Global ice volumes at the Last Glacial Maximum and early...

Global ice volumes at the Last Glacial Maximum andearly Lateglacial

Kurt Lambeck *, Yusuke Yokoyama, Paul Johnston, Anthony PurcellResearch School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia

Received 7 February 2000; accepted 12 July 2000

Abstract

Observations of sea levels during the Last Glacial Maximum (LGM) at localities far from the former ice marginsconstrain the global change in ice volume from the LGM to the present at about 52U106 km3. Regional studies of sea-level change from observations near and within the margins of the former ice sheets constrain ice volumes of theindividual ice sheets and have led to an imbalance between the global estimate of ice volume and the sum of theindividual ice-sheet volumes. The latter estimates are reliable only when the observational record from localities close tothe ice mass extends well into Lateglacial times, which is generally not the case for the major ice sheets. Ice volumesduring the LGM and earliest part of the Lateglacial period can therefore be substantially increased without affecting thepredictions of Lateglacial and Postglacial sea level in a significant manner, provided that a rapid reduction in ice volumeoccurred in early Lateglacial time. New far-field data for LGM and Lateglacial sea-level change indicates that a rapidrise in sea level of about 15 m occurred at about 16 500^16 000 14C (or 19 200^18 700 calibrated) years ago. This leads tothe inference that during the LGM the ice sheet volumes of the major ice sheets were greater than inferred from regionalrebound analyses and that rapid reductions in volume occurred at the termination of the LGM. The timing of thisoccurrence does not coincide with any recognised Heinrich event, although pulses of ice-rafted debris originating fromboth northern ice sheets do occur in some high latitude cores. An Antarctic contribution to the post-LGM melting eventalso cannot be ruled out, the timing coinciding with evidence for the onset of warming in southern latitudes and theaddition of meltwater into the Southern Ocean. ß 2000 Elsevier Science B.V. All rights reserved.

Keywords: sea-level changes; last glacial maximum; glacial extent; eustacy; meltwater

1. Introduction

The Last Glacial Maximum (LGM) was a timewhen large ice sheets covered the continental landmasses of North America and Europe and whensea levels globally stood lower than today. It is an

interval in Earth climate history that is distinctlydi¡erent from present conditions, yet it occurredsu¤ciently recently for reliable and quanti¢ableevidence of the climate to be preserved in sedi-ment and ice records. This period becomes, there-fore, important for testing climate models underconditions that are quite di¡erent from those oftoday; models that are also used for predictingfuture trends in climate change (e.g. [1,2]). Animportant element in understanding the LGMconditions is the timing of this event and of the

0012-821X / 00 / $ ^ see front matter ß 2000 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 2 - 8 2 1 X ( 0 0 ) 0 0 2 2 3 - 5

* Corresponding author. Tel. : +61-2-6249-5161;Fax: +61-2-6249-5443; E-mail: [email protected]

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ice distribution and ice volumes at this and Late-glacial times. This is the issue addressed in thispaper through an evaluation of sea-level changeduring the LGM^Lateglacial interval.

Few direct measurements exist of the thicknessof ice formerly over the continents. For small icesheets such as that over the British Isles, it hasbeen possible to quantify the ice thickness by dat-ing the formation of weathering pro¢les on moun-tain peaks that stood above the ice at the time ofthe LGM, while in some localities of Antarctica,it has been possible to measure the change in icethickness since the LGM by dating remnant mar-ginal moraines. But in North America and Fen-noscandia, locations of the largest latest Pleisto-cene ice cover, no mountain peaks stood outabove the ice domes and in these cases, only mini-mum estimates of ice thickness can be inferred.Instead, to estimate past ice volumes, recourseto glaciological modelling is necessary and thisrequires a series of assumptions concerning thesupply of ice-forming moisture, ablation condi-tions, and thermal bed-rock and stress states atthe base of the ice cover. Independent checks onLGM and Lateglacial ice thickness estimates areclearly desirable and it has long been recognisedthat observations of crustal rebound and sea-levelchange provide such constraints: as the ice sheetsmelted in post-LGM times, the crust underlyingthe ice rebounded, sea levels rose or fell depend-ing on their locality, and shorelines advanced orretreated concordantly. Observations of sea-levelchange and shoreline migration, coupled with ob-servations of the ice retreat, provide the basis forestimating not only parameters de¢ning the earthrheology but also ice volumes during the LGMand Lateglacial times. Sea-level data from the for-merly glaciated regions (from near-¢eld sites) pro-vide some constraint on the nearby ice volumesand observations far away from the former icesheets (far-¢eld sites) constrain the total volumeof land-based ice over time (e.g. [3^7]).

Far-¢eld observations of sea level during thetime of maximum glaciation are indicative of aprolonged period when sea level was nearly con-stant, from about 19 ka BP (U1000 years beforepresent) or earlier, to 16.5 ka BP, followed by ashort period of very rapid sea-level rise, of about

15 m in less than 500 years [8]. (All ages are inradiocarbon years because much of both the sea-level and ice-retreat data are referred to this timescale and only in the ¢nal section is the calibratedtime scale used.) This evidence comes from boththe coral record from Barbados and from newsedimentological^palaentological records fromstable continental shelves [9^11]. Together, theyplace a reliable constraint on the total land-basedice volume during this interval.

Analyses of sea-level change from localitiesnear and within the margins of the former icesheets, for eastern Laurentia [3], Laurentia as awhole [4,5], Scandinavia [6] and the Barents^Kara seas [7], have led to the conclusion thatthe corresponding ice-sheet volumes at the LGMand/or Lateglacial time are usually less than thevolumes assumed for the ice models (e.g. [12^14])used in the rebound calculations, models that aregenerally characterised as single-domed, thick andwith quasi-parabolic ice-height pro¢les. A conse-quence of these analyses is that the sum of theregional land-based ice-volume estimates is lessthan the total volume inferred from the far-¢eldLGM sea levels and that other ice sheets experi-enced a substantial reduction in volume so as tomake up for the `missing' melt-water [14^15]. Thisled to the postulate that Antarctica contributedmore than 107 km3 to the global ocean volume[14], an amount equal to the di¡erence in ice vol-ume between the Denton and Hughes LGM mod-el for Antarctica [13] and the volume estimatedfrom the present ice sheet [16]. Direct tests ofthis hypothesis have not been possible because,while Late Holocene rebound appears to havebeen quite substantial in several localities alongthe Antarctic coast, the available sea-level evi-dence is inadequate to permit a comprehensiveinversion of changes in overall Antarctic ice vol-ume to be made [17]. A limitation of the regionalrebound inversions for ice volumes is that theproblem is not well constrained for Lateglacialand LGM times and the resulting volume esti-mates for the individual ice sheets for this earlyperiod can be quite uncertain unless there is ad-equate early sea-level information from sites with-in the former maximum ice limit [18].

It is the new results for the sea levels in the far

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¢eld and the poor resolution for the LGM vol-umes of the individual ice sheets that leads to thefollowing scenario that may not require as large aLGM Antarctic ice volume as suggested above:Ice sheets during the LGM were larger than in-ferred from the regional rebound analyses, butthese volumes were retained for only a relativelyshort time period before a rapid reduction in vol-ume occurred at about 16.5^16 ka BP. The icethicknesses of the individual ice sheets deducedfrom the regional studies of the northern hemi-sphere ice sheets, constrained by late- and post-glacial sea-level information, are appropriate forLateglacial times only, rather than for the LGMand earliest Lateglacial. The inference then is thatone or more of these ice sheets experienced a sub-stantial reshaping and loss of mass at about 16.5^16 ka BP, raising global sea level at this time byabout 15 m. Thus an equivalent amount of extraice could be stored in one or other of the northernice sheets during the LGM rather than requiringthat it be stored in Antarctica.

This is the primary issue that is explored in thispaper, using mainly the Scandinavian data as ex-ample with the understanding that the Laurentianice sheet may have experienced similar changes.Speci¢cally the question to be addressed is : canmore ice be placed into the LGM ice sheets with-out introducing inconsistencies with the inferencesdrawn from the local rebound evidence? Of thetwo major northern ice sheets, the Scandinavianrecord for rebound is the better one for such anevaluation because the observations in several in-stances extend well into the Lateglacial period andin one instance into the LGM [6], whereas theobservational sea-level record for Laurentia,where the ice cover persisted into more recenttime, is generally of shorter duration [19]. Anyconclusions reached about the limits of the earlynorthern ice sheets will be at least equally validfor inferred ice volumes for Antarctica during theLGM where the rebound record does not extendmuch beyond 8000 years BP [17].

A second and related issue, addressed brie£y, isthe source of the meltwater at 16.5^16 ka BP. If itcan be established from the far-¢eld analyses thatthe ice sheets were larger at the LGM than in-ferred from the regional studies, the absence of

good local rebound data for this time does notpermit a determination to be made of which icesheet provided the meltwater source. Ocean sedi-ment records do record the occurrence of in£ux ofland-based ice into the oceans through their ice-rafted debris [20] or oxygen isotope signals [21]but the high northern-latitude sediments do notcontain unambiguous records of this early meltingevent. Possibly the Antarctic ice sheet was respon-sible, as has been suggested for a later meltwaterpulse [22].

2. Total ice volumes since the Last GlacialMaximum

Sea-level change information from far-¢eld sitesprovides an estimate of changing ocean volumesand hence of the total ice sheet volume with twoprovisos: that (i) the observation site is free fromtectonic movements or that these movements canbe corrected for; and (ii) corrections have beenmade for the glacio-hydro-isostatic contributionsto local sea-level change.

The sea-level equation for a tectonically stablearea is [23,24]

vj rsl � vj e � vj i � vj w �1�

where vjrsl(B,t) is the height of the palaeo seasurface relative to the present and is a functionof position B and time t. vje(t) is the `ice-volume-equivalent sea-level change' (de¢ned by Eq. 3, be-low), or simply the equivalent sea-level change,associated with the change in ocean volume re-sulting from the melting or growth of land-basedice sheets on a deformable earth [23,24]. The vji

and vjw are the glacio- and hydro-isostatic con-tributions to sea-level change from the isostaticcrustal displacement and associated planetarygravity-¢eld or geoid change. Both vji and vjw

are functions of position and time. The waterdepth or terrain elevation at time t at any locationB, expressed relative to coeval sea level, is

h�B ; t� � h�B ; t0�3vj rsl�B ; t� �2�

where h(B,t0) is the present-day (t0) bathymetry or

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topography at B. The palaeoshorelines occurwhere h(B,t) = 0. Both isostatic terms in Eq. 1are functions of the earth rheology. Also, the gla-cio-isostatic term is a function of the ice massthrough time and the hydro-isostatic term is afunction of the spatial and temporal distributionof the water load: of the relative sea-level varia-tion and of the migration of shorelines.

The term vje(t) relates to the total change inland-based ice volume Vi according to

vj e�t� � b 1

b o

Zt

1Ao�t�

dV idtdt

�3�

where Ao(t) is the ocean surface area and bi, bo

are the average densities of ice and ocean water,respectively. The ocean surface area in Eq. 3 is afunction of time because of the shifting shorelinesas the relative position of land and sea is modi¢edand because of the retreat or advance of groundedice over shallow continental shelves and seas. The¢rst dependence is a function of earth rheologyand ice-load geometry which together determinethe local rate of sea-level change. The second timedependence is a function of the location of the icelimits and whether the ice sheets are located aboveor below coeval sea level. Hence the relationshipbetween ice volume Vi and equivalent sea levelvje is weakly model dependent. It should benoted that with these de¢nitions, the ice volumein Eq. 3 includes the ice grounded on the shelvesand which displaces ocean water. It should also benoted that the ice-volume-equivalent sea level de-¢ned by Eq. 3 is not the same as eustatic sea levelwhich is usually de¢ned as the globally averagedchange in ocean level. This distinction arises fromthe changing depth and shape of the ocean basinsand, even when melting has ceased and the oceanvolume is constant, the ocean basin geometry con-tinues to be modi¢ed by the isostatic adjustmentof the land and sea £oor. In consequence vji andvjw are non-zero when averaged over the oceansat any time t [23^25] and the di¡erence is notinconsequential. Writing

vj i�B ; t� � 6vj i�B ; t�sAo � N j i�B ; t� �4a�

vj w�B ; t� � 6vj w�B ; t�sAo � N j w�B ; t� �4b�

where 6 s Ao denotes the average value over theocean surface Ao at time t and Nji;w denote thespatial dependence part of the two isostatic terms,then the eustatic sea level is

vj eus�t� � vj e�t� �6vj i�B ; t�sAo�

6vj w�B ; t�sAo �5�

In evaluating these ocean-averaged values, thetime dependence of the ocean surface area againneeds to be taken into consideration. (These lasttwo terms are a more precise de¢nition of theconversion from the sea-level equivalent to eu-static sea level drop used in Denton and Hughes([13], p. 274).) We use vje(t) here rather thanvjeus(t) because it is the former that gives a directmeasure of ice volume through Eq. 3. (Some in-consistency has crept into the usage of the termeustatic sea level to which the senior author hascontributed. Initially the distinction between thevje(t) and vjeus(t) was maintained (e.g. [14,24]),but in some more recent papers (e.g. [26]), the ice-volume-equivalent sea level was dropped in fa-vour of eustatic sea level, mainly because of theclumsiness of the former term.)

If both the ice distribution through time andthe earth's response to loading are known, thenthe equivalent sea level, and ice volumes throughEq. 3, follow from observed relative sea levelsvjobs

rsl according to

vj e � vj obsrsl 3�vj i � vj w� �6�

where the vji and vjw are the model-dependentisostatic corrections from Eq. 1. The accuracywith which vje can be established depends onthe accuracy of the local sea-level observationand on the accuracy with which the isostatic cor-rections can be made. For sites far from the icemargins these latter terms represent 10^15% ofthe sea-level signal for the LGM and Lateglacialtimes and if the corrective terms can be evaluatedwith an accuracy of 10% the resulting uncertaintyintroduced into vje is of the order 1^2 m, smallerthan most observational uncertainties for the gla-cial stages.

Valuable data for the evaluation (Eq. 6) of the

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LGM and Lateglacial equivalent sea level are thedepth^age relationship of fossil corals from Bar-bados [9,10]. This locality has been subject to ver-tical tectonic movement, but this has been cor-rected for using the elevation and age of theLast Interglacial (5e) shoreline as a measure ofthe average rate of vertical movement [27]. Twocorals (Porites sp.) occur at a corrected depth ofaround 130 m and have been dated at between18.5 and 17 ka BP. The main period of early coralgrowth (Acropora sp.) appears to have occurredlater, after about 16 ka BP, and these corals nowoccur in water depths of about 110 m. It is thetwo older corals, rather than the second group,that we believe mark the LGM and that theyounger group is representative of immediatepost-LGM conditions (see below). The coralsmark a lower limit to sea levels at this locality,the actual sea level having been as much as 5^8 mabove the Acropora corals at the time of theirgrowth and possibly more for the Porites corals.

Another important indicator of past sea levels

is the age and depth of sediments or peats thatmark the transition from terrestrial or lagoonalconditions to marine conditions as sea level rosefrom its LGM lowstand to its present level. In theprotected palaeo Bonaparte Gulf of northwesternAustralia, this evidence has been undisturbed andpreserved and has provided detailed evidence ofthe sea-level change throughout the LGM andLateglacial [11,28].

Fig. 1 illustrates the LGM and early Lateglacialice-volume-equivalent sea levels inferred from thevarious data sources based on the relationship Eq.6 and nominal earth- and ice-model parametersdiscussed below. Also shown are the correspond-ing land-based (including grounded) ice volumes.The observations for the time of maximum glaci-ation, both the coral data from Barbados and thesediment data from the Bonaparte Gulf, are indi-cative of a prolonged period when equivalent sea-level was constant, from 19 ka BP or earlier, until16.5 ka BP. This is followed by a period of veryrapid sea-level rise, of about 15 m in less than500 years after which the sea-level rise was lessrapid due to the more gradual and more uniformdecay of the ice sheets.

3. Crustal rebound and sea-level change in theformerly glaciated regions

Sites where the sea-level or crustal rebound sig-nal is most sensitive to the thickness of the iceload are those near the centres of former glacia-tion (near-¢eld sites), but the observational recordis limited in time to the ice-free period only. Ob-servations from near the ice margins for the LGMand early part of the Lateglacial period are there-fore few. Of the two major northern ice sheets, theScandinavian one is the better for rebound anal-ysis because the observational record of sea-levelchange is more complete and in several instancesthe record extends into the Lateglacial period andin one instance into the LGM.

3.1. Fennoscandia

Earlier studies [4,29] concluded that ice modelssuch as that proposed by Denton and Hughes [13]

Fig. 1. The upper and lower limits (dashed lines) of the ice-volume-equivalent sea level inferred from observed sea levelsfrom northern Australia and Barbados. The open circles re-fer to brackish water fauna and the solid circles refer to shal-low marine fauna from northern Australia [11]. Two olderobservations from the same region [28] are shown by thecrosses. The Barbados corals are shown as open triangles[9,10]. The right hand axis gives the corresponding volume ofland-based ice, including ice grounded below sea level on theshelves.

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contained more ice than is acceptable by the sea-level data. In this latter, glaciologically arguedmodel, the maximum ice thickness at the LGMexceeds 3000 m and is centred over the Gulf ofBothnia. But for a very wide range of earth-modelparameters it leads to an excessive rebound [6]with consequences that the Baltic Sea is predictedto have been open to the Arctic Ocean in Late-glacial times when the ice had retreated from Fin-land, that much of Finland remained submergeduntil Mid and Late Holocene time, and that theBaltic remained open to the Atlantic at the timesof the fresh-water Baltic Ice Lake and AncyllusLake, all inconsistent with observational evidence[30]. The outcome of inversions for both earth-rheology and ice thickness estimates is that duringthe LGM and Lateglacial time, the ice is relativelythin over eastern and southern Scandinavia andthat the ice height increases relatively slowly withdistance from the ice margin when compared withthe steeply domed models with thick quasi-para-bolic pro¢les of Denton and Hughes [13]. In thenorth and west, the ice-height pro¢les appear tobe more consistent with such quasi-parabolicmodels [6,30]. Fig. 2 compares the ice thicknessesfor the thin-ice model with the LGM model pro-posed by Denton and Hughes for a section acrossScandinavia. This comparison clearly illustratesthe very di¡erent ice volumes contained in thesetwo ice models.

In the inversion [6] for the Scandinavian icevolume it has been assumed that ice-height pro-¢les remain similar throughout the deglaciationphase, implying that basal conditions controllingthe ice-height pro¢les have remained unchangedthrough time. Because few early-Lateglacial ob-servations exist, tests of this assumption are fewalthough the few ice-margin observations that areavailable from the Norway coast (e.g. from An-dÖya) indicate that the model predictions under-estimate the rebound [6]. Thus a greater ice vol-ume is appropriate in at least northernScandinavia for this early period and one scenariois that during the LGM, the Scandinavian icesheet overall contained more ice than is inferredfrom the rebound inversions: that thicker icecould be supported during the LGM because theconditions at the base of the ice sheet were ini-tially favourable for this, i.e. cold and rigid, butthat in early Lateglacial time a change in basalconditions occurred leading to a rapid thinningof the ice and ice-thickness pro¢les that aremore consistent with those inferred from the in-version of the sea-level data (Fig. 2) [31]. Therapid rise in the ice-volume-equivalent sea levelnoted from the far-¢eld localities (Fig. 1) suggeststhat this transition could have occurred in theshort interval 16.5^16 ka BP.

Fig. 3 illustrates the time dependence of the icevolume (model S0) resulting from the inversion of

Fig. 2. Ice-height pro¢le across Scandinavia at the Late Glacial Maximum according to: (i) Denton and Hughes [13]; and (ii) themodel that is consistent with the inversion of sea-level data from the region [6].

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the Scandinavian sea-level data [6] as well as thatof the preliminary ice model (S1) [9] that wasbased on the Denton and Hughes LGM model[13] and on published ice retreat reconstructions[32,33]. The three other models (S2^S4) di¡erfrom S0 only in their ice content during theLGM and earliest Lateglacial time. These variantsare not necessarily intended to have physicalmeaning, rather, they are introduced to establishthe sensitivity of the rebound predictions to theearly part of the ice history. In models S2 and S3,

the ice at the time of the LGM is assumed tofollow the ice thickness pro¢les of Denton andHughes, but their amplitudes have been scaledby 0.7 such that the maximum ice thickness isabout 2400 m [29]. In S2, the maximum ice per-sists from 19.0 ka BP until 16.5 ka BP at whichpoint it is reduced everywhere and linearly overthe next 500 years to the ice thicknesses of modelS0 at 16 ka BP. This model implies that a rela-tively thick ice sheet did initially develop over theGulf of Bothnia and Finland, but that at 16.5 kaBP, it rapidly decreased in volume with the centreof loading shifting westwards. Model S3 is thesame as S2 except that the duration of theLGM is longer, with maximum ice volumes ¢rstattained by 23 ka BP. Model S4 is constructed ina similar way to S2 except that the full Dentonand Hughes [3] model is used for a short-livedLGM which then decays to the model S0 in theinterval 18.5^16 ka BP. All of these European icemodels include a Barents^Kara ice sheet [7]. Oth-er ice sheets used in the calculation include amodi¢ed ICE-1 ice sheet [34] for the westernhalf of the northern hemisphere (see below), anda model for Antarctica based on the di¡erencebetween the Denton and Hughes [13] model andthe present ice sheet [16], scaled down so as tocontribute 25 m to equivalent sea level at thetime of the LGM and whose rate of melting isin phase with that of the northern hemisphere.

The earth model parameters adopted for thepreliminary calculations are those discussed inearlier analyses of European sea-level observa-tions and which have been found to give a satis-factory agreement between observations andpredictions. The model used here (E0) is charac-terised by a lithosphere of e¡ective elastic thick-ness Hl of 65 km, an upper mantle with an aver-age e¡ective viscosity Rum of 4U1020 Pa s,extending from the base of the lithosphere downto 670 km depth, and a lower mantle with anaverage e¡ective viscosity Rlm of 1022 Pa s. (Thisnominal earth model di¡ers in a small and unim-portant for present purposes way from the opti-mum solution inferred in [6]).

Fig. 4 illustrates the predicted sea levels for thepast 20 000 years at four representative sites inScandinavia. (Fig. 5 illustrates the location of

Fig. 3. Ice volumes of (a) Scandinavian and (b) North Amer-ican ice models since the LGM. In a, S0 corresponds to themodel inferred from the inversion of the Scandinavian sea-level data [9] and S1 is an adaptation of the Denton andHughes ice model [13]. S2^S4 are variants of S0 in which icevolumes are enhanced during the Last Glacial Maximum. Inb, L0 is adapted from ICE-1 [34] and L1 and L2 are variantsof this model, di¡ering in the amount by which ice volumeshave been increased during the Last Glacial Maximum.

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these and other sites, along with the limits of theice sheet at the time of the LGM.) The arrows forthe predicted curves at each site indicate the ageof the oldest evidence of sea-level change at thatsite. Models S2 and S3 lead to nearly identicalpredictions throughout Holocene and Lateglacialtimes and the di¡erences become notable only forthe LGM and earlier. Hence the assumed dura-tion of the LGM is not critical for the predictionsof Lateglacial and more recent sea levels. At mostof the localities, the di¡erences in the predictionsof sea level, based on ice model S0 and S2, remainrelatively small for the period of observation andcomparable to the uncertainty estimates of theobservational data (cf. [6]). Where this is not sois for Óra®svatn (AndÖya) where the record ex-tends back to 18 ka BP [35]. (Here there is aninconsistency in the model in that at this timethe ice limit is assumed to have stood near the

outer edge of the continental shelf [32], whereasthe northern end of AndÖya appears to have al-ready been ice free by this time. Similar inconsis-tencies occur in Lateglacial times at some otherNorwegian coastal locations (e.g. in J×ren [6]),and this emphasises the need for an improvedchronology for the ice margin and its retreat.For present purposes, these inconsistencies areembarrassments rather than being of serious con-sequence.) Otherwise, for most sites with observa-tional data, little distinguishes the predictionsbased on models S0 and S2. At both Óra®svatnand Brusand (J×ren), predictions based on modelS4 do di¡er substantially from those based on S0,indicating that there is a limit to the amount of icethat can be introduced into the LGM withoutperturbing the Lateglacial predictions in a signi¢-cant manner.

Fig. 6 illustrates the comparisons of observed

Fig. 4. Predicted sea levels at four locations in Scandinavia (see Fig. 5a for locations) according to di¡erent ice models (de¢nedin Fig. 3, and including the standard models for the other ice sheets). The arrows indicate the oldest observations in the region.

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and predicted sea levels for the large Scandinavianobservational data base [6] for the three modelsS0, S2 and S4. The best agreement between ob-servations and predictions occurs for model S0 asis expected because the ice model was the result ofthe inversion of this sea-level data base and for aearth model similar to that used here. For theother two models, the distributions of the normal-ised residuals

�vj obsrsl 3vj pred

rsl �=c �7�

where vjobsrsl and vjpred

rsl are vectors of the observedand predicted sea-level values and c is a vector ofstandard deviations of the former, become in-creasingly skewed, indicating that, particularly

for S4, the predictions, based on the nominalearth model E0 used, overestimate the rebound.This does raise the question whether the ice mod-els inferred from the rebound analysis are depen-dent on the earth-model parameters, whether forthe model S2, for example, there is a set of three-layered earth-model parameters that leads to abetter agreement with the observations thandoes the combination (E0, S0). This will need fur-ther investigation.

3.2. North American ice sheet

Glaciological models of the Laurentian icesheet at the time of the last peak glaciation sug-gest that this ice sheet, excluding the Cordilleranand Innuitian contributions, contained enough iceto globally raise sea level by between about 40and 110 m [12,13,36] and considerable divergenceof views remain about the ice thickness throughtime. The use of sea-level observations to con-strain models of the ice load here have generallybeen less successful than in the case of Scandina-via because the quantitative evidence for reboundis mostly limited to the eastern and northern partsof the former ice margin. Nevertheless, di¡erentanalyses [3,4,37] have all led to a similar conclu-sion, that thick, single-domed, quasi-parabolicpro¢led ice sheets, that persist over North Amer-ica until early Holocene time, result in an over-estimation of the rebound and that substantialreductions in ice volumes are required for Late-glacial times. Nakada and Lambeck [38] con-cluded that the ice thickness of the Laurentidepart of the ICE-1 model [34] needed to be scaleddown to about 70% of its initial values in orderfor the predictions to match reasonably the ob-served sea-level changes in the Hudson Bay area.Likewise, the more comprehensive analysis byTushingham and Peltier [4] resulted in an icemodel (ICE-3G) whose thickness over the sameregion at 10 ka BP is signi¢cantly less than thatcontained in ICE-1 at the same epoch, althoughboth models have similar, but not identical, icethicknesses here for the LGM. However, evenmore than in the case for Fennoscandia, inver-sions of the available sea-level data resolve onlypoorly the early part of the ice record because the

Fig. 5. Locations of sites corresponding to the predictions il-lustrated in Figs. 4 and 7 and model ice limits at time ofLast Glacial Maximum. (a) Scandinavia: 1 = Óra®svatn, An-dÖya, 2 = Aî ngermana«lven, 3 = Brusand (J×ren), 4 = Oslofjor-den. (b) North America: 1 = Churchill, 2 = Ottawa Island,3 = Boston.

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observational evidence within and near the icelimit does not extend far back in time. Withinthe Hudson Bay area, for example, the regiondid not become ice free until about 8000 yearsBP and the record does not predate this time.Hence, analogously with the Scandinavian exam-

ple, it is possible to introduce more ice into theearly part of the Laurentian LGM ice sheet with-out this making a signi¢cant impact on the com-parison of predicted and observed sea-level varia-tions for Holocene time.

Predictions for sea-level change at a number of

Fig. 6. Observed versus predicted sea levels and histograms of the normalised residuals (de¢ned by Eq. 7) for earth model E0and three Scandinavian ice models S0, S2, S4.

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representative North American sites are illus-trated in Fig. 7 for ice models that di¡er only intheir volumes before early-Lateglacial time. (Fig.3b illustrates their ice-volumes and Fig. 5b givesthe locations of three of the sites for which thepredictions are made.) Model L0 is based on ICE-1 [34] smoothed and interpolated onto a 1³ lati-tude by 1³ longitude spatial grid and a 1000 yeartime grid, with a pre-LGM record that follows thepattern of £uctuations inferred from the N18O ma-rine record and the Huon reef data [39]. ModelL1 is the same as L0 after 16.0 ka BP, but the icethickness from 16.5 ka BP back into pre-LGMtime is everywhere scaled upwards by a factor of

1.4 and with a linear transition between 16.5 and16 ka BP. Model L2 is another variant of L1 inwhich the ice thickness from 0 to 14 ka BP is thesame as in L0, the same as L1 for 16.5 ka BP andearlier, and with the transition from 16.5 to 14 kaBP occurring in two steps; initially rapid over500 years starting at 16.5 ka BP and then at areduced rate from 16 to 14 ka BP. As for theScandinavian case, these ice models are not basedon any particular physical arguments but are in-troduced only to examine the in£uence of theearly melting history on sea-level predictions inLate- and Postglacial times.

From the comparisons in Fig. 7 it is clear that

Fig. 7. Predicted sea levels at four North American localities (see Fig. 5 for localities of the Hudson Bay sites of Churchill andOttawa Island). Predictions are based on earth model E0 and Laurentian ice models L0, L1, L2. Standard ice models are in-cluded for the other ice sheets.

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the rebound predictions are insensitive to theearly melting history, particularly for the last8000 years for which most of the observationaldata from within the maximum ice limit exists.In the Hudson Bay area, for example, the dataextend back to only about 7 ka BP and all threemodels lead to very similar sea-level predictionsfor this interval. For sites close to the maximumice margin, such as Boston, the record extendsback to about 12 ka BP but, here also, the pre-dictions based on the three models di¡er byamounts that are less than the combined uncer-tainties arising from the observational data andfrom inadequate knowledge of the local detailsof the ice sheet. Southwards, the record extendsfurther back, to about 15 ka BP along the coast ofVirginia, but at these distances from the ice sheetthe isostatic terms are of second order and theobservations have little power to discriminate be-tween the di¡erent LGM models (cf. the predictedsea levels for Miami in Fig. 7). Hence, from re-bound inversions alone, the LGM ice volumes canbe increased by up to at least 40% over that in theinitial model without leading to signi¢cant dis-crepancies in sea-level predictions for Postglacialtimes, provided that this additional ice is removedearly in Lateglacial time.

4. Discussion

The above indicative analysis for the Scandina-vian and North American rebound illustrates thatwhen evidence for past sea-level positions is ab-sent for LGM and early Lateglacial times for lo-calities close to or within the limits of formermaximum glaciation, the ability to estimate max-imum glaciation ice volumes for the individual icesheets is limited (Figs. 4 and 7). This conclusion iseven more true for the Antarctic ice sheet with itsvery limited sea-level data base [17]. In contrast,high resolution data for this period from localitiesfar from the ice margins do provide a good con-straint on the total volume of ice and of the rateof melting (Fig. 1). In particular, this evidenceindicates that a rapid rise of sea level occurredat about 19 ka BP (calibrated), raising the levelby about 15 m in as little as 500 years or less. (All

ages in the discussion section now refer to thecalibrated time scale [40].) Ice sheets over eitherScandinavia and North America in which a rapidand substantial reduction in ice volume occurredat this time, lead to rebound that is consistentwith the observational evidence from within theformer ice margins and, in fact, is required bydata from AndÖya. In the case of Scandinavia,the rebound evidence dictates a relatively thinice sheet over the eastern and southern regionsin Lateglacial time and the inference is that aninitially thick ice sheet became unstable at about19 ka BP that, while discharging a substantialvolume of ice into the oceans, resulted in thechange of ice thickness pro¢les over the easternand southern parts of the ice dome (cf. Fig. 2).Physically, this suggests that basal conditionswere initially cold and frozen but that basal thaw-ing commenced as early as 19 ka BP (cf. [31,36]).There was never enough ice in the Scandinavianice sheet to alone explain the 15-m sea-level risenoted for this period (Fig. 1) and this implies thatthe Laurentide ice sheet, or possibly the Antarcticice sheet, must have experienced a comparablecollapse at about the same time, possibly a desta-bilising consequence of the rising sea level fromone ice sheet adjustment on the other.

Fig. 1 compares observed and predicted ice-vol-ume equivalent sea-level change where the latter isbased on the northern hemisphere ice models S2and L2 and the nominal Antarctic ice modelwhose volume change since the LGM has beenuniformly scaled down from a maximum of 37 m[14] to 25 m of equivalent sea level. That is, onlythe northern hemisphere ice sheets are assumedhere to have participated in the rapid ice-volumereduction event at 19 ka BP. The predictions rep-resent quite well the rapid change at the end ofthe LGM, although the magnitudes of the pre-dicted sea levels for both the LGM and Lategla-cial are less than the observed values, suggestingthat the ice volumes of the individual ice sheetscould be further increased for the early part of theLateglacial.

Rapid changes in relative sea level since thetime of the LGM have been previously reported.Fairbanks [9], for example, inferred from the Bar-bados coral record a rise of about 25 m between

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14.7 ka BP and 13.7 ka BP, denoted as Meltwaterpulse 1A (Mwp-1A) (see also [40]), and Blanchonand Shaw [41] inferred, from the same coral evi-dence, a rise of 13.5 m in less than 300 yearswithin this interval. Possibly there is a chronologyproblem with the Lateglacial and LGM data. Allages for the northwest Australian data have beenAMS radiocarbon dated [11]. Many of the faunalspecimens lived in brackish water conditions sothat reservoir corrections should be less thanthat for full-marine fauna. For the latter a correc-tion of about 1000 years appears appropriate forLGM conditions [42] and 400 years has beenadopted for the LGM brackish-water samples.Possibly the radiocarbon time scale is not linearat times of the rapid sea-level rise. This time scaleis based on an assumption of equilibrium beingestablished between 14C production in the atmos-phere and uptake in the oceans (ignoring othersinks), with a major part of this uptake occurringduring the subduction of surface waters in theNorth Atlantic. This North Atlantic deep waterformation is sensitive to changes in the salinityand temperature of the surface waters and theinjection of fresh water will a¡ect the rates andsites of the deep water formation and also changethe balance between rates of 14C production anduptake. Hence non-linearities in the 14C time scalecan be anticipated, as occurred at the time of theYounger Dryas [40], but this is unlikely to lead toerrors of the magnitude required if the terminal-LGM meltwater pulse is the same as Mwp-1A,and the two must be seen as distinct events ofrapid sea-level rise.

Clark et al. [22] examined possible origins forthe Mwp-1A and their arguments are equally val-id for the `terminal-LGM Mwp', reported here,whose £ux of freshwater input is 0.3^0.4U106

m3 s31, about the same as that inferred forMwp-1A. If the origin of the meltwater is theLaurentian ice sheet, then the only plausible es-cape route for the majority of this water into theNorth Atlantic is by ice calving and transport viathe Hudson Strait, there being no likely mecha-nism that can melt large volumes of ice quicklyenough to escape via the Mississippi drainage sys-tem [22]. Like Mwp-1A, the large £ux of water

into the ocean at the end of the LGM does notappear to have left a clear and consistent geo-chemical signal in the ocean sediments in contrastto the smaller in£uxes associated with Heinrichevents seen in the North Atlantic [20], the majorpost-LGM event H-1 occurring well after the ter-minal-LGM meltwater pulse. These events areseen as sharp peaks in the relative abundance ofice-rafted debris as well as in planktonic foramin-ifera signatures that are indicative of cooling andfreshening of the surface waters. However, suchpeaks are not restricted everywhere to the timingof the established Heinrich events and a similarpeak occurs in some sediment cores at the time ofthe terminal-LGM meltwater pulse. For example,in core SU90-24 [43], the amount of ice-rafteddebris deposited at this time is similar to, or great-er than, that deposited at times corresponding tosome of the recognised Heinrich events. Such apeak is also seen in Nordic seas cores [44], indi-cating that it may be quasi-synchronous for thetwo major northern ice sheets.

Clark et al. [22] have suggested that the sourceof the Mwp-1A may have been the Antarctic icesheet. They review the limited evidence for, anddivergent views on, the post-LGM history of thisice sheet and note, interalia, that Antarctic icevolumes could have been substantially larger atthe LGM without this being detectable from ob-servations of rebound of the continent's margin.Recent evidence of raised shorelines from theVestfold Hills and elsewhere indicates that a sub-stantial reduction in ice volume must have oc-curred in Lateglacial times [17], but the observa-tional record does not extend su¤ciently far backin time to provide a useful constraint on the icevolumes for the earlier period. The N18O signal inone deep-sea core from the Southern Ocean [45],as well as in the Vostok ice core [46], indicate thatwarming in the southern hemisphere may havestarted quite abruptly at about 20 calibrated kaBP (about 16.7 radiocarbon ka BP) and a partialdispersal of the ocean-bordering ice sheet mayhave followed soon after. This would be consis-tent with evidence from the N18O signal in diatomsof meltwater input into the Southern Ocean dur-ing the last cold stage [47].[AC]

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