Late Devensian and Holocene records of relative sea-level...

*Corresponding author. Tel.: 0044-191-374-2496; fax: 0044-191-374-2456.

E-mail address: [email protected] (I. Shennan).

Quaternary Science Reviews 19 (2000) 1103}1135

Late Devensian and Holocene records of relative sea-levelchanges in northwest Scotland and their implications for

glacio-hydro-isostatic modelling

Ian Shennan!,*, Kurt Lambeck", Ben Horton!, Jim Innes!, Jerry Lloyd!, Jenny McArthur!,Tony Purcell", Mairead Rutherford!

!Environmental Research Centre, Department of Geography, University of Durham, Durham DH1 3LE, UK"Research School of Earth Sciences, The Australian National University, Canberra, ACT 0200, Australia

Abstract

Raised tidal marshes and isolation basins (lakes that were once connected to the sea) in northwest Scotland record changes inrelative sea level following deglaciation during the Late Devensian to the present. The Kentra to Arisaig area, which was covered byrelatively thick ice (c. 900 m) at the Last Glacial Maximum (LGM), shows a regression from a marine limit between 36.5 m OD and40 m OD at c. 15.9 kyr cal BP (range 15.6* 16.3 kyr cal BP) through to an early-Holocene minimum. A range of sites in the same arearecord a mid-Holocene maximum, indicative of mean sea level c. 6.5 m above present. The maximum is not a well-developed and shortduration highstand as predicted by a number of models, but is an extended period,&8.0 } 5.0 kyr cal BP, with sea level within c. 1 m ofthe maximum. Sites to the north, in Kintail, show no Late Devensian record because much of the area lies within the Younger Dryasice limit. The altitude of the mid-Holocene maximum in Kintail is not well constrained, but occurred 7.9 } 8.1 kyr cal BP. Furthernorth, sites on the Applecross peninsula record a Late Devensian fall in sea level and a Holocene maximum for mean sea level nohigher than c. 3.0 m above present. In Coigach, the furthest north of the new sites and well outside the Younger Dryas Ice limit, there isno evidence recorded of Late Devensian sea levels above present. The Holocene maximum here was around c. 2.5 m above present.

These observations of sea-level change, all standardised to change in mean sea level relative to present, constrain the glacio-hydro-isostatic rebound model parameters. Earth models comprising three mantle layers, with lateral viscosity and elastic parameters, givea satisfactory description of rebound. The parameters H

-(lithosphere thickness)"65 km, g

6.(upper mantle viscosity)"4]1020 Pa

14C seconds and g-.

(lower mantle viscosity)"1022 Pa 14C seconds give the best overall agreement but discrepancies betweenobservations and predictions remain. An increase of 10% in ice thickness north of the Great Glen, compared to the previous optimumice model, provides good agreement for many sites but important discrepancies remain for the northern sites and indicateinadequacies in the model of the British ice sheet. Several alternative ice models are examined but the various combinations of earthand ice-model illustrate the non-uniqueness of the solution. A combination of more extensive ice limits, especially onto the HebrideanShelf and West Shetland Shelf, and some changes to ice thicknesses over the mainland should produce a better agreement, but thespatial coverage of observations remains a limitation to producing a unique solution. The characteristics of the Holocene highstand,age, duration and amplitude, at the di!erent sites refutes the assumption that globally deglaciation ceased abruptly 7000 yr ago. Theobservations are consistent with an ice model that includes c. 3 m of melting over the last 7000 yr. ( 2000 Elsevier Science Ltd. Allrights reserved.

1. Introduction

Previous studies from northwest Scotland providea rich record of Late Devensian and Holocene relativesea-level changes from around 12 kyr 14C BP to the

present. The main features are a rapid, c. 9 mm/14C yr,fall of sea level before 10 kyr 14C BP, an almost station-ary level in the early Holocene, a rise to a mid-Holocenemaximum and then falling in the Late Holocene (e.g.Shennan et al., 1995a). This general form is the result ofthe interplay of isostatic rebound and eustatic sea-levelrise and this interplay has been quantitatively modelledfor di!erent parts of the Earth (e.g. Lambeck, 1993a, b;Peltier and Andrews, 1976; Peltier, 1998). Observationsof relative sea-level change provide constraints on both

0277-3791/00/$ - see front matter ( 2000 Elsevier Science Ltd. All rights reserved.PII: S 0 2 7 7 - 3 7 9 1 ( 9 9 ) 0 0 0 8 9 - X

components, "rstly on the isostatic rebound and there-fore on the mantle rheology model and ice model para-meters, and secondly on the eustatic change, that is, onthe magnitudes of grounded ice volumes and rates ofmelting of the global ice sheets.

Observational constraints from much of northwestScotland (Fig. 1) on past models have been limited toa few isolated data points and on assumed ages for someof the principal shorelines, in particular the `MainRock Platforma and the `Main Postglacial Shorelinea(Peacock, 1970; Robinson, 1977; Sissons and Dawson,1981; Dawson, 1988; Lambeck, 1993a, b, 1995 and refer-ences therein; Stone et al., 1996). Broad agreementbetween the general form of observed and predictedrelative sea-level changes has been achieved but signi"-cant discrepancies also have been identi"ed (Fig. 2)and indicate that more precise observations could pro-vide important constraints on the Late Devensian icesheet over Scotland. More observations are now avail-able, based on investigations of a range of palaeoenviron-ments that record relative sea-level changes (Fig. 1 andTable 1). From this range of palaeoenvironments thetidal marshes and isolation basins provide the most re-liable, precise sea-level index points. In contrast, wetlandenvironments that formed behind coastal sand dunes orgravel barriers contain important evidence of coastalevolution, but the sea-level change component is noteasily separated from the e!ects of storms or variations insediment supply.

The aims of this paper are to compare these observa-tions with the model predictions, to test the validity of thelatter and then infer from any discrepancy improvementsto the model parameters. Finally we assess the implica-tions of the results for palaeocoastline reconstructionsbeyond the immediate area of NW Scotland.

2. The 5eld data

The area of northwest Scotland examined lies betweenArdnamurchan and the Beauly Firth (Fig. 1), with new"eld data collected from "ve areas on the west coast. Thisselection was based on the following reasons. Over muchof Scotland there are well developed morphologicalshoreline features whose ages are poorly constrained andin particular there is a lack of radiocarbon dated relativesea-level data of Late Devensian age. Recent studies fromthe Arisaig area (Fig. 2 and Table 1) show that in thenorthwest well constrained records can be obtained andthere is a range of palaeoenvironments preserved thatrecord relative sea-level change. Comparisons of obser-vations and model predictions of relative sea-levelchange suggest that there is uncertainty over the dimen-sions of the Late Devensian ice over northwest Scotland(Lambeck, 1995; Shennan et al., 1995a; Ballantyne et al.,1998).

From initial "eld and laboratory investigations ofsome 50 sites we selected those sites that were likely toprovide precise sea-level index points. Details of themethods employed for establishing the age-height rela-tionships of the sea-level indicators have been previouslypublished (references in Table 1) and we present here onlythe summary litho- and bio-stratigraphy. Full details willbe published elsewhere. All of the new sea-level indexpoints (Table 2) are from either isolation basins or fromnow elevated tidal marshes. Table 2 shows the verticalrelationship of each index point to the estimated tidelevel at which it formed and the di!erences for such levelsbetween the various sites.

Descriptions of sediments in the "eld followed Troels-Smith (1955), but those shown on the "gures are modi"edto include our interpretation of the sequences followingbiostratigraphic analysis and simpli"ed for the sake ofclarity of reproduction. Preparation of samples formicrofossil (pollen, dino#agellate cysts, diatoms,foraminifera and thecamoebians) analysis follows stan-dard methods (Moore et al., 1991; Palmer and Abbott,1986; Scott and Medioli, 1980) and, unless indicated inthe text or "gures, the data shown are percentages basedon a minimum count of 200 individuals per level.

Our "eld sites fall into "ve areas: Kentra, Arisaig,Kintail, Applecross, and Coigach (Fig. 1). For each areawe present new data and a reconstruction of relativesea-level change based on the new and previously pub-lished data. Table 2 includes all the sea-level index pointsfrom the "ve areas. All dates are listed with both conven-tional radiocarbon ages and calibrated ages based onStuiver and Reimer (1993), their method A, using 95%con"dence limits. We also applied the revised calib-ration of Hughen et al. (1998) for 8.9 to 12.7 kyr 14C BP.While the two calibrations match at 8.9 kyr 14C BP, and9.9 kyr cal BP, they show a 400 yr di!erence for a sampledated 12.7 kyr 14C BP. This makes no fundamentalmodi"cation to the interpretations of the sequences de-scribed the following sections. All radiocarbon-datedsamples mentioned in the text and shown on microfossildiagrams are abbreviated to the minimum and maximumcalibrated ages shown on Table 2. The preliminary modelpredictions presented in later sections are all based onthe radiocarbon time scale, the time scale also used tode"ne the history of the ice sheets. Use of the radiocarbontime scale for the model predictions is discussed later.Table 2 also shows the indicative meaning of each indexpoint, i.e. the present tide level represented the indexpoint, interpreted from the litho- and bio-stratigraphicdata. These data also show the tendency of sea level,negative for a reduction in marine in#uence and positivefor an increase, from which a relative fall or rise of sealevel may be indicated. The indicative meanings allowdirect comparison of di!erent types of index points bystandardising the altitude to relative sea level (RSL)change from present (Table 2), with an error term that

1104 I. Shennan et al. / Quaternary Science Reviews 19 (2000) 1103}1135

Fig. 1. Location map of the "eld study area, with insets of the sites from which new sea-level data are described.

includes the sum of all the quanti"ed height errors, in-cluding "eld levelling, present tide heights, and inter-pretation of the indicative meaning (total error"J(e2

1#e2

2#2e2

n)).

2.1. Kentra

The only new information is re-dating of the isolationcontact for the basin at Ardtoe. The original radiocarbon

I. Shennan et al. / Quaternary Science Reviews 19 (2000) 1103}1135 1105

Fig. 2. Observations of relative sea-level (RSL) change for the Kentra} Arisaig area provides an independent test of models of Late Deven-sian and Holocene isostasy, ice loads and relative sea-level change. Theobservations are from a number of recent publications (summarised byShennan et al., 1995a, b, 1999a) and were not used in the calibration ofthe models used for the predictions (Lambeck, 1995). Predictions andobservations show good agreement in the general form of relativesea-level change through time, but with signi"cant di!erences in themagnitude and age of the turning points and the age of the rapid LateDevensian relative fall in sea level. The predicted altitude of the mid-Holocene maximum is in close agreement with the observations,though the latter record a much #atter peak, i.e. of longer duration. Thedi!erences between the predictions and observations could indicatea larger ice mass, by approximately 15%, in the area to the NW of theGreat Glen at the last ice maximum, in comparison to current ice sheetreconstructions (Lambeck, 1995). A larger ice mass could also explainthe di!erences between the predictions and observations from Fear-nbeg and around Inverness (Firth and Haggart, 1989; Lambeck, 1995;Shennan et al., 1996a).

date was for a 3 cm slice directly above the isolationcontact analysed using conventional radiocarbonmethods (Shennan et al., 1996b), whereas the new date isan AMS date for a 1 cm thick sample on the isolationcontact. This provides a better age, older by over 700 yr(Table 3), for the relative fall of sea level across the sill ofthe basin because the original sample obviously includesmore post-dating the isolation of the basin.

Apart from the relative fall of sea level recorded atArdtoe, and a limiting date from Kentra Moss core 32(Shennan et al., 1995b) the relative sea-level record issparse until the fall from the mid Holocene maximum,after which it is well constrained. (Fig. 3).

2.2. Arisaig

The rocky glacially eroded landscape of the Arisaigarea provides a series of rock-lipped depressions thathave accumulated shallow marine, intertidal, lacustrineand terrestrial sediments since the time of deglaciation.Previous studies (Shennan et al., 1993, 1994, 1995a, b,1996a, b, 1999a) securely constrain relative sea-level cha-

nges during the Holocene and back to approximately12 kyr 14C BP (c. 14 kyr cal BP) in the Late Devensian,with the highest index point from the isolation basin atRumach Meadhonach, sill at 17.8 m OD. Further "eldsurveys revealed a series of isolation basins up to UpperLoch Dubh, sill at 36.5 m OD (Fig. 4). At Lochana Chleirich, sill just above 40 m, diatom analyses recordno marine sedimentation. Therefore, we infer that themarine limit in this area lies between these two altitudes.This "ts well with the terraces and banks of shingle andsand, interpreted as raised beaches, at 41 m OD justnorth of Arisaig (Peacock, 1970). All of the new datacome from basins that show very similar lithostratigra-phy, comparable with that from Upper Loch Dubhwhich, from base to top comprises: (1) basal blue greyclay silt with a trace of sand; (2) green grey silty organiclimus; (3) thin blue grey silt with sand; (4) green brownorganic limus with herbaceous detritus; (5) brown Sphag-num peat; (6) dark brown herbaceous peat with wood. Inaddition, the original cores from the basins at Loch nanEala and Rumach were resampled and re-dated using theAMS radiocarbon technique.

Diatom analyses for each of the new basins, and theforaminifera and charophyte oogonia where present,show that in each case the transition between lithostrati-graphic units 1 and 2 represents part of the isolationprocess (Fig. 5). The samples dated come from the lithos-tratigraphic boundary (i.e. the lowest level withinsu$cient organic material to date). Variations in basinhydrology, balancing tidal input against freshwater dis-charge, and organic productivity will in#uence both theage and the indicative meaning of the index point. How-ever, the altitude parameter is well constrained by thestaircase of basins. Where the lithostratigraphic bound-ary, and therefore the dated sample, is coincident withthe decline from marine-dominated diatom assemblages,the radiocarbon age is always the oldest for the cluster ofbasins at similar altitudes, for example Lochan nan TriChriochan, Loch Dubh and Loch a Mhuilinn (Fig. 5).These date an earlier stage in the isolation process com-pared to the other basins. The scatter of sea-level indexpoints (Fig. 6) is consistent with these variations, allow-ing for indicative meanings from mean high water ofspring tides for those samples recording the later stage ofthe isolation process, and mean high water of neap tidesfor those relating to the earlier stage.

In addition, the oldest dates from the highest basins,Upper Loch Dubh and Lochan nan Tri Chriochan, con-strain the ice sheet reconstructions, giving a minimumage (c. 15.5 to 16.25 kyr cal BP) for deglaciation in thearea. Freshwater, including halophobic species charac-terise the higher clastic layer, unit 3. This accumulatedduring the Younger Dryas (Loch Lomond) Stadial whenan ice sheet reached to within 6 km of the site.

The relative sea-level plot for the Arisaig area (Fig. 6)also includes seven replacement dates obtained using


Table 1Published studies and sites presented in this paper with radiocarbon-dated reconstructions of relative sea-level change in north and northwestScotland

Area and sites Type of palaeoenvironment Summary of relative sea-level record Reference

KentraKentra Moss Tidal marshes Late Holocene RSL fall Shennan et al. (1995b)Ardtoe Isolation basin Late Devensian RSL fall Shennan et al. (1996b)

ArisaigLoch nan Eala Isolation basins Late Devensian RSL fall, early Holocene rise,

late Holocene fallShennan et al. (1994)

Glenancross Wetland and barrier Mid Holocene RSL maximum Shennan et al. (1995a)Mointeach Mhor Wetland and barrier Mid Holocene RSL maximum Shennan et al. (1995a)Gartenachullish Wetland and barrier Early Holocene RSL rise Shennan et al. (1999a)Rumach Isolation basins Late Devensian RSL fall Shennan et al. (1993, 1996a)7 new sites Isolation basins Late Devensian RSL fall This paper

KintailLoch nan Corr Isolation basin Early Holocene RSL rise through to Late

Holocene RSL fallThis paper

Kirkton Tidal marsh Late Holocene RSL fall This paper

ApplecrossFearnmore Tidal marsh Late Holocene RSL fall This paperFearnbeg Isolation basin Late Devensian RSL fall Shennan et al. (1996a)

CoigachDubh Lochan Isolation basin Early Holocene RSL rise through to Late

Holocene RSL fallThis paper

Loch Raa Tidal marsh Late Devensian RSL fall This paperBadentarbat Wetland and barrier Mid Holocene barrier evolution and sea-level

trendThis paper

Wick River Estuarine tidal marshes Mid Holocene RSL rise, late Holocenemaximum then fall

Dawson and Smith (1997)

Dornoch Firth Estuarine tidal marshes RSL fall to early Holocene minimum, riseto mid-Holocene maximum then fall

Smith et al. (1992)

Beauly Firth Estuarine tidal marshes RSL fall to early Holocene minimum, riseto mid Holocene maximum then fall

Firth and Haggart (1989)

Scapa Bay, Orkney Wetland and barrier Holocene barrier evolution and sea-level trend De La Vega and Smith (1996)

AMS rather than conventional radiocarbon techniques(Table 3). Although not dated directly, biostratigraphicdata constrain the altitude of the Late Devensian / earlyHolocene sea-level minimum. Dino#agellate cyst anddiatom evidence from the Rumach VI basin (Shennanet al., 1999a) show that highest tides and surges crossedthe sill throughout the accumulation of the organic sedi-ment from which the lower boundary dates the relativefall of sea level and the upper boundary the rise (Table 1).The microfossil assemblages constrain the altitude of theearly Holocene relative sea-level minimum to c. 2.5 to3.0 m above present. These data help resolve the debateregarding the age and mode of formation of the `MainRock Platforma (Main Lateglacial Shoreline). Althoughthis fossil shore platform is better developed at sitesfurther south, there are numerous fragments betweenKentra and Arisaig around 5 m OD (Dawson,1988,1994). For comparison with the relative sea-levelplot (Fig. 6) this represents 2.6 } 4.7 m above presentassuming the shoreline was formed between mean tide

level and mean high water of spring tides. Numerousauthors support a model of rapid coastal erosion duringthe Younger Dryas (e.g. Dawson, 1988, 1994; Stone et al.,1996). Fig. 6 shows relative sea level within this heightrange for a long period: while gradually falling throughthe Younger Dryas (c. 11.7 to 13 kyr cal BP), through theearly Holocene minimum, and for much of the rise to themid-Holocene maximum. This allows for a model withrapid coastal erosion during the Younger Dryas followedby a long period of intertidal erosion and transportprocesses under interglacial conditions.

2.3. Kintail

Loch nan Corr and Kirkton provide complementaryand contrasting evidence of Holocene relative sea-levelchange. Bennett and Boulton (1993) record the YoungerDryas (Loch Lomond) Stadial ice limit between the twosites, although May et al. (1993) suggest a possible limitfurther west. Loch nan Corr is an isolation basin at the


Tab

le2

Sea-

leve

lin

dex

poin

ts

Lab

ora

-to

ryco

de

14C

age

BP$

1pC

alib

rate

dag

eyr

calB

PA

ltitud

ean

dth

ickn

ess

Indi

cative

mea

nin

g,to

OD

and

rela

tive

totide

leve

lT

enden

cyof

sea

leve

lR

SLch

ange

from

pres

ent

max

.m

ean

min

.m

OD

mm

OD

mm$

erro

r

Ken

tra

Ken

tra

Mos

s21

-1SR

R47

2210

8040

1063

966

927

3.87

0.03

2.88

MH

WST

#0.

50}

0.99

0.21

Ken

tra

Mos

s21

-2SR

R47

2313

7045

1336

1288

1182

3.75

0.02

2.73

MH

WST

#0.

35}

1.02

0.21

Ken

tra

Mos

s21

-3SR

R47

2414

8040

1413

1345

1295

3.66

0.03

2.58

MH

WST

#0.

20}

1.08

0.21

Ken

tra

Mos

s3-

1SR

R47

3222

5545

2346

2251

2139

5.05

0.02

2.88

MH

WST

#0.

50}

2.17

0.21

Ken

tra

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s3-

2SR

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3324

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2358

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2.58

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#0.

20}

2.42

0.21

Ken

tra

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3530

6545

3368

3296

3089

6.39

0.02

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MH

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50}

3.51

0.21

Ken

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3631

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3.77

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s39

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3034

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3.99

0.21

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tra

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s38

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2835

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4.32

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4.88

0.21

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4.47

0.21

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2809

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Fig. 3. Relative sea level (RSL) observations from the Kentra area.Data from Table 2, giving altitudes standardised to change relative topresent. The j symbol indicates a maximum limit for RSL based on thebase of a peat layer from which microfossil data show that it formedabove sea level at Kentra Moss (Shennan et al., 1995b).

eastern end of Loch Duich (Fig. 7), whereas Kirkton isa raised tidal marsh 12 km to the northwest on the northshore of Loch Alsh, approximately 3 km west of anexposure of clay, with a Holocene marine fauna, approx-imately 1.5 m above high water mark described byBaden-Powell (1937).

2.3.1. Loch nan CorrThe rock sill of the basin is at #2.70 m OD, only

0.08 m above present mean high water of spring tides.Core LC96-2, from the edge of the lake, provides a com-prehensive record of relative sea-level change well illus-trated by the foraminiferal and thecamoebianbiostratigraphy (Fig. 8). The site lies within the YoungerDryas ice limit (Bennett and Boulton, 1993; May et al.,1993), and therefore we should expect only a Holocenerecord. The date from the lowest organic deposit,9.25}9.65 kyr cal BP (Table 2), agrees with this but weinfer that the complete record is not present in coreLC96-2 because there is no record for the period back tothe opening of the Holocene and no bio-stratigraphicevidence of a transgression into the basin following iceretreat. A core from the centre of the lake is more likely toinclude sediments covering this part of the sequence butwe have yet to obtain one.

From 770 cm to 746 cm the transition from mainlylagoonal foraminifera to nearshore shelf species indicatesan increase in tidal input to the basin, representing a rela-tive rise in sea level. The maximum tidal input, andtherefore maximum sea level, occurs at 678 cm(7.9}8.1 kyr cal BP), indicated by minimum frequencies ofsaltmarsh and lagoonal species and a diverse assemblageof nearshore shelf species (Fig. 8 shows only the two mostabundant species). After this the basin becomes slowlyisolated from tidal input, illustrated by the followingsequence of dominant assemblages: nearshore shelf spe-

cies Cibicides lobatulus and Elphidium macellum; a la-goonal assemblage dominated by Haynesina germanica;saltmarsh species Jadammina macrescens and Miliamminafusca; freshwater thecamoebians dominated by Cen-tropyxis aculeata. The lower boundary of the latter as-semblages is dated 0.55}0.725 kyr cal BP. From themicrofossil assemblages we attribute di!erent indicativemeanings for the dated samples (Table 2), ranging frombelow mean sea level, when nearshore shelf species dom-inate, gradually through the stages of isolation to thepresent, where the sill is just above mean high water ofspring tides.

The two dates from 678 cm are signi"cant. The agesare identical, yet one is a date an a sample of the bulksediment, an organic limnic mud, and the other on testsof the calcareous foraminifera Cibicides lobatulus. Thesesuggest that in shallow marine marginal environmentssuch as isolation basins, the mixing of sea water is suchthat the marine reservoir e!ect is negligible. Alterna-tively, the reservoir e!ect may be o!set by old carbon inthe limnic mud, but we have no evidence to discriminatebetween these explanations.

2.3.2. KirktonA series of 12 cores (Fig. 7) extending almost 500 m

landward from the current tidal marsh shows a stratigra-phy directly comparable to that described at KentraMoss (Shennan et al., 1995a, b). All cores "nished in sandor gravel or were stopped on rock. Above the sand orgravel there is a partly organic partly minerogenic unit.This has a variable grain size distribution, ranging fromclay to "ne gravel in di!erent proportions in di!erentcores. The minerogenic component "nes and decreasesup core to a humi"ed surface peat with herbaceous root-lets and Sphagnum macrofossils. Peat cutting over recentcenturies has removed much of the surface peat and thisrestricts the choice of cores for biostratigraphic andradiocarbon analysis. Cores KT96-6 and KT96-11 havesu$cient undisturbed surface peat and together covermost of the altitudinal range of the transition from thepeat to the underlying minerogenic sequence, betweenapproximately 3.0 and 3.8 m OD. Current MHWST is2.57 m OD.

No diatoms or foraminifera are preserved in eithercore but the pollen assemblages provide a comprehensiverecord of relative sea-level fall in both cores (Fig. 9).Comparison with the assemblages from Kentra Moss(Shennan et al., 1995a,b; Innes et al., 1996) provides theindicative meaning for the four radiocarbon dated sea-level index points (Table 1). The lowest dated sample ineach core records a regressive sequence from minerogenictidal #at sedimentation to salt marsh, typi"ed byabundant Plantago maritima pollen, at &20 cm aboveMHWST. The upper index point from KT96-11, witha pollen assemblage dominated by Gramineae, risingAlnus, and Plantago maritima at low and declining


Fig. 4. Arisaig site map, showing the locations of isolation basins sampled and their sill altitudes (m OD). The insets show for one basin, Upper LochDubh, the reconstruction of the basin stratigraphy from a transect of boreholes. One location, in this case core 4, was then selected to represent thesequence and resampled to provide sediment for further analyses. The same approach was used for each basin.

frequencies, represents a level &50 cm above MHWST(approximately HAT). The uppermost pollen sample in-dicates the continued regression with the "rst sign ofraised Sphagnum bog. The sequence from KT96-6 showsa comparable regressive succession, with dominantGramineae and Cyperaceae, Plantago maritima at lowand declining frequencies, followed by the transition dir-ectly to a Calluna mire which represents approximatelyHAT and is dated by the upper index point.

The ten sea-level index points from Loch nan Corr andKirkton show a consistent record (Fig. 10). Since Kirkton

is 12 km northwest of Loch nan Corr there is likely to besome di!erential glacioisostatic movement between thetwo sites but this may lie within the error range of thereconstructed relative sea levels.

2.4. Applecross

At the northern end of the Applecross peninsula twosites, Fearnbeg and Fearnmore (Fig. 11), provide a recordof Late Devensian and Holocene relative sea-levelchange.


Fig. 5. Summary of microfossil (diatom, foraminifera and charophyte), radiocarbon and altitude data for seven isolation basins from the Arisaig area.The altitude refers to the rock sill of the basin. Calibrated ages are shown in Table 2. In each case the date comes from the transition from clasticsediment to organic limus. Diatom salinity classes, based on % total diatoms counted at each level, show trends from the most marine species(polyhalobian class), through brackish (mesohalobian), to more freshwater (oligohalobian) and salt-intolerant species (halophobe). Foraminifera andcharophyte oogonia indicate respectively marine and freshwater conditions in the basin. The microfossil data help de"ne the indicative meanings(method described in Shennan et al., 1999a) used to calculate the changes in relative sea level shown in Table 2 and Fig. 6.


Fig. 6. Relative sea level (RSL) observations from the Arisaig area.Data from Table 2, giving altitudes standardised to change relative topresent. The j symbol indicates a minimum for RSL based on bio-stratigraphic evidence from the lowest isolation basin, Rumach VI(Shennan et al., 1999a).

2.4.1. FearnbegFearnbeg is an isolation basin with a sill at 5.7 m OD

(Fig. 11b). Diatom analyses show gradual isolationthrough more than 20 cm of clastic and then moreorganic sediments (Shennan et al., 1996a). Two AMSradiocarbon ages replace the original conventional date,which had a large standard error (Tables 2 and 3). Thesetwo dates record a relative fall in sea level of about 1.5 m.The older sample (c. 14.0}14.7 kyr cal BP) has a diatomassemblage which indicates that the sill of the basin wasbelow MTL, whereas the assemblages from the youngersample (c. 13.7}14.3 kyr cal BP) indicate that the sill wasaround MHWNT. There is no evidence for a Holocenetransgression back into the basin. This suggests the mid-Holocene relative sea-level maximum lies below 5.7 mOD, an observation supported by the evidence fromFearnmore (below) where the highest level sea-level indexpoint is at 5.17 m OD (core FM96-18, Table 2 andFig. 11). Shoreline fragments to the east, at the head ofLoch Torridon (Fig. 1) lie at 7.07 m OD (Robinson,1977). Assuming they formed at a level at or above meanhigh water of spring tides the di!erence in height iscompatible with estimates of the shoreline gradient (e.g.Firth et al., 1993).

2.4.2. FearnmoreAt Fearnmore surface peat overlying organic sands

occurs in small valleys between low rock ridges. Coretransects show that close to the present shoreline thesurface herbaceous peat grades downward througha sandy, silty peat with abundant herbaceous rootlets, toa slightly organic sand. The altitude of the peat-sandtransition increases away from the shore until the sandysilty peat unit disappears and the herbaceous peat restsdirectly on a coarse sand or sand and gravel. Recent

cutting of the surface peat limits the choice of cores formicrofossil and radiocarbon analyses. Core FM96-18records the highest altitude of the sandy silty peat unit(Fig. 11). Samples for pollen and diatom analyses showthat in the cores where the peat lies directly on a coarsesand or sand and gravel the peat formed in a freshwaterbog environment. In core FM96-18 pollen, diatom andforaminifera data (summarised in Fig. 12) record a re-gressive sequence from tidal #at, indicative of the con-temporaneous MHWST, through salt marsh to raisedbog, at about contemporaneous HAT, comparable withthose described from Kentra Moss and Kirkton. Regulartidal inundation, indicated by the upper limit of marshforaminifera and transition to freshwater diatoms, ceasedc. 4.4}4.8 kyr cal BP (Fig. 12). Occasional inundation byextreme tides continued until the development of raisedbog, illustrated by the rise in Sphagnum spores andhalophobic diatoms at 157 cm, #5.17 m OD. Thesedata concur with the observation from Fearnbeg, thatthe Holocene relative sea-level maximum was less than5.70 m OD.

Below the altitude of FM96-18 pollen and diatomsamples from the base of the peat show that a compara-ble regressive sequence occurs in the cores down to thepresent shore. Only core FM96-52, from an adjacenttransect in the small valley adjacent to the one shown inthe transect, had su$cient surface peat remaining toprovide an uncontaminated radiocarbon date. Two sam-ples from the regressive sequence in FM96-52 give datedsea-level index points for the transition from tidal #atthrough salt marsh (Table 2).

The six sea-level index points from Fearnmore andFearnbeg record Late Devensian and late Holocene rela-tive falls in sea level but no direct evidence from theintervening period during part of which sea level wouldhave risen (Fig. 13).

2.5. Coigach

Although much of the coastline of Coigach compriseslow cli!s there are a number of sheltered embaymentswith accumulations of unconsolidated sediments. Fieldinvestigations reveal three main types of sites: an isola-tion basin; a raised tidal marsh; and a number of wet-lands behind gravel barriers. While the "rst two usuallyprovide excellent sea-level index points, the latter fre-quently reveal complex interrelationships between sedi-ment supply, coastal processes and relative sea-levelchange (e.g. Shennan et al., 1999a). The sequences atDubh Lochan, Loch Raa, and Badentarbat record a his-tory of Holocene relative sea-level change (Fig. 14). Inaddition, a well-de"ned raised shoreline occurs at c. 5.2 mOD around Achnahaird Bay. Current MHWST at Ul-lapool some 30 km to the southeast is 2.45 m OD and2.30 m OD at Loch Nedd, 30 km to the north}northeast.


Fig. 7. Kintail sites, showing details of Kirkton and Loch nan Corr(locations shown in Fig. 1). (a) transect of cores at Kirkton, stratigraphyof the raised marsh sequence, and location of cores sampled for furtheranalyses, 6 and 11. (b) location details for the isolation basin at Loch nanCorr. Soft ground conditions and open water prevented sampling of atransect of cores, so only one entire core, LC96-2, was completed (lithol-ogy shown in Fig. 8). The out#ow stream crosses the rock sill of the basin.

2.5.1. Dubh LochanDubh Lochan is a small lake in a small embayment on

the east side of Achnahaird Bay. The lake discharges into

the bay via a stream that cuts through a small vegetatedgravel ridge down to a rock sill visible at 3.69 m OD.

A stratigraphic survey reveals a basin behind the rocksill (Fig. 14a). In the deepest part of the basin there isa sequence that comprises a basal sand, a lower limuswith a 2 cm intercalated organic silt horizon, a grey sandwith abundant gastropods and foraminifera, a brownlimus with a silt component that decreases upcore, and"nally a surface herbaceous peat.

Pollen, foraminifera and thecamoebian assemblagesrecord the following sequence of environmental changes(Fig. 15). Above the unfossiliferous basal sand the lowerlimnic unit contains freshwater microfossils, especiallyPediastrum, Myriophyllum alterniyorum and charophyteoogonia. Changes in the abundance of Cyperaceae, Em-petrum and Juniperus pollen suggest that the intercalatedorganic silt represents the Younger Dryas Stadial. Thetop of the lower limnic unit is abrupt in all cores in whichit is overlain by grey sand. None of the microfossils in thislimnic unit suggest any saline input into the lake at thattime. In contrast the overlying grey sand contains a richassemblage of gastropods and calcareous foraminifera,especially Cibicides lobatulus. We interpret these data asindicative of a rising relative sea level that led to theconstruction of a small gravel barrier across the outlet.As sea level continued to rise the barrier was brokenaround 8.1}8.4 kyr cal BP, and tidal waters entered thebasin, eroding the upper surface of the freshwater limusthat is dated 9.7}10.0 kyr cal BP (Table 2 and Fig. 15).A regression is well underway by 5.9}6.2 kyr cal BP, thetransition from the grey sand to the overlying silty limuswhich contains abundant marsh foraminifera. The re-gression continues until c. 4.6}5.0 kyr cal BP when thebasin is isolated from tidal input across the sill andfreshwater thecamoebians replace the marsh foraminif-era. As with Loch nan Corr, we interpret the microfossilassemblages to assign the indicative meanings for thedated samples, in this case from below mean high waterneap tides, following the breakthrough of the barrier, tomean high water of spring tides by the "nal isolation(Table 2). Late Devensian marine features around LittleLoch Broom, around 27 km south, at 15.5 } 17 m OD(Sissons and Dawson, 1981) apparently contrast with thesequence from Dubh Lochan. Allowing for their `provis-ional gradient of 0.33 } 0.39 m/kma (p. 123), there oughtto be pre-Younger Dryas shallow marine or inter-tidalsediments in the basin. In order to test this hypothesisfurther, the basal sand sequence will require further in-vestigation since no microfossils have been observed inthe samples collected so far.

2.5.2. Loch RaaAt the south end of Achnahaird Bay, Loch Raa and

Loch Vatachan lie in the low area below the coll toBadentarbat Bay. Transects of cores at the southern endof Loch Raa reveal a sequence of peat above minerogenic


Fig. 8. Summary microfossil (foraminifera and thecamoebians) diagram from Loch nan Corr. Only those species reaching '10% total count areshown. Lithology modi"ed from Troels-Smith (1955): cross-hatching * organic limus; L L L * silt and clay; horizontal dashes * dark, highlyhumi"ed organic deposit; dots* sand. Details of the radiocarbon dates, shown as calibrated age ranges and taken at the levels indicated, in Table 2.The sill of the basin is at 2.70 m OD.

sediments directly comparable with the previously de-scribed sites at Kentra Moss, Kirkton and Fearnmore. Athigher elevations, above c. 5.20 m OD, the surface peatlies directly on sand. Single pollen and diatom samplesfrom the peat-sand boundary above this altitude (coresLR96-6 and 7) reveal freshwater environments. This pro-vides a limiting altitude for the mid-Holocene relativesea-level maximum, about 2.6 m above present assuming

a similar tidal range to today. It is also at the samealtitude at the raised shoreline around Achnahaird Bayfor which a similar age and origin is therefore assumed.As the altitude of the peat-sand boundary decreases atransitional organic silt occurs between the peat andthe sand (Fig. 14b). In cores LR96-4, !1 and !8 thepollen and diatom assemblages show regressive se-quences from tidal #at through tidal marsh to freshwater


Fig. 9. Summary microfossil (pollen, spores and dino#agellate cysts) diagram from Kirkton, core 96-6 (Fig. 9a) and core 96-11 (Fig. 9b). Showing taxareaching '10% total land pollen and additional taxa indicating the transition from intertidal to saltmarsh and bog environments. Below 80 cm (Fig.9a) coarse sand prevented further sampling. Lithology modi"ed from Troels-Smith (1955) L L L * silt and clay; dots * sand; horizontal dashes* dark, highly humi"ed organic deposit; vertical dashes* herbaceous root macrofossils. Details of the radiocarbon dates, shown as calibrated ageranges and taken at the levels indicated, in Table 2.

Fig. 10. Relative sea level (RSL) observations from the Kintail area.Data from Table 2, giving altitudes standardised to change relative topresent. The four index points from the raised tidal marsh at Kirktonare those with the small vertical error bars.

bog c. 4.2}4.8 kyr cal BP (Fig. 16 and Table 2), with sealevel then falling to present. The height } age scatter theyreveal cannot be resolved without further investigations.

2.5.3. BadentarbatThis coastal wetland with a small lagoon lies behind

a gravel barrier that extends across the small valley at thehead of Badentarbat Bay (Fig. 14c). Diatom assemblages

show a transition from a low energy marine/brackishlagoon to a freshwater environment, and "nally a suc-cession to bog (Fig. 17). The calibrated age, 5.7}5.9 kyrcal BP, records the end of the brackish phase. The datedsediment accumulated in an unknown depth of water.The age most probably relates to the "nal stage of barriermigration, closing o! a tidal connection to the back-barrier environment. Although barrier migration is in-#uenced by sea-level change there are other controllingprocesses, such as sediment supply. The dated samplecannot be accurately related to the contemporaneoustide level.

The sea-level index points from Loch Raa and DubhLochan (Fig. 18) and the shoreline around AchnahairdBay constrain the mid-Holocene sea level to a maximumof no more than&2.5 m above present with the regressionunderway by 5.9}6.2 kyr cal BP. The date from Baden-tarbat suggests that barrier migration was closely relatedto relative sea-level rise and the Holocene maximum.

2.6. Further sites in north and northwest scotland

Previous studies from the Beauly Firth (Firth andHaggart, 1989), the Dornoch Firth (Smith et al., 1992),Wick River (Dawson and Smith, 1997) and Scapa Bay,Orkney (De La Vega and Smith, 1996) provide radiocar-bon dated relative sea-level index points (Table 4, and


Fig. 11. Detail of the Fearnmore and Fearnbeg sites in Applecross (general locations, Fig. 1). (a) Fearnmore, showing the location of cores, thosesamples for further analyses, 18 and 52, and a reconstructed stratigraphic section of the raised tidal marsh. (b) Fearnbeg, showing the location of cores,core 1 sampled for further analyses, and a reconstruction of the basin stratigraphy for the east-west transect. The sill of the basin is at 5.70 m OD atcore 22, east of which the rock surface drops to the intertidal zone.

Fig. 19) that constrain model predictions (e.g. Lambeck,1995). In addition, morphological shoreline data providefurther constraints, although they have not been directlydated and are not detailed here. The Beauly Firthradiocarbon-dated index points record a Late Devensianrelative fall in sea level, an early Holocene rise to a mid-Holocene maximum around 7 m above present. Theheight of the mid-Holocene maximum decreases north tobelow 5 m in the Dornoch Firth, and at the Wick Riverthere is no clear maximum but relative sea level was justabove present for some of the mid- to late-Holocene. InOrkney it is di$cult to eliminate the in#uence of barrierdevelopment on sedimentation but nevertheless the datareveal no Holocene sea level above present. Further

constraints on model predictions come from the limitedHolocene evidence available from the Shetland Isles (e.g.Hoppe, 1965; Birnie et al., 1993) and the outer Hebrides(e.g. Ritchie, 1966, 1985; Gilbertson et al., 1996). Bothareas record relative submergence.

3. Models

High resolution glacio-isostatic rebound models havepreviously been developed for the British Isles and com-pared with a large data set of relative sea-level indicatorsfor England, Wales and Scotland (Lambeck, 1993a, b)and for Ireland (Lambeck, 1996). Comparisons of the


Tab

le3

Sea-

leve

lin

dex

poin

tsre

-dat

edus

ing

AM

Sm

ethod

s.D

etai

lsin

ital

ics

for

the

orig

inal

sam

ples

publis

hed

in(S

henn

anet

al.,

1994

,199

5b,19

96a,

b).

Lab

ora

tory

code

14C

age

BP$

1pC

alib

rate

dag

eyr

calB

PA

ltitud

ean

dth

ickn

ess

Indi

cative

mea

nin

g,to

OD

and

rela

tive

totide

leve

lT

enden

cyof

sea

leve

lR

SLch

ange

from

pres

ent

max

.m

ean

min

.m

OD

mm

OD

(m)

m$

erro

r

Ken

tra

Ard

toe

94}1

AA

2809

512

540

9015

109

1471

014

329

20.6

00.

011.

19M

HW

NT

}19

.41

0.40

Ard

toe

SRR

5167

1204

011

014

429

1404

013

707

0.03

Ari

saig

Loch

nan

Eal

a92}65

AA

2809

942

4550

4868

4832

4579

6.27

0.01

1.18

MH

WN

T}

5.12

0.40

Loch

nan

Eal

a66

B}1

SRR

4741

4010

5047

8744

7943

530.

04

Loch

nan

Eal

a92}65

AA

2810

081

1575

9251

8990

8716

6.27

0.01

0.93

MH

WN

T}0.

25#

5.37

0.40

Loch

nan

Eal

a66

B}2

SRR

4742

8195

4593

6291

4790

670.

04

Loch

nan

Eal

a92}20

0BA

A28

097

8925

6510

013

9925

9689

5.20

0.01

1.18

MH

WN

T#

4.02

0.40

Loch

nan

Eal

a01

UB

3634

8743

149

9996

9747

9440

0.04

Loch

nan

Eal

a92

-200

BA

A28

096

1025

070

1234

712

060

1134

75.

200.

011.

18M

HW

NT

}4.

020.

40Lo

chna

nE

ala

01U

B36

3310

060

8612

109

1134

011

001

0.04

Rum

ach

Ioch

dar

92}5B

AA

2809

210

980

8513

086

1290

012

705

9.30

0.01

1.18

MH

WN

T}

8.12

0.40

Rum

ach

Ioch

dar

5SR

R48

6210

755

9012

885

1269

012

462

0.04

Rum

ach

Mea

dho

nac

h92}12

AA

2809

312

605

8515

193

1480

414

419

17.8

00.

011.

18M

HW

NT

}16

.62

0.40

Rum

ach

Mea

dhon

ach

UB

3643

1182

014

514

037

1390

513

437

0.03

Rum

ach

IV93}F

5A

A28

094

1273

085

1537

815

001

1458

516

.30

0.01

1.18

MH

WN

T}

15.1

20.

40R

umac

hIV

SRR

5170

1194

010

514

137

1397

513

817

0.03

App

lecr

oss

Fea

rnbeg

,FB93}1

AA

2810

112

280

7514

714

1434

014

037

5.70

0.01

1.23

MH

WN

T}

4.47

0.54

Fea

rnbe

gSR

R51

7111

920

125

1429

313

900

1355

60.

02


Fig. 12. Summary microfossil (pollen, spores, foraminifera and diatoms) diagram from Fearnmore, core 96-18 (Fig. 12a) and summary pollen diagram,core 96-52 (Fig. 12b). Showing taxa that indicate the transition from intertidal to saltmarsh and bog environments. Frequencies are calculated as% total land pollen, % total foraminifera or % total diatoms counted. Lithology modi"ed from Troels-Smith (1955) L L L * silt and clay; dots* sand; horizontal dashes* dark, highly humi"ed organic deposit; vertical dashes* herbaceous root macrofossils. Details of the radiocarbon dates,shown as calibrated age ranges and taken at the levels indicated, in Table 2.

observations with predictions has led to estimates of therheological response parameters for the mantle (Lam-beck et al., 1996) as well as to estimates of the ice thick-ness and the extent of the ice margins (Lambeck,1991, 1995). The resulting models give a satisfactorydescription of sea-level change across the region except

that signi"cant discrepancies between observations andmodel predictions were noted for northern Scotland,particularly in the Beauly Firth area, where the modelpredictions underestimated the rebound. This led to thesuggestion that the ice thickness in the north of theadopted model were inadequate although the dearth of


Fig. 13. Relative sea level (RSL) observations from the Applecross area.Data from Table 2, giving altitudes standardised to change relative topresent. Absence of any marine sediments in the Fearnbeg basin afterthe isolation dated by the two Late Devensian index points indicatesthat even the highest tides during the period of the Holocene maximumdid not cross the sill of the basin at #5.70 m OD (Table 2), whichsuggests that mean sea level was no higher than &3.0$0.5 m abovepresent. The sediments at Fearnmore, and their biostratigraphy, sug-gest that the upper limit of Holocene saltmarsh sediments is at core 18(Figs. 11a and 12a), where the regressive sequence from intertidal #at toraised bog occurs between #4.91 and #5.17 m OD. These raisedmarshes indicate a Holocene maximum mean sea level approximately2.1$0.4 m above present (Table 2).

Fig. 14. Coigach site map, showing details for Dubh Lochan, LochRaa, and Badentarbat (locations shown in Fig. 1). (a) Dubh Lochan,showing the location of cores, core 17 sampled for further analyses, anda reconstructed stratigraphic section of the basin. (b) Loch Raa, show-ing the location of cores, those samples for further analyses, 1, 4 and 8,and a reconstructed stratigraphic section of the raised tidal marsh. (c)Badentarbat, showing the location of cores, 1R sampled for furtheranalyses, and a reconstructed stratigraphic section of the back barriersediments (it was not possible to di!erentiate whether cores ended onrock or large gravel or boulders).

quantitative sea-level information for northern andnorthwestern Scotland did not make it possible to beprecise about this de"ciency.

Earth models comprising three mantle layers givea satisfactory description of the rebound and a greaterstrati"cation is not required to explain the observationalevidence for the relative sea-level change of Britain (Lam-beck et al., 1996). The chosen earth model comprises anelastic lithosphere of e!ective thickness H

-, an upper

mantle extending from the base of the lithosphere to themajor 670 km seismic discontinuity with an e!ective vis-cosity of g

6., and a lower mantle with an e!ective viscos-

ity of g-.

. Within each of these three layers the densityand elastic moduli vary with depth in accordance withseismic models of the mantle. Phase boundaries andother discontinuities within the mantle are assumed tobehave as material boundaries on the time scales inquestion but models with isobaric boundary conditions(Johnston et al., 1997) lead to essentially the same solu-tions for the three mantle parameters H

-, g

6., g

-.. Only

models with lateral homogeneous viscosity and elasticparameters are considered.

The ice model, BR-D, for the British Isles is based onthat developed in Lambeck (1993b) but in which the icethickness north of the Great Glen has been increasedby about 10% because of the discrepancy betweensea-level model predictions and observations in theBeauly Firth area (Lambeck, 1995). The ice model

for Scandinavia is based on the recent analysis byLambeck et al. (1998) and the models for the other majorice sheets are the same as discussed in Lambeck (1993b).The ice loads over the British Isles and Fennoscandia arede"ned on a 25]25 km grid, whereas the more distantice sheets are de"ned on a 100]100 km grid, mostly atintervals of 1000 yr since the time of the Last GlacialMaximum (LGM) and at longer intervals for the earlierperiod.

The melt water from the global ice sheets is distributedinto the oceans and the concomitant loading e!ects take


Fig. 14. Continued.

into account the time dependence of the shape of thesebasins, as well as the condition that the ocean surface isan equipotential surface at all times. The total ice andwater mass is conserved throughout. Both the ice andwater loads are expressed with a spatial resolution ofharmonic degree 256, higher degree expansions not beingrequired. Changes in the equipotential surface, and hencesea level, caused by changes in the Earth's rotation dur-ing the deglaciation and post-glaciation stages (Milneand Mitrovica, 1996) are not included since this e!ectintroduces minimal spatial variation in the sea-level re-sponse over the small area under consideration. Theeustatic sea-level function adopted is from Nakada andLambeck (1988) and recent analysis (Fleming et al., 1998)has shown that this provides an adequate approximationto the time-dependence of the land-based ice volumessince the time of the LGM. This function includes an

increase in ocean volume over the past 6000 yr so as toincrease eustatic sea level by 3 m, with most of thischange occurring between 6 and 2 ka BP. In the prelimi-nary comparisons of model predictions with observa-tions discussed in the following section, this increase forthe past 6000 yr has not been included.

The preliminary model predictions presented in thefollowing section are all based on the radiocarbon timescale, the time scale also used to de"ne the history of theice sheets. The mantle viscosity estimates are thereforegiven in units of Pa 14C seconds, a not wholly trivialdistinction since the time scale during the past 20 000 orso years di!ers from the calendar time scale by about15% (e.g. Stuiver and Reimer, 1993; Hughen et al., 1998).Provided that the radiocarbon time scale di!ers from thecalendar time scale only in a linear way, and providedthat the same time scale is used throughout, the use of the


Fig. 15. Summary microfossil (pollen, freshwater algae, foraminifera and thecamoebians) diagram from Dubh Lochan, showing taxa that illustrate thechanges in saline water input into the basin. Pollen taxa Empetrum and Juniperus corroborate the age of the lowest radiocarbon date. Chenopodiaceaeand Plantago maritima pollen indicate salt marsh environments fringing the basin. Pollen of Myriophyllum alterniyorum, colonies of the freshwater algaPediastrum and freshwater thecamoebians indicate two episodes of freshwater environments. Foraminifera illustrate changes in the degree of marineincursion into the basin. Frequencies are calculated as % total land pollen and % total foraminifera#thecamoebians counted. Lithology modi"edfrom Troels-Smith (1955): cross-hatching - organic limus; L L L* silt and clay; dots* sand. Details of the radiocarbon dates, shown as calibrated ageranges and taken at the levels indicated, in Table 2. The sill of the basin is at 3.69 m OD.

former does not change the results. Any non-linearities inthe radiocarbon time scale do not introduce signi"canterrors into the analysis (Lambeck, 1998), provided thatrealistic error estimates are assumed. Di$culties arisingfrom possible `plateaua e!ects of the radiocarbon timescale, in for example, earliest Holocene time (e.g. Stuiverand Reimer, 1993; Hughen et al., 1998) are not resolved ifall ages are converted to the calendar time scale becauseall the observational evidence is given with respect toradiocarbon time.

Where direct comparisons are made between the ob-servations and predictions, the latter are for the exactgeographic co-ordinates and times of the observed datapoints, even though observations from a given localitymay be plotted on the same age}height diagrams.

3.1. A preliminary comparison of predicted and observedsea levels

Fig. 20 illustrates the comparisons of the predicted andobserved values for the new data from the northwestcoast of Scotland. In these preliminary comparisons be-tween predictions and observations, the former are basedon the &best-"tting' earth-model for the British Isles ofLambeck (1998) (model E-0, Table 5), on the ice model

BR-D, and without the eustatic sea-level correction. Thedata are divided into sub-regions corresponding to thefour main localities for the observational data, (i) Kentraand Arisaig are shown on the same "gure because thedi!erences are small and give a longer time series, (ii)Kintail, (iii) Applecross, and (iv) Coigach. Within eachlocality the predictions are made for the speci"c siteco-ordinates corresponding to each observation suchthat the spatial variation in the rebound across the local-ity is re#ected in a loss of smoothness in the height}agefunction particularly for Late Devensian time (e.g. for theKentra and Arisaig sites).

The observational accuracies p0

of the shoreline indi-cators are estimated according to

po"Mp2

h#p2

r#(df/dt)2p2

tN1@2

where p2h

is the height-measurement variance, p2r

is thevariance associated with the uncertainty in the reductionof the sea-level indicator to mean sea level at the epoch inquestion, df/dt is the predicted rate of change in sea-levelchange at the epoch in question and p2

tis the variance of

the age determination. For pta value of twice the formal

standard deviation of the radiocarbon age determinationis adopted. p

his usually small but should include any


Fig. 16. Summary microfossil (pollen, spores and foraminifera test linings preserved in the pollen preparations) diagram from Loch Raa, core 96-1(Fig. 16a), core 96}4 (Fig. 16b) and core 96}8 (Fig. 16c). Showing taxa that indicate the transition from intertidal to saltmarsh and bog environments.Frequencies are calculated as % total land pollen. Lithology modi"ed from Troels-Smith (1955) L L L* silt and clay; dots* sand; horizontal dashes* dark, highly humi"ed organic deposit; vertical dashes* herbaceous root macrofossils; diagonal dashes* wood root macrofossils. Details of theradiocarbon dates, shown as calibrated age ranges and taken at the levels indicated, in Table 2.


Fig. 17. Summary diatom diagram from Badentarbat showing species '10% total diatom valves. The individual species shown are included withinthe summary graphs of salinity classes, from the most marine species (polyhalobian class), through brackish (mesohalobian), to more freshwater(oligohalobian) and salt-intolerant species (halophobe). Lithology modi"ed from Troels-Smith (1955): cross-hatching* organic limus; L L L* siltand clay. Details of the radiocarbon date, shown as calibrated age range and taken at the level indicated, in Table 2.

uncertainty arising from the relation between the levell-ing datum and mean sea level, and a value of 0.5 m hasbeen adopted. p

rtakes into consideration any uncertain-

ties arising from di!erences in tidal conditions at the pastepoch from present conditions and a value of 2 m hasbeen adopted here.

For Kentra-Arisaig and Kintail (Fig. 20a and b) agree-ment between predictions and observations is satisfac-tory except that the predicted highstands at 6 ka 14C BPexceed the observed values by a few metres, a discrepancythat would be largely removed if the eustatic correctionterm is applied. At the other two localities, the agreementbetween observations and predictions is unsatisfactory inthat the observed Late Devensian data points lie consis-tently above the predicted values. At both Applecrossand Coigach the predicted Late Devensian and earlyHolocene levels are below present-day sea level, incon-

sistent with the observational evidence. Similar Late De-vensian discrepancies have been previously noted forother localities in the Wester Ross area (Lambeck, 1993b)although the available observational evidence then waslimited to nominal ages for some of the raised shorelines(e.g. Sissons and Dawson, 1981). Such discrepancies forthe more western of the localities, lying near the icemargin during Late Devensian time, could, in principle,be a consequence of the adopted earth-model parametersbeing inappropriate or of the ice-load model being inad-equate. Thus the earth-model and ice-model depend-encies of the predictions will "rst be examined.

3.2. Earth-model dependence

The parameters E-0 summarised in Table 5 yield pre-dictions of sea-level change that give the best overall


Fig. 18. Relative sea level observations from the Coigach area. Datafrom Table 2, giving altitudes standardised to change relative to pres-ent. The data record a rise in relative sea level during the early Holo-cene to a maximum that is represented by both the morphologicalevidence, the raised shoreline around Achnahaird Bay, and the strati-graphic evidence shown here by the dated index points. The mor-phological shoreline is not dated directly, but shown on the graph witha minimum age taken from the evidence for falling sea level in the basinat Dubh Lochan.

agreement with the observational data for the BritishIsles, but their uncertainties remain relatively large. Thusto examine whether the discrepancies between observa-tions and predictions noted above may be attributable tothe choice of earth-model parameters, predictions arealso made for a series of parameters that encompass theoptimum values (models E-1 to E-6, see Table 5). Theresults are illustrated in Fig. 21 for the above four subsetsof the observational data. All predictions are based onthe BR-D ice model for the British Isles (see above).

At all localities, the dependence of the predicted sealevels on the lower-mantle viscosity is relatively minor(models E-5 and E-6; Fig. 21) and any variation in sea-level prediction within the range of 5]1021}3]1022 Pa14C s does not lead to an improved comparison with theLate Devensian data from Applecross, nor with the earlyHolocene data from Coigach. Likewise, within the rangeof uncertainties in the estimate of the upper-mantle vis-cosity (models E-3 and E-4; Fig. 21) the predictions donot lead to much improvement in the comparisons forthe Applecross and Coigach localities.

The dependence of the predictions on the value of thelithospheric thickness (H

-) is more signi"cant. Thus mod-

els with a low H-(model E-1) leads to a Late Devensian

prediction for Applecross (Fig. 21) that is consistent withthe observed value, but it does lead to a prediction for themid-Holocene highstand that much exceeds the observedvalue. In addition to the observations shown in Fig. 21,the fact that there is no mid-Holocene transgression intothe basin at Fearnbeg (see discussion above) the high-stand must be below the altitude of the single LateDevensian observation which is from the same basin. ForCoigach an even lower value for H

-is required if the

discrepancy there is attributed to an inadequate choice ofearth-model parameters. Such low H

-models do yield

predictions that are inconsistent with the observations atKentra, Arisaig and Kintail (Fig. 21). Also it is the LateDevensian and early-Holocene part of the observationalsea-level record for localities elsewhere in northern Brit-ain that constrains the value for H

-adopted in model

E-0.No combination of earth-model parameters, at least

not within a range that is consistent with the data fromthe British Isles in general, leads to improved predictionsfor the northern sites of Coigach and Applecross.

A general inference that can be drawn from bothFigs. 20 and 21 is that the discrepancies between observa-tions and predictions are greater for the northern sites ofCoigach and Applecross, than for the more southernlocalities of Kentra, Arisaig, and Kintail. This trend issimilar, but more accentuated, to that previously notedmainly for northeastern Scotland in the models ofLambeck (1993b, 1995). This points to inadequaciesin the ice-sheet model used rather than to major in-adequacies in the earth models. In particular, becausethe magnitude of the discrepancies change over rela-tively short distances, this points to the limitations beingin the British ice sheet rather than in the more distant icesheets.

3.3. Ice sheet model dependence

The ice model BR-D used in the above predictionsof relative sea-level change is based on: (i) empiricalobservations of the ice margin at the time of maximumglaciation and during the subsequent retreat, (ii) a fewestimates of ice thickness at the time of maximum gla-ciation, and (iii) the assumption that the ice-height pro-"les can be characterised by quasi-parabolic functions(Lambeck, 1993b). Considerable uncertainty remains inthe ice model. In the context of the present investigationquestions remain about the limits and thickness of the iceover northern Scotland, including the extent of ice overthe Orkney Islands and northeastern Caithness, the loca-tion of the ice margins to the west and northwest ofScotland, and the ice thickness over the Outer Hebrides.Some of these are resolved by Ballantyne et al. (1998) butsimilar data are needed for a much larger area. Other icemodels proposed for the British Isles di!er considerablyfrom BR-D in terms of the volumes of ice containedwithin them and the main purpose of this section is toexamine the sensitivity of the sea-level predictions to thechoice of ice model and to determine whether inferencescan be drawn from the observations of sea-level changeabout the past ice volumes.

Several alternative ice models are examined. A modelthat can be considered to be a maximum reconstructionis that of Boulton et al. (1977). In this model the ice sheetextends across the North Sea to adjoin the Scandinavian


Table 4Relative sea-level observations from Wick River (Dawson and Smith, 1997), Dornoch Firth (Smith et al., 1992), Beauly Firth (Firth and Haggart, 1989),and Scapa Bay, Orkney (De La Vega and Smith, 1996)

Laboratorycode

14C age BP$1p Calibrated age yr cal BP Altitude andthickness

Tendencyof sea level

RSL change frompresent

max. mean min. m OD m m$error

Wick RiverWick River 53 B81152 6770 80 7693 7560 7439 !3.11 0.03 # 4.60 0.21Wick River 10 B81155 7070 80 7992 7855 7672 !1.02 0.02 # 2.51 0.21Wick River 10 B81157 5940 60 6893 6757 6661 1.05 0.02 ! !0.67 0.21Wick River 23 B81156 6830 70 7738 7622 7488 1.14 0.02 # !0.35 0.21Wick River 10 B81163 2160 80 2342 2138 1937 1.30 0.01 ! !0.42 0.21Wick River 87 B81154 2130 100 2344 2114 1870 1.64 0.02 ! !0.08 0.21Wick River 23 B81159 4400 50 5248 4924 4852 1.71 0.02 G 0.02 0.70Wick River 87 B81153 1110 70 1171 983 917 1.72 0.02 # #0.23 0.21Wick River 23 B81162 1130 50 1165 1036 936 1.85 0.02 # #0.36 0.21Wick River 30 B81161 1490 60 1287 1350 1520 2.3 0.03 ! !0.58 0.21Wick River 31 B81160 970 50 744 918 961 2.44 0.2 # #0.95 0.21Wick River 10 B81158 4420 80 4835 4985 5300 1.23 0.2 # !0.26 0.21

Dornoch FirthCreich!1, HB36 SRR3690 9560 55 11149 10994 10687 !2.09 0.03 ! !4.49 0.21Creich-2, HB36 SRR3691 7860 55 8948 8566 8439 !1.12 0.03 # !3.22 0.21Creich-3, HB11 SRR3692 7930 55 8982 8686 8545 2.65 0.03 # #0.55 0.21Creich-4, HB7 SRR3693 6950 55 7895 7713 7628 5.37 0.03 # #3.27 0.21Creich-5, HB7 SRR3694 6930 55 7888 7690 7616 5.63 0.03 ! !3.23 0.21Creich-6, HB16 SRR3695 7055 50 7929 7860 7715 5.21 0.03 # #3.11 0.21Dounie-2, HB56 SRR3787 5190 65 6171 5930 5757 6.29 0.01 ! !3.89 0.21

Beauly FirthBarnyards 3B HV10010 9200 100 10566 10307 10163 1.99 0.05 ! !0.65 0.21Barnyards 14B BIRM1123 9610 130 11217 10944 10444 6.64 0.05 ! 3.99 0.21Barnyards 14B BIRM1122 5510 80 6449 6297 6113 8.81 0.05 ! 6.17 0.21Moniak 4B BIRM1127 7430 170 8500 8167 7848 6.82 0.05 # 4.18 0.21Moniak 4B BIRM1126 7270 90 8179 8035 7847 7.23 0.05 ! 4.59 0.21Moniak 4B BIRM1125 7100 110 8115 7905 7653 7.40 0.05 # 5.05 0.21Moniak 4B BIRM1124 4760 90 5656 5527 5299 8.76 0.05 ! 6.12 0.21

Scapa Bay, OrkneyScapa Bay SB23 not known 4820 90 5732 5590 5319 !0.32 0.02 Limiting !0.95 0.88Scapa Bay SB23 not known 5140 90 6170 5910 5665 !1.08 0.02 !? !1.71 0.88Scapa Bay SB23 not known 5730 60 6706 6500 6407 !1.40 0.02 #? !3.33 0.50Scapa Bay SB23 not known 6940 60 7894 7700 7616 !3.48 0.01 !? !5.08 0.50Scapa Bay SB23 not known 8540 80 9785 9490 9382 !5.10 0.01 Limiting !5.73 0.88Scapa Bay SB23 not known 9860 80 11502 11000 10948 !5.69 0.02 Limiting !6.32 0.88Scapa Bay SB33 not known 6720 60 7631 7540 7431 !2.27 0.01 !? !3.87 0.50Scapa Bay SB33 not known 6950 50 7891 7713 7632 !2.36 0.01 ! !3.96 0.50

ice sheet as well as extending out to the edge of thecontinental shelf to the west and north of Scotland.Frozen-bed basal conditions were assumed such that theice thickness, following quasi-parabolic functions, in-creases rapidly with distance inwards from the ice mar-gin. The maximum ice thickness attained in this model isabout 1900 m. This model is denoted here as BR-A anddetails about the assumed time-dependence of the iceretreat are discussed in Lambeck (1993a); Fig. 10). Ina second model by Boulton et al. (1985) more mobile

basal conditions were assumed such that the ice thicknessincreases less rapidly with distance in from the ice marginthan is the case for BR-A. The ice sheet in this case doesnot extend across the North Sea to the Norwegian icesheet, nor does it extend as far north onto the continentalshelf as BR-A. The maximum ice thickness is also muchreduced, to about 1100 m at the time of the maximumglaciation. This model, denoted here as BR-B, corres-ponds to a minimum reconstruction of the ice sheet overthe British Isles (see Fig. 8 of Lambeck, 1993a). The ice


Fig. 19. Relative sea level observations from four locations in northernScotland (locations on Fig. 1). Data from Table 4, giving altitudesstandardised to change relative to present. Table 4 gives the originaldata sources. The Beauly Firth and Dornoch Firth record a fall inrelative sea level from the Late Devensian to the early Holocene, thena rise to a mid-Holocene maximum and a fall to present. The data fromWick River show a Holocene rise to just above present in the lateHolocene. The earliest part of the Orkney record comprises two limit-ing dates, i.e. MSL was below the levels indicated, followed by a seriesof index points that illustrate a generally rising trend but not reachingabove present.

retreat assumed that this model is similar to that adoptedfor BR-A, being based on the ice margin isochrones ofAndersen (1981).

Because the model BR-A was found to yield reboundpredictions that were inconsistent with most of the obser-vational evidence (Lambeck, 1991, 1993a), a third modelBR-C was developed in which the ice margins at the timeof the maximum glaciation were assumed to coincidewith Andersen's ice limits at 16 000 BP such that thecentral North Sea was ice free and the northern andnorthwestern ice margins are closer to shore than is thecase for BR-A. The maximum ice thickness of this inter-mediate model is about 1500 m. The fourth model BR-Dis that previously discussed. All models have the sameloading history prior to the LGM and the distant icesheets are the same in all cases.

Fig. 22a compares the ice thickness pro"les for the fourmodels along an east}west section at latitude 573N andthis illustrates well the large range of the estimates of icevolumes contained within each of these models. Earlierstudies have indicated that models such as BR-A andBR-C lead to a gross overestimation of the reboundacross the British Isles, irrespective of the choice of earthmodel, and that the ice thicknesses have to be substan-tially reduced in order for the rebound predictions to becomparable with the observed values. Thus, for presentpurposes only, the three models BR-A, BR-B and BR-C,have been scaled such that they have the same ice thick-ness as BR-D of about 1200 m at the point in the pro"le(about 43W, Fig. 22b) where the maximum ice thicknessis achieved. These scaled models (denoted by the sub-

script4

e.g. BR-A4), illustrated in Fig. 22c and d indicate

that models BR-A4

and BR-C4

contain substantiallymore ice over western Scotland at the time of the LGMthan do the other two models. In particular, the ice in themodels BR-A

4and BR-C

4extends much further west-

wards than in the other two models, with model BR-A4

extending to the edge of the continental shelf (becausemodel BR-C at the glacial maximum has the same icethickness as model BR-A at 16 000 BP, by de"nition ofthe former model, the scaled BR-C

4model actually con-

tains more ice in Late Devensian time than the scaledBR-A

4model, even though both have the same ice thick-

ness at 18 000 BP).Fig. 23 illustrates the predictions for the four localities,

all based on the earth-model E-0 but di!ering in thechoice of ice model. In all cases the scaled models BR-A

4and BR-C

4overestimate the rebound, for both the Holo-

cene and the Late Devensian parts of the observationalrecord, and the ice volumes contained in these models areexcessive. If a thick ice sheet extended as far west andnorth as assumed in model BR-A

4then this would only

be consistent with the rebound evidence if the retreatoccurred much earlier and faster than proposed in theisochrone reconstructions by Andersen (1981), such thatmuch of the concomitant relaxation was completed bythe time of the oldest sea-level data at about 12 00014C BP. Predictions based on the minimum model BR-B

4underestimate the Late Devensian rebound and the sealevels occur above present level only for a short intervalbefore about 12 500 14C BP at Kintail and Kentra} Arisaig. At Applecross and Coigach, this model pre-dicts no raised shorelines during any part of the LateDevensian. The Late Devensian observation fromApplecross and the early Holocene observations fromCoigach are more consistent with predictions based ona larger ice model, between BR-D and BR-A

4and BR-C

4.

Thus ice volumes in the minimum ice model are inad-equate throughout, with the discrepancy between obser-vation and prediction being greatest for the northernlocalities.

Predictions of Late Devensian relative sea level basedon model BR-D gives, as previously noted (Fig. 21),satisfactory agreement with observations at the Arisaigand Kintail localities, whereas the di!erences becomelarger for the more northern sites. This model also fails topredict Late Devensian highstands at Coigach, a clearcontradiction with the observations of Sissons and Daw-son (1981). Di!erences in predictions, at all localities,between the two models BR-B and BR-D are substan-tially greater than the observational accuracies of the sealevels, despite the relatively minor di!erences in the re-spective ice pro"les as illustrated in Fig. 22b. This indi-cates the considerable sensitivity of the reboundparameters to the choice of ice model and that accuratesea-level observations can provide signi"cant constraintson ice models provided that (i) the data are spatially


Fig. 20. Comparison of predicted (solid line) with observed (open circles with error bars) sea-level change for (a) Kintail, (b) Kentra } Arisaig, (c)Applecross, (d) Coigach. The predictions are based on earth model E-0 (Table 5), ice model BR-D, with a nominal eustatic sea-level function in whichall melting had ceased by 6000 BP.

Table 5Earth model parameters

Earth model LithospherethicknessH

-(km)

Upper mantleviscosityg6.

Pa 14C s

Lower mantleviscosityg-.

Pa 14C s

E}0 65 4]1020 1022

E}1 50 4]1020 1022

E}2 100 4]1020 1022

E}3 65 3]1020 1022

E}4 65 5]1020 1022

E}5 65 4]1020 5]1021

E}6 65 4]1020 3]1022

well-distributed, and (ii) the dependence on the rheologi-cal parameters can be resolved.

The model predictions for Applecross and Coigachindicate that the ice volumes are likely to have beensomewhere between those described by the models BR-

C4and BR-D. A simple upwards scaling of the ice thick-

ness in model BR-D does not, however, lead to muchimprovement between observations and predictions be-cause the northen sites lie close to the model ice marginin early Late Devensian time and hence near the positionwhere the rebound signal is close to zero. To increasefurther the rebound at these sites requires that the icemargins extended beyond the limits assumed in modelBR-D (e.g. Stoker et al., 1993; Ballantyne et al. (1998)).Models with extended ice limits, such as BR-C, and inwhich the ice thickness is reduced further than the factor0.8 assumed above, do lead to better agreement betweenpredictions and observations. This is illustrated in Fig. 24for the two northern localities, for here the sites liewell within the maximum ice margin of this model. Thescaling required is, however, not uniform, being about 0.5for Kentra } Arisaig, 0.6 for Applecross and 0.7 forCoigach, indicating that proportionally more ice is re-quired to the north of Coigach than to the south.A simple scaling of the model BR-C by these factors


Fig. 21. Predicted sea-level change for (a) Kintail, (b) Kentra } Arisaig, (c) Applecross, (d) Coigach, based on the di!erent earth models (E-1 } E-6)summarised in Table 5. Models E-1 and E-2 illustrate the marked dependence of the predictions on lithospheric thickness; models E-3 and E-4 indicatethe e!ect of increasing the upper-mantle viscosity from 3]1020 Pa 14C s to 5]1020 Pa 14C s. Dependence on lower-mantle viscosity (compare E-5with E-6) is less. Open circles with error bars show the observed sea-level values.

suggests that ice thickness may have been as much as300 m greater over the Coigach area than over theKentra } Arisaig } Kintail region.

At all four localities, the model predictions, irrespectiveof the choice of ice model, indicate a well developed andshort duration highstand at about 6000 yr BP, a result ofthe assumption that all deglaciation ceased globally atthat time and that no further increases in ocean volumeoccurred. A number of studies have shown, however, thatthis is unlikely to have been the case, that a small amountof melting may have continued into more recent times(e.g. Nakada and Lambeck, 1988; Lambeck, 1998; Flem-ing et al., 1998) with the consequence that the mid-Holocene highstand is reduced in amplitude, less sharplyde"ned, and occurs earlier than otherwise predicted.Fig. 25 illustrates the predictions for the four localities.The predictions marked (i) refer to the earth model E-0,the ice model BR-D and the eustatic correction appliedfor the past 7000 yr (The corrections for the earlier period

remain uncertain and have not been used here). Agree-ment with the observed values is improved although themid-Holocene observations still lie below the predictedvalues at all localities. This is unlikely to be a conse-quence of the corrective term being too small in ampli-tude because, if larger, the ubiquitous highstandsobserved along most continental margins that lie farfrom the former ice sheets would vanish (e.g. Lambeck etal., 1990). Alternatively, it could be a consequence ofinappropriate earth-model parameters. From Fig. 21, forexample, it can be seen that a small increase in lithos-pheric thickness or a small decrease in upper mantleviscosity would su$ce to reduce the mid-Holocene high-stand by a few meters. This is further illustrated in Fig. 25by the curves (ii) corresponding to a model in which thelithospheric thickness has been increased from 65 to70 km and the upper mantle viscosity has been reducedfrom 4]1020 Pa 14C s to 3.5]1020 Pa 14C s, parametersthat lie within the uncertainty estimates of the earth


Fig. 22. Ice thickness pro"les across northwestern Scotland along latitude 573 north, (a) and (c), and longitude 43 west, (b) and (d), for the four icemodels discussed in text: (a) and (b) original ice thickness; (c) and (d) scaled ice thickness such that ice heights are the same at 573N, 43W.

model E-0. Disagreement between the observations andpredictions for the Late Devensian at Kentra } Arisaig,however, is now increased. This could be accounted forby an increase in ice volume as is further illustrated inFig. 25 by the curves (iii) in which the predictions arebased on the modi"ed earth model used for (ii) and an icemodel that lies midway between BR-D and BR-C

4.

Agreement with observed sea levels is improved for Kin-tail for these model predictions. The rebound is overes-timated at Kentra } Arisaig and Applecross but it is stillunderestimated at Coigach, indicating again the need tointroduce more ice into the model for northernmostScotland.

These various combinations of earth and ice-modelparameters illustrate the non-uniqueness of the solutioneven when the data set is spatially limited. But if uniquesolutions for the ice distribution cannot be inferred,the inference that the ice mass of the model BR-D needsto be increased in northernmost Scotland is consistentwith the discrepancies between observed and predictedsea levels previously noted for the Beauly Firth region

(Lambeck, 1993b). Thus the assumption made in con-structing the ice model BR-D, that the northeasternpart of Caithness was ice free at the time of the LGM,based on the geomorphological interpretations ofSutherland (1984) and Bowen et al. (1986) is unlikely tobe valid and a substantial thickness of ice must haveexisted over both Caithness and the Orkney Islandsat that time. Numerous studies now suggest more ex-tensive ice limits, beyond Caithness and Orkney, ontothe Hebridean Shelf and West Shetland Shelf (e.g.Hall and Bent, 1990; Peacock et al., 1992; Stoker et al.,1993; Hall, 1995, 1996; Ballantyne et al., 1998). A combi-nation of more extensive ice limits and slightly reducedthicknesses over the mainland indicated in the ice sheetreconstructions of Ballantyne et al. (1998) may pro-duce the overall increase in ice mass to model the LateDevensian and Holocene sea-level observations de-scribed above.

Some limits may be placed on the extent of the iceto the north by the limited observations of sea-levelchange in the Outer Hebrides and Shetland. At the former


Fig. 23. Predicted sea-level change for (a) Kintail, (b) Kentra }Arisaig, (c) Applecross, (d) Coigach based on di!erent ice models. The earth model in allcases is E-0. Open circles with error bars show the observed sea-level values.

Fig. 24. Predicted sea levels for (a) Applecross and (b) Coigach based on earth model E-0 and the scaled ice model b * BR-C with b "0.8, 0.6 and 0.4.Model BR-C

4in Figs. 22 and 23 is BR-C scaled with b "0.8. Open circles with error bars show the observed sea-level values.


Fig. 25. Predicted sea-level change at (a) Kintail, (b) Kentra } Arisaig, (c) Applecross and (d) Coigach for (i) earth-model E-0 and ice model BR-D, (ii)the same as (i) but with the modi"ed earth model (H

-"70 km; h

6."3.5x1020 Pa 14C s), (iii) same as (ii) but with an ice model that is intermediate

between BR-D and BR-C4

(b"0.8). Open circles with error bars show the observed sea-level values.

locality raised shorelines are absent (Ritchie, 1966, 1985;Gilbertson et al., 1996). Models such as BR-A and BR-Cpredict elevated mid-Holocene sea levels throughout theOuter Hebrides and this was one of the reasons forfavouring smaller ice models in Lambeck (1993b). ModelBR-D does not predict raised shorelines for the OuterHebrides. Raised shorelines have not been observed inShetland either, where sea levels appear to have beenrising throughout the Holocene (Flinn, 1964; Hoppe,1965; Firth and Smith, 1993; Smith, 1993). Quantitativedata are limited but the evidence does favour models inwhich the ice thickness over these islands was relativelyminimal.

Improved evidence for past sea-level change, parti-cularly for the Late Devensian period, for localities innorthern Scotland is clearly desirable if improved con-straints are to be placed on the northern limits of theBritish ice sheet, but they are only one element of thebroader solution sought. Improvements relating to more

than the northern part of the ice model are essential ifpreviously noted discrepancies for other parts of theBritish Isles (Lambeck, 1995) are to be solved. Forexample, initial analyses, based on ice model BR-D, earthmodel E-0 and deglaciation globally continuing after7000 yr ago, now predict Holocene sea levels abovepresent in Northumberland that are consistent with re-cent observations (Shennan et al., 1999b, c, Lambeck,1995). Changes to ice sheet extent, thickness and patternof retreat modify sea-level predictions for locations dis-tant from the areas where these changes are made. Inter-dependencies between earth model, ice model andeustasy model parameters can only be resolved withanalyses covering areas larger than those described hereand there is little gain to our understanding of theseinterdependencies in producing a model solution thatincorporates only the sea-level observations describedhere and the new ice sheet parameters for the samegeographical area (e.g. Ballantyne et al., 1998).


The improved spatial and temporal distributions ofsea-level index points resulting from research over thelast "ve years, in particular for Scotland and northernEngland, and the recent information on ice sheet dimen-sions usher in the next phase of research. New, quantitat-ive ice models for the whole British Isles ice sheet shouldinclude realistic sub-glacial topographies, to resolve thedi!erences between models based on ice thickness andreconstructions of ice-sheet altitudes. This is critical be-cause the parameter sought is ice mass for each locationand time interval, yet ice thickness, ice-sheet altitude andland surface altitudes are of the same order of magnitudefor northern Britain at the LGM. These ice models andnew sea-level data from critical areas and time periodsare necessary to progress further the integration of di!er-ent linked earth } ice } ocean models (e.g. Lambeck et al.,1998; Peltier, 1998) with reliable "eld and laboratoryobservations.

Acknowledgements

The major part of this work was completed underNERC grant GST/02/761, part of the Land}Ocean Inter-face Study (LOIS). Radiocarbon dates with AA andCAM laboratory codes were provided under the LOISproject. This is LOIS Publication number 603 and also isa contribution to IGCP Projects 367 and 437.

Additional information was obtained from projectsfunded by the Commission of the European Communi-ties, Directorate General for Science, Research and De-velopment (DG XII), Environment Programme, as partof `Climate Change and Coastal Evolution in Europea(EV5V-CT94-0445), `Impacts of Climate Change andRelative Sea-Level Rise on the Environmental Resourcesof European Coastsa (EV5V-CT93-0258), `Relative Sea-Level Changes and Extreme Flooding Events aroundEuropean Coastsa (EV5V-CT93-0266) and `ClimateChange, Sea-Level Rise and Associated Impacts in Euro-pea (EPOC CT-90-0015). The authors thank FrankDavies, Derek Coates and Brian Priestley for samplepreparations, Niamh McElherron for help in producingthe manuscript, and Steven Allan and David Humefor cartographic work. Frances Green, Antony Long,Ian Sproxton and Kevin Walker provided signi"canthelp with "eldwork. Finally we thank Callum Firthand Douglas Peacock for their excellent suggestions forimproving the paper in their reviews of the originalversion.

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