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Quaternary Science Reviews 28 (2009) 1831–1849

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Quaternary Science Reviews

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Modeling ice sheets from the bottom up

T. Hughes*

Department of Earth Sciences, Climate Change Institute, University of Maine, Bryand Global Sciences Center, Grove Street Extension, Orono, ME 04469-5790, USA

a r t i c l e i n f o

Article history:Received 6 November 2008Received in revised form25 May 2009Accepted 6 June 2009

* Tel.: þ1 207 581 2198; fax: þ1 207 581 1203.E-mail address: terry.hughes@maine.edu

0277-3791/$ – see front matter � 2009 Elsevier Ltd.doi:10.1016/j.quascirev.2009.06.004

a b s t r a c t

Three facts should guide ice-sheet modeling. (1) Ice height above the bed is controlled by the strength ofice-bed coupling, reducing ice thickness by some 90 percent when coupling vanishes. (2) Ice-bedcoupling vanishes along ice streams that end as floating ice shelves and drain up to 90 percent of an icesheet. (3) Because of (1) and (2), ice sheets can rapidly collapse and disintegrate, thereby removing icesheets from Earth’s climate system and forcing abrupt climate change. The first model of ice-sheetdynamics was developed in Australia and applied to the present Antarctic Ice Sheet in 1970. It treatedslow sheet flow, which prevails over some 90 percent of the ice sheet, but is the least dynamiccomponent. The model made top-down calculations of ice velocities and temperatures, based on knownsurface conditions and an assumed basal geothermal heat flux. In 1972, Joseph Fletcher proposed a six-step research strategy for studying dynamic systems. The first step was identifying the most dynamiccomponents, which for Antarctica are fast ice streams that discharge up to 90 percent of the ice. Ice-sheetmodels developed at the University of Maine in the 1970s were based on the Fletcher strategy andfocused on ice streams, including calving dynamics when ice streams end in water. These modelscalculated the elevation of ice sheets based in the strength of ice-bed coupling. This was a bottom-upapproach that lowered ice elevations some 90 percent when ice-bed coupling vanished. Top-downmodeling is able to simulate changes in the size and shape of ice sheets through a whole glaciation cycle,provided the mass balance is treated correctly. Bottom-up modeling is able to produce accurate changesin ice elevations based on changes in ice-bed coupling, provided the force balance is treated correctly.Truly holistic ice-sheet models should synthesize top-down and bottom-up approaches by combiningthe mass balance with the force balance in ways that merge abrupt changes in stream flow with slowchanges in sheet flow. Then discharging 90 percent of the ice by ice streams mobilizes 90 percent of thearea so ice sheets can self-destruct, and thereby terminate a glaciation cycle.

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1. Introduction

This review primarily traces the trajectory of my glaciologicalcareer, which began in 1968. Consequently, those who influencedmy career the most are cited prominently. My apologies to otherprominent glaciologists. A half-century ago, glaciology was beingconverted from a descriptive branch of geology to an analyticalbranch of physics. Analytical reconstructions of ice sheets beganwith the parabolic profile of an ice sheet having a constant basalshear stress on a horizontal bed (Nye, 1951). Next, the basal shearstress was allowed to vary with ice velocity determined bya constant surface accumulation rate and whether ice moved bycreep over a frozen bed (Haefeli, 1961) or by sliding over a thawedbed (Nye, 1959), using the newly published flow law (Glen, 1955)and sliding law (Weertman, 1957a) of ice. These treatments

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produced elliptical ice-sheet profiles on a horizontal bed. Ablationrates were added and both accumulation and ablation rates wereallowed to vary in later refinements (see Hughes, 1998, Figure 5.10).In all these treatments, gravitational ice motion was resisted bya basal shear stress proportional to the product of ice height abovethe bed and ice surface slope. The resulting ice surface was high andconvex, even when moderate bed topography was included. Theirdependence on the surface mass balance made them top-downmodels that produced nearly steady-state ice sheets. The ice sheetsof Antarctica and Greenland today are nearly in steady state overall,within the accuracy of the surface mass balance. These ice sheetshave high convex surfaces where slow sheet flow prevails, asassumed in the analytical models. The Antarctic Ice Sheet oftenends as floating ice shelves because ice accumulation over virtuallyits entire surface allows it to advance into the sea, where icebergcalving provides the primary ablation mechanism. Weertman(1957b) provided the first analytical derivation of the low andessentially flat surface of a floating ice shelf. In his derivation,

T. Hughes / Quaternary Science Reviews 28 (2009) 1831–18491832

gravitational ice motion is resisted by a longitudinal tensile stressproportional to the height of ice floating above sea level.

2. Modeling ice sheets from the top down

Numerical ice-sheet modeling was inaugurated by WilliamBudd, Richard Jenssen, and Uwe Radok in 1971. They developeda steady-state flowline model which they applied to the AntarcticIce Sheet in order to derive variations of temperature, stress, andvelocity with depth, using measured ice heights above the bed, iceelevations above sea level, ice surface accumulation rates, and icesurface temperatures (Budd et al., 1971). From these data, theirmodel plotted ice trajectories and timelines with depth alongsurface flowlines, and calculated either basal ice temperaturesbelow the melting point or basal ice melting rates at the meltingpoint for specified rates of the basal geothermal heat flux. Doublingthe geothermal heat flux converted a ubiquitously frozen bed intoa largely thawed bed. Widespread changes from a frozen toa thawed bed also resulted from moderate changes in conditions atthe ice surface. An outer basal freezing zone was introduced beyondthe inner basal melting zone in subsequent applications of themodel to prevent widespread ice-bed decoupling as the basal waterlayer thickened (Sugden, 1977).

Budd and Radok were meteorologists who saw interactions ofthe ice surface with the atmosphere as the critical boundarycondition in modeling ice sheets. Budd et al. (1971) specifiedsurface conditions in order to determine basal conditions. Theirswas a top-down model in which the surface mass balance combineswith the force balance to offset gravitational motion with basal dragthat resists motion. By that constraint, their model applied only toslow sheet flow. This is known as the ‘‘shallow-ice’’ approximation(Hutter, 1983). Their pioneering work set the stage for developinggridpoint ice-sheet models that were three dimensional and timedependent. Time-dependent modeling showed that present basalthermal conditions are determined primarily by past surfaceconditions, not present conditions, even if surface changes frompast to present are only moderate. These models also simulate onlyslow sheet flow, which prevails over some 90 percent of ice sheets,past and present. In sheet flow, gravitational flow is resistedprimarily by basal drag, as quantified by the basal shear stress.Since past surface conditions are poorly known for present icesheets, and unknown for former ice sheets, top-down modelscannot deliver reliable basal conditions for 90 percent of the bedbeneath ice sheets. For example, when a state-of-the-art threedimensional time dependent top-down model was applied to theAntarctic (Huybrechts, 1990, 1992) and Greenland (Huybrechts,1994, 1996) ice sheets, it was unable to generate the amount anddistribution of basal water that has been mapped by radar soundingin both Antarctica (Siegert et al., 1996) and Greenland (Oswald andGogineni, 2008), unless the model used a distribution of basalgeothermal heat flux that forced a fit. Basal water controls ice-bedcoupling, and therefore the height and stability of ice sheets. Basalwater cannot support a basal shear stress, so gravitational flow isnot resisted by basal drag when basal ice is no longer in contactwith the bed. As a consequence, progressive reduction of ice-bedcoupling by basal water converts the high convex surface ofa grounded ice sheet into the low and flat surface of a floating iceshelf. The ice sheet has destroyed itself when the ice shelf disin-tegrates into icebergs. Disintegration of an ice shelf is alsoa consequence of eliminating ice-bed coupling where the ice shelfis grounded laterally in a confining embayment and where the iceshelf is pinned locally to the sea floor, producing ice rumples or icerises on the ice-shelf surface above each pinning point. Confinedand pinned ice shelves are common where the Antarctic Ice Sheetadvances into the sea and becomes afloat.

The top-down models for sheet flow by Budd et al. (1971) andlater top-down models were incompatible with important fielddata from Antarctica, much of it collected by tractor-train traversesduring the International Geophysical Year (IGY) in 1958 andbeyond. The traverses measured ice elevations, temperatures, andaccumulation rates at the surface and ice heights above the bedalong traverse routes. The data, traverse routes, and geographicalfeatures appeared on the 1970 map, Antarctica, published by theAmerican Geographical Society. Contoured bed topographic datashowed that most of the West Antarctic Ice Sheet was groundedbelow sea level on the Antarctic continental shelf (Bentley andOstenso, 1961), leading Mercer (1970) to propose that it was aninherently unstable ‘‘marine’’ ice sheet. Contoured surface eleva-tion data showed the East Antarctic Ice Sheet had the convexsurface produced by steady-state models of sheet flow, but theWest Antarctic Ice Sheet had a concave surface. Perhaps the WestAntarctic Ice Sheet was far from steady state and in fact was in anadvanced stage of gravitational collapse that produced the lowfloating ice shelves surrounding it. My response to this possibilityappeared in four monographs, in 1972, 1973, 1974, and 1975, underthe acronym ISCAP (Ice Streamline Cooperative Antarctic Project),all of which posed the question, ‘‘Is the West Antarctic Ice Sheetdisintegrating?’’ Was the West Antarctic Ice Sheet not onlycollapsing into ice shelves, but would the ice shelves then disin-tegrate into icebergs, thereby removing the West Antarctic IceSheet from the global climate system, and flooding the world oceanwith icebergs that, in melting, would cool ocean surface water andtherefore reduce the ocean-to-atmosphere heat exchange thatdrives atmospheric circulation? Could a new glaciation cycle thenbegin?

3. The Fletcher memorandum

Incorporated in my ISCAP bulletins was a research strategy forstudying dynamic systems proposed by Joseph Fletcher in aninternal memorandum when he headed the Office of PolarPrograms at the National Science Foundation (Fletcher, 1972).Fletcher recommended research that answered six questionsdirected at how any dynamic system operates. His six questions andmy answers for the Antarctic Ice Sheet that also apply to all icesheets are:

1. What are its most dynamic parts? Answer: ice streams,including their calving fronts when ice streams end groundedin water or as floating ice tongues often imbedded in iceshelves.

2. What factors force motion in these parts? Answer: gravityresisted by ice-bed coupling and atomic bonding in ice.

3. Which of these factors vary over time? Answer: ice-bedcoupling and breaking atomic bonds during iceberg calvingevents.

4. What physical processes cause the time variations? Answer:processes that weaken or strengthen ice-bed coupling and thatlead to and cause calving of ice.

5. Can these processes be quantified theoretically? Answer: yes,but the processes are poorly understood and the theories mustbe holistic, including transitions from sheet flow to stream flowto shelf flow and the dynamics of calving.

6. What experiments will test the theories? Answer: experimentsdesigned to gather broad comprehensive data over theAntarctic Ice Sheet, especially in West Antarctica and relyingheavily on satellite technology, combined with field studiesthat include deep drilling and are concentrated on ice streamsand their calving fronts where rapid changes in behavior areobserved, with all data being input to computer models

Fig. 1. The marine ice instability at marine ungrounding lines of ice sheets (Weertman,1974). Top left: the base of right-triangles are equal basal ice and water pressures, theheights of these triangles are heights of ice and water above the base, the areas of thesetriangles are opposing longitudinal gravitational driving forces in ice and water perunit transverse width, the pulling force is the difference between these areas, shown asthe dashed triangle. Top right: the longitudinal pulling force is the area of the dashedtriangles and is proportional to the square of ice thickness. Bottom: as the ungroundingline retreats, the pulling force increases on a downsloping bed and decreases on anupsloping bed because the floating ice thickness increases and then decreases.

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designed to replicate observed behavior and to projectbehavior into the future when internal and external forcingmay change.

The ISCAP bulletins applied my answers to Fletcher’s questionsin a research strategy for the Antarctic Ice Sheet as a dynamicsystem that was changing most noticeably in West Antarctica. Myanswers were based on glaciological, geophysical, and geologicalfield studies in Antarctica during and after the InternationalGeophysical Year in 1958. Much of the glaciological and geophysicalresearch was directed by Charles R. Bentley and published inVolume 16 of the Antarctic Research Series of the AmericanGeophysical Union (Crary, 1971). Because ice streams discharge 90percent of Antarctic ice, instabilities in ice streams make the entireAntarctic Ice Sheet inherently unstable and subject to rapidcollapse, collapse that was largely complete in its marine WestAntarctic sector that has a concave surface and is mostly groundedbelow sea level. Field studies of glacial and marine geology in theDry Valleys of the Ross Sea embayment by Denton et al. (1968,1971), on East Antarctic outlet glaciers through the TransantarcticMountains into the embayment by Mercer (1968, 1972), and in theWeddell Sea embayment by Anderson (1972) confirmed collapse offormer marine ice sheets in these parts of West Antarctica. Fieldstudies of surface lowering along the Byrd Station Strain Network inthe center of West Antarctica by Whillans (1972, 1973) provideddirect evidence that collapse was still underway.

Newly developed airborne radar sounding technology wasapplied to the West Antarctic Ice Sheet, showing that the concavesurface was a consequence of major ice streams (Robin et al., 1970a)and that basal water was abundant where these ice streams hada nearly flat surface, as though here the ice streams were afloat,making these portions ‘‘pseudo ice shelves’’ (Robin et al., 1970b).Concave ice streams draining the West Antarctic Ice Sheet suppliedfloating ice shelves, so ice streams seemed to be the vehicles bywhich gravitational collapse converted the high convex surface ofnearly steady-state sheet flow into the low flat surface of shelf flow.The ISCAP bulletins were designed to test this hypothesis. Theircontents were subsequently published in refereed journals(Hughes, 1973, 1975, 1977) and as a book chapter (Hughes, 1998,Chapter 3). They presented a case for studying ongoing gravita-tional collapse of the West Antarctic Ice Sheet.

Glaciologists began studying the ice streams mapped by Robinet al. (1970a). Early results were presented at a conference spon-sored by the American Association for the Advancement of Science(AAAS) at the University of Maine on 8–10 April 1980, as recordedby Horne (1980). These studies led to The West Antarctic Ice SheetInitiative (WAIS) funded by the U.S. National Science Foundation(NSF) as a long-term investigation of this possibility (Bindschadler,1991). Results over the next decade were presented at a ChapmanConference sponsored by the American Geophysical Union (AGU)and held at the University of Maine on 13–18 September 1998(Bindschadler and Borns, 1998). More recent results are presentedin Volume 77 of the AGU Antarctic Research Series (Alley andBindschadler, 2001). WAIS workshops have been held annuallysince 1993.

The ISCAP bulletins explored two mechanisms for gravitationalcollapse. The first mechanism was gravitational collapse progress-ing inward from marine margins of the West Antarctic Ice Sheet.Collapse was triggered by rising sea level, beginning 18,000 yearsago, and accelerated by disintegration of floating ice shelves formedduring collapse. Ross Ice Shelf occupies a confining embayment andis pinned to the sea floor at places identified by ice rumples and icerises on the surface (Hughes, 1972, 1973). Surface velocities alongthe north–south leg of the Ross Ice Shelf Survey (Dorrer et al., 1969)were less than velocities for ice entering the Ross Ice Shelf from

West Antarctica, based on mass-balance measurements available atthe time (Bull, 1971). Perhaps a confined and pinned ice shelf canbuttress the ice streams supplying it. Then, if the ice shelf dis-integrated, perhaps ice streams would rapidly downdraw theremaining ice sheet until it became afloat. If the bed under these icestreams sloped downward into the ice sheet, retreat of the ice-shelfgrounding line would force ice streams to retreat. Weertman (1974)published the essence of this retreat mechanism (Fig. 1) andThomas (1977) quantified the processes driving retreat (Fig. 2).Thomas and Bentley (1978) applied the mechanism to modelcollapse on the former marine ice sheet in the Ross Sea Embaymentwhen ice-bed uncoupling began 18,000 years ago with rising globalsea level. They assumed the convex surface of sheet flow extendedto the grounding line of Ross Ice Shelf, as it does for ice ridgesbetween ice streams. De Angleis and Skvarka (2003) documentedretreat when part of Larsen Ice Shelf disintegrated.

In the second mechanism for gravitational collapse, heads ofconcave ice streams retreat and drag the marine ice-shelfgrounding lines with them (Hughes, 1974, 1975). This seemedpossible, based on the theory for cyclic surging mountain glaciersdeveloped by Robin and Weertman (1973), applied to account fornearly flat sections, ‘‘pseudo ice shelves,’’ of West Antarctic icestreams reported by Robin et al. (1970b). Ice-bed uncoupling bydeepening basal water under the flat sections would migrateupstream if the pressure gradient of basal water decreased upslope,causing the maxima in surface slope between each flat section tomigrate upslope. This process may now be underway in WestAntarctic ice streams (Bindschadler, 1997) and it causes the icestreams to retreat. In both cases, collapse of the ice sheet is deter-mined by conditions at the bed, specifically ice-bed uncoupling. Tocapture these mechanisms, which depart radically from steady-state conditions, models should be constructed from the bottom up.

4. Reconstructing former ice sheets for CLIMAP

The International Decade of Ocean Exploration (IDOE), 1970–1980, was underway when my ISCAP bulletins were circulating and

Fig. 2. Processes triggering gravitational collapse of marine portions of an ice sheet(Thomas, 1977). The ungrounding line migrates across basal sills due to (a) ice thinningduring an ice-stream surge, (b) lowering the sill due to glacial erosion or ongoing beddepression under the weight of ice, (c) rising sea level that lifts floating ice, (d) meltingthe upper or lower surfaces of floating ice, and (e) accelerated calving causing a calvingbay to migrate up the ice stream.

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an awareness was taking root that ice sheets may be the mostvulnerable component of Earth’s climate system (Hollin, 1972). Amajor part of IDOE was CLIMAP (Climate: Long-range Investigation,Mapping, and Prediction). CLIMAP provided glaciologists with anopportunity to become part of the large scientific communityengaged in documenting and understanding global climate change.George Denton at the University of Maine (UM) was chargedprimarily with reconstructing ice sheets at the Last GlacialMaximum (LGM) for 18 ka BP, but also with disintegrating themarine West Antarctic Ice Sheet during the preceding EemianInterglacial at the Last Interglacial Maximum (LIM) for 125 ka BP.Denton recruited me for these tasks. The top-down model of icesheets developed by Budd et al. (1971) was not suited to the CLI-MAP tasks, so I developed a bottom-up approach for reconstructingand disintegrating ice sheets. James Fastook and David Schillingcontributed mightily to this effort. We incorporated the marine iceinstability (Weertman, 1957a,b; Thomas, 1977) in conducting theLIM experiment.

The primitive models of atmospheric circulation used by CLI-MAP required three boundary conditions that only ice sheets couldprovide. These models needed (1) the areal extent of ice sheets (and

sea ice) as albedo input, (2) the volume of ice sheets to obtain thereduced ocean surface area in the ocean-to-atmosphere heatexchange, and (3) the elevation of ice sheets to obtain the surfacetopography that may re-direct surface winds and the jet stream. Asa glacial geologist, Denton could provide the areal extent of icesheets, but he needed a glaciologist to determine their volume andelevation at the LGM, and a mechanism to collapse the WestAntarctic Ice Sheet to obtain the Eemian sea level 6 m higher thanat present at the LIM. The only numerical model for ice sheetsavailable at that time was the flowline model Budd et al. (1971) haddeveloped for the Antarctic Ice Sheet. My ISCAP bulletins high-lighted defects in that modeling approach, the primary defect beingtheirs was a top-down model of sheet flow in which the amountand distribution of basal water was very sensitive to the surfacetemperature and accumulation rates and the basal geothermal heatflux. None of this information was available for former ice sheets tobe reconstructed for CLIMAP. However, these data are of minorimportance in reconstructing former ice sheets because theprimary result CLIMAP needed was ice elevations above the bed.That depends on the strength of ice-bed coupling, which could bedetermined from the glacial geology Denton was providing,a bottom-up approach.

Bottom-up modeling requires distinguishing between ‘‘first-order’’ and ‘‘second-order’’ glacial geology. First-order glacialgeology consists of a glacial imprint on the deglaciated landscapethat becomes more pronounced with each cycle of Quaternaryglaciation due to repeated processes of nearly steady-state glacialerosion and deposition. Second-order glacial geology is producedover time during the last glacial retreat. It overprints first-orderglacial geology. Most glacial geologists at that time were mappingand dating second-order glacial geology. For this reason, our ice-sheet reconstructions based on first-order glacial geology wererejected when we presented them at the International Symposiumon Dynamics of Large Ice Masses, sponsored by the InternationalGlaciological Society and held in Ottawa, Canada, in 1978. Wesubsequently published our CLIMAP work in book form, The LastGreat Ice Sheets (Denton and Hughes, 1981). It is necessary topresent the rationale for our bottom-up approach based on first-order glacial geology that determines ice-bed coupling and there-fore ice elevations above the bed. In the bottom-up approach, theunknown surface conditions and basal geothermal heat flux at theLGM and LIM, and the previous history of an ice sheet, are virtuallyirrelevant in determining the size and shape of former ice sheets.

Ice-bed coupling weakens when a frozen bed becomes thawedbeneath an ice sheet. For slow sheet flow, basal thawing lowers theice surface by about 20 percent. Thawing begins in bed hollows,from which progressive thawing expands and eventually envelopsbed hills as ice flows across a melting bed. When ice flows acrossa freezing bed, hilltops are frozen first and hollows last. Completefreezing raises the ice surface by about 25 percent and restores thesurface above a frozen bed. Therefore, melting and freezing bedsconsist of a mosaic of frozen and thawed patches which aredetermined primarily by bed topography. Ice surfaces above bothfrozen and thawed beds are high and convex. Melting and freezingzones along an ice-sheet flowline produce respectively more steepand less steep ice surface slopes in the flow direction, but theoverall ice surface remains convex (Fig. 3).

Once the bed is wholly thawed, continued basal melting willsubmerge the wet bed, first in hollows but progressive submer-gence eventually envelops hills as well. Since bed topographyincludes linear channels formed by tectonic activity or by subaerialand submarine erosion processes before the ice sheet existed,drowning of the bed will preferentially occur along channels. Theresulting ice-bed decoupling will allow overlying ice to move fasteralong these channels because resistance to gravitational motion is

Fig. 3. Response of ice elevation and ice trajectories to ice-bed coupling linked to basalthermal conditions (Denton and Hughes, 1981, Chapter 5). For sheet flow, the icesurface lowers 20 percent as a frozen bed thaws and rises 25 percent as a thawed bedfreezes (broken surface lines). Frozen beds are white. Thawed beds are black. Basalshear stresses sO are higher for creep (sO)C over a frozen bed and lower for sliding (sO)S

over a thawed bed (broken tau lines). Top: ice elevations and trajectories as ice movesfrom a frozen bed on an upland plateau across melting and freezing beds to a frozenbed under a surface ablation zone on land. Bottom: ice elevations and trajectories as icemoves from a thawed bed in a marine embayment across freezing and melting beds toa thawed bed under a marine ice stream that becomes afloat. Melting and freezingbeds are shown as a mosaic of thawed (black) and frozen (white) patches.

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weakened by the deepening basal water. Fast currents of ice inthese channels will become ice streams imbedded in the ice sheet,especially toward ice margins where thinning sheet flow is forcedto increasingly conform with bed topography. Ultimately, up to 90percent of ice in an ice sheet is discharged by ice streams. It is

unclear whether stream flow begins when basal water submergeshills lower than a critical size, supersaturates till or sediments toa critical depth, or drowns bedrock bumps up to a ‘‘controllingobstacle size’’ in the Weertman (1957a) theory of basal sliding.

Progressive reduction of ice-bed coupling along channels wherebasal water progressively drowns the topography of a hard bed,mobilizes the till or sediments of a soft bed, or both, will producethe lowering concave surface of ice streams that ends with the lowflat surface of ice tongues in water or as the low convex surface ofice lobes on land. Basal water draining around the perimeter of anice lobe allows partial ice-bed recoupling and gives the lobe its lowconvex surface. If ice tongues enter an embayment, they can mergeto become a floating ice shelf that is grounded along the sides of theembayment or at basal pinning points within the embayment. Inthis way partial ice-bed coupling continues into the embayment,and allows the ice shelf to buttress the ice streams (Thomas,1973a,b). Most West Antarctic ice streams enter the Ross Sea andWeddell Sea marine embayments, where their floating ice tonguesmerge to become the buttressing Ross and Ronne–Filchner iceshelves.

The former LGM ice sheets of North America and Eurasia werecentered on Hudson Bay in North America and over the Gulf ofBothnia, Barents Sea, and (in my opinion) Kara Sea in Eurasia, allisostatically depressed by the weight of overlying ice. Postglacialraised beaches and negative gravity anomalies are first-orderfeatures that locate these centers of ice spreading at the LGM whenthe ice load was greatest. They are first-order glacial features. Beingmarine water bodies originally, the ice domes that formed abovethem probably rested on a largely thawed bed in the deepest water.From these centers, ice moved across exposed Precambrian crys-talline shields from which the remaining overlying layer of sedi-mentary rock has been removed by Quaternary glacial erosion, aftereons of subaerial erosion. Since these shields are spattered withlakes, which would have been thawed patches under the ice, the icesheets moved across a freezing bed that was a mosaic of thawedand frozen patches. These eroded shields are first-order glacialfeatures. Beyond the shields, rock and regolith eroded from thethawed patches are deposited over the largely un-eroded sedi-mentary rock cover, producing looping end moraines. This band ofdepositional moraines is a first-order glacial feature. The biggestlooping moraines lie beyond troughs eroded in the sedimentaryrock cover. Today, these troughs are often occupied by linear lakeson land (notably the Great Lakes in North America). Along marineice margins, the troughs are linear straits and inter-island channelstoday. The troughs were occupied by ice streams at the LGM and arefirst-order glacial features. Fast stream flow produced a melting bedthat cut across the freezing bed between ice streams. Each cycle ofQuaternary glaciation reinforced the imprint of these first-orderglacial features on the deglaciated landscape (Hughes, 1981a;Hughes et al., 1981). In North America, the Laurentide Ice Sheetcentered on Hudson Bay merged with a Cordilleran Ice Sheet whichhad a frozen bed beneath ice divides along the crests of mountainranges and a thawed bed in valleys on the flanks of these ranges,giving an overall melting bed from ice divides to ice margins asa first-order glacial feature.

In the CLIMAP Eemian modeling experiment at the LIM, theThomas (1977) marine instability mechanism at ice-streamungrounding lines was applied to the CLIMAP West Antarctic IceSheet at the LGM (Stuiver et al., 1981). Rising sea level since theLGM triggered the marine instability, causing ungrounding lines toretreat up the concave CLIMAP ice streams (Fig. 4). The ice sheetcollapsed into ice shelves on its eastern and western flanks,producing the Weddell Sea embayment occupied by the Ronne–Filchner Ice Shelf and the Ross Sea embayment occupied by theRoss Ice Shelf. Subsequent collapse occurred on its northern flank,

Fig. 4. : Gravitational collapse of the West Antarctic Ice Sheet during Terminations of Quaternary glaciation cycles modeled for CLIMAP at the LIM (Denton and Hughes, 1981,Chapter 10). Ice is downdrawn by progressive ice-bed uncoupling along ice streams occupying the shaded submarine troughs. Stages of collapse proceed from the glacial maximum(A), to progressive collapse in marine embayments of the Ross, Weddell, and Amundsen seas (B and C), to collapse of the central West Antarctic Ice Sheet (D), to disintegration ofbuttressing ice shelves produced during collapse (E).

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producing an equally large embayment in the Amundsen Sea whenungrounding lines migrated up Thwaites and Pine Island glaciersinto the heart of West Antarctica. Pine Island Bay is the beginning ofthat embayment today. Final collapse occurred following disinte-gration of the confined and pinned ice shelves that formed asungrounding lines retreated. These ice shelves had buttressed theretreating ice streams. This LIM experiment could apply equally tothe present Holocene Interglacial, and projects ongoing collapse ofthe West Antarctic Ice Sheet into the future. Collapse is entirely dueto ice-bed uncoupling that progresses up lowering concave icestreams and allows calving bays to discerp the downdrawn ice.

Ice-bed uncoupling can also proceed from the interior of icesheets along ice streams to ice margins, as had been modeled forthe Laurentide Ice Sheet in Hudson Bay and its ice stream in HudsonStrait (MacAyeal, 1993; Calov et al., 2002). When a frozen bedthaws, ice-bed coupling is largely lost in these models, and the ice-sheet collapses and spreads until surface lowering brings coldinterior ice into contact with the bed, causing the bed to freeze sosurface ice accumulation can restore the original ice elevation.These ‘‘binge/purge’’ cycles can be tuned to mimic Heinrich (1988)events for quasi-periodic rapid discharges of icebergs from theLaurentide Ice Sheet. No changes in ice surface temperature andaccumulation rates are required, not even changes linked to thelowering ice surface. Changing surface conditions take millennia toaffect the basal thermal regime (Whillans, 1981), so surface changeshave little effect on these essentially bottom-up processes linked toabrupt ice-bed decoupling and recoupling.

The CLIMAP bottom-up approach to ice-sheet modeling focusedattention on ice streams. Since ice streams discharge up to 90percent of ice from past and present ice sheets, modeling ice-stream dynamics correctly can generate changes in the size andshape of ice sheets that are big enough and fast enough to triggerrapid changes in global climate and sea level. Changes of this kindare well documented for former ice sheets (Denton and Hughes,1981; Mayewski et al., 1997), and even now are becoming manifestin present ice streams in Antarctica (Thomas et al., 2004) andGreenland (Thomas, 2004). Top-down models controlled by thesurface mass balance are often unable to advance the Laurentide IceSheet below the Great Lakes at the Last Glacial Maximum (LGM),which did happen, without also advancing the Cordilleran Ice Sheetalmost to Mexico, which didn’t happen. This is because ice eleva-tions at the center of the Laurentide Ice Sheet over Hudson Baymust be high enough, from a positive mass balance, to force sheetflow across the Great Lakes. With ice streams occupying the deeptroughs of the Great Lakes, the southern Laurentide margin israpidly advanced by greatly reducing ice-bed coupling whensummer meltwater in the surface ablation zone reaches the bed,probably through crevasses (Zwally et al., 2002). This processwould be greatly accelerated by heavy summer rainfall over thesouthern Laurentide ablation zone (Bromwich et al., 2004).The ablation zone, not the accumulation zone, controls advance ofthe ice margin by controlling ice-bed decoupling. In the ablation,zone, therefore, surface conditions can directly influence basalconditions, with no time lag. Such is not the case in the accumulationzone.

5. The Peltier challenge

The CLIMAP reconstructions of ice sheets at the LGM were usedby climate modelers throughout the decade of the 1980s until 1994,when W. Richard Peltier presented another approach to recon-structing LGM ice sheets in his paper, ‘‘Ice Age Paleotopography’’(Peltier, 1994). He had developed models of global isostasy in whichthe lengths of Earth radii changed as the load of ice and water overEarth’s surface changed during glaciation cycles. His radii had

a viscous response in the mantle and an elastic response in thelithosphere to changing surface loads. This allowed him to deter-mine mantle viscosities and lithosphere flexures which he thenused, in a circular way, to calculate the changing height (calculatedice load) of ice at the end of these radii from the known changingareal extent of ice sheets and changing sea level (measured waterload) during the last deglaciation. Glaciologists weren’t needed. Hepublished his ice elevations on the Internet at precisely the loca-tions climate modelers preferred in their General CirculationModels (GCMs) of Earth’s atmosphere. In my view, Peltier’s chal-lenge has been good for glaciology. Competition is always good, andhis approach compels glaciologists to examine more critically thedefects in their approach to ice-sheet modeling.

The Achilles’ heel in Peltier’s approach was threefold: (1) hismodel depends on the rheology of Earth’s interior, a rheologywhich can never be known as accurately as the rheology of icesheets, (2) only vertical motion in the mantle and lithosphere istreated, and (3) only a slow isostatic response is delivered forchanges in ice sheets when rapid climatic responses to rapidchanges in ice sheets are of most interest. In (1), Peltier treats icesheets as a purely static load on Earth’s surface. As a consequence ofignoring ice-sheet modeling, his ice sheets tend to be too thin toaccount for the known lowered sea level at the LGM and, contraryto the glacial geological record, his ice sheets are more like ice slabsof nearly constant thickness than even the idealized elliptical icesheets permit for constant accumulation rates. In (2), adding thelinear viscous radial extensions in Earth’s mantle to linear elasticflexures in Earth’s lithosphere allows Peltier to use Green functionsto generate spherical harmonics on Earth’s surface that could belinked to known changing sea levels worldwide as the loads of iceand water changed during the last deglaciation. A more robustmodel would allow elastic–viscoplastic lithosphere flexure, allowlateral variations in nonlinear mantle viscosity as surface loadschanged, and allow nonlinear viscoplastic mantle creep to varylaterally and interact with moving lithosphere plates and mantleconvection currents (Koons and Kirby, 2007). In (3), Peltierprovided no mechanisms for controlling ice elevations by speci-fying the strength of ice-bed coupling, coupling that weakensdrastically as basal ice melts and ultimately allows ice sheets todestroy themselves. Rapid changes in the size and shape of icesheets in response to basal decoupling are not possible in Peltier’smodel, so it cannot be used in studying causes of abrupt climatechange. Peltier has modified his old approach to include mecha-nisms for ice-bed decoupling, based on glacial geology (Peltier,2004; Tarasov and Peltier, 2004).

The CLIMAP ice sheets also had an Achilles’ heel. The gravita-tional driving stress for sheet flow in ice sheets is proportional tothe product of ice height above the bed and ice surface slope. Thisdriving stress was equated with the basal shear stress resistinggravitational motion in the CLIMAP ice sheets. Generating theconcave CLIMAP ice streams by letting the basal shear stressdecrease along ice streams also made the gravitational drivingstress decrease, because both ice height above the bed and icesurface slope decrease along a concave ice stream. That was unre-alistic because marine ice streams typically end as floating icetongues which may or may not be imbedded in confined and pin-ned ice shelves. For floating ice, the gravitational driving stress isproportional to ice height above water and it is equated with thelongitudinal tensile stress in an ice tongue (Weertman, 1957b). Thistensile stress is reduced when the ice tongue is imbedded in an iceshelf confined laterally and pinned locally to the bed (Thomas,1973a,b). Therefore, resistance to gravitational motion in an icestream should allow a downstream transition from basal shear tolongitudinal tension, with the tensile stress actually reaching up icestreams and pulling ice out of the ice sheet. Including this stress in

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the longitudinal force balance introduced the ‘‘pulling power’’ of icestreams.

6. The ‘‘pulling power’’ of ice streams

The bed was not only fully thawed under the CLIMAP icestreams, basal water progressively drowned bed topographydownstream. Progressive drowning would produce a ‘‘floatingfraction’’ of ice that increased downstream. In hollows it mighteven produce the ‘‘pseudo ice shelves’’ along West Antarctic icestreams reported by Robin et al. (1970b). When ice was fully afloat,the ice stream would become an ice shelf. Therefore, the concavesurface profiles of ice streams were bottom-up reflections of majorice-bed uncoupling as the floating fraction increased from essen-tially zero under the high convex surface of sheet flow to essentiallyone under the low flat surface of shelf flow. The Achilles’ heel in theCLIMAP ice streams could be ‘‘healed’’ by making the floatingfraction of ice the primary variable in modeling stream flow. Sheetflow alone cannot collapse an ice sheet and terminate a glaciationcycle. Stream flow can because most of the ice, up to 90 percent, ispulled out by ice streams. In his treatment of ice shelves, Weertman(1957b) showed that the tensile gravitational ‘‘pulling’’ stress ina flat ice shelf is determined by the height of ice floating abovewater, not by the product of ice thickness and ice surface slope,which is zero for a flat ice shelf. So as the floating fraction of iceincreases along an ice stream, the gravitational driving stresschanges from being determined by the product of ice thickness andsurface slope (which applies to sheet flow) to being determined bythe height of ice floating above water (which applies to shelf flow).

Gravitational thinning in Weertman’s ice shelf is resisted bya longitudinal tensile stress that is a ‘‘pulling stress’’ on the icestreams that supply an ice shelf. If stream flow is transitionalbetween sheet flow and shelf flow, this pulling stress should extendup ice streams and ‘‘pull’’ ice out of ice sheets. Linking the floatingfraction of ice along an ice stream to the decrease in basal shearstress that resists sheet flow and the increase in longitudinalpulling stress that resists shelf flow quantifies how ice streams pullice out of ice sheets. I called this ‘‘the pulling power of ice streams,’’pulling power being the product of the longitudinal gravitationalpulling force and the longitudinal ice velocity (Hughes, 1992).Bottom-up ice-sheet modeling linked to the pulling power of icestreams has been developed further since then (Hughes, 1998,2003, 2009a,b). It remains a work in progress. The pulling powerconcept is now being applied to ice streams in Greenland andAntarctica that have suddenly increased their ice discharge inrecent years, behavior for which conventional glaciology theoryhad no explanation solely in terms of sheet flow resisted by basaldrag. Those working on this problem all take the pulling power ofshelf-like flow into account, including the acceleration of marineice streams when a buttressing ice shelf disintegrates (e.g., Van derVeen, 1985, 1987; MacAyeal, 1989; Hulbe and MacAyeal, 1999;Hindmarsh and LeMeur, 2001; Marshall et al., 2002; MacAyealet al., 2003; Hulbe et al., 2004; Thomas, 2004; Thomas et al., 2004;Dupont and Alley, 2005a,b; Marshall, 2005; Schoof, 2007; Hofstede,2008).

In my approach to pulling power, as it exists now, ice-beduncoupling produces a floating fraction of ice under ice streamsthat increases from being essentially zero for a frozen bed or smallfor a thawed bed where sheet flow predominates, to unity or closeto unity as stream flow develops, and remains at or close to unitywhen ice streams merge with floating ice tongues or confined andpinned ice shelves, but decreases toward zero when ice streamsend as ice lobes grounded on land and beneath which basal watercan escape (Hughes, 2009a,b). All stresses in the direction of iceflow depend on the floating fraction of ice. These stresses are basal

and side shear and longitudinal tension and compression. Basalshear dominates in slow sheet flow, longitudinal tension dominatesin unconfined shelf flow, but all stresses appear in stream flow andconfined shelf flow. The floating fraction of ice is the part of the iceoverburden that is supported by basal water and for which longi-tudinal gravitational motion is resisted by longitudinal tension inthe ice. The remaining part is supported by the bed, so that longi-tudinal gravitational motion is resisted by basal and side shear andlongitudinal compression, all of which occur along ice streams andin confined or pinned ice shelves.

Physically, the floating fraction of ice can be an ambiguousquantity at the bed. Is it the submerged fraction of rolling bedtopography, supersaturated regions of basal sediments or till, thedrowned fraction of bedrock bumps that are smaller than thecontrolling obstacle size in theories of basal sliding, or all of these?The important point is that the floating fraction is linked to parts ofthe bed that are unable to resist longitudinal gravitational motionby generating basal or side shear or longitudinal compression.

Perhaps the best way to illustrate the floating fraction of ice iswith a cartoon that shows areas of wet thawed or drowned beds inblack and areas of dry frozen beds in white, with flow radiatingfrom both marine and terrestrial ice domes, including verticallongitudinal cross-sections along selected flowline transects thatshow ice trajectories (Fig. 5). In slow sheet flow, the bed is generallywet under a marine ice dome over an embayment and dry undera terrestrial ice dome over a plateau. Ice streams begin near themarine dome but begin far from the terrestrial dome. Ice streamsmoving landward end as ice lobes and ice streams moving seawardend as ice shelves. Between ice streams, a freezing zone surroundsthe marine dome and a melting zone surrounds the terrestrialdome, with these zones consisting of a mosaic of wet and drypatches. Wet patches become elongated lakes or marine channelsin flow directions as ice velocity increases. Dry patches that thawbecome elongated drumlins or roches moutonees as velocityincreases. Eskers form in the braided drainage systems near icemargins and under ice lobes.

7. Modeling a glaciation cycle from the bottom up

Bottom-up ice-sheet modeling allows reconstructing a fullglaciation cycle based on first-order glacial geology (Hughes, 1996).This was presented at a symposium honoring Johannes Weertmanwhen he turned seventy. Since the symposium volume did notreach many glaciologists, the work was presented again in IceSheets (Hughes, 1998), which described the glacial geology on pages239–250 in Chapter 9 and produced the reconstructed ice sheets onpages 307–317 in Chapter 10. In these reconstructions, the basalshear stress balanced gravitational forcing in sheet flow, but instream flow the basal shear stress was gradually replaced by thelongitudinal tensile stress along ice streams as providing primaryresistance to gravitational forcing. Northern Hemisphere ice sheetswere reconstructed for six stages in a generalized Quaternaryglaciation cycle based on the last cycle: (1) the initial advance of icesheets, (2) their extent during interstadials, (3) their advance frominterstadial to stadial positions, (4) their extent during stadials, (5)their retreat from stadial to interstadial positions, and (6) theircollapse during Termination of the glaciation cycle. Ice elevationsabove the bed depend mainly on ice-bed coupling assigned to eachstage.

Pleistocene ice sheets were nucleated at high northern latitudesin both terrestrial and marine environments where permafrost iscontinuous, even on broad Arctic continental shelves (Hughes,1986a). Therefore these ice sheets had a high height-to-area ratioduring their initial advance because a frozen bed maximized ice-bed coupling.

Fig. 5. : The flow regime linked to ice-bed coupling for an idealized ice sheet (Hughes, 1998, Chapter 9). Left: surface ice flowlines (solid lines) and the surface equilibrium line(dashed line) linked to wet bed conditions where ice-bed coupling is weakened in sheet flow (mosaics of black patches) and largely lost in stream flow (solid black areas). Right:flowline transects along the main ice divide (AA), from the main ice saddle (BB), from an ice dome above a marine embayment (CC), and from an ice dome above a highland plateau(DD), showing ice trajectories (solid lines) for beds that are wet (W), dry (D), freezing (F), and melting (M), and regions of debris-charged refrozen basal ice (shaded areas).

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Initial advance was primarily over Precambrian shields studdedwith lakes. These lakes would have been thawed patches under thespreading ice sheet. The largest lakes arc around the edges of theshields and are furthest from centers of ice spreading, so theywould be interconnected pro-glacial lakes during interstadialswhen the advancing ice sheets halted long enough to produce anisostatically depressed trough along their landward margins at theedge of the shields.

Beyond the shields and surrounding the centers of ice spreadingare straits and inter-island channels extending seaward and the arcof large linear lakes extending landward. These linear troughswould have been occupied by ice streams that advanced the ice-sheet margins during transitions from interstadials to stadials.

These transitions are triggered when complete thawing of the bedtakes place under the centers of spreading on the shields. Thawingoccurs because the increasing ice overburden finally crushesbasal ice into water, causing reduced ice-bed coupling (crushing isphysically observed as a reduction in ice volume and meltingtemperature). The resulting partial gravitational collapse shot icestreams into the surrounding troughs during stadials. The exposedshields have ubiquitous erosion features produced by ice sliding overa wholly thawed bed. This proves that thawed patches originallyconfined to the smattering of lakes on the shields expanded overthe entire shield at glacial stadials, causing general ice-sheetlowering and spreading, without a great change in ice mass.

As ice over the shields lowered, colder ice would move towardthe bed and restore the previous pattern of thawed patches ina frozen matrix. That would shut down the ice streams and allowinterior ice to thicken. Rock and rubble eroded from shields andalong the linear troughs when these areas were wholly thawed were

deposited as ice-rafted sediments after icebergs calved from marineice streams, and were deposited as looped moraines at the lobatetermini of terrestrial ice streams. Successive recessional moraineswould form after terrestrial ice streams shut down and their lobesretreated during transitions from stadials to interstadials.

When ice lowered sufficiently, calving bays would migrate upstagnating marine ice streams and eventually carve out marineembayments that were formerly centers of ice spreading. Calvingbays carve out the heart of the accumulation zone of an ice sheet,and forcedforcedtermination of the glaciations cycle. Calving alsodiscerps terrestrial ice margins ending in proglacial lakes.Following deglaciation, sites of greatest isostatic rebound and ofstrongly negative gravity anomalies would identify sites of majordomes at the glacial maximum, as distinct from the last remainingice domes on land after final gravitational collapse of ice saddles inmarine embayments.

These then constitute the first-order features useful in modelinga glaciation cycle: (1) the present distribution of permafrost, (2) thepresent distribution of lakes on Precambrian shields, (3) troughsradiating seaward and landward from these shields, (4) the arealextent of ubiquitous glacial scouring on shields that over timeexposes the shields, (5) lobate recessional moraines at the ends oflandward troughs beyond the shields, and (6) centers of greatestpostglacial isostatic rebound. Each of these six features is associatedwith a particular stage of a glaciation cycle, and they shouldtherefore guide ice-sheet modeling of the cycle from the bottom up.In this modeling activity, ice-bed coupling deduced from thesefeatures is the primary control on ice elevations above the bed.Surface temperatures and accumulation rates, which are largelyunknown, are very much secondary controls on ice elevations. If

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the first-order glacial geology and geomorphology that controlseach stage of the glaciation cycle are converted into correct varia-tions in ice-bed coupling, the resulting elevations of the ice sheetsabove the bed will be correct, regardless of conditions at the icesurface, prior changes in the size and shape of the ice sheets, or thepattern of the geothermal heat flux over the glaciated landscapeunder the ice sheets.

The key to bottom-up modeling of ice sheets is linking glacialgeology and geomorphology to ice-bed coupling that dominateseach stage of the glaciation cycle. In addition to identifying whichfirst-order features of the glaciated landscape control a given stage,second-order glacial features can be ‘‘peeled off’’ the first-orderlandscape in layers that ‘‘stack’’ these features in a time trans-gressive manner from the youngest to the oldest (Boulton et al.,1985; Boulton and Clark, 1990; Hughes, 1998, Figures 9.24, 9.25,and 9.26). Joan Kleman of Stockholm University has taken thisapproach to a new level by developing a time–space topology thatpeers into the past along all flowline transects of former ice sheetsuntil that ‘‘look’’ is blocked by more recent events of glacial erosionor deposition that erase the older features (Fig. 6). These second-order features are often glacial lineations of various kinds that alignin directions of ice flow at the time the lineations were imprintedon the landscape. They show whether the bed was frozen, thawed,or a mosaic of frozen and thawed patches that correlate with basalfreezing and melting zones. By applying time–space topology tovarious parts of the former Scandinavian and Laurentide ice sheets,Kleman has taken the concept of ice-bed coupling under former icesheets at various times in their history to a new level (Kleman,1990, 1992, 1994a,b, 2008; Kleman et al., 1992, 1994, 1997, 2008;Kleman and Borgstrom, 1996; Kleman and Stroeven, 1997; Klemanand Hattestrand, 1999; Kleman and Glasser, 2007; De Angelis andKleman, 2008; Clark and Stokes, 2001; Stokes et al., 2007; Stokeset al., 2009).

With this bottom-up approach, there is no need to know thepast climate history that determines the surface temperatures andaccumulation rates, and partly determines the basal geothermalheat flux, at a given stage in the glaciation cycle. Top-down modelsthat trace their pedigrees to Budd et al. (1971) depend critically onall these conditions. Yet it remains true that the changing size andshape of ice sheets during a full glaciation cycle cannot be modeledwithout using the top-down approach.

8. Combining top-down and bottom-up modeling strategies

Modeling ice sheets needs the top-down approach because thatapproach employs the mass-balance equation that controls how icesheets advance and retreat over time. When snow precipitationaccumulates year by year over highland plateaus or on sea ice, sosurface snow is compressed into ice at depth, the ice eventuallybecomes thick enough to thin and spread under its own weight.Merger of these ice spreading centers can produce an ice sheet withterrestrial and marine portions (Hughes, 1986a, 1998, Figure 1.9).Marine portions formed initially from sea ice are necessary forgrounded ice to occupy marine embayments so terrestrial portionsformed initially in highlands will not end by calving along marineshorelines. Gravitational thinning of ice is more than compensatedby continued surface accumulation of snow, so spreading iceadvances until landward ice margins melt and marine or lacustrineice margins calve as fast or faster than ice moves forward. This is thefirst-order effect of the mass balance. A bottom-up modelingapproach is not useful until an ice sheet is already in place, so ice-bed coupling can be treated as a first-order effect in controlling iceelevations above the bed.

A bottom-up application of the top-down University of MaineIce Sheet Model (UMISM) developed by James Fastook (Fastook,

1987, 1992, 2009) is used by Canadian and Scandinavian glacialgeologists to provide a glaciological explanation for glacial geologythey map that was produced by the Laurentide and Scandinavianice sheets during the last glaciation cycle. Since I am familiar withUMISM, I will use it as an example of the advantages of combiningtop-down and bottom-up modeling approaches. UMISM generatesice sheets in the map plane, using specified surface temperaturesand accumulation or ablation rates as model input, obtained bydirect measurement for present ice sheets and as output frommodels of atmospheric circulation or by other means for past icesheets. In this sense it is a standard top-down model. Temperaturesat depth are calculated vertically from specified surface tempera-tures and accumulation or ablation rates, and are linked to verti-cally averaged horizontal ice velocities by way of the flow law of ice,such that mass and energy are conserved. The temperature field isused to determine if the bed is frozen or thawed and, if thawed, tocalculate basal melting and freezing rates. For a thawed bed, slidingvelocities can be calculated from a variety of sliding laws modifiedto convert the calculated amount of basal water into a water depththat progressively drowns bedrock bumps or supersaturatesdeformable till and sediments. Both processes decouple ice fromthe bed. The combined velocities of basal sliding, a mobilizeddeformable bed, and vertically averaged creep in ice become thehorizontal ice velocity in the mass-balance equation. A positive ornegative mass balance at model gridpoints requires ice to thickenor thin at these sites to sustain mass continuity. Ice thickening orthinning rates over time are obtained from the difference betweenthe surface accumulation or ablation rates of ice (and basal freezingor melting rates) and thickening or thinning rates of ice due toconvergence or divergence of ice flow caused by gravitationalmotion. The rheology of a soft deforming bed is not included inUMISM, but it is generally included in other top-down models(Marshall, 2005). Treatments of deforming beds under WestAntarctic ice streams appear in Volume 77 of the AGU AntarcticResearch Series (Alley and Bindschadler, 2001), which includesa comprehensive study of wet deforming till by Kamb (2001). Alsosee discussion by Hooke (2005, Chapters 7 and 8).

UMISM and other top-down models based on the shallow iceapproximation progressively add velocities obtained from flow andsliding laws to get the cumulative mass-balance velocity and the icethickness profile used in the mass balance for transporting ice inthe direction of the downsloping ice surface, for prescribed rates ofsurface ice accumulation and ablation entered as model input. Asnoted by Van der Veen (1987) and Hofstede (2008), however, theconcave profile of ice streams introduces reduced velocities in theflow and sliding laws which depend on a gravitational drivingstress proportional to the product of ice height above the bed andice surface slope in the shallow ice approximation. For a positivesurface accumulation rate, the mass-balance ice velocity increasesas the driving stress decreases, because both ice thickness and slopedecrease along an ice stream as the surface goes from convex forsheet flow to concave for stream flow. This introduces negativelongitudinal strain rates that reduce ice velocities based on thedriving stress, whereas ice velocities based on the mass balanceincrease continuously for the calculated downslope ice thicknessprofile. Poorly known quantities in the flow and sliding laws,especially in sliding laws, can be ‘‘tuned’’ to force the two velocitiesto match. This problem points to a breakdown in the shallow iceapproximation that may be corrected by gradually replacingresistance by basal drag with resistance by longitudinal tension,both linked to the flotation height of ice through the longitudinalgravitational force (Hughes, 2009a,b). The amount of basal watercalculated in UMISM and a version of the Johnson (2002) model ofsubglacial hydrology are used to move basal water from sources tosinks. The gravitational driving stress, proportional to the product

Fig. 6. Geomorphic systems associated with an ice sheet (Kleman, 1994a,b, Figure 7, reproduced with permission). Top: an ice sheet is sectioned to show velocity profiles for creepover a frozen (dry) bed and sliding over a thawed (wet) bed, flowline trajectories, the surface mass-balance regime, and the basal thermal regime. Dry bed, wet bed, and marginalmeltwater geomorphic systems are shown for one-dimensional symmetry. Bottom: a demonstration of how time–space histories can be deduced by observing geomorphiclandforms along transects such as I–II. The actual history is shown in (a), the line-of-sight along a given transect is shown in (b), what can be seen along all possible lines-of-sight isshown in (c), and what can be seen in sectors A, B, C, and D is shown in (d).

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of ice thickness and surface slope, is balanced only by the local basalshear stress in the shallow ice approximation. Therefore, UMISM isa sheet-flow model even thought the mass balance and subglacialhydrology combine to concentrate ice motion along linear basaldepressions that generate stream flow. To introduce longitudinaltension that allows ice streams to pull ice out of ice sheets, UMISMhas a parameter called a ‘‘Weertman’’ that represents the pullingpower of marine ice streams at their (un)grounding lines, withvalues increasing from zero to unity down an ice stream or asa buttressing ice shelf disintegrates, with unity providing thepulling force for an unconfined ice shelf, following Weertman(1957b). The ‘‘Weertman’’ generates concave ice-stream profiles inUMISM, and thereby aleviates the problem of negative longitudinalstrain rates noted by Van der Veen (1987) and Hofstede (2008). Amore complete treatment of this problem requires solution of thefull momentum/equilibrium equation, as Sargent (2009) has done.Her solution can be imbedded in UMISM for stream flow andconfined or pinned shelf flow.

Glacial geology, often undated, reveals changing directions of iceflow and changing basal thermal conditions before and after theLGM. These data are then used as ‘‘targets’’ that UMISM attempts to‘‘hit’’ by adjusting variables in the model within acceptable limits.These variables are parameters in the flow and sliding laws of ice,conditions at the ice surface (temperatures and rates of ice accu-mulation or ablation), and conditions at the bed (temperatures,water volume and distribution, rates of basal freezing or melting,and the geothermal heat flux). For a Scandinavian application, seeNaslund et al. (2003a,b). For Laurentide applications, see Clarhall(2002) and De Angelis (2007). In this way, the concept of first-orderand second-order glacial geology developed for CLIMAP is used byUMISM to target basal processes and understand the glacial historyof former ice sheets.

MacAyeal (1992) developed the first model for turning WestAntarctic ice streams on and off in an irregular way, as basal tillthaws and loses its cohesion under thickening ice and refreezes toregain cohesion under thinning ice. In top-down models, changesin ice-bed coupling are determined primarily by changing theamount and distribution of basal water that is produced by changesin the surface temperature and mass balance over time, for a givendistribution of the basal geothermal heat flux. Modeling changes inthe size and shape of ice sheets over time must employ a top-downapproach, because bottom-up modeling calculates ice elevationssustained by ice-bed coupling anchored to basal thermal condi-tions. These conditions ultimately depend on surface conditions fora specified pattern of the basal geothermal heat flux. Surfaceconditions change during a glaciation cycle, so the basal thermalconditions will also change, including the geothermal heat flux,which changes as the insulating ice thickness changes over time.For rapid surface lowering of the kind modeled for Termination ofa glaciation cycle, these long-term effects are less important thanrepeating episodes of basal freeze–thaw processes of the MacAyeal(1992) kind or episodes of repeating discharge of impounded basalwater, as proposed by Erlingsson (1994, 2006, 2008) for rapiddrainage of subglacial lakes. Sudden drainage of this kind has beenreported by Stearns et al. (2008) at the head of Byrd Glacier in EastAntarctica, with a rapid increase in ice velocity, probably as dis-charged water causes additional ice-bed uncoupling to propagatedown the ice stream.

Gravity easily thins thick ice after it loses contact with the bed,so a grounded ice sheet 3 km thick under its interior ice domes isonly 300 m thick after it becomes afloat, for the same surface massbalance. This is because, for the same ice thickness, the longitudinaltensile stress for floating ice is ten times larger than the basal shearstress for grounded ice, so reducing ice thickness by a factor of 10equates the two stresses that resist gravitational spreading. Any

reduction of ice thickness for grounded ice results in a rise in globalsea level. To accomplish this surface lowering by way of ice streams,resistance to gravitational spreading has to change from beingdominated by the basal shear stress for sheet flow at the head of icestreams to being dominated by the longitudinal ‘‘pulling’’ stresswhen ice streams become afloat as shelf flow.

9. Modeling basal thermal conditions underpresent ice sheets

Nearly all studies of ice streams have been in West Antarctica,where the bed is largely below sea level (Alley and Bindschadler,2001). These ice streams lie on soft deforming marine sedimentsmobilized into till. Maintaining ice streams of this kind requiresa continual supply of soft sediments if the ice streams remainlargely in place. West Antarctic ice streams are believed to beretreating along submarine troughs from positions near thecontinental shelf edge at the LGM (Fig. 3), with soft marine sedi-ments occupying the troughs (Anderson, 1999). This may havestrongly biased our understanding of ice-stream dynamics. Many ifnot most Antarctic and Greenland ice streams today pass throughfjords as outlet glaciers, and may remain in place in their fjordseven as ice margins advance and retreat. This was also the case formany ice streams draining former ice sheets. For such ice streams,soft marine sediments should have been removed by glacialerosion. Without mechanisms for resupplying sediments, thesewould be rock-floored ice streams. Very little fieldwork has focusedon these ice streams. The study of a former rock-floored stream byStokes and Clark (2003) on the Dubawnt swarm should informfieldwork; also see De Angelis (2007). Our concepts of ice-streamdynamics may need major revisions when these studies are done.

Essential data for studying ice streams in their full complexityinclude gridded seismic sounding of the kind being done for Rut-ford Ice Stream in West Antarctica (Smith and Murray, 2009), andapplications of seismic streamer technology to ice streams. Equallyimportant is deep radar sounding capable of mapping the amountand extent of basal water, and therefore of ice-bed coupling andperhaps even the geothermal heat flux, as has been done alongradar flightlines crisscrossing the northern Greenland Ice Sheet(Oswald and Gogineni, 2008). Jakobshavn Isbrae, KangerdlugssuaqGlacier, and Helheim Glacier are probable rock-floored ice streamsthat occupy Greenland fjords and have doubled their velocities inrecent years (Stearns and Hamilton, 2007; Joughin et al., 2008).These should be mapped by seismic and radar sounding, andmonitored continually by satellite sensors. Deep drilling to the bed,as done for West Antarctic ice streams, is possible (Engelhardt andKamb, 1997, 1998).

Basal thermal regimes can be mapped under present ice sheetsby linking ice elevations to ice-bed coupling. Using this linkage,basal thermal zones (frozen, freezing, melting, and thawed condi-tions at the bed) were mapped under the Antarctic Ice Sheet wheresurface and bed topography were known with sufficient accuracyalong flowbands in sheet flow, taking variable flowband widths andsurface accumulation rates into account (Wilch and Hughes, 2000).Martin Siegert compared places where the bed was determined tobe wholly thawed with the known locations of subglacial lakesdetected by radar, and found a strong match (Siegert, 2001). Thegeothermal heat flux was not needed in this approach.

Johnson (2002) developed a finite-element map-plane model ofsubglacial hydrology, based on a solution of the Manning equation,that he coupled to UMISM to map flow of basal water from sourcesto sinks beneath the Antarctic Ice Sheet for various rates of thegeothermal heat flux. His model generated subglacial lakes thatmatched those detected using radar (Siegert, 2001), and locatedwhere other subglacial lakes would be, with some subsequently

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found. His model also drove subglacial water toward bed channels,resulting in enhanced ice-bed decoupling so stream flow developedin ice above the channels. Pulses in discharge of impoundedsubglacial water generated pulses in stream flow.

Linking ice elevations to ice-bed coupling for stream flow wasused to map the floating fraction of ice beneath Byrd Glacier, one ofthe fastest East Antarctic ice streams with the biggest ice drainagebasin (Reusch and Hughes, 2003). Surface wave-like undulationshaving the appearance of stacked terraces correlated with thefloating fraction of ice along the bed, after correcting for variationsof bed topography. As with sheet flow, surface elevations in streamflow are primarily determined by the degree of ice-bed coupling.The relatively level portions of the wave-like surface of Byrd Glacierwere matched with the greatest floating fraction of ice, therebyquantifying the concept of ‘‘pseudo ice shelves’’ for the levelportions of West Antarctic ice streams proposed by Robin et al.(1970b) and based on radar sounding. This correlation remainedafter a ‘‘bookkeeping’’ error was corrected (Hughes, 2009b).

Hofstede (2008) applied the ice-bed coupling concept to modelrecent lowering of Jakobshavn Isbrae in Greenland, followingdisintegration of a buttressing ice shelf in Jakobshavn Isfjord in2002. He used a flowline version of the flowband model thatpartitions a geometrical representation of the longitudinal gravi-tational driving force among local basal and side shear stresses,longitudinal tensile stresses upstream, and longitudinal compres-sive stresses downstream, all resisting gravitational flow and alllinked to the floating fraction of ice (Hughes, 2009a,b). The flowlinewas along a flightline down the center of Jakobshavn Isbrae thatdelivered surface and bed radar reflections. Side shear stressesvanish along the center of ice streams, so the effects of side andbasal drag were assigned to the basal shear stress. Hofstede’smodel was able to reproduce the known thinning of JakobshavnIsbrae after its ice shelf disintegrated. An increase in the floatingfraction of ice accompanied surface lowering, giving a direct linkbetween a reduction of ice thickness and a reduction of ice-bedcoupling over time.

Aitbala Sargent, a doctoral student advised by James Fastook,has modified the MacAyeal/Morland equations for ice shelves toinclude a basal shear stress to get equations that also apply to icestreams. This amounts to a solution of the full equilibrium/momentum equations that modelers have long sought, since theice-shelf application already includes stresses in the map plane forside shear and for longitudinal and transverse tension andcompression (Sargent, 2009; Sargent and Fastook, 2008). The Sar-gent equations apply to ice streams in a standard top-down ice-sheet model. Resistance to gravitational stream flow is reduced ina bottom-up application that increases the ‘‘Weertman’’ floatingfraction under ice streams and eliminates basal pinning pointsunder ice shelves. This solution is being imbedded in UMISM.

Among innovative ways of thinking, may I include thermalconvection below the density inversion of the Antarctic andGreenland ice sheets as the origin of ice streams (Hughes, 2009c)?A gravitational buoyancy force below the density inversion gener-ates a buoyancy stress that is about one-third the gravitationaldriving stress for advective sheet flow. The buoyancy stress istherefore theoretically large enough to cause thermal convectiveflow in ice below the density inversion. When superimposed onadvective flow, the pattern of convective flow would be aligned inthe direction of advective flow. The most efficient pattern would befor warm basal ice to rise in narrow curtains that would be thelateral shear zones of ice streams, with ice sinking slowly in the icestream between shear zones. That lowers the surface of ice streamsand allows basal water to flow toward ice streams, thereby furtherdecoupling ice from the bed and increasing stream flow. The cyclingconvective flow would spiral downstream at a rate controlled by

the advective ice flow, but it could be measured in principle. If it isfound to occur and to be significant, then thermal convectionshould be included in ice-sheet models.

10. Modeling West Antarctic collapse from the bottom up

The six kinds of first-order features useful in modeling ice sheetsfrom the bottom up to capture stages in past glaciation cycles arealso useful in capturing basal conditions for the Greenland andAntarctic ice sheets at present. The present size of these ice sheetsshould be close to stage 5, when the ice sheets are in recession fromforward positions during the LGM. Whether these ice sheetscontinue recession to stage 6 and a full Termination remains anopen question. The West Antarctic Ice Sheet is the leading candi-date for this event.

In stage 5, interior ice has lowered, bringing cold upper ice intocontact with the bed and partly freezing a ubiquitously thawed bedat state 4 so that isolated thawed patches remain, most promi-nently as subglacial lakes in bedrock hollows. That this conditionnow exists beneath the Greenland Ice Sheet has been demonstratedfrom basal radar data (Oswald and Gogineni, 2008). Subglaciallakes, also located by radar sounding, are widespread beneath theAntarctic Ice Sheet (Siegert et al., 1996). Johnson (2002) developeda model of subglacial hydrology coupled to UMISM that generatednumerous known subglacial Antarctic lakes. Robin Bell, in a lectureat the Center for Remote Sensing of Ice Sheets (CReSIS) at theUniversity of Kansas on 1 November 2006 titled, ‘‘East Antarctica:An Ice Sheet Controlled By Lakes and Mountains,’’ explored theimplications of these bed conditions for ice-sheet stability ifsubglacial lakes can link up and generate ice streams. Stearns et al.(2008) presented evidence from precision ice elevation changesmapped by Earth-orbiting satellites showing that subglacial lakeslinking up under Byrd Glacier right now are causing a substantialincrease in ice velocity.

With these new methods for mapping the amount and extentof basal water, including linked subglacial lakes (‘‘pseudo iceshelves’’), it now becomes possible for top-down models to usebasal water as bottom-up input and calculate the geothermal heatflux as output, as Koons and Kirby (2007) have done for tectonicsystems. Then sites of high geothermal heating can be used assources for basal water in bottom-up modeling of subglacialinstabilities which, coupled to models of subglacial hydrology,allow basal water to ‘‘carry’’ the overlying ice at accelerating rates.Transport of basal water from geothermal sources to sinks at ice-shelf grounding lines should generate stream flow in overlyingice. Ice streams, therefore, become the primary vehicles fortransporting subglacial water from sources to sinks, sinks beingboth marine ice tongues, possibly imbedded in ice shelves, andterrestrial ice lobes from which basal water drains away. Thisdemonstrates that ice streams must be modeled correctly.

The best natural laboratory for modeling the interactionbetween top-down and bottom-up process is the West Antarctic IceSheet, which is in an advanced stage of gravitational collapse, and isunderlain by a Cenozoic volcanic province in its central subglacialhighlands. A probable high geothermal heat flux in the highlandswould provide the source of subglacial water that enters icestreams moving toward sinks for that water (Blankenship et al.,2001). Long fast concave ice streams drain West Antarctic ice onthree sides, east, west, and north (Fig. 7). Again, modeling icestreams and subglacial hydrology correctly becomes paramount.Both require modeling basal processes correctly. Data input fromthe bed is as important as data input from the surface.

The West Antarctic Ice Sheet was one-third of the Antarctic IceSheet at the LGM (Fig. 1), but after Holocene gravitational collapseof its Ross Sea and Weddell Sea sectors, it is only one-tenth of the

Fig. 7. : The Antarctic Ice Sheet today. Broken lines show ice drainage divides for Pine Island Glacier (P) and Thwaites Glacier (T) draining West Antarctic ice into Pine Island Bay,Foundation Ice Stream (F) and Mercer Ice Stream (M) draining East Antarctic ice through the Bottleneck into Ronne–Filchner and Ross ice shelves, Byrd Glacier (B) draining EastAntarctic ice into Ross Ice Shelf, and Lambert Glacier (L) draining East Antarctic ice into Amery Ice Shelf. Heavy dashed lines show projected retreat routes of Pine Island andThwaites glaciers through the Bottleneck into East Antarctica as they downdraw and collapse the West Antarctic Ice Sheet.

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Antarctic Ice Sheet today (Fig. 7). During collapse, ice poured intoboth the Ross Sea and Weddell Sea sectors from three sides, south,east, and west, and left from the remaining side, north. Today, EastAntarctic ice enters only through the Bottleneck and ice leaves WestAntarctica on its north, east, and west flanks. It has gone fromgaining ice on three sides and losing ice on one side to gaining iceon one side and losing ice on three sides. This has to be an unstablesituation, and today the West Antarctic Ice Sheet is in an advancedstage of gravitational collapse. Ice leaving on the east and west sidesis buttressed by the respective Ronne–Filchner and Ross ice shelves,but ice leaving on the north side enters the ice-free Pine Island Baypolynya in the Amundsen Sea, which provides no buttressing. Forthis reason Pine Island Bay may be ‘‘the weak underbelly of theWest Antarctic Ice Sheet’’ (Hughes, 1981b).

How much of the remaining West Antarctic Ice Sheet willcollapse and how soon? How high and how fast will global sealevel rise? How much East Antarctic ice will pour through theBottleneck as West Antarctic ice lowers? The Bottleneck (60 W–135 W at 84 S) is the junction connecting the grounded east andwest components of the Antarctic Ice Sheet (Fig. 7). Thiel Moun-tains in the middle of the Bottleneck diverts most East Antarctic iceinto Ronne–Filchner Ice Shelf by way of Foundation Ice Stream onthe east and into Ross Ice Shelf by way of Mercer Ice Stream on thewest. Little East Antarctic ice now enters West Antarctica, so theWest Antarctic Ice Sheet can be considered as losing ice on threesides and gaining ice only from the top. The rise in sea level will be3–5 m if the ice sheet collapses to sea level, depending on whetherbuttressing ice shelves disintegrate (Fig. 1). This is not the worst-case scenario.

If the West Antarctic Ice Sheet collapses into Pine Island Bay, asanticipated, two giant ice streams, Pine Island Glacier and Thwaites

Glacier, will retreat and may eventually reach the two entrances tothe Bottleneck on the east and west sides of Thiel Mountains(Fig. 7). Then they may merge with Foundation and Mercer icestreams and continue to migrate into East Antarctica and dischargean unknown amount of East Antarctic ice (Fig. 8). In the worst-casescenario, they could throw the entire East Antarctic Ice Sheet intoa negative mass balance that may put it on the road to total grav-itational collapse and a 65 m rise in sea level. That answers the‘‘how high’’ question.

An answer to the ‘‘how fast’’ question depends on what happensto the ice shelves that buttress the West Antarctic Ice Sheet as itcontinues to collapse. Holocene collapse began about 7000 BP(Anderson and Shipp, 2001), apparently continues today, andproduced the huge Ross and Ronne–Filchner ice shelves thatbuttress most of the remaining grounded one-third of the ice sheet.If Pine Island Bay remains an ice-free polynya as it opens to thesouth, following downdrawn retreat of Pine Island and Thwaitesglaciers, these ice streams should continue to move at their presentvelocities of several kilometers per year, and may even speed up asthey merge with Foundation and Mercer ice streams, pass throughthe Bottleneck, and tap into much higher East Antarctic ice. As theypull out East Antarctic ice, discharge of East Antarctic ice by otherice streams supplying Ronne–Filchner and Ross ice shelves shoulddiminish and may even stop, if these ice streams through theTransantarctic Mountains have high fjord-like headwalls, as doesByrd Glacier, the largest ice stream (Hughes, 1998, Figure 3.20). Inthat case, the Ronne–Filchner and Ross ice shelves will be deprivedof ice input from these ice streams and the resulting negative massbalance may lead to catastrophic ice-shelf disintegration. The icestreams that remain active will then be unbuttressed and can pullout even more East Antarctic ice.

Fig. 8. : Possible partial gravitational collapse of the East Antarctic Ice Sheet. Present ice elevations are contoured every 0.5 km. Broken contour lines show possible ice elevationsbefore partial gravitational collapse of East Antarctic ice into Amery Ice Shelf, and after partial gravitational collapse of East Antarctic ice through the Bottleneck into an ice-free WestAntarctica. Heavy black lines enclose possible collapsed portions of the East Antarctic Ice Sheet. Collapse obtained using Equation 11.34 in Hughes (2009b).

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Far fetched? Look at Byrd Glacier, the largest of these ice streamsthrough the Transantarctic Mountains (Fig. 7). It has a hugedrainage basin, as large as the West Antarctic Ice Sheet, drawing icefrom the three highest interior ice domes of East Antarctica. Glaciererratics and scoured bedrock that can be dated using cosmogenicnuclides are found all along its fjord through the mountains atelevations 1000 m above Byrd Glacier. So Byrd Glacier has thinnedand lowered by at least 1000 m, and that is why it has acquired sucha vast ice drainage basin. Yet it is still buttressed by Ross Ice Shelf.The ‘‘how fast’’ question is answered by removing buttressing iceshelves. Calving bays accomplish this task most rapidly (Thomas,1977; Hughes, 2002; MacAyeal et al., 2003; Hulbe et al., 2004).

11. Calving bays

Lambert Glacier lies across the East Antarctic ice divide oppositethe Bottleneck (Fig. 7). Lambert Glacier discharges into Amery IceShelf, which has a drainage basin even larger and much lower thanthe drainage basin of Byrd Glacier. Ice may have lowered 3000 mwhere Lambert Glacier enters Amery Ice Shelf (Fig. 8). If we treatAmery Ice Shelf as a giant ice stream that has lost contact with itsbed, retaining partial basal contact only along Lambert Glacier andother tributary ice streams, then it enters an ice-free polynya in theIndian Ocean. Like Pine Island and Thwaites glaciers, and unlikeByrd Glacier, it is then unbuttressed and can pull out much more iceas a result. That would explain why it has such a broad and low icedrainage basin, and that is what could happen across the EastAntarctic ice divide if Pine Island and Thwaites glaciers passed,unbuttressed, through the Bottleneck and into East Antarctica.

When ice downdrawn by ice streams become afloat, water-filledbottom crevasses can extend upward close to sea level and air-filledtop crevasses can extend downward close to sea level. Floating ice

calves when they meet (Kenneally and Hughes, 2006). This is thecase in an arid polar environment and it is an essentially bottom-upprocess because bottom crevasses fracture up to 90 percent of theice thickness. If surface melting is extensive, water-filled topcrevasses can propagate through the whole ice thickness. JohannesWeertman was first to treat both cases (Weertman, 1973, 1980).These and other processes are active in calving bays (Thomas, 1977;Hughes, 2002; MacAyeal et al., 2003).

Jakobshavn Isbrae drains about seven percent of the GreenlandIce Sheet, has long been the fastest known ice stream, and becomesafloat in Jakobshavn Isfjord. A calving bay has migrated some 30 kmup the fjord since 1850 AD, the end of the Little Ice Age (Weidickand Bennike, 2007). Several seasons of observations suggesteda series of positive feedback mechanisms called the JakobshavnEffect (Hughes, 1986b). The ‘‘pulling power’’ of an ice stream inextending flow produces ubiquitous surface crevasses whichabsorb much more solar energy than does smooth surface ice,thereby enhancing surface melting so surface meltwater can reachthe bed by way of the ubiquitous crevasses, accelerate basal slidingand, once ice becomes afloat, accelerate the calving rate. Theseprocesses have accelerated in recent years. The calving bay hascarved away the ice shelf and the unbuttressed ice stream ismoving nearly twice as fast (Thomas, 2004; Joughin et al., 2008).

Jay Zwally and five colleagues first observed the connectionbetween increased midday summer melting and increased icevelocity on the smooth ice surface just north of Jakobshavn Isbrae(Zwally et al., 2002). This is now called the Zwally Effect and itshould accelerate most Greenland ice streams. It may have causedrapid advance of the southern margin of the Laurentide Ice Sheet atthe LGM, where a climate simulation generated heavy summerrainfall (Bromwich et al., 2004). The Zwally Effect is unlikely in thecold Antarctic environment, but other positive feedbacks in the

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Jakobshavn Effect should be active if a calving bay follows PineIsland and Thwaites glaciers into the Bottleneck. As East Antarcticaice pouring through the Bottleneck lowers, the calving bay maymigrate up Pine Island and Thwaites glaciers and begin to carve outthe heart of the East Antarctic Ice Sheet. The heart of the LaurentideIce Sheet was carved out 8000 years ago when a calving baymigrated up a giant ice stream in Hudson Strait and entered Hud-son Bay (Hughes et al., 1977; Denton and Hughes, 1981, Figure 8.8).With most of its accumulation zone gone, the Laurentide Ice Sheetcollapsed in 200 years, leaving three isolated ice caps on land abovesea level.

All aspects of the above scenario take place with no change insurface temperatures and accumulation or ablation rates exceptthose associated with the lowering ice surface. Therefore, thescenario is controlled by conditions at the base of ice and bottom-up modeling is required to capture the ice-sheet response tochanging these conditions. For the floating ice shelves, changingbasal conditions by enhanced basal melting frees basal ice frompinning points that enable the ice shelves to buttress ice streamssupplying them with ice. Enhanced basal melting is now wide-spread under Antarctic ice shelves (Jacobs et al., 1996; Rignot andJacobs, 2002).

Calving bays can remove the pinning points by removing the iceshelves, which is what triggered the doubled discharge fromJakobshavn Isbrae in Greenland after its ice shelf disintegrated in2002. This was first demonstrated by NASA glaciologist, RobertThomas (Thomas, 2004). Hofstede (2008) used a bottom-upapproach to model the same observations.

As basal melting allows ice streams to pull more Antarctic iceinto the sea, the resulting rise in sea level can also float Antarctic iceshelves free from their basal pinning points. Basal conditions thatwould allow ice streams to discharge more ice center aroundexpanding the supply of water under the ice streams. This wouldallow the ice streams to both widen and lengthen. Even withoutexpanding the water supply, glacial erosion of a till or sedimentblanket, and then of bedrock pinning points that project up intobasal ice, will free overlying ice to slide more swiftly over whateverbasal water is available.

If an ice stream joins an ice shelf at a bedrock sill, retreat of theice-shelf grounding line over the sill increases the ice thickness, andtherefore the height of ice floating above sea level. The ‘‘pulling’’force of the ice shelf on the ice stream increases as the square of thisheight, so more ice is pulled out and the grounding line may retreateven faster if the bed continues to deepen (Fig. 1). This retreat oversills can be caused by a surging ice stream that thins ice upstream,by lowering of the sill due to delayed isostatic sinking and glacialerosion, by rising sea level, and by melting basal ice, all with nochange in surface conditions unrelated to surface lowering (Fig. 2).

These are the processes that give ice sheets a measure of inde-pendence from other components of Earth’s climate system, yetallow ice sheets to control the system by discharging enormousamounts of ice into the ocean in a short time. It takes eighty degreesof sensible heat in ocean surface water to supply latent heat neededto melt one gram of an iceberg, and these icebergs can be tens tothousands of cubic kilometers in volume, weighing billions ofmetric tons. If they are discharged by the hundreds to thousands ina few centuries, they may trigger sustained global cooling over thattime (Hughes, 2004). The heat needed to bring these icebergs up tothe melting point, and then melt them, is supplied primarily byocean surface water to the depth of the draft of the icebergs. Thisheat is then unavailable to sustain the ocean-to-atmosphere heatexchange that drives global climate. Rapid disintegration of iceshelves (MacAyeal et al., 2003; Hulbe, et al., 2004) and calving ofgiant icebergs (Kenneally and Hughes, 2006) should becomea major focus of glaciological research. Ice shelves may also be

discerped by large oceans swells that are known to pass underAntarctic ice shelves (MacAyeal et al., 2006). These mechanismsallow ice sheets to trigger rapid changes in the ocean and atmo-sphere. The West Antarctic Ice Sheet is where all these interactingtop-down and bottom-up processes can be studied and thenmodeled to simulate its ongoing gravitational collapse.

12. Discussion

This review is based primarily on my own experiences inglaciology in a career now spanning four decades. It began at TheOhio State University in 1968. I had no knowledge of glaciology.Paterson (1969), in his first edition of The Physics of Glaciers,provided my initial education. In 1970 the American GeographicalSociety published its map, Antarctica, which changed my perspec-tive forever. The first-order concave profile of the West Antarctic IceSheet, in sharp contrast to the overall convex profiles of the EastAntarctic Ice Sheet and the Greenland Ice Sheet, led me to suspectthat it was in an advanced stage of gravitational collapse. If so, wascollapse ongoing? The Fletcher (1972) memorandum provided theanchor for answering that question. I composed and circulated fourISCAP bulletins designed to address the question, using a quantumjump in data from Antarctic meteorology, geophysics, glaciology,glacial geology, and marine geology, dating from the InternationalGeophysical Year in 1958.

My bulletins led to my move to the University of Maine in 1974,where I was given the task of reconstructing global ice sheets at theLGM and to model total gravitational collapse of the West AntarcticIce Sheet at the LIM as part of CLIMAP during the 1970–1980International Decade of Ocean Exploration (Denton and Hughes,1981). To accomplish that task, I had to develop a way to recon-struct ice sheets from the bottom up, based on ice-bed couplingdeduced from glacial geology at the LGM, rather than employ a top-down model that depended on unknown surface conditions.Simulating total collapse of the West Antarctic Ice Sheet at the LIMbrought James Fastook into glaciology, and began a collaborationthat continues to this day. Fastook developed his University ofMaine Ice Sheet Model (UMISM), which combines the essentials oftop-down and bottom-up modeling.

Peltier (1994) inspired me to more forcefully re-direct mythinking from the CLIMAP view that ice sheets at the LGM and theLIM defined boundary conditions bracketing maximum perturba-tions of a fundamentally stable global climate. After CLIMAP, Ibegan to view ice sheets as fundamentally unstable and able tocontrol climate change, especially rapid climate change, throughthe instabilities inherent in ice sheets. I found these instabilities asresiding primarily in the periphery of ice sheets, allowing the ice-sheet interiors to remain relatively stable until the instabilitieswere able to penetrate the core regions and Terminate a glaciationcycle, thereby warming global climate. This led me to assignparticular features of first-order glacial geology and relatedgeomorphic features on a deglaciated landscape to specific stagesof a glaciation cycle, not just to the LGM (Hughes, 1996, 1998). Thenice-bed decoupling under the central core lowered the interior icesurface and shot out ice streams at the LGM without a large changein ice volume, whereas in the CLIMAP ice sheets, an increase in icevolume caused the ice sheets to advance to the LGM ice margins.

I now believe the CLIMAP simulation of gravitational collapse ofthe West Antarctic Ice Sheet, in order to account for sea level 6 mhigher at the LIM, should have been allowed to propagate throughthe Bottleneck into the East Antarctic Ice Sheet. This propagationcan also take place during the present interglacial, with anunknown increase in sea level. Rapid collapse of sectors of theGreenland and Antarctic ice sheets is the focus of my contribution toCReSIS. This is a new problem to solve that will draw on insights

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gained from both top-down and bottom-up modeling strategies.Future models should include the dynamics of calving bays tocomplete the destruction of ice sheets, as was the case for theLaurentide Ice Sheet and may become possible for the East AntarcticIce Sheet with prolonged climate warming. A central part of thisstrategy should be coupling the isostatic response to rapid loweringof ice sheets to a holistic model that treats the lithosphere andmantle as one coupled system in which both lateral and verticaldeformation interact with thermal convective flow driving platetectonics and with the dynamics of Earth’s oceans, atmosphere, andecology. The rheology should include nonlinear flow laws linkingstrain rates to driving stresses, so that the effective viscosity canchange by orders of magnitude laterally, not just vertically. Theresulting synthesis will be truly holistic for all dynamic process inthe Fletcher (1972) research strategy.

Acknowledgements

Extended discussions with James Fastook, Robert Thomas, andKees van der Veen demonstrated the need for this review. BeverlyHughes processed the manuscript. Johan Kleman provided a veryuseful review. Support was provided by NSF and NASA through theCenter for Remote Sensing of Ice Sheets (CReSIS), University ofKansas.

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