Peregrinations of the Greenland Ice Sheet divide in the last glacial cycle: implications for central Greenland ice cores

Peregrinations of the Greenland Ice Sheet divide in the lastglacial cycle: implications for central Greenland ice cores

Shawn J. Marshall a;*, Kurt M. Cu¡ey b

a Department of Geography, University of Calgary, 2500 University Dr NW, Calgary, Alta., Canada T2N 1N4b Department of Geography, University of California, 501 McCone Hall, Berkeley, CA 94720, USA

Received 12 October 1999; accepted 24 March 2000

Abstract

The superb quality of the climate chronology archived in the Summit, Greenland ice cores (GRIP, GISP2) testifiesthat the Greenland Ice Sheet divide has been generally stable through the last glacial cycle. The ice sheet has experienceda broad range of paleoclimate conditions, ice sheet margin configurations, and internal dynamical adjustments inglacialînterglacial transitions, however. It is unlikely that the Summit region escaped shifts in ice divide position,geometry, elevation, and flow characteristics. Details of this dynamical history are important to several aspects of icecore studies. The magnitudes of pure and simple shearing, reconstruction of vertical ice velocity, the explicit location ofthe ice divide, and the divide `residence time' at different locations are all of interest in interpretation of climaticvariables and physical properties of ice in the ice cores. We apply a three-dimensional, thermomechanical ice sheetmodel to examine the evolution of these dynamical variables over the last 160 kyr in central Greenland. While a high-elevation ice dome is present in the Summit region throughout the simulation, ice divide migrations of up to 150 km arepredicted. All points in the vicinity of the Summit ice cores, including the modern divide, have been subject to flowlineshifts and variable, non-zero shear deformation during the adjustment from glacial to Holocene conditions, from ca. 10ka to the present. Modelled divide peregrinations and strain rate history are consistent with the observed disturbance ofdeep ice in the GRIP and GISP2 ice cores, which has muddled paleoclimate reconstructions for the last interglacial(Eemian) period in Greenland. Dynamical excursions are also evident north of the modern summit, where the NGRIPice core is currently being drilled [Dahl-Jensen et al., J. Glaciol. 43 (1997) 300^306]. However, the prevailing flowdirection and deformation regime at the NGRIP site are much more stable than those at GRIP and GISP2 in thesimulations. Combined with the greater depth of ice at this site, this lends cautious optimism to the hope that Eemianice at NGRIP may contain an intact record of Eemian climate. ß 2000 Elsevier Science B.V. All rights reserved.

Keywords: Greenland ice sheet; ice movement; paleoclimatology; Summit Greenland; GISP2; GRIP

1. Introduction

The GRIP and GISP2 deep ice cores from

Summit, Greenland provide a remarkably detailedperspective on the past 100 kyr of climate history[2^4]. Unfortunately, climate interpretations areuncertain beyond this age in the Summit ice cores,due to disruption of the deep ice stratigraphy.In particular, inferences about climate of the last(Eemian) interglacial period, ca. 135^110 ka, have

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* Corresponding author. Tel. : +1-403-220-4884;E-mail: [email protected]

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proven controversial [5,6]. In search of an undis-turbed, detailed record of Eemian climate, theUniversity of Copenhagen group has initiatedthe North Greenland Ice Core Project (NGRIP),and a new deep ice core is currently being drilledon a ridge 316 km NNW of the GRIP (Summit)drill site [1]. Calculations in [1] suggest thatEemian ice will be higher above the bed at theNGRIP site, which might lower the likelihoodof dynamically induced stratigraphic disruption.

This paper concerns the large-scale (regional)ice dynamical context for these important sites.We use a three-dimensional thermomechanicalice sheet model [7] to construct a history of ice£ow and surface topography in the Summit re-gion. Modelling illuminates the potential patternand range of climatically and dynamically induceddivide migrations through the last glacial cycle inGreenland. It also provides quantitative estimatesof strain rate history and £owline variability atthe ice core sites. This history cannot be viewedas literally true due to uncertainties in the model(particularly in forcings such as the spatial distri-bution of accumulation rate), but is nonetheless apowerful guide for understanding the Summit andNGRIP sites.

Ice surface topography is particularly impor-tant near an ice core site because there are twodistinct deformation regimes associated with anice divide [8,9]. Beneath the summit1 is a divide-£ow regime, characterized by dominance of pureshear and a vertical velocity that decreases rapidlywith depth. Away from the summit is the £ank-£ow regime, with dominantly simple shear and avertical velocity that decreases less rapidly withdepth. Ice stratigraphy and strain history di¡ersigni¢cantly in ice underlying divide- and £ank-£ow regimes. The evolution of Summit regiontopography is therefore relevant to several impor-tant components of the Greenland ice core stud-ies. These include:

1. Understanding the spatial pattern of isochrons,as inferred from radar surveys. Upward warp-ing of isochrons will occur beneath a stable icedivide (the `Raymond bump') [8,10]. No suchbump is seen under the modern Greenlandsummit [11,12]. The lack of a Raymondbump could result from migration of the sum-mit, from enhanced accumulation at the sum-mit, or from linear-viscous behavior of ice atthe low stresses beneath the divide. Further,improved understanding of isochron evolutionis permitting new inferences about the dynamichistory of ice sheets (e.g. [13]). These methodswill be applied to central Greenland, and thecomparison to model-based estimates will bevaluable.

2. Inferring some important climate parameters,temperature and accumulation rate historiesin particular. The vertical velocity pattern isimportant for these studies. If, for example,the GRIP site which now has divide £owused to have £ank £ow, the change in verticalvelocity structure when the transition occurredshould be considered in these analyses.

3. Understanding stratigraphic disruption. Thedisturbed deep ice in the Summit cores appearsto have been subject to large-scale folding[14,15], but the underlying mechanisms are un-certain. One possibility is that a signi¢cantchange in regional ice £ow direction deformedand overturned pre-existing stratigraphic hori-zons [16]. Another possibility is that a rapidchange in divide position overturned a Ray-mond bump previously developed under a¢xed summit (H.P. Jacobsen, unpublished cal-culations, University of Washington). A thirdpossibility is that very localized variations ofviscosity cause warping of isochrons, whichare then overturned if the simple shear rate ishigh relative to longitudinal stretching rate[14,15,17]. For investigating this latter case, itis important to know whether major increasesin shear strain rate are likely to have occurredalong £ow paths leading to the ice core sites.

4. Understanding the NGRIP site. The NGRIPdrill site is located on a gentle ridge, in a topo-graphic setting which is likely to have mini-mized £ow excursions [1]. It is therefore a

1 We use the terms `divide' and `summit' interchangeably, inreference to the time-varying maximum-elevation point in theice sheet. When capitalized, `Summit' refers to the ¢xed geo-graphical location of the GRIP and GISP2 ice cores, thepresent-day summit region in Greenland.

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promising place for a deep ice core, but it ismore than 300 km from the modern ice divide.Changes in ice sheet dynamics and geometrycould have a substantial impact on NGRIP'ssource ice and the deformational environmentat the NGRIP location.

With these four motivations in mind, we use themodel calculations to answer several speci¢c ques-tions. For how long has the ice sheet summit beenmaintained at its present position? If the summithas migrated, what path did it likely follow? Havethere been substantial changes in £ow direction atthe ice core sites? Has the magnitude of sheardeformation been substantially greater in thepast? Is the NGRIP site vulnerable to major icedynamic changes? Anandakrishnan et al. [9]raised some of these questions, and demonstratedthat the ice divide position in Greenland is sensi-tive to whole ice sheet dynamics. Our investiga-tion should be considered a three-dimensional,time-dependent extension of the steady-state £ow-line calculations in [9]. It is useful to address thesequestions in a three-dimensional model becausethe integrated strain history and the details of£owline evolution require knowledge of the ex-plicit spatial evolution of the Summit region.

Numerous three-dimensional model studieshave examined the last glacial cycle in Greenland(e.g. [18^23]), addressing questions of large-scaleice sheet evolution. These investigations indicatethat there has been signi¢cant variability inGreenland ice volume and geometry over thepast 160 kyr. Divide migration is observed inthese simulations, and is discussed in [23], butlittle attention has been given to the history ofshear £ow at depth, switches between divide-and £ank-£ow regimes, or the integrated dynam-ical history. Our ice sheet model is similar tothose applied in [18^23], but we quantify and an-alyze patterns of divide migration and strain ratehistory with a focus on implications for the Sum-mit and NGRIP ice cores.

The paleoclimate history that we use as a modelforcing also represents an important departurefrom previous studies. Past air temperatures, TA,in [18^23] are based on time series of proxy cli-mate indicators in Greenland, in particular ice

core N18O records. Recent modelling studies [20^23] assign paleotemperature perturbations atSummit using a TA(N18O) transfer function de-rived from the modern spatial distribution of airtemperature and N18O in Greenland. Importantnew insights from the Summit ice cores suggestthat this transfer function is inappropriate for as-sessment of paleotemperature at the Summit sites.Inversion of borehole temperature history in boththe GRIP and GISP2 boreholes gives solid evi-dence for a last glacial maximum climate at Sum-mit that is roughly 20³C colder than the Holocene[24^27]. This dramatically modi¢es prior estimatesof 10³C that are predicted from traditional iso-tope^temperature calibrations. We adopt the re-vised TA(N18O) relationship of Cu¡ey and Clow[27] in all model experiments. Recent results fromSeveringhaus and co-workers provide strong sup-port for this revised isotope^temperature ther-mometry [28,29].

2. Model description

We apply ¢nite di¡erence discretizations on aregular Cartesian grid with 20 km resolution. De-¢ne horizontal co-ordinates (x, y), with x positiveeastwards and y positive northwards. Consider icesurface topography, hs, ice thickness H, and bedtopography, hb, such that hs(x,y,t) = hb(x,y,t)+H(x,y,t). Present-day bed and ice topographyare compiled at 20 km [18,30] and were madeavailable through the Greenland model intercom-parison study of the European Ice Sheet Model-ling Initiative (EISMINT) (personal communica-tion, C. Ritz, 1998; [22]).

2.1. Ice sheet model

We use a time-dependent, three-dimensionalthermomechanical ice sheet model [7], designedafter Huybrechts [30,31]. Assuming a constantice density bI, the local mass balance is :

D hs

D t� DDxj�vjH� � _b �1�

where vj is the vertically averaged horizontal ve-

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locity ¢eld and bç is the mass balance rate (ice-equivalent accumulation minus ablation). Astandard Glen's £ow law formulation relatesstrain rates to stress ¢elds in the ice [32,33], withsoftening of the e¡ective ice viscosity (`£ow en-hancement') used here as in previous modellingstudies to crudely account for the rheologic e¡ectsof impurities and fabrics in the ice sheet. We donot prescribe basal sliding in the numerical experi-ments described in this paper.

The temperature ¢eld solution T(x,y,z,t) is de-rived from the balance of internal energy and in-cludes advection, di¡usion, and strain heating dueto the internal deformation of ice. De¢ne ice ther-mal conductivity k(T), speci¢c heat capacityc(T), and thermal di¡usivity U(T). Using the in-compressibility condition, Dkvk = 0, the local en-ergy balance is:

DTD t� 3vk

DTDxk� U �T�D

2TD z2�

1b Ic�T�

D kDT

DTD z

� �2

� x d�T�b Ic�T� �2�

where xd describes strain heating due to the in-ternal deformation of ice:

x d�T� � 2B�T� �b Ig ND jhsN�hs3z��n�1� �3�

Bed isostatic adjustment is modelled through alocal, damped return to isostatic equilibrium[34,35] :

D hb

D t� 3

hb3hb0

d� b Ihs � bWN HW

bBd

� ��4�

where bW and bB are water and bedrock densities,respectively. The latter term in NHW accounts forchanges in water layer thickness associated withsea level £uctuations and water loading of de-pressed crust during early stages of ice sheet re-treat. We use a relaxation time scale (e-foldingtime) of d= 3000 yr.

Greenland ice dynamics have been well studiedby the distinguished modelling groups in Brusselsand Grenoble [18^22,30,36,37]. Similar modelshave been developed and applied to Greenland

by other groups, examining general questionsabout large-scale ice sheet evolution [22,23,38].Aside from the paleoclimatic forcing and ourline of inquiry, our simulations are similar tothose in previous Greenland modelling studies.The values of physical and model parameterswere adopted from the EISMINT intercompari-son study [22], and are summarized in Table 1.Ice dynamics and thermal evolution are solvedasynchronously, with model time steps of 2^4 yrfor the implicit dynamical solution, and 10^20 yrfor thermodynamic updates. Model experimentspresented in this paper run from 160 ka to thepresent, and we use the ¢t to observed present-day ice volume and area as a criterion to guide usin all model experiments.

2.2. Ice sheet mass balance

We calculate mass balance, bç , using the annual

Table 1Physical and model parameters

Parameter Value De¢nition

a 0.0693 ³C31 exponential factor,accumulation^temperaturelapse rate

B0c 5.7U1035 Pa33

yr31Glen £ow law constant,T6310³C

B0w 2.735U1011 Pa33

yr31Glen £ow law constant,Ts310³C

E 5 £ow enhancement factorg 9.81 m s32 gravitational accelerationn 3 Glen £ow law exponentnx 83 longitudinal grid dimensionny 141 latitudinal grid dimensionnz 20 vertical grid dimensionQc 60 000 J mol31 creep activation energy of

ice below 310³CQw 139 000 J mol31 creep activation energy of

ice above 310³CQG 0.053 W m32 geothermal heat £uxR 8.314 J mol31 K31 ideal gas law constantLN 0.0065 ppt m31 elevationîsotope lapse rateL 30.0075³C m31 atmospheric temperature

lapse ratevx =vy 20 km horizontal grid resolutionvt 2^4 yr dynamic time stepvtTD 10^20 yr thermodynamic time stepbB 3300 kg m33 average crustal densitybW 1028 kg m33 density of waterbI 910 kg m33 density of ice

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degree-day method [39,18,30]. Given summer tem-peratures, mean annual air temperatures, and pre-cipitation rates over the ice sheet, this methodestimates surface melt and the fraction of precip-itation to fall as snow. Paleoclimatic conditionsare speci¢ed based on perturbations to modernclimatology, with present-day precipitation ratesderived from Ohmura and Reeh [40]. Mean annu-al and summer temperatures over Greenland havebeen compiled by Ohmura [41] and parameterizedfor modelling studies by Huybrechts et al. [30].These formulations and datasets are the ones em-ployed in the EISMINT Greenland model inter-comparison study [22]. We add a subgrid meltparameterization that accounts for the range ofelevations in a cell [42]. This scheme improvesthe ¢t to present-day Greenland ice volume andarea at the end of the glacial cycle integration.Di¡erences in ice volume from tests with thestandard cell-centered degree day melt calculationare typically a few percent.

Basal melting and iceberg calving on marinemargins are included in the mass balance calcula-tion. We compute calving as a function of waterdepth, ice thickness, and ice sti¡ness (tempera-ture), as described in [35], although calving for-mulations have little impact on model studies inGreenland.

2.3. Paleoclimatology

We estimate paleotemperature history at theGreenland ice divide based on the GISP2 bore-hole temperature record for the past 98 kyr [27].Prior to 98 ka, isotope^temperature thermometryis required to estimate air temperature at the di-vide. We apply the transfer function of Cu¡eyand Clow [27], using an isotopic record describedbelow. Borehole temperatures and isotopic valuesinclude a climatic signal and a contribution fromelevation changes at the divide, via isotopic andatmospheric temperature lapse rates [43]. We as-sume that the Summit ice cores archive atmos-pheric conditions at the roving (dynamical) dividelocation, rather than their spatially ¢xed present-day sites. We therefore track the location andaltitude of the migrating divide in the model, in

order to correct for these elevation e¡ects andextract the climatic signal from the Summit tem-perature reconstruction. This is an approxima-tion, and a rigorous approach would require aniterative ìnversion' of sorts to locate the true ori-gin of the source ice in the GRIP and GISP2 icecores; source locations would di¡er for each core,and would shift in time. This kind of tracer anal-ysis is technically feasible, but we do not believe itto be warranted for the paleotemperature correc-tion; modelled elevation changes in the divide re-gion are less than a few 100 m in the last 100 kyr,and elevation histories are similar at GRIP,GISP2, and the time-varying model divide. Thecorresponding elevation-lapse rate correctionsare therefore not very sensitive to assumptionsabout source ice location.

The climatic temperature shift that results fromthis elevation correction, vTc, is applied uni-formly in space. Mean annual air temperatures,TA�x; y; t�, are then perturbed from modern val-ues (t = 0) based on this baseline climatic shift andlocal elevation changes:

TA�x; y; t� � TA�x; y; 0� � vT c�t��

L �hs�x; y; t�3hs�x; y; 0�� 5�

We apply a uniform temperature lapse rate,L=30.0075³C m31, as an estimate of free-airconditions in Greenland's dry, polar atmosphere.

Precipitation rates P(x,y,t) are perturbed frompresent-day ¢elds as a function of air tempera-ture, assuming an exponential dependence afterRitz et al. [21]:

P�x; y; t� � P�x; y; 0� exp�a�TA�x; y; t�3

TA�x; y; 0��Umin 1:5;9 hs�x; y; t� � 0:0019 hs�x; y; 0� � 0:001

� ��6�

where a = 0.0693³C31 in our study, giving a 75%reduction in Summit accumulation rate with a20³C cooling. The ¢nal factor approximates thein£uence of changes in ice surface slope 9hs, ofimportance for orographically driven precipita-tion at the margins.

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2.4. Isotopic record

The ice core isotopic record in central Green-land is exceptional for the last 100 kyr, with tre-mendous agreement between the GRIP andGISP2 ice cores. However, stratigraphic disrup-tion of deep ice in the Summit ice cores precludesdirect application of GRIP and GISP2 isotopechronologies prior to ca. 100 ka. While this periodof time is not important to the analyses and con-clusions in this paper, we attempt to improve onapplication of the Summit records by constructinga synthetic isotopic history for this period. We dothis by blending the GRIP ice core record withthat from Vostok, Antarctica. The GRIP N18Ohistory for the period 97.8 ka to the present [2]is combined with an arti¢cial N18O chronologythat has the shape of the Vostok deuterium iso-tope record for the interval 160^97.8 ka [44]. Theminimum and maximum N18O values in this peri-od are taken from the GRIP ice core; these abso-lute values are not questioned in the GRIP re-cord, it is the chronology which isindecipherable. The resultant N18O history is plot-ted in Fig. 1.

The GRIP/Vostok record is characterized by arelatively stable Eemian interglacial period, withconditions similar to or warmer than the Holo-cene during the interval 132^117 ka. These attrib-utes of the last interglaciation are imported fromthe Vostok record (e.g. [44^46]). While Vostokbears the imprint of southern hemisphere condi-tions, the major interstadial^stadial climate oscil-lations observed in the Summit cores in the lastglaciation (ca. 100^10 ka) all have counterparts(although asynchronous) in the Antarctic ice cores[47]. This is convincing evidence for global man-ifestation of high-amplitude, millennial-scale cli-mate oscillations. Climatic records from oceansediments and from calcite deposits in Devil'sHole [48] also suggest that the last interglacialperiod was relatively stable (as seen in Antarcti-ca), and indicate a broad global signature of high-amplitude climate variations. We assume that thischaracter can be extrapolated to the Eemian peri-od. If this is true, the `style' of the last interglaci-ation in Greenland must have resembled that inAntarctica. We therefore argue that the Vostokice core gives a better representation of globalclimate variability than the Summit cores priorto 100 ka.

It should be noted that north Atlantic sedimentcore records would provide a reasonable alterna-tive to application of the Vostok record; the re-sulting synthetic isotope history would be verysimilar. Implications of the GRIP/Vostok isotoperecord are discussed in Cu¡ey and Marshall [49].The major conclusions in this paper are not de-pendent on this early part of the climate forcinghistory, as it is the more recent evolution of theice sheet that is critical to disturbing deep ice.

3. Simulations and analysis

Simulations require an initial distribution of icetopography and temperature. We spin up an ini-tial model by: (1) starting with present-dayGreenland ice thicknesses, topography, and clima-tology (air temperatures, ice-equivalent accumula-tion rates), (2) introducing a 6³C cooling at allpoints to re£ect cold glacial conditions that pre-vailed ca. 160 ka, (3) integrating forward for 200

Fig. 1. Synthetic `GRIP/Vostok' oxygen isotope record usedfor model forcing (solid line), derived from a blend of icecore records from Vostok, Antarctica and GRIP (dashedline).

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kyr with this ¢xed cold climate to give equilibriumice thickness, bed topography, and ice tempera-ture ¢elds. Simulations were then run from 160ka to the present, with time-varying climate con-ditions updated at 100 yr intervals. The initial

condition of the ice sheet is somewhat arbitrary,and is based on the approach of previous studies.A steady-state cooling of 10³C would better re-£ect the recalibrated temperature history in cen-tral Greenland; we calculate a mean temperatureof 341.9³C at Summit over the last 160 kyr (Fig.2a). This represents a 10.4³C depression from cur-rent conditions, and could be considered to be the`mean' long-term temperature experienced at theSummit sites. Mean glacial conditions, from theperiod 100^20 ka, correspond to a cooling of13.1³C. The choice is not critical in the currentstudy, as our focus is the last 40 kyr of ice sheethistory. There is little memory of initial condi-tions at this time. We also note that an equilibri-um spinup is an idealization in any case; it is notpossible to reconstruct an internal temperaturedistribution and ice sheet geometry that truly re-£ects conditions ca. 160 ka, without detailedknowledge of climates prior to this.

Fig. 2a,b depicts the 160 kyr record of air tem-perature and accumulation rate at the roving icedivide location. These are the forcing functionswhich result from application of the GRIP/Vos-tok isotopic record, the Cu¡ey and ClowTA(N18O) relationship [27], and Eqs. 5 and 6.The resultant ice area, volume, and divide eleva-tion histories are plotted in Fig. 2c,d. Snapshotsof ice sheet surface topography at 127 ka, 21 ka,

Fig. 2. Modelled glacial cycle time series. (a) Air temperatureat the ice divide, ³C. (b) Ice-equivalent accumulation rate atthe ice divide, m yr31. (c) Total ice sheet volume (solid line,1015 m3) and area (solid line, 1012 m2). (d) Elevation historyat the modelled divide (solid line) and the modern summitposition, m.

Fig. 3. Snapshots of modelled surface topography. (a) Eemian minimum con¢guration, 127 ka. (b) Last glacial maximum, 21 ka.(c) Present day. (d) Present day, observed.

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and the present day are presented in Fig. 3. Thesedepict the Eemian minimum, the last glacial max-imum, and the modern ice sheet con¢gurations,with associated ice volumes of 0.78, 3.79, and2.78U1015 m3 of ice, respectively. The observedpresent-day volume of ice in Greenland (Fig. 3d)is 2.83U1015 m3 [21].

Our Eemian minimum construction is severelydiminished relative to previous model studies andrelative to modern interglacial conditions. This isa consequence of the isotope^temperature rela-tionship that we apply, and the result is discussedin detail in [49]. Despite the dramatic ice volumevariations, the core of the ice sheet in centralGreenland persists throughout the integration.The elevation and position of the ice divide areremarkably stable. This is a robust result from aspectrum of simulations with di¡erent isotope^temperature relationships and isotopic histories.

3.1. Surface geometry in the Summit region

Fig. 4 plots a close-up look at the observed andmodelled present-day Summit region, with loca-tions of the GRIP, GISP2, and NGRIP ice coresites indicated. The model is predictably over-

smoothed relative to reality, partially due to thedi¡usive model physics and partially a result ofthe smoothed (20 km) bedrock topography ¢eldsthat serve as model input. The simulated dividestructure and location is nevertheless satisfactory,with the GRIP site near the modelled summit,GISP2 on a gentle, westward-dipping £ank ofthe summit, and NGRIP positioned on a ridgestriking northwestwards from the divide. Slopeamplitudes range from 0.001 to 0.0015 (0.06^0.09³) at the three sites, an accurate rendition ofmodern surface slopes at the GISP2 and NGRIPsites. In reality, these two sites are presently expe-riencing gentle £ank (shear) £ow, while thepresent-day GRIP site is in a divide-£ow regime,with negligible surface slope. The model fails tocapture this precisely, with the simulated present-day divide in Fig. 4b displaced 72 km northeast ofthe true Summit. We name this point `mGRIP', asit is the model's representation of the GRIP site.To avoid confusion, the geographic location ofthe GRIP drill site is referred to as `gGRIP' inthe remainder of the paper.

In Nature, ice sheet geometry is determined bynumerous factors, including bed topography, icetemperature history, ice rheology, margin position

Fig. 4. Enlarged view of present-day surface topography in the Summit region. (a) Observed. (b) Modelled. GRIP, GISP2, andNGRIP ice core sites are noted, as well as the modelled divide location, mGRIP.

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and history, accumulation patterns, accumulationrate history, and the presence of fast-£ow regionsin an ice sheet, which lower ice surface, increasingice £ux to a region (e.g. the Jakobshavn Isbr× icestream in west Greenland). Given these complexenvironmental controls, the approximations in theice sheet model, and the simpli¢ed climate history,it is unsurprising that the true Summit location isnot simulated. Fig. 4 is generally encouraging inour view, and we argue that the failure to predictthe divide in precisely the right location does notlimit the interpretations that follow. However, itis important to focus attention on the mGRIP siteas well as gGRIP, as the £ow evolution atmGRIP may be of foremost relevance in inter-preting model implications for the GRIP icecore. Simulations have been repeated to trackstrain rate and elevation histories at the mGRIPlocation, and analyses below are carried out atboth the mGRIP and gGRIP locations.

Fig. 5a,b depicts surface topography ¢elds inthe divide region in the Eemian and late glacialice sheet. Migration of the divide is evident inthese end-member snapshots, with the Eemiansummit displaced about 150 km to the northeast.The modelled ice divide at 21 ka is within 20 kmof gGRIP. Fig. 5c shows the modern modelled

surface topography, overlain by contours of icedivide `residence time'. Peregrinations of the icedivide are con¢ned to a narrow band bridgingthe Eemian and late glacial states of Fig. 5a,b.For much of the last glacial cycle (approximately70 kyr) the modelled summit hovers in close prox-imity to gGRIP. The simulations suggest an inter-esting bimodal glacial/interglacial pattern for theice sheet divide, with the present-day divide(mGRIP) located near its Eemian position, de-spite the substantial di¡erences in Eemian andHolocene ice sheet geometry (cf. Fig. 3a,c).

The trajectory of the modelled divide over thelast 10 kyr is rather interesting. During the lastglacialînterglacial transition, ca. 9^8.5 ka, the di-vide migrates quickly from its southwestern, gla-cial location to occupy a position 20^30 kmnortheast of mGRIP for most of the Holoceneperiod. At approximately 1.5 ka in the simula-tions, the divide begins meandering back to thesouthwest. The mGRIP site is the location thatintercepts the ambulatory divide at time 0 in themodel; it is not special otherwise, and has everyappearance of being a short-term host for the di-vide. Ongoing summit migration can be expectedin the centuries ahead. The NGRIP site resides ona gentle northwesterly ridge throughout this peri-

Fig. 5. Snapshots of modelled surface topography in the Summit region. (a) Eemian minimum con¢guration, 127 ka. (b) Lastglacial maximum, 21 ka. (c) Present day. The duration of divide òccupation' at di¡erent points in the model is plotted in (c), in-tegrated over the full 160 kyr integration. (x,y) point (0,0) is referenced to the GRIP site.

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od of readjustment in the Summit region,although the NGRIP site steepens during theEemian when the northern £ank of the ice sheetencroaches (Fig. 5a). The ice divide is still up-stream during this interval, so no abrupt changesin the chemical or physical properties of thesource ice are to be expected.

3.2. Surface gradient evolution

Surface gradients at the mGRIP, gGRIP,GISP2, and NGRIP sites were monitored at 100yr intervals through the glacial cycle integration,giving a detailed representation of the evolutionof slope amplitude and aspect (Fig. 6 and Table2). Mean conditions of the last 160 kyr are domi-nated by the glacial con¢guration of Fig. 5b. Sur-face gradient evolution through the entire 160 kyrintegration is shown in Fig. 6a^d, with NGRIP

Fig. 6. Time series of surface gradient evolution at the gGRIP (heavy black line), GISP2 (dashed line), and NGRIP (thin blackline) ice core sites and the modelled present-day divide, mGRIP (gray line). (a) North^south slope, positive for northward dip,m/km. (b) East^west slope, positive for westward dip, m/km. (c) Slope amplitude, [(Dxhs)2+(Dyhs)2]1=2, m/km. (d) Slope aspect, de-grees. 0³ is eastward, 90³ northward, 180³ westward, and 270³ southward. NGRIP is plotted alone in the series of curves on theright. (e^h) Expanded view of (a^d), showing only the last 20 ka.

Table 2Slope and aspect statistics

gGRIP GISP2 NGRIP mGRIP

Slope aspect (³)a :Mean 150 170 131 152S.D. 26 20 14 13Minimum 80 126 90 127Maximum 224 223 168 198Modern 179 191 138 194Slope amplitude (U103)Mean 1.18 1.22 1.41 1.21S.D. 0.40 0.46 0.60 0.33Minimum 0.54 0.79 0.81 0.32Maximum 3.64 3.89 4.31 3.27Modern 1.18 1.54 1.59 0.35aMeasured counter-clockwise from East (0³).

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isolated on the right hand side. The last 20 kyrat all four locations is expanded in Fig. 6e^h.Slope amplitudes are of order 0.001 (0.06³) atall four locations during glacial and Holocenetimes, increasing to V0.004 during the Eemian(Fig. 6c).

An interesting and potentially important aspectof the slope evolution is illuminated in Fig. 6a,b,which decomposes the surface gradient into zonal(x) and meridional (y) components. Flow at theNGRIP site is always northwesterly (Dyhs 6 0 andDxhs s 0), with more northerly £ow during theEemian. Flow directions shift more dramaticallyat the mGRIP, gGRIP, and GISP2 sites, however.All three locations reside west of the roving modeldivide through most of the integration (Fig. 6b;Dxhs s 0), with the exception of a short early Hol-ocene interval when the divide migrates to nearthe GISP2 site. There is a notable interglacial/gla-

cial contrast in the north^south slope at the Sum-mit sites, evident in both the Eemian and earlyHolocene periods (Fig. 6a,e). The mGRIP,gGRIP, and GISP2 sites tilt northward(Dyhs 6 0) during the glacial period, shifting to asoutherly aspect (Dyhs s 0) during interglaciations.

Fig. 6d,h plots the evolution of slope azimuth,Q, at all four sites, measured counter-clockwisefrom East (i.e. 0³ represents eastward tilt, 90³northward, and 180³ westward). Slope azimuthsillustrate the tilt inferences discussed above. TheNGRIP site experiences the least variability, withnorthwesterly to northerly £ow prevailingthroughout the integration (QW130³) and a stan-dard deviation of only 14³ in £ow direction, com-pared to 26³ at the gGRIP site. There is a gradual20^30³ rotation of £ow at the NGRIP site duringthe Holocene, but the glacial^deglacial transitionat NGRIP is gentle. The mGRIP, gGRIP, and

Fig. 7. Time series of surface velocity and strain rate history at the gGRIP (heavy black line), GISP2 (dashed line), and NGRIP(thin black line) ice core sites and the modelled present-day divide, mGRIP (gray line). (a) (u,v) velocity components in the (x,y)directions, m yr31. (b) Expanded view of (a), showing the last 20 kyr. (c) Flank-£ow index, f, over the last 160 kyr. (d) Ex-panded view of (c), showing the last 20 kyr. (e) Normalized simple shear strain, S/S0, over the last 160 kyr. (f) Expanded viewof (e), showing the last 20 kyr.

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GISP2 sites all have greater variability in slopeazimuth, a result of the bimodal glacial/intergla-cial geometry in the divide region. The most sig-ni¢cant £ow excursions occur in the Eemian, withroughly 90³ variations in slope aspect at each site.Following this period, however, from ca. 90 ka tothe present, slopes are relatively stable. A north-westerly aspect typi¢es the three sites during theglacial period (QW150³), followed by an abruptPleistocene^Holocene transition, ca. 9 ka. As dis-cussed below, we highlight and implicate thisdeglacial dynamical adjustment in the Summit re-gion as being of particular importance for strati-graphic disruption in the gGRIP and GISP2 icecores.

Neglecting details of the individual evolutions,all three geographical positions in the Summit re-gion (gGRIP, GISP2, and mGRIP) experiencedsimilar histories. The Eemian was a period of sub-stantial £owline adjustment throughout the icesheet, accompanied by steepening in the divideregion. Variability in slope amplitudes was muchless over the last 110 kyr, but slope azimuths me-ander throughout this time. The important con-clusion is that no location in the Summit region

was static through the last glacial period and gla-cialînterglacial transition. The reorganization ofdivide geometry accompanying the Pleistocene/Holocene deglaciation was the most signi¢cantevent of the last 100 kyr in central Greenland.

3.3. Flank £ow vs. divide £ow

Surface velocity ¢elds associated with the slopeevolution are plotted in Fig. 7a, with (u,v) repre-senting the (x,y) velocity components, respec-tively. Slopes in the entire divide region, as wellas NGRIP, are gentle, giving £ow velocities ofonly 1^4 m yr31 through most of the integration.The Eemian period is an exception, with roughly10-fold increases in velocity predicted at each site.There is strong northward £ow at NGRIP andsouthwestward £ow at the Summit sites duringthis interval. Fig. 7b plots the last 20 kyr of thesetime series, providing a better view of modelledvelocities during the Pleistocene^Holocene transi-tion. The glacialînterglacial £ow reversals at thegGRIP and GISP2 sites are evident ca. 8.5 ka,although £ow velocities at the gGRIP site arevery modest, approximately 1 m yr31. Flow at

Fig. 8. (a) Basal shear stress (non-dimensional) based on the analysis of Raymond [8], in the range (0,20) ice thicknesses fromthe divide. Dashed line: gravitational driving stress. Solid line: empirical curve ¢t to basal shear stress modelled by Raymond [8],¢gure 5b. (b) Pure shear strain rate, P, and simple shear strain rate, S, within eight ice thicknesses of the ice divide, based onthe basal shear stress in (a). Strain rates are dimensionless in this analysis. (c) Flank-£ow index f calculated from P(x/H) andS(x/H) in (b). See text for elaboration. (d) Kinematic (thin line) and modelled (heavy line) £ank-£ow histories at the the GRIPsite. (e) As in (d), but at the mGRIP site.

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the mGRIP site in the Holocene is less than 0.5 myr31.

To examine model strain rates and quantify thetransitions between £ank £ow and divide £owmore rigorously, we de¢ne a depth-dependent£ank-£ow index:

f �z� � S�z�S�z� � P�z� �7�

where S(z) and P(z) indicate the strain rates as-sociated with simple shear and pure shear at ele-vation z :

S�z� � 12

D uD z

� �2 � D v

D z

� �2

� �1=2

�8a�

P�z� � DwD z

�� D uD x� D vD y

�� 8b�

for vertical velocity w(z). The divide-£ow regimeis characterized by negligible simple shear stress,SW0, while simple shear deformation dominatespure strain in the £ank-£ow regime [8,9]. Fromthe de¢nition of Eq. 7, f = 0 for divide £ow andfC1 under £ank £ow. Raymond's investigation[8] suggests that most of the transition from di-vide to £ank £ow occurs within four ice thick-nesses of the divide, or just 12 km in the case ofGreenland's Summit region. We therefore antici-pate that the numerical model, with a 20 km grid,is unable to resolve true divide £ow. Put anotherway, even the model Summit has non-zero slopein general, with Ss 0. The present-day mGRIPsite has a £ank-£ow index of f = 0.7; this is theclosest the ice sheet model comes to a divide-£owregime.

Nevertheless, model-derived P and S valuesvary interestingly with time in the Summit region,making the £ank-£ow index a useful metric. Wecalculate model strain rates from (4) at a height of300 m above the bed, archiving these values every100 years for the 160 kyr integration. This re-quires interpolation of the modelled velocity pro-¢les to the 300 m level, as thickness of thestretched vertical layers in the model changeswith time to re£ect changes in ice thickness. Weuse a cubic spline interpolation to represent the

non-linear velocity pro¢les which occur at depthin the ice sheet. We monitor strain rates at the 300m level because disturbances in the Summit icecores begin at close to this height above the bed.

Fig. 7c,d plots f(t) at the ice core locations. Asexpected, all four sites are characterized by £ank£ow through most of the integration, with fs 0.9.The index is highest at the NGRIP and GISP2sites, which never approach divide £ow in themodel. Fig. 7d illustrates the Pleistocene^Holo-cene transition, with the gGRIP site showing atransition towards divide £ow as the modelledSummit passes over the site ca. 9 ka. The mGRIPlocation tends towards divide £ow, fW0.8, as theHolocene progresses.

The absolute magnitude of simple shearing isalso relevant to potential disturbance of the icecore sites, as well as the development of ice fabricin the cores. Fig. 7e,f presents the history of shearstrain rates, S, normalized by the modelledpresent-day value, S0. The Eemian period wasan obvious excursion, with a 30-fold increase insimple shear strain at mGRIP and approximately12-fold increases at gGRIP. The GISP2 site has ahigher modern S0 value, so the Eemian increase inshear strain rate is more modest. As seen in Fig.7f, strain rates in glacial conditions are less thanmodern at all sites save mGRIP, S/S0W0.5. S/S0

at mGRIP is about 2.5 times the present value.Trends reverse in the Pleistocene^Holocene tran-sition, with reduced shearing at mGRIP but three-to four-fold increases over about 1000 years at thegGRIP and GISP2 sites. Strain rates double atNGRIP through the Holocene, but the increaseis gradual. These results indicate that variabilityin shear straining during deglaciation is higher atthe mGRIP, gGRIP, and GISP2 sites.

3.4. Theoretical £ank-£ow estimation

The £ank-£ow assessment in Fig. 7c is limitedby the fact that model discretization precludesproper resolution of divide £ow. As an alternativeto model-derived strain rates, we consider estima-tion of a vertically averaged value £ank-£ow in-dex, f �t�, based on the divide-£ow analysis ofRaymond [8] and the distance of the geographicalgGRIP and mGRIP sites, dg(t) and dm(t), from

EPSL 5466 19-5-00


the roving or dynamic model divide. We estimatethe subgrid location of the dynamic model dividethrough a bicubic interpolation of the surface top-ography ¢eld in a ¢xed 220U240 km2 region thatcontains the roving summit (cf. Fig. 5c). The di-vide is identi¢ed as the highest point in the inter-polated topography ¢eld, using a 2 km subgridgrain. dg(t) and dm(t) are calculated at 100 yr in-tervals through the 160 kyr integration.

Calculation of f �d�t�� requires a relationship forS(d) and P(d), which we develop through adap-tation of Raymond's analysis. Non-dimensional-izing and expressing horizontal distance as x/H,Raymond examined ice £ow within 20 ice thick-nesses of the divide, x/Hn(0,20). He de¢ned anarbitrary but realistic ice surface on a £at bed:

hs�x� � H h03K 0xH3

12L 0

xH

� �2� �

�9�

where h0 = 1.15, K0 = 4.095U1033, and L0 = 0.4U1033. Gravitational driving stress calculated fromthis expression is dd =3bIghsDxhs, plotted in Fig.8a (dashed line). With a no-slip condition at thebase, this expression can be equated to basalshear stress, db. Raymond's ¢nite element simula-tions illustrate that this expression no longer de-scribes db in the divide-£ow regime at x/H6 4,where DxhsC0. To empirically approximate Ray-mond's predictions of basal shear stress, we gen-erate the synthetic curve shown in Fig. 8a, db = Aln (x/H+1). This closely resembles Raymond's ¢g-ure 5b [8].

Using this synthetic db relationship, we calcu-late horizontal surface velocities assuming a sim-pli¢ed isothermal relationship:

us � 2BHn� 1

d nb �

2BHn� 1

�A ln �x=H � 1��n �10�

where B is the vertically averaged ice sti¡ness co-e¤cient in Glen's £ow law for ice [32,33], and n isthe £ow law exponent, typically taken to be 3. Beventually falls out in the calculation of f below,so we do not need to tailor this to ice rheologiesin the Greenland Summit region. From Eq. 10,Dxus and DzuWus/H can be calculated. Assumingice incompressibility, Dzw =3Dxu, we can therefore

derive approximate expressions for S(x/H) andP(x/H) in Eq. 8. Fig. 8b plots these two ¢eldsin the vicinity of the ice divide, x/Hn(0,8).S(x/H) increases monotonically beyond thispoint, while P decreases. The crossover from di-vide to £ank £ow suggested by this curve is atxW3.5H, consistent with the inferences of Ray-mond, although P still represents a discerniblefraction of total strain up to ca. 10 ice thicknessesaway.

The associated vertically averaged £ank-£owindex, f (x/H), is plotted in Fig. 8c. We calculatethis index out to a distance of 40 ice thicknesses,beyond which we assign f = 1. From the dg(t) anddm(t) histories, and taking H = 3000 m, we canthen estimate f �t� indirectly, and independent ofthe modelled strain rates (Fig. 7c). Fig. 8d,e plotsa comparison between £ank-£ow histories gener-ated by the modelled velocities and the o¥ineanalysis (¢ne lines) at the gGRIP and mGRIPsites. These can be thought of as dynamic andkinematic measures of f �t�, as the latter methodis based only on d(t) histories and the £ank-£owindex of Fig. 8c. The kinematic calculation ne-glects factors such as accumulation rate history,ice viscosity variations, and dynamical transientsthat bear on pure shear. The stepped appearanceof the kinematically determined f �t� history inFig. 8d,e re£ects the discrete nature of dg(t)and dm(t). The two di¡erent f �t� reconstruc-tions are similar overall, however, with £ank£ow prevailing, f s 0.8, through most of the in-tegration. With reference to Fig. 8c, this indicatesthat the dynamic divide is usually more than25^30 km from the gGRIP and mGRIP sites.Occasional intervals of pure divide £ow are pre-dicted at mGRIP, corresponding to momentswhen the ice divide passes through this location(dm(t)6 10 km).

Our conclusion from these results is that themodel-derived strain rates give a reasonable indi-cation of f �t�, and our inferences about £ank vs.divide £ow are not quali¢ed by the model resolu-tion. Peregrinations of the divide brought allpoints in the Summit region into a £ank-£ow-dominated regime at some time in the last 20 kyr;no location experienced pure divide £ow through-out this period.

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4. Discussion

The history of divide migration concurs withthe results of Anandakrishnan et al. [9], who sug-gested the likelihood of shifts from divide to £ank£ow in the Summit region. We ¢nd that theseshifts correspond to glacial and interglacial geo-metric modes, with the most substantial dynami-cal variations in the divide region occurring dur-ing transitions between glacial and interglacialstates. Peregrinations of the divide are less than150 km in our simulations, and less than 63 kmover the last 110 kyr. There is a noteworthy £owexcursion during the last deglaciation, however.The modelled ice divide circles the modern Sum-mit location over the past 20 kyr: (1) occupying aglacial maximum position southeast of the gGRIPsite, (2) migrating to points southwest of gGRIPduring the Pleistocene^Holocene transition, ca.15^10 ka, then (3) stabilizing to the northeastfor the past 7 kyr. Divide mobility of this sort isconsistent with the lack of a stratigraphic Ray-mond bump at the Summit site [11,12], a featureassociated with sti¡ ice in a pure divide-£ow re-gime (cf. [8,10]).

Firm conclusions about ice core disruption can-not be made, as we remain uncertain as to themechanism(s) of disturbance. We have not at-tempted to explicitly model folding processes. Asdiscussed in Section 1, however, stratigraphic dis-turbance in the Summit ice cores may be a resultof divide migrations or £owline shifts [9,14,16].While the model fails to precisely simulate themodern Summit location, the conclusion of a me-andering divide is a signi¢cant result. We alsosuggest that £ow reversals at the Summit sitewere likely, with potentially disruptive shifts in£ow direction during glacial^deglacial transitions.A reversal of this sort during the last deglaciation,as predicted by the model, may have been partic-ularly e¡ective at disturbing deep ice at the Sum-mit sites. Major stadialînterstadial oscillations(cf. Fig. 1) throughout the late glacial periodmay have incurred a similar divide response. An-other factor that makes Summit ice susceptible todisruption is the peculiar rheology associated withdivide £ow [8] ; the low stress regime beneath di-vides causes sti¡ening of the ice, relative to ice

undergoing shear £ow [32]. Alternations betweendivide and £ank environments could therefore in-troduce vertical gradients or discontinuities in theice rheology and fabric, presenting stratigraphichorizons and e¡ective viscosity contrasts thatmight overturn under shear [14,15,17].

These features of the ice dynamical history ^shifts between divide and £ank £ow, glacialînter-glacial £ow reversals, and the peculiar nature ofdivide ice ^ are relevant at the mGRIP, gGRIP,and GISP2 sites. The NGRIP ice core location isprobably free of disturbances motivated by theseprocesses, as it resides in a persistent northwest-erly shear-£ow environment and is well removedfrom the ice divide. Surface gradients at NGRIPdo change in amplitude and orientation duringthe Pleistocene^Holocene transition, however,with a westerly rotation of roughly 30³ in mod-elled £ow direction over the past 10 kyr (Fig. 6d).The NGRIP ice core may therefore be susceptibleto stratigraphic disturbances that originate from£owline shifts [16]. This is a possible cause offolding in deep ice, so we cannot make strongconclusions about stratigraphic integrity atNGRIP. Modelled £owline shifts are gradual atNGRIP, however, which will suppress overturn-ing. Combined with the greater distance of Eem-ian ice above the bed at NGRIP [1], we supportthe Danish optimism that the NGRIP core maycontain an improved record of Eemian climate.

There are several cautionary notes on the mod-el reconstruction. Model resolution is not su¤-cient to give a de¢nitive simulation of divide per-egrinations. Given su¤ciently detailed bedrockinformation, a nested high-resolution study ofthe Summit region would be constructive. Uncer-tainties in the model are di¤cult to quantify, andmany glaciological complexities are necessarilyover-simpli¢ed (e.g. ice deformation is isotropic,longitudinal stresses are neglected, basal £ow andice streams are not modelled). Ice in the GRIPand GISP2 boreholes is highly anisotropic, andthis would a¡ect strain rates and the £ank-£owindex in a complex way. Paleoclimatic uncertain-ties are probably of even greater importance thanall of these e¡ects [22]. While temperature andaccumulation conditions at the Summit sites arewell constrained over the last 100 kyr, the climate

EPSL 5466 19-5-00


history at other points in the ice sheet is un-known. The geographical distribution of paleocli-mate perturbations is certain to be more complexthan the uniform shifts that we apply. In partic-ular, snow accumulation patterns may havechanged signi¢cantly with ice sheet geometryand North Atlantic conditions.

A further cautionary note concerns the specu-lative climate in central Greenland prior to 100ka. Both isotope thermometry and isotopic his-tory are controversial in this period, and ice sheetreconstructions in the Eemian are particularlysensitive to the way these are treated in models.There is therefore considerable uncertainty inmodel reconstructions in this early period, inour model as in all previous investigations. Wehave explored parameter space extensively in sim-ulations of the last climatic cycle, however, andanalyses and conclusions regarding the past V50kyr of divide history are essentially independentof the interglacial state of the ice sheet. If it is truethat stratigraphic disruption occurred when icewas deep (a presumed prerequisite for the thinice layers and high stresses involved in structuraldeformation), then late glacial and deglacial £owexcursions are what matters for ice core disrup-tion. In particular, we implicate the £owline shiftsand divide migration associated with the last gla-cial^deglacial transition, ca. 9 ka. Dynamically,the ice sheet has little memory of the Eemian icesheet con¢guration at this time. The GRIP/Vos-tok isotopic record that we have introduced andthe choice of isotope^temperature relationshipprior to 100 ka therefore have little bearing onour main conclusions.

5. Conclusions

One should not interpret the modelled ice sheetevolution as an accurate historical reconstruction,but the following distillates are unlikely to changewith model revisions. The Greenland Summit po-sition has moved signi¢cantly through time in thelast 100 kyr, but never (excepting the modernsummit) enough to cause a signi¢cant increasein shear strain rates along £ow paths leading tothe present ice core sites (the reduction of strain

rates due to the lower glacial age accumulationrates being a more important factor). The summitposition was likely quite stable through the last 60kyr of the glacial climate, but then shiftedabruptly during deglaciation (the latter supports[9]). There is probably no location for which di-vide £ow has persisted throughout the past 20kyr, and a signi¢cant change in the vertical veloc-ity pattern probably occurred beneath the modernSummit site during deglaciation. Changes in £owdirection accompanying the summit shift, and theshift itself, are plausible causes for the absence ofa Raymond bump beneath Summit, and forstratigraphic disruption of Eemian ice in theGRIP and GISP2 cores. Incorporating these in-sights into models for fold generation (e.g. [14^17]) may help to further understand these struc-tural features.

The NGRIP site is a remarkably stable ridge,and we cannot argue for dramatic changes in £owdirection or magnitude at NGRIP over the past100 kyr. Because this site resides in a continuous£ank-£ow environment, its £ow history di¡ersfrom that at mGRIP, gGRIP, and GISP2 inways that may be important to structural forma-tion. This does not mean that the deep ice atNGRIP has been immune to signi¢cant dynami-cal changes or stratigraphic disruption, but iscause for cautious optimism.

Substantial changes in ice sheet geometry dur-ing the Eemian interglacial climate likely oc-curred, as suggested by Koerner [50]. This doesnot cast doubt on NGRIP's ability to supply anundisturbed record for the middle and late Eem-ian, but suggests that undisturbed pre-Eemian,and possibly early Eemian, records may neverbe recovered from the Greenland Ice Sheet.

Acknowledgements

We thank Catherine Ritz, the European ScienceFoundation (ESF), members of the European IceSheet Modelling Initiative (EISMINT), and GRIPand GISP2 project members. The thoughtful com-ments of Richard Alley and an anonymous re-viewer improved the manuscript. S.J.M. is sup-ported by a Post-Doctoral Fellowship from the

EPSL 5466 19-5-00


Natural Sciences and Engineering ResearchCouncil of Canada (NSERC) and the ClimateSystem History and Dynamics Program(CSHD), co-sponsored by NSERC and the At-mospheric Environment Service of Canada. Thispaper stemmed from discussion at the annual sci-enti¢c meeting of the Northwest Glaciological So-ciety.[EB]

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Documents

Peregrinations of the Greenland Ice Sheet divide in the last glacial cycle: implications for central Greenland ice cores