kg K−1 and CT = 0.0742 K MPa−1, the above expression givesdZB/ds = −1.62 dZS/ds. (For CT = 0.098 K MPa−1 the coefficient is reducedfrom 1.62 to 1.30.)

Implications of Equation 14 are that drainage pathways that exceed the criticalslope threshold are likely to seal up by freezing (Hooke 1991) and that if contin-uous water flow occurs under conditions of supercooling, the rate of subglacialsediment accretion can be greatly enhanced (Alley et al. 1997). This process hasbeen invoked to explain the huge volume of entrained sediment associated withice-rafted sedimentation during Heinrich events (Andrews & MacLean 2003), andit has been suggested (Alley et al. 2003) that glaciohydraulic supercooling can actas a stabilizing feedback on glacial erosion, limiting the amount of overdeepeningthat can develop. Contrasting the glaciohydraulic freezing threshold condition withthe hydraulic ponding threshold, dZB/ds = −10 dZS/ds leads to the conclusion

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that the glaciohydraulic freezing condition is the more stringent one because itbecomes important at smaller values of adverse bed slope.

4.1.2. REGELATION INFILTRATION Intrusion of ice into subglacial sediment couldbe an important process for englacial entrainment of bed material. The process hasbeen studied experimentally (Iverson & Semmens 1995) by applying a normal loadto a specially prepared ice block that contained a basal layer, intended to representan ice-saturated sediment, overlain by a layer of pure ice. The lower surface ofthis sample block was in contact with a water-saturated layer of sediment. Resultscan be summarized by the relation vr = Ks(pi − pw)/ρigHsi (Iverson & Semmens1995, Iverson 2000), where vr is the infiltration rate (m s−1), Ks is a constantrepresenting the apparent conductivity (m s−1) of sediment to ice, pi is the iceoverburden pressure acting at the upper boundary of the ice-saturated sedimentlayer, pw is the water pressure in the water-saturated sediment layer, and Hsi isthe thickness of the ice-saturated sediment layer. Noting that pe ≈ pi − pw, theice infiltration rate becomes small at low effective pressure as well as when thethickness of ice-entrained sediment becomes large. If the substrate is a fine-grainedsediment the regelation infiltration process is likely to stall.

4.1.3. ICE ACCRETION BY FROST HEAVE PROCESSES Frost heave processes, bestknown for their role in permafrost, can be active beneath glaciers and contributeto basal accretion of subglacial meltwater and sediment (e.g., Christoffersen &Tulaczyk 2003a,b). The operation of such processes is linked to a puzzling phe-nomenon: In freezing soils, pore water is drawn toward the freezing front. Inspec-tion of Equation 7 offers some insight into how this counter-intuitive behavior canoccur. If, at equilibrium, ice pressure exceeds the water pressure, then equilibriumis achieved by lowering the temperature of the water, effectively supercooling thewater relative to the equilibrium temperature T0 that would apply if the two pres-sures were equal. Thus supercooling and low water pressure go hand in hand. It isimportant to recognize that the pressure difference pi − pw in Equation 7 pertainsto the thermodynamic equilibrium of ice and water and is unrelated to pe, whichquantifies the buoyancy effects.

A satisfying explanation of frost heave, based on the phenomenon of premelting,has been advanced (e.g., Dash et al. 1995, Wettlaufer & Worster 1995, Rempelet al. 2004) and clearly summarized by Rempel et al. (2004): “Soil and ice grainsrepel each other across the interfacially premelted liquid films as a consequenceof the same intermolecular forces that give rise to these films. Low pressure isthus generated in the films, which draws in surrounding water, as into a withdrawnpiston.” Figure 4 illustrates the migration of water toward a freezing front underthe influence of this suction. For a permeable medium, the magnitude of the waterflux associated with the thermomolecular pressure gradient is

qw = − KH

ρwg

(ρiL

T0∇T

), (15)

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266 CLARKE

where the hydraulic conductivity KH depends strongly on the volume fractionof water in the pore space. Migration of water toward a freezing front does notnecessarily result in sediment entrainment. For ice to infiltrate intergranular porespace the radius of curvature Rc of the ice-water phase boundary must be less thanthe pore throat radius Rp (Figure 4). If this condition is not satisfied then ice willaccrete at the ice-bed contact but will not invade the sediment. The radius conditionfor ice infiltration of the soil skeleton can be rewritten as Rp > 2γiwT0/ρiL(T0 −T ), where T0 is the bulk melting temperature (Rempel et al. 2004); when thesupercooling T0 − T is large, ice can infiltrate finer-grained sediment than whenthe supercooling is small.

Much recent work on frost heave, including that of Christoffersen & Tulaczyk(2003a,b), has been based on the Miller model (e.g., Miller 1980), which hasbeen shown to have an incorrect microphysical justification. The main point ofdifference between the Miller model and contemporary explanations concerns theattribution of the differential pressure in Equation 7, which, in a previous section,was written pi−pw = γiwκ + pT(d). Miller attributes the difference to the capillarypressure γiwκ , whereas Dash and colleagues show that pT, the disjoining pressureassociated with premelting, accounts for the difference. It is unclear the extent towhich previous work is undercut by these new insights.

4.2. Hydromechanical Processes

The fast flow processes of sliding and sediment deformation are both activated byhigh water pressure and thus are affected by the operation of the subglacial watersystem. In turn, these mechanical processes are frictional and, through the vBτB

term in Equation 5, produce meltwater and open the possibility of a positive feed-back. Although decreased effective pressure promotes fast sliding and lowers thestrength of subglacial sediment, it does not necessarily follow that weak subglacialsediment will be deforming; when overlying ice is nearly afloat (pe ≈ 0) the bedis largely decoupled from the overlying ice so that the shear stress transmitted tothe sediment can be very low. How this trade-off is negotiated at various levels ofeffective pressure is an important question that lacks an intuitive answer.

Many valley glaciers manifest diurnal and seasonal cycling of subglacial waterpressure, so beneath these glaciers the effective pressure can vary over a widerange. Observations from beneath Storglaciaren, Sweden, reveal that when effec-tive pressure decreases, the flow rate increases, while simultaneously the strain ratein subglacial sediment decreases (Iverson et al. 1995). In this case, high water pres-sure weakens the substrate, but the dominant effect is to reduce the shear stress thatis transmitted to the bed and increase the rate of sliding over it. Measurements ofthe sliding contribution to the total flow of fast-flowing West Antarctic ice streamsindicate that the partitioning between sliding and sediment varies spatially andtemporally, with sliding contributing 80%–100% of the flow at sites on WhillansIce Stream and 20% of the flow at a site on Bindschadler Ice Stream (Kamb2001). Although subglacial sediment deformation is clearly an important fast-flow

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process, there is a growing suspicion that its importance has been overstated (e.g.,Piotrowski et al. 2001).

4.2.1. HYDRAULIC JACKING AND HYDROFRACTURE Subglacial water and sedimentshare in the task of supporting the ice overburden. If the water system is sheet-likethen the overburden pressure pi is partitioned on the basis of the area fractions αs

of solid surfaces and αw of water in contact with the ice, where αw + αs = 1. Thepartitioning of overburden pressure between solid clasts and subglacial water istherefore pi = αs ps + (1 − αs)pw, where ps is the pressure transmitted to the soilskeleton. A large difference between ps and pw cannot be sustained because thereis a strong tendency for pw to be near ps so that pw ≈ pi and ps ≈ pi. In situationswhere a sheet-like system coexists with subglacial conduits, the partitioning ofoverburden pressure can be more complicated, and for temporally varying conduits,the partitioning will vary with time. For example, the drop in subglacial waterpressure at the leading edge of downglacier-propagating mini-surges of VariegatedGlacier (Kamb & Engelhardt 1987) can be readily explained in terms of hydraulicjacking acting along the flow axis of the glacier. Water pressure in the fast-flowingzone approached or exceeded the ice overburden pressure and, at the leading edgeof the propagating zone, decreased the load supported by water and bed solids inthe region immediately downflow from this edge.

Transverse hydraulic jacking has been observed at Trapridge Glacier, Canada(Murray & Clarke 1995), where pressure sensors in close proximity to a waterconduit mimicked the water pressure fluctuations in the conduit but with oppositepolarity, in effect yielding a subglacial seesaw. An extreme example of transversejacking was reported by Nolan & Echelmeyer (1999) for Black Rapids Glacier,USA. This glacier is known to rest on a sedimentary substrate (Truffer et al. 1999)and there is compelling evidence that the seismic properties of its substrate canchange dramatically with time. During a 45-day observation interval in 1993,three subglacial outburst floods swept through the study area, and each of thesecoincided with transient decreases in the seismic wave speed. Nolan & Echelmeyer(1999) concluded that during the outburst floods the water pressure in the floodconduit became so high that it lifted the ice ceiling of the conduit, reducing the loadtransferred to the glacier bed in the region adjacent to the conduit. So great werethe changes in seismic properties associated with these repeated unloadings of thebed that they could only be explained by assuming that the subglacial sedimentbecame temporarily unsaturated in water and that part of the sediment pore spacewas filled with air exsolved from the pore water. This process can occur rapidly andis completely reversible. Thus, following a flood, when the conduit water pressurereturns to its preflood value, the substrate can return to a state of full saturation.

For valley glaciers during the winter season the meltwater supply to subglacialconduits is greatly reduced and conduits tend to seal up. Under these circumstancesany fracture processes that lead to a change in the volume of the subglacial watersystem can produce sudden pressure impulses. Because of the incompressibilityof water, even small changes in volume can produce large changes in pressure.

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A short-lived pressure event beneath Trapridge Glacier, Canada, which was prob-ably initiated by faulting of the glacier, produced a water pressure pulse thatexceeded 8 MPa in a region where the ice overburden pressure was 0.5 MPa(Kavanaugh & Clarke 2000). Hydrofracture, water pressure–induced ice fracture,is a closely related process and a likely cause of the glacier seismicity associatedwith mini-surges (Kamb & Engelhardt 1987), the opening of subglacial waterpathways, and the establishment of a hydraulic connection between the surfaceand bed of glaciers (Boon & Sharp 2003).

4.2.2. WATER-COUPLED SEDIMENT TRANSPORT Subglacial sediment transport pro-cesses have not received much attention, but there is good reason to believe thatthe standard literature on suspended sediment transport in subaerial channels (e.g.,Garcia & Parker 1991) can be directly applied. Bed load transport is unlikely to bea significant process except in well-developed subglacial conduits and during highdischarge events. The main consequences of water-coupled subglacial sedimenttransport processes are to erode soft sedimentary beds and alter their mechani-cal and hydraulic properties by the selective removal of fine-grained sediment.Without fines-removal the comminution process tends to be self-limiting and theregelation infiltration process is suppressed.

5. PRODUCTS AND PUZZLES

5.1. Behavioral and Material Products

Interactions among subglacial processes can stimulate intriguing flow behavior,including cyclic oscillations and on-off switching of fast-flow processes. Theseinteractions also yield material products such as ice streams and glacial bedforms.

5.1.1. SWITCHES AND OSCILLATORS Of the many kinds of switches that can op-erate subglacially, the most fundamental ones are those that control switchingfrom one subglacial environment to another. The cold-warm switch is dominatedby thermal processes at the ice-bed boundary and has received considerable at-tention. For hard-bedded glaciers, this switch enables basal sliding (neglecting asmall contribution from cold-bedded sliding); for soft-bedded glaciers, it can acti-vate sliding and sediment deformation. The hard-soft switch can operate beneathsediment-based glaciers if the substrate is capable of switching from a compactedstiff state to a dilated soft state. Both the cold-warm and hard-soft switches have, atvarious times, been invoked to explain temporal and spatial switching of fast-flowprocesses.

The transition from slow to fast flow across the margins of ice streams is abruptand can be viewed as evidence for a spatial switch in subglacial processes (seeFigure 1) that selects between ice stream and ice sheet morphologies. Ice streamsare also subject to a temporal switch: Kamb Ice Stream stopped roughly 150 years

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ago and Mercer and Whillans Ice Streams are currently decelerating (Joughin et al.2002) and could conceivably switch to a slow-flow state. The exact nature of theseswitches is unknown, but there is no lack of possibilities, ranging from a switch inmechanical properties, when subglacial sediment fails or ceases to fail, to a switchin thermal conditions at the ice-bed interface.

Free oscillations in the flow rate of glaciers are characteristic of the episodicfast-flow events known as surges (Raymond 1987), during which the flow velocitycan increase 10–1000-fold. At a much larger scale, the quasi-cyclic oscillations ofthe Laurentide Ice Sheet known as Heinrich events (Hemming 2004) could presentan example of surge-like behavior of ice streams that drained the ice sheet to theLabrador Sea. Kamb (1987) proposed that the temporal switch that triggered glaciersurging was associated with a switch in the subglacial drainage morphology froma pipe-like system (Equation 4) that efficiently evacuates water from the bed to aninefficient sheet-like linked cavity system that operates at low effective pressure.Surge termination occurs when the drainage morphology switches back to a pipe-like configuration. Morphological switching of the subglacial water system is alsothought to underlie glacier motion changes during the winter/spring transition invalley glaciers (e.g., Stone & Clarke 1996, Harper et al. 2002, Mair et al. 2002,Anderson et al. 2004).

5.1.2. SELF-ORGANIZATION Contemporary ice sheets reveal a strong tendency tosegregate into distinctive regions dominated by either sheet or streaming flow(e.g., Figure 1). On the basis of their numerical ice sheet modeling studies, Payne& Dongelmans (1997) view this as evidence for self-organization of the thermaland mechanical processes that control temperature at the ice-bed contact. Fromthis perspective, ice streams are the spontaneous expression of a pattern-formingmechanism and do not require inhomogeneities in subglacial topography or ge-ology to initiate or enable their formation. Under steady forcing, the ice sheetsmodeled by Payne & Dongelmans (1997) do not establish a steady state but in-stead manifest complex spatial and temporal variability, with ice streams turningon, shutting down, and interacting in a complex manner. If the possibility of spatialfluctuations is inhibited, for example, if unfavorable bed topography or substrategeology prevent ice streams from changing their spatial position, they continue tofluctuate—but only in time (Fowler & Johnson 1996, Payne & Dongelmans 1997).By this thinking, episodic surging of topographically controlled valley glaciers andice streams is an expected outcome of their spatial constraints.

The undrained plastic bed model introduced in Tulaczyk et al. (2000b) exploresthe hypothesis that soft-bedded ice streams that are actively deforming their bedsdo not require a subglacial drainage system and store their meltwater in a porouszone of thickness Hs within subglacial till rather than at the ice-bed contact. Thus,in Equation 5, they replace ∂ Hw/∂t by Hs∂e/∂t and discard terms involving thewater transport flux qA

w. With these assumptions, together with the critical stateassumption, the consequence of excess meltwater production is to increase thevoid ratio of the sediment e and, for a failing sediment, to reduce its strength τu.

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For a failing bed, the basal shear stress τB is identical to its shear strength, soreducing the strength of the substrate also reduces the magnitude of the frictionalheating at the interface (represented by vBτB in Equation 5). However, reducedwater production reduces the void ratio e and increases strength. Thus to maintaina steady state, ice streams must adjust the physical properties of their substrate ina delicate manner to produce enough frictional melting to maintain the flow. Theinteresting point is that for a fast-flowing ice stream, there are stabilizing feedbacksthat work to slow down the flow if it is too fast and to speed it up if it is tooslow.

Although the details remain imprecise, self-organization seems like a usefulconcept when considering how subglacial processes conspire to produce a frac-tal grain size distribution in subglacial sediments and a characteristic roughnessspectrum over hard beds (Hubbard et al. 2000). Conceivably, glaciers organize theproperties of their substrates to minimize the amount of geomorphic work thatthey must perform.

5.1.3. LANDFORMS Subglacially generated landforms, although incidental prod-ucts of the operation of subglacial processes, are interesting from a variety ofperspectives. The subject of glacial geomorphology has a long history and thesubglacial processes that give rise to several features (e.g., eskers) are reason-ably well understood, but ignorance predominates. Drumlins (Figure 2) remaincontroversial and bewildering despite the substantial scientific literature devotedto discovering how they are formed. Throughout the past decade, such questionshave captured the interest of mathematically inclined glaciologists who see soft-bedded streamlined bedforms such as drumlins, lineations, and transverse ribbedmoraines as expressions of fluid dynamical instabilities in the deforming substrate(e.g., Hindmarsh 1998, 1999; Fowler 2001; Schoof 2002). The work has a dauntingmathematical level, uncertain relevance, but potentially interesting implications.There is a suggestion that instabilities in a viscous subglacial layer must be hi-erarchical, with an initial instability that produces roll-like transverse bedforms(Schoof 2002); a second instability would therefore be required to produce three-dimensional streamlined bedforms.

5.2. Some Puzzles

It would be wrong to leave the reader with an impression that glaciology is amature science, now dedicating itself to minor janitorial tasks. Glaciologists areinspired by the knowledge they have gained—much of it very recent—but theyare challenged by what remains to be understood. A sampling of some burningquestions is given below.

5.2.1. DEEP DEFORMATION Under normal circumstances, the effective pressure inwater-saturated subglacial sediment is expected to increase with depth in the sedi-ment layer because of the contrasting densities of water and the solid soil skeleton.

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Thus, by Equation 11, the weakest sediment should be that which is highest up thesoil column and closest to the ice-bed contact. In this light, the interpretation ofsediment deformation measurements by Truffer et al. (2000) beneath Black RapidsGlacier, Alaska, is highly disconcerting. As part of a program to use commercialwireline drilling to retrieve sediment from a 7- m-thick subglacial till layer (Trufferet al. 1999) they installed tilt cells (Figure 3c) at depths of 0, 1, and 2 m in thissubstrate and observed changes over 410 days. At the study site, roughly 50%–65% of the glacier motion is contributed by basal motion (sliding and/or sedimentdeformation), yet almost the entire amount of basal motion was occurring at adepth below that of their deepest tilt cell, possibly in localized shear layers deepwithin the sediment or by sliding at the contact between sediment and underlyingbedrock. The research group that conducted these studies has unique expertise inthe installation of subglacial instruments, and there is no reason to doubt their meth-ods or conclusions. Taken as a measure of progress in understanding subglacialdeformation processes, these results are discouraging.

5.2.2. TO BE OR NOT TO BE Across the margins of ice streams there is a rapidspatial transition from sheet-flowing ice (∼10 m year−1) to stream-flowing ice(∼1 km year−1), which is sharply delineated in Figure 1. Tracing the ice streamsupflow reveals their arterial character, with numerous branching tributaries, butfrom this longitudinal perspective it is difficult to precisely identify the positionof ice stream onset. Following the criteria of Bindschadler et al. (2001), the lon-gitudinal onset separates regions where the ice flow rate increases with increasingdriving stress τD (sheet flow) and a region where the flow rate increases with de-creasing driving stress (stream flow). Applying these definitions, one can surmisethat in the sheet-flowing region creep deformation of ice is the dominant motionprocess, whereas in the stream-flowing region basal motion processes dominate.The question that remains is whether the onset position is fixed by topographicand geological factors or, as Payne & Dongelmans (1997) might have it, free tomigrate up or down the axis of the ice stream. Topographic control is not a generalfeature of onset regions and some form of geological control seems likely. Air-borne geophysical surveys and seismic surveys in the onset region of Kamb IceStream (Bell et al. 1998, Anandakrishnan et al. 1998) suggest the presence of ageological boundary, with stream flow occurring over a sediment-filled basin. Ge-ological controls on the genesis of subglacial landforms have also been suggested(e.g., Rattas & Piotrowski 2003).

5.2.3. CATCH AND RELEASE DRAINAGE Ice streams flow over warm substrates, butnot much is known about their drainage systems. The idealized undrained plasticbed model (Tulaczyk et al. 2000b) does not require a drainage system. Yet thepaleo-ice stream in Figure 2 appears to have had one (O Cofaigh et al. 2002)and contemporary ice streams are known to discharge subglacial meltwater intothe global ocean. New evidence suggests that the drainage system beneath ice

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streams can contain water pockets capable of storing and releasing large volumesof subglacial meltwater (Gray et al. 2004). An examination of changes in the surfacetopography of Kamb Ice Stream, which is currently shutdown, and BindschadlerIce Stream, which is currently active, reveals large and rapid vertical displacementsof the surface of both ice streams. The affected regions have areas ranging from 25–125 km2 and show as bull’s-eyes in radar interferometric phase patterns; analysisof the subglacial fluid potential (defined in Equation 1) suggests cycles of pondingand release of water from one pond to the next.

5.2.4. LEAPING GLACIERS An extreme form of stick-slip sliding has been proposedto explain curious earthquakes that seem to be associated with glaciers (Ekstromet al. 2003). The seismic source mechanism for these events appears to differ fromthat of conventional tectonic earthquakes and is consistent with downslope slidingof a substantial mass of ice over an interval of 30–60 s. The source mechanismand strength can be estimated from seismic records and expressed in terms of anequivalent product of mass and displacement. For one event, with a source locationnear Dall Glacier, Alaska, the mass-displacement product was 1.3 × 1014 kg m,corresponding to 10 km3 of ice displaced by 13 m in roughly 1 min. Glaciologistshave yet to observe such behavior in a valley glacier.

6. CONCLUDING REMARKS

In writing this review, one of my most challenging tasks was to identify someexclusion principles. I had hoped to touch on topics that ranged from subglacialelectrokinetics, which account for curious subglacial electrical phenomena, to sub-glacial chemical and biological processes, which might influence the atmosphericconcentrations of carbon dioxide and methane. In the end, I decided to highlightprocesses that are clearly relevant to glacier dynamics and to the generation ofsubglacial landforms and to downplay work that seems primarily mathematical,computational, or narrative in character. I resisted the temptation of writing a sci-entific history, choosing to emphasize new results at the expense of old ones—theapproximate boundary of new and old being set at 1990.

ACKNOWLEDGMENTS

I thank Bruce Buffett, Poul Christoffersen, Denis Cohen, Tim Creyts, JulianDowdeswell, Laurence Gray, Jane Hart, Neal Iverson, Ian Joughin, KirkMartinez, Colm O Cofaigh, Alan Rempel, Martin Truffer, Christian Schoof, andJohn Wettlaufer for a variety of contributions that have helped improve this review.Financial support from the Natural Sciences and Engineering Research Councilof Canada (NSERC) has allowed me to spend a great deal of time working onglaciers and pondering their mysteries.

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The Annual Review of Earth and Planetary Science is online athttp://earth.annualreviews.org

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Figure 1 Arterial character of West Antarctic ice streams. Labels identify the Mercer (A),Whillans (B), Kamb (C), Bindschadler (D), and MacAyeal (E) ice streams. Satelliteimagery from the Canadian Space Agency. Slightly modified from Joughin et al. (2002);copyright by American Geophysical Union (2002).

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P1: KUV

March 23, 2005 16:53 Annual Reviews AR233-FM

Annual Review of Earth and Planetary SciencesVolume 33, 2005

CONTENTS

THE EARLY HISTORY OF ATMOSPHERIC OXYGEN: HOMAGE TOROBERT M. GARRELS, D.E. Canfield 1

THE NORTH ANATOLIAN FAULT: A NEW LOOK, A.M.C. Sengor,Okan Tuysuz, Caner Imren, Mehmet Sakınc, Haluk Eyidogan, Naci Gorur,Xavier Le Pichon, and Claude Rangin 37

ARE THE ALPS COLLAPSING?, Jane Selverstone 113

EARLY CRUSTAL EVOLUTION OF MARS, Francis Nimmo and Ken Tanaka 133

REPRESENTING MODEL UNCERTAINTY IN WEATHER AND CLIMATEPREDICTION, T.N. Palmer, G.J. Shutts, R. Hagedorn, F.J. Doblas-Reyes,T. Jung, and M. Leutbecher 163

REAL-TIME SEISMOLOGY AND EARTHQUAKE DAMAGE MITIGATION,Hiroo Kanamori 195

LAKES BENEATH THE ICE SHEET: THE OCCURRENCE, ANALYSIS, ANDFUTURE EXPLORATION OF LAKE VOSTOK AND OTHER ANTARCTICSUBGLACIAL LAKES, Martin J. Siegert 215

SUBGLACIAL PROCESSES, Garry K.C. Clarke 247

FEATHERED DINOSAURS, Mark A. Norell and Xing Xu 277

MOLECULAR APPROACHES TO MARINE MICROBIAL ECOLOGY ANDTHE MARINE NITROGEN CYCLE, Bess B. Ward 301

EARTHQUAKE TRIGGERING BY STATIC, DYNAMIC, AND POSTSEISMICSTRESS TRANSFER, Andrew M. Freed 335

EVOLUTION OF THE CONTINENTAL LITHOSPHERE, Norman H. Sleep 369

EVOLUTION OF FISH-SHAPED REPTILES (REPTILIA: ICHTHYOPTERYGIA)IN THEIR PHYSICAL ENVIRONMENTS AND CONSTRAINTS,Ryosuke Motani 395

THE EDIACARA BIOTA: NEOPROTEROZOIC ORIGIN OF ANIMALS ANDTHEIR ECOSYSTEMS, Guy M. Narbonne 421

MATHEMATICAL MODELING OF WHOLE-LANDSCAPE EVOLUTION,Garry Willgoose 443

VOLCANIC SEISMOLOGY, Stephen R. McNutt 461

ix

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March 23, 2005 16:53 Annual Reviews AR233-FM

x CONTENTS

THE INTERIORS OF GIANT PLANETS: MODELS AND OUTSTANDINGQUESTIONS, Tristan Guillot 493

THE Hf-W ISOTOPIC SYSTEM AND THE ORIGIN OF THE EARTH ANDMOON, Stein B. Jacobsen 531

PLANETARY SEISMOLOGY, Philippe Lognonne 571

ATMOSPHERIC MOIST CONVECTION, Bjorn Stevens 605

OROGRAPHIC PRECIPITATION, Gerard H. Roe 645

INDEXESSubject Index 673Cumulative Index of Contributing Authors, Volumes 23–33 693Cumulative Index of Chapter Titles, Volumes 22–33 696

ERRATAAn online log of corrections to Annual Review of Earth andPlanetary Sciences chapters may be found athttp://earth.annualreviews.org

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