Geophys. J. Int. (1993) 115, 960-990

Glacial rebound of the British Isles-11. A high-resolution, high- precision model

Kurt Lambeck Research School of Earth Sciences, The Australian National University, Canberra ACT 0200, Australia

Accepted 1993 May 10. Received 1993 May 7; in original form 1992 September 11

SUMMARY Observations of ice movements across the British Isles and of sea-level changes around the shorelines during Late Devensian time (after about 25 000 yr BP) have been used to establish a high spatial and temporal resolution model for the rebound of Great Britain and associated sea-level change. The sea-level observations include sites within the margins of the former ice sheet as well as observations outside the glaciated regions such that it has been possible to separate unknown earth model parameters from some ice-sheet model parameters in the inversion of the glacio- hydro-isostatic equations. The mantle viscosity profile is approximated by a number of radially symmetric layers representing the lithosphere, the upper mantle as two layers from the base of the lithosphere to the phase transition boundary at 400 km, the transition zone down to 670 km depth, and the lower mantle. No evidence is found to support a strong layering in viscosity above 670 km other than the high-viscosity lithospheric layer. Models with a low-viscosity zone in the upper mantle or models with a marked higher viscosity in the transition zone are less satisfactory than models in which the viscosity is constant from the base of the lithosphere to the 670 km boundary. In contrast, a marked increase in viscosity is required across this latter boundary. The optimum effective parameters for the mantle beneath Great Britain are: a lithospheric thickness of about 65 km, a mantle viscosity above 670 km of about (4-5) lo2"Pa s, and a viscosity below 670 km greater than 4 x lo2' Pas. Key words: British Isles, glacial rebound, mantle viscosity, sea-level.

The recognition that Scotland had been ice covered in the 1 INTRODUCTION recent geological past goes back to A. Agassiz in 1840, and In an earlier paper (Lambeck 1993a, referred to hereafter as A. Geikie in 1865 produced a map of the ice-movement Part I) it was established that the complex pattern of directions that is quite similar to the reconstruction by sea-level indicators that formed around the British coastline Sissons (1976) more than 100 years later (Price 1983). during the past 15 000 years, provides an important data set Despite the much greater information base now available, for estimating the mantle response to changes in surface knowledge of the ice sheets at the time of, and subsequent loading produced by the melting of the Late Devonsian ice to, the last glaciation remains limited. Denton & Hughes sheet over the region, and by the concomitant rise in (1981, p. 311), for example, conclude in a more general sea-level produced by the melting of the much more context that 'our most important conclusion is that the voluminous ice sheets of Fennoscandia and Laurentia. It distribution of Late Wisconsin-Weichselian ice sheets is not was established that both the effective lithospheric thickness well known'. Sissons (1981) concludes that 'after 140 years and a simple depth dependence of effective mantle viscosity of research it is surprising how little we really know about can be inferred from the observational data. Furthermore it the extent of the last Scottish ice sheet and associated was shown that certain constraints on the areal extent and events'. With this state of affairs it is perhaps a bold or thickness of the ice sheet can also be inferred from the foolish action to propose any model for the last British ice observations of past sea-levels. Simple models were sheet but this has been done here in the spirit of developed that illustrated the principal characteristics and establishing, (1) what information is required for the requirements for a model of the glacio-hydro-isostatic glacial-rebound calculation, (2) what information about the rebound that is consistent with the observational evidence. ice sheet can be extracted from the observations of relative

960 Glacial rebound of the British Isles-I1 961 sea-level change, (3) what information can be extracted timing of this occurrence remains uncertain and may not from these observations about the Earth’s response to have been synchronous along all fronts. Sissons (1981), for surface loading, and (4) what information about coastal example, suggested that the ice sheet over northern evolution can be extracted from these rebound models. The Scotland was stationary or even retreating at a time when it first two questions have been examined in Part I which was still advancing southwards over England. In East established the need for a relatively high-resolution ice Yorkshire, the ice sheet may have continued to advance model in order to yield satisfactory predictions of the until about 18 000 yr BP, the Dimlington Advance, (Penny, temporal and spatial changes in sea-level observed in the Coope & Catt 1969; Rose 1985), whereas the advance from British Isles, particularly in Scotland. the Irish Sea across Cheshire and Shropshire probably In this paper a new detailed ice-sheet model for the Late occurred earlier, at perhaps 22 000 yr BP. A nominal date of Devensian ice sheet has been developed (Section 2) from 22000yrBP has been adopted here for the time of the time of maximum glaciation to the end of the Loch maximum glaciation of the entire British Isles region, with Lomond Advance ice sheet soon after 10000yrsBP, only minor changes in ice volume occurring up to about together with an approximate model for the ice movements 18 000 r BP. Andersen’s (1981) estimate of the areal extent during Middle Devensian time after 50 000 yr BP. In Section of the [ce sheet at this time does require some modification. 3 the observational evidence for past sea-levels in Scotland, Thus, the accumulating evidence that the North Sea was England, Wales and the Channel coast of northern France largely ice free during Late Devensian time (=26000- has been reviewed, and a series of relative sea-level curves 10000yrBP) is accepted and the British ice sheet is has been established for sites both within and without the assumed to have terminated at the Wee Bankie Moraine off former glaciated region. To address the third question raised the coast of eastern Scotland (Eden, Holmes & Fannin above, this observational data base, together with the new 1978; Sutherland 1984) (Fig. 1) and to have been stationary ice-sheet model, provide the input for the inversion in here between about 22000 and 18000yrBP. The Nor- Section 4 of the equations defining the glacio-hydro- wegian evidence also points to the Scandinavian ice sheet isostatic sea-level change through time. Certain ice-model not having extended across the North Sea as far as Scotland parameters are also determined in this inversion. In the and to the existence of an ice-free corridor between the two inversion the earth model is defined by realistic depth- ice sheets during the last glacial maximum (e.g. Larsen & dependent elastic moduli and density as determined by Sejrup 1990; Sejrup et al. 1987). The Shetland Islands seismological methods and by a depth-dependent radially appear to have been largely unaffected by the lastest symmetric linear viscosity structure for the lithosphere, Scottish and Scandinavian ice sheets and any evidence for upper mantle, transition zone and lower mantle. Section 5 glaciation and ice transport across them is interpreted as discusses the resulting earth- and ice-model parameters. being the result of a local ice sheet or of an earlier glacial This section also includes some preliminary comparisons of cycle (Sissons 1981; Sutherland 1991). In the proposed the predicted sea-level changes since the last glacial model (Fig. 2) the Orkney Islands and parts of Caithness maximum with the observed changes, but a more complete and Buchan were ice free during the Late Devensian discussion of some of the geomorphological consequences (Sutherland 1984; Hall & Connell 1991) and the nearby ice will be given elsewhere. front is assumed to have been stationary between about 22000 and 18000yr BP (Figs 1 and 2a). The Outer Hebrides supported its own ice sheet (Peacock 1991) and 2 A NEW ICE-SHEET MODEL the western limit does not extend as far across the shelf as it The predictions in Part I based on the ice model derived does in the models of Andersen (1981) or Boulton et al. from the Boulton et al. (1977) and Andersen (1981) results (1977) in which the Outer Hebrides ice is an integral part of indicated that major modifications to the ice sheet are the main ice sheet and extends across the continental shelf required. Also, since these reconstructions new evidence of as far as St Kilda (Sutherland, Ballantyne & Walker 1984). the ice movements across Great Britain and the surrounding Instead the Outer Hebrides ice as assumed to have retreated shallow sea-floor has accrued and this has been used to to a local ice sheet and cleared the Minches after about develop a new model for the last maximum glaciation and 18 000 yr BP (Fig. 2a). Also, the extent of the ice into the subsequent retreat. The principal changes from the Sea of the Hebrides and the Malin Sea is considered to have Andersen (1981) isochrone model and the Boulton et al. been the result mainly of outflows from the Little Minch and (1977) reconstruction concern the extent of the ice cover the Firth of Lorne (Davies, Dobson & Whiting 1984) and to over the continental shelf and the North Sea, the initial rates have been less extensive than proposed in the Andersen or of retreat of the ice and the ages attributed to some of the Boulton et al. models. features defining the position of the retreating ice margin, Furthermore, in this model the Scottish ice moved across and the initial thickness of the ice sheet at maximum the north Channel of the Irish Sea but did not penetrate far glaciation. into Ireland during Late Devensian time (Stephens, Creighton & Hannon 1975; Hoare 1991). Instead, the ice Timing, areal extent and ice thickness of the Late flow was deflected southwards to form the Irish Sea Glacier Devensian maximum glaciation which extended as far as the southern entrance to St George’s Channel (e.g. Garrard & Dobson 1974; Eyles & The maximum extent of the ice sheet over the British Isles McCabe 1989), fed also from the east by an ice sheet appears to have been reached between about 25000 and centred over Wales and from the west by the Irish ice sheet. 20 000 yr BP (e.g. Huddart, Tooley & Carter 1977; Bowen The ice front across southern Ireland has been taken to & Sykes 1988; Eyles & McCabe 1989) although the precise coincide with the South of Ireland Moraine and is given an 962 K. Lambeck

Figure 1. Location map of main geographic areas mentioned in text and the limit of the ice sheet at the last glacial maximum. The major terminal moraines are: (1) Wee Bankie Moraine; (2) South of Ireland Moraine; (3) Galtrim Moraine; (4) Drumlin Readvance Moraine and its extension into the Irish Sea. age of 22000yr BP (Eyles & McCabe 1989). The initial 17000yr BP (McCabe, Haynes & MacMillan 1986; Bowen northwards retreat of the ice across southern Ireland and the et al. 1986). Irish Sea is assumed to have been rapid such that by The southern limit of the ice sheet over Wales and 18000yr BP the ice margin stood north of the Galtrim England appears to be reasonably well constrained and the Moraine and at the Isle of Man (Stephens & McCabe 1977) limits given by Andersen (1981) have been largely adopted (Figs 1 and 2a), consistent with ice-free conditions having here, with ice-free conditions existing locally in both existed in northeastern Wales by this time (Bowen 1973). Pembroke and Glamorgan (e.g. radiocarbon dates BM 374 Along the western margin in Ireland the ice sheet -is and Birrn-340 of 18 460 and 22 350 yr BP respectively). The assumed not to have extended much beyond the present ice cover over Wales and dominated by a local ice sheet that shoreline such that the coastal fringe was ice free before formed over the high ground and coalesced to the west and Glacial rebound of the British Isles-II 963

T = 22000 aBP T=18000aBP

T = 16ooo aBP

Figure 2. Isochrones and ice-thickness estimates for the retreat of the ice sheet over the British Isles at selected epochs (a) from 22000 to 12 750 yr BP and (b) for the Loch Lomond Advance and subsequent retreat. Growth of this new ice cap is assumed to have started at 12 500 yr BP. north with ice that advanced down the Irish sea basin from of northeast England, through eastern Lincolnshire, to the Scotland. The flow across Shropshire and Cheshire northern edge of Norfolk and into the southern North Sea terminated at Wolverhampton (e.g. Thomas 1989) but there south of Dogger Bank (Boulton et af. 1985; Long et al. does appear to be a potential problem of timing here for if 1988). It is assumed here that this ice flow was a relatively the ice had retreated from the southern part of the Irish Sea; short-lived phenomenon or surge and that it had vanished by 18 000 yr BP the maximum advance into Shropshire, fed soon after 18 000 yr BP (see Fig. 2). by ice flow from the Irish Sea, would have occurred earlier Two contrasting views of the last glacial maximum ice and a nominal date of 22 000 yr BP has been adopted for this thickness over the British Isles are exemplified by the advance. The ice front has been identified in the Peak maximum and minimum ice sheet reconstructions of District at the southern end of the Pennines and the more Boulton et al. (1977, 1985) (see, Fig. 7 of Part I). In their recent evidence is consistent with Andersen’s identification. maximum model the ice thickness exceeds 1800 m and the The evidence for eastern Yorkshire suggests that a Late ice sheet covers the peaks of the highest mountains. Others Devensian ice flow occurred over the Holderness Peninsula have argued for much thinner ice such that the higher 964 K. Lambeck

mountain tops were exposed as nunataks. Geomorphologi- cal evidence such as striae, erratics and trim lines can in some instances place constraints on maximum ice thickness (e.g. Ballantyne 1984) and they point to values of typically 1000-1200 m over Central Scotland. Thus Sutherland (1991) expresses a consensus view that the maximum ice thickness here is unlikely to have exceeded much more than 1300m. On the Outer Hebrides, estimates of ice thickness are of the order of 400m (Peacock 1980) while the evidence of an absence of erratics on the higher peaks in the Southern Uplands of Scotland suggest that here the ice thickness is unlikely to have exceeded about 1OOOm. Ice thickness estimates for the Central Plain of Ireland are about 400-500m according to Watts (1977) with the higher mountains standing out as nunataks. Such reduced ice-thickness estimates also appear to be consistent with the evidence from flow direction indicators that point to a polycentric ice sheet with at least two major ice foci, one over Rannoch Moor in the north and the other over the Southern Uplands in the south (Figs 1 and 2a), and a number of subsidiary ice centres over Scotland, northern England and Ireland.

Ice retreat during Late Devensian time After 18000yrBP the ice retreat is assumed to have occurred without major standstills or readvances until about 12 500 yr BP when the ice sheets had vanished throughout Britain and Ireland. In eastern Scotland, the retreat of ice is marked by numerous Late Devensian shorelines formed at the ice margin, by the deposition of marine sediments and by glacial outflows, although the age control on these features is limited. Thus at time of the formation of the East Fife Shorelines, the ice margin had retreated across the low grounds of eastern Fife, Kincardine and eastern Lothian and locally may have retreated up the Forth and Tay valleys (see Fig. 3 of Part I and Fig. 4 later for locations). Of this series of shorelines, the youngest, (the East Fife 6 shoreline), has been associated with the deposition of the arctic-fauna- bearing marine Errol Beds with a nominal age of 14 750 yr BP (Paterson, Armstrong & Browne 1981) and this is adopted here. By the time of the formation of the Main Perth Shoreline, nominally at about 13 500 yr BP (Paterson et al. 198l), ice had retreated up the Forth and Tay River valleys and areas such as the upper Teith Valley west of Stirling were ice free by 12 750 yr BP (Gray & Lowe 1977). In contrast, in Andersen’s reconstruction the ice front at 14 000 yr BP was still to the east of the Wee Bankie Moraine and did not retreat to eastern Fife until about 13 500 yr BP (see Fig. 9 of Part I). The oldest Late Devensian radiocarbon age recorded in northeastern Scotland is 16 630 f 650 yr BP for deposits offshore from Banff (Sissons 1981) and this area is assumed to have been ice free by this time. The Cromarty and Moray Firths may have been occupied by ice until about 13 500 yr BP (Peacock, Graham & Wilkinson 1980) and the ice front is considered to have stood near the upper Moray Firth at about this time. As emphasized by Firth (1989), the age of the ice movements across this region is poorly C constrained, but the evidence does suggest an ice margin at 14 000 yr BP that lies considerably further to the west than Figure 2. (Continued.) assumed by Andersen (1981), consistent with other evidence Glacial rebound of the British Isles-Il 965 from the Spey Valley of rapid ice retreat from the eastern 1974). The extent of the resulting Loch Lomond Advance Highlands by about 13 500 yr BP (Sissons & Walker 1974). ice sheet has been well documented for the Western In southwestern Scotland the ice retreated to the north of Highlands with the ice again extending down to the Clyde the Solway Firth and most of the Southern Uplands are estuary and into the upper valleys of the Forth and Tay believed to have been ice free well before 13000yrBP rivers (Sissons 1974, 1981). Local ice sheets developed over (Lowe & Walker 1977; Bishop & Coope 1977). Also, the Inner Hebrides islands of Mull and Skye but no major evidence from western Scotland sites such as Cam Loch glaciation appears to have occurred beyond the Western (Pennington 1977), southwest Mull (Walker & Lowe 1982) Highlands of Scotland. Ice thicknesses were never sufficient and Lochgilphead (Peacock et al. 1977), suggest that much to cover the higher peaks and the morphological indicators of the coastal area of western Scotland was ice free before suggest values of 400111, reaching 600m locally (Sissons 13 000 yr BP. Taken together, the evidence suggests that a 1974; Thorp 1986). Elsewhere in the British Isles only minor very large part of Scotland was ice free at or soon after ice sheets formed as mountain glaciers at the time of this about 13000yrBP (Sissons 1981; Price 1983) and by cold stage. Fig. 2(b) illustrates the adopted isochrones for 12500yrBP, the Late Devensian ice sheet is assumed to this short-lived advance and retreat in which all glacier ice have vanished everywhere over Scotland. Hence the late was finally gone by 9500 yr BP. Glacial retreat over west and southern Scotland in this model occurs significantly earlier than suggested by Ice model for 22 000-9500 yr BP Andersen's model in which much of the region was still ice covered at 13 000 yr BP (Fig. 9 of Part I). Ice heights through time have been established using eqs 4 In Ireland, the early retreat of the ice sheet from south to and 5 in Part I, and the same procedure as discussed in Part north is assumed to have been rapid, based on an age of I. At the time of maximum glaciation t,,, the heights 17 000 yr BP for the Main Drumlin or Kell Drumlin Moraine hmax(tmax)at the ice foci, are based on the estimates (McCabe 1987; McCabe et al. 1987) rather than the discussed above and, with smaxestablished from the 14 000 yr BP adopted by Andersen (1981). The northern maximum ice limits, this determines the coefficient di)(eq. limits of the 'Drumlin event' moraines (Fig. 1) are taken 4b of Part I) for profiles (i = 1 . . . 9) radiating out from the to define the ice limit at 17000yrBP along the northern ice centres. The maximum ice heights at these foci for and north-western margins (McCabe et al. 1986) and by subsequent epochs t are given by 14 000 yr BP Ireland appears to have been largely ice free (McCabe 1987; Carter 1982). Retreat of ice from the Irish 1 h,,,(t) = - c "(i)[s:;x(t)]"'. Sea is also assumed to have been rapid, consistent with the Ji 17 000 yr age for the Kells Drumlin Moraine extension on to the sea-floor (Stephens & McCabe 1977), so as to have been Ice heights along the profiles then follow from eq. 5 of Part ice free by about 15 000 yr BP. I). Fig. 2 illustrates the resulting model at selected time Few precise constraints appear to exist on the retreat of intervals. Altogether, the model of Late Devensian ice the ice across Wales and England during the Late Glacial. retreat is defined at the time of maximum glaciation of Ice-free conditions may have occurred in northwestern 22000yrBP, then at 1OOOyr time steps from 20000 to Yorkshire as early as 17 000 yr BP (Gascoyne, Schwarz & 14000yr inclusive and thereafter at 500 year intervals until Ford 1983) and, apart from local residual ice sheets such as 9500 yr BP. The resulting ice model has been digitized with that over Cumbria, the main ice sheet appears to have a spatial resolution of 0.25" in latitude by 0.5" in longitude, retreated north of the Scottish border by 15000yrBP. or approximately 25 km by 25 km. Cumbria itself is assumed to have been ice free by 13500yr BP (Gale 1986) and all glacier ice over Wales Lower-middle Devensian glacial cycles vanished before 14 000-13 500 yr BP (Haynes et al. 1977; Musk 1986). During Early Devensian time, before about 50 000 yr BP, Figure 2(a) illustrates the proposed isochrones for the ice much of England and Ireland appears to have been ice free sheet over the British Isles from 22000yrBP to (e.g. Shotton 1977; McCabe 1987). There also appears to be 12 750 yr BP. In addition to the arguments and observations little evidence for early Devensian glaciation in Scotland summarized above, other information used to construct before this time (e.g. Bowen et al. 1986) although some these isochrones have included the Late Devensian patterns authors have suggested that the build-up of the ice sheet of frontal retreat over northern England given by Boulton, over Scotland may have started as early as 75000yrBP Smith & Morland (1984) and the patterns of longitudinal (Sutherland 1984). Price (1983) has drawn a tentative and radial features, primarily drumlins and striae, left by the summary of environmental conditions in Scotland and retreating ice (Boulton et al. 1985). suggests that glacial/periglacial environments existed here during 78 000-65 000 yr BP and again during 55 000- 50 000 yr BP, with interstadiai conditions between these two The Loch Lomond Readvance cold intervals as well as in the interval 50000-45000BP. The period of climatic improvement that started at about Renewed ice-sheet development over Scotland possibly 14 000-13 500 yr BP and which led to the rapid collapse of occurred in the interval of 45 000-32 000 yr BP. Palaeo- the Late Devensian ice sheet came to an end by about temperature records, particularly mean summer tempera- 12 500 yr BP and was followed by a gradual climatic cooling, ture, provides an indicator of the likelihood of ice-sheet culminating with the Loch Lomond Stadia1 in Scotland growth during Devensian time. Such temperature records between about 10 800-10 300 yr RP (Price 1983; Sissons have been proposed by Coope, Morgan & Osborne (1971) 966 K. Lambeck

l8 particular problems of interpretation of which have been discussed in the volumes edited by van de Plassche (1986), Smith & Dawson (1983), Tooley & Shennan (1987) and Pirazzoli (1991). An important source of information, particularly for change during the latter part of the Holocene, is from the aquatic and herb flora of peats defining marine transgressions or regressions. Often these peats are intercalated with marine or freshwater sediments so that it becomes possible to deduce both the position of past shorelines and indicators of whether sea-levels were rising or falling at the time of deposition. In other examples, '- I , .. I Western the past shorelines are inferred from the position of fossil ' Scotland ,r--- intertidal or shallow-water marine molluscs, or from erosional features left when the sea retreated, such as the 4 rock platforms and shingle beaches found in western t I Scotland. Generally, the height formation will not 0- correspond to mean sea-level, the reference level used in all 3 model calculations, and the successful interpretation of the s' 0.1 ; observations in terms of sea-level change requires a b I knowledge of the relation of the stratigraphic boundaries or 0 .-p 0.2 - shoreline features to sea-level. Thus the peat sequences E corresponding to the freshwater-to-marine transgressions, -2 will usually correspond to a level near mean high-water 0.3 : spring (MHWS) tide although the actual formation range P about this level may be quite large (e.g. Shennan 1986) as well 0.4 - as a function of tidal amplitude (e.g. Heyworth & Kidson 1982). Additional uncertainties result if the peats formed in a backswamp rather than in an open coastal environment, 50 40 30 20 10 0 because in the former case the formation height may be near time ( xlo00 years BP) the middle of the tidal range rather than near the MHWS Figure 3. Palaeotemperature records for central England and level. Compaction of the peats and consolidation of the western Scotland (top) and the equivalent sea-level function for the underlying sediments add still further uncertainty to the past 50000 yr (bottom). inferred sea-levels. Other shoreline markers present a for lowland England, by Price (1983) for western Scotland, similar range of problems. For example, shingle beaches and by McCabe (1987) for Ireland (Fig. 3) and, within define a maximum level that generally lies above MHWS observational uncertainties, the results for the three regions tide because of storm activity and the highest astronomical exhibit similar fluctuations so that a simple relationship tide level may provide a more appropriate reference height. between temperature and ice-sheet extent can be estab- In contrast in situ molluscs define a lower part of the tidal lished. For example, average summer temperatures in range or a limiting depth below the tidal range, depending central lowland England in the interval 50 000-30 000 yr BP on species. Because of these different formation levels it is do not appear to have dropped below those at sites near the important that all shoreline markers are reduced to the same edge of the ice sheet during the last glacial maximum and it level, particularly in a region such as the Solway Firth where can be assumed that the ice sheet did not extend far south the tidal range presently exceeds 10m, or in the Bristol into England at any time in this interval. At 35 000 yr BP, as Channel where it exceeds 14 m. Mean tide level is the most well as at 27 000 yr BP, temperatures were similar to those appropriate level for this and all shoreline information will at 15000yrBP and the extent of the ice sheet at these be reduced to this level, with the questionable assumption earlier epochs is assumed to have been the same as that at made that the tidal range has remained constant throughout 15 OOO yr BP. Fig. 3 illustrates the resulting equivalent a time interval in which major changes in sea-level have sea-level curve for the British ice sheet for the past occurred in environments of indented shorelines and 50 000 yr BP and it compares well with the model previously variable topography. Because the tidal range can vary derived from the evidence of ice movements across the significantly within a region, corrections have been applied northwest shelf of Scotland and across the North Sea (Eden individually to the data points at each location using the et al. 1978) (Fig. 13 of Part I). Insofar as sea-levels are tidal amplitude information compiled by Shennan (1992). predicted only for the Late- and Postglacial stages such The height measurements of the shorelines are usually approximate models for the earlier glacial cycles suffice (see expressed relative to the British Ordinance Datum (OD) at Part I). Newlyn in the south of England. Zero-height OD does not generally coincide with mean sea-level (MSL) which lies at 3 A SUMMARY OF OBSERVATIONS OF up to 0.35 m OD in northern England and up to 0.5m OD in SEA-LEVEL CHANGE Scotland and all heights have been reduced to MSL using the corrections given by Thompson (1980) except in a few Quantitative evidence for sea-level change along the coast of instances where heights refer to a local datum in which case Great Britain comes from a variety of different sources, the the reference is assumed to approximate MSL. Glacial rebound of the British Isles-II 967

The quoted precision of the height determinations based sequences of East Fife. Fig. 4(a) illustrates the shoreline on the peat evidence is generally small, of the order of isobases, contours of constant shoreline elevation above the 0.1 m, but the accuracies of the inferred sea-levels will be present OD height datum, based primarily on the considerably lower, of the order of flm or more when Cullingford & Smith analysis and on the elevations of the some of the above-mentioned uncertainties are taken into top of the Errol and St Abbs Beds in the Tay and Forth consideration. These error estimates are comparable to the valleys. No reductions to MSL have been made at this stage. amplitudes of the minor oscillations in sea-level inferred, for Another conspicuous elevated beach and shoreline example, by Tooley (1978) or Shennan (1986) and the latter throughout southeast Scotland is the Main Perth Beach are considered as local ‘noise’ superimposed on the more (Sissons & Smith 1967; Sissons, Smith & Cullingford 1967) regional sea-level trends. The resulting sea-level trend is, and associated shoreline (MPS). Again, quantitative age therefore, represented by a smooth curve through the MSL information for this shoreline is lacking and its age is estimates with upper and lower limits indicated by the inferred to be about 13 500 yr BP from evidence of the ice spread of depths of the individual observations and by the front which stood near the shoreline during a temporary halt accuracy estimates of the observations. in the ice retreat (Paterson 1974; Sissons 1974). In East Fife All ages used for the shorelines and sea-levels correspond the MPS has been identified at elevations below the EF-6 to the conventional radiocarbon time scale because the beaches (Smith, Sissons & Cullingford 1969) but the history of the movements of the ice sheets are almost wholly correlation is based on elevations and gradients rather than defined within the same time scale. Fractionation and on quantitative evidence. The corresponding isobases of the reservoir corrections will generally have been made or MPS shorelines are illustrated in Fig. 4(b). estimated. Age constraints for some of the major shorelines The best defined shoreline of all in the Forth valley is the recorded in Scotland are poor and inferred rather than Main Postglacial Shoreline defined by the abutment of the based on direct radiocarbon ages and the inferences of ages present flat valley floor, the ‘carse’ surface, against the by correlating shoreline fragments from one area to another higher adjacent ground. These carse clays were deposited in introduces further uncertainty, particularly because the an estuarine environment during a time of relative sea-level formation of a shoreline need not be synchronous; rise and are overlain in some localities by peats carbon diachronous formation being suggested by both the dated at 6500 yr BP. This determines the time of the end of observational evidence (Morrison et al. 1981) and by the transgressive phase and the formation of the Main rebound modelling (Lambeck 1991). Postglacial (MPg) Shoreline (Sissons 1967a). It is also well defined in the Tay and Earn River valleys and along the Tay Firth (Cullingford, Caseldine & Gotts 1980; Morrison et al. Southeast Scotland 1981), in East Fife and along coastal areas as far north as This area encompasses the Forth and Tay valleys and the Ythan valley in Aberdeenshire (Smith et al. 1980, 1985). adjacent coastal areas from the English border (near The precise age of the shoreline remains uncertain and the Berwick) to about Aberdeen (Fig. 4). Well-developed culmination is variously reported as between 6800 and elevated shorelines occur up to elevations of about 40 m and 5700 yr BP although its formation may not be synchronous. these are believed to post-date the last ice retreat across the Smith et al. (1985), for example, suggest that the shoreline area from east to west. The main raised shorelines are the decreases in age by as much as 500yr from the upper Tay East Fife group, the Perth sequence and the postglacial and Earn River valleys to East Fife. A nominal age of features, some of which have been correlated across the 6000yr BP is adopted and Fig. 4(c) illustrates the regions using their morphological, stratigraphic and corresponding isobases. sedimentary characters, as well as their heights and While the cane clays form a remarkably uniform deposit gradients. Along the river valleys the evidence for change in some layering and lamination does occur. One persistent sea-level is primarily in the form of marine deposits, peats, feature near the top of the sequence is a thin silty-to- or erosional features, but only in a few instances has it been fine sand layer constrained in age by peats above and below possible to establish time series for the sea-level change. it dated at about 7000 f 200 yr BP. It is found in the upper The East Fife Shorelines were initially mapped by Forth valley (Sissons & Smith 1965), in East Fife (Morrison Cullingford & Smith (1966). Six separate beaches have been et al. 1981), near Montrose (Smith et al. 1980), and in the identified in the sequence, each of which terminates in Ythan valley (Smith, Cullingford & Brooks 1983). Sissons outwash plains with the break in slope between the beach or (1983) and Smith et al. (1985) have suggested that this terrace and the back slope marking the shoreline. The feature may have been produced during a major storm surge lowermost feature East Fife 6 (EF-6) Shoreline extends while Dawson, Long & Smith (1988a) and Long, Smith & furthest westward and it has been suggested that it Dawson (1989) have suggested that it may have been correlates with the Errol Beds in the Tay estuary (Paterson deposited by a tsunami generated by a major submarine et al. 1981) where they occur to the west of Perth, and the St landslide in the Norwegian Sea. Irrespective of its cause, the Abbs Beds in the Forth Estuary where they have been uniqueness of this layer makes it an ideal shoreline marker recognized as far west as Inverkeithing (Paterson et al. 1981; for a well-defined instant in time. Fig. 4(d) illustrates the Sissons & Rhind 1970). Based on age estimates of these ‘Tsunami’ isobase from localities where it has been clays, Browne (1980) tentatively associates an age of identified and from elevations given by Long et al. (1989). 14 750 yr BP with the EF-6 Shoreline, a suggestion that is The reference height for this shoreline is unknown but the adopted here. Further north, Cullingford & Smith (1980) MHWS tide level is adopted. have identified the same shoreline sequence on the basis of Cores taken through the carse clays in the Forth valley the correlation of their heights and gradients with the have revealed a number of buried beaches, the deepest and 968 K. Lambeck

I I 50 40 30 20

Figure 4. Isobases of the major shorelines identified in eastern Scotland. (a) The East-Fife 6 Shoreline, (b) the Main Perth Shoreline, (c) the Main Postglacial Shoreline, (d) the 7000 yr BP ‘tsunami’ Shoreline, (e) the Main Late Glacial Shoreline. most extensive of which is a gravel layer backed by cliffs that sea-level may have stood at this height for a formed by marine erosion of older tills. This is the Buried considerable duration. Gravel Beach of Sissons (1967a) or the Bothekennar Gravel Figure 5 illustrates the time series of the change in (Browne et al. 1984). The shoreline, defined by the base of shoreline heights for three locations with all heights reduced these buried cliffs and referred to as the Main Late Glacial to MSL. The Arnprior results of Sissons & Brooks (1971) (MLg) Shoreline, has been identified from near Grange- have been extended to late glacial time by a linear extrapola- mouth in the west where it occurs near present sea-level to tion of the MLg and MP shorelines of Sissons (1974) about near Berwick in the east where it occurs at -18mOD 10 km and 20 km respectively beyond the western limits at (Sissons 1974). It post-dates the Main Perth Shoreline and which they have been observed. The upper Tay Forth result pre-dates the overlying sediment deposited at about for the localities of Bridge of Earn and Glencarse is from 10 300 yr BP (Sissons 1967b). The extent of erosion suggests Cullingford et al. (1980) and from the data points from Glacial rebound of the British Isles-II 969

I because no direct age measurements exist for the actual shorelines before about 9000 yr BP and the older ages are all inferred from relationships between the retreating ice front across the region and shoreline development. The results for Arnprior and Errol both indicate the occurrence of small oscillations in sea-level between about 10 000 and 8000 yr BP corresponding to the three Buried Shorelines of Sissons (1967a and b) (see also Paterson et al. 1981). The age of the first of these, the High Buried Shoreline, is constrained by pollen ages as having formed at about 10 200 f 100 yr BP, soon after the formation of the Main Late Glacial Shoreline. The second, the Main Buried Shoreline, is constrained in age by both pollen and radiocarbon age as about 9600 yr BP I MLg and the youngest, the Low Buried Shoreline, is constrained -10 ' I in age as 8700 yr BP (Sissons & Brooks 1971). Within the 15 10 5 0 firths of eastern Scotland, at least, sea-level fluctuations (b)60 exhibit a complex sequence of oscillations in earliest Holocene time. Fig. 5 also illustrates the envelopes of the (Earn, Abernethy, Glen Carse) adopted sea-level curves for the three localities, all referred to MSL, and the associated accuracy estimates. The standard deviations for the older shorelines (EF-6, MPS) are 5 m while for the MLg and Buried Shorelines accuracies of 3m and for the MPg and Tsunami Shorelines values of between 1 to 2m have been adopted depending on the quality of the original observations. Figs 4 and 5, with the former shoreline heights reduced to present MSL, summarize the eastern Scotland sea-level observation data that will be used below for estimating glacial-rebound parameters. -20 15 10 5 0 Northeast Scotland (c) 50 .LI) Errol Most evidence for past sea-levels in this area comes from the & (Firth of Tay) . shores of the Cromarty, Moray, Inverness and Beauly Firths (Fig. 6) and this has been reviewed by Firth (1989) for Late Devensian time and by Firth & Haggart (1989) for Holocene time. Within the inner Moray Firth a sequence of beaches of

1 -20' ...... ' 15 10 5 0 time (~1000years BP) 58.0" Figure 5. Time series of height-age relationships of former shorelines (relative to MSL) at (a) Amprior, (b) Bridge of Earn and Glencarse, (c) Errol. Also illustrated are the envelopes of the inferred sea-level change for these localities. In (a) and (c) HBS, j MBS and LBS refer to the high-, main- and low-buried shorelines respectively.

Paterson et af. (1981) for the MP and the top of the marine L 1 I I clays identified with the EF-6 Shorelines. The Errol curve, 40 50 to the east of Glencarse, is from Paterson et al. (1981) and Figure 6. Location map for northeast Scotland and (inset) the includes the EF-6 Shoreline height taken from their heights of the ILg-4A Shoreline. (1) Beauly Firth, (2) Firth of height-distance diagram for the Tay Firth shorelines. It Inverness, (3) Cromarty Firth, (4) Dornoch Firth, (5) Munlochy needs to be emphasized that these curves are less accurate Bay, (6) Beauly, (7) Inverness, (8) Nairn, (9) Banff, (10) Fort than may be implied by the generally consistent pattern George, (11) Wick. 970 K. Lambeck

Late Devensian age reach altitudes of over 30m, and 7000 yr BP, now appear to be well below present sea-level possibly as high as 42m (Synge 1977), associated with the (Hoppe 1965; Flinn 1964). The observational data base used westward retreat of the ice from Nairn to Inverness. Firth for the Moray region consists of the sea-level curve for the (1989) has identified at least 10 Late Glacial sequences, upper Beauly Firth (Fig. 7) and the elevations of the referred to collectively as the Inverness Late Glacial (ILg) LIg-4A, MLg, Tsunami, and the IF-1 shorelines along the Shorelines of which the best defined are the Ilg-4A and Inverness and Moray Firths. Ilg-5A surfaces with gradients of about 0.4 m km-' in an approximately northeasterly direction (Fig. 6). Direct age information for these shorelines is not available. They must Western Scotland post-date the retreat of the last ice cover and this places an This area includes the Inner and Outer Hebrides and the age constraint on ILg-4A of about 13 500 yr BP correspond- mainland coast from Wester Ross in the north to the Firth ing to the deglaciation of Cromarty (Firth 1989), although of Clyde, Kintyre and Arran in the south. Evidence for Peacock (1974) suggests that this deglaciation may have sea-level change in this region is distinctly different from occurred later. A nominal age of 13500yrBP is adopted that in the southeastern region, reflecting the differences in here, equivalent to the Main Perth Shoreline of the Forth geology and sediment supply and the fact that the west coast region (Firth 1989). Firth & Haggart (1989) have also has been subjected to a greater degree of glacial erosion and identified a buried erosional surface covered by sediments scouring than the east coast. Raised shorelines and elevated dated at 9610f 130yrBP. This surface is terminated at marine sediment deposits have been recognized throughout some locations by the base of a cliff line and they suggest the region at elevations up to 100m but no systematic that it corresponds to the Main Late Glacial Shoreline of studies for their origins and ages have yet been published. southeastern Scotland. This association is also adopted here. Some of the elevated deposits are believed to be of A detailed examination of the Beauly evidence by pre-Devensian age while others may hav been emplaced as a Haggart (1986) and Firth & Haggart (1989) has indicated result of glacier action (Synge 1977; Dawson 1984). that after about 10 000 yr BP small sea-level oscillations Well-developed rock platforms at up to 50 m OD also attest occurred that are similar to those reported for the upper to higher shorelines at some time in the past but these also Forth valley (Fig. 7). The 'Tsunami Shoreline' has also been are of uncertain age (Sissons 1982, 1983; Dawson 1984). identified here as well as in Munlochy Bay, Dornoch Firth One region where a variety of fossil-bearing Late Glacial and Wick (Long et al. 1989) and its age is constrained to lie sediments have been preserved is in the Clyde Firth and between 7430 f 120 and 7270 f 90 yr BP (Haggart 1986). Clyde River. A useful data set is from the Ardyne locality The culmination of the early Holocene transgression forms (see Fig. 9b for location) where Peacock, Graham & the Inverness Flandrian Shoreline (IF1) and is defined by Wilkinson (1978) have examined the heights and ages of in estuarine flats, terraces and shingle ridges along the margins situ marine bivalves and their relationship with the of the firths of the region, attaining a height of about maximum elevations of the same sedimentary units in 9-10 m OD near Beauly and sloping in a north-northeast nearby localities. They succeeded in estimating the sea-level direction with a gradient of about 0.07mkm-'. The curve from about 12000 to 10000yrBP and while formation time is between 7100 and 5500 yr BP and Haggart uncertainties are large (Fig. 8a), this result indicates a rapid (1986) suggests an age of about 6400 yr BP and correlates it fall followed by a nearly constant level for about 1500yr. with the Main Postglacial Shoreline of the Forth-Tay Other data points for the region include in situ marine region. Further north, elevated shorelines of Late Holocene molluscs dated at 13 780 f 124 yr BP (Browne, McMillan & age have not been identified in Caithness or in the Orkney Graham 1983) and a series of peat and mollusc dates Islands while in Shetland, shorelines formed at 6000- between about 13 000 and 8000 yr BP. The in situ n~ollusc (points 1-3 in Fig. 8a) represent lower limits and, by analogy with the Ardyne results, could be up to 20 m below sea-level (see radiocarbon dates GU-12, Birm-122, SRR- 479). Point 4 is also based on marine shells but the height Beauly Firth has been reduced to sea-level using nearby morphological indicators (Baxter, Ergin & Walton 1969). Points 5 and 6 (Bishop & Dickson 1970) represent lower limits whereas h ', ' points 7 and 8 (Bishop & Coope 1977) define upper limits. vE 3 20- t',' The level at 6000yrBP is based on a number of e . 8',' observations throughout the firth and associated lochs and \' sounds, although nowhere is the shoreline defined with precision (e.g. Jardine 1986; Boyd 1986; Gemmell 1973). For a wide range of plausible ice and earth models, the predicted regional variability for the sites within the Firth of Clyde region are generally smaller than the uncertainties associated with the observations, and the data points can be combined into a single sea-level curve (Fig. 8a) that is representative of the region between Dumbarton and Ardyne. (See also Fig. 21 of Part I). Figure 7. Time series of height-age relationship in the upper Other quantitative data for establishing part of a sea-level Beauly Firth region and the inferred sea-level change envelope. curve, come from the Lochgilphead region of Argyll Glacial rebound of the British Isles-II 971

(a) 40

(weslern Scotland) 550fl 30 -E regional . -2 20 P . 3e 10

0.

15 13 11 9 7 5

(b) 60

\Oban-Lome (western Scotland) 50

" 15 10 5 0 time (~1000years BP)

Figure 8. (a) Height-age relationships for sea-level indicators in the Clyde Firth and the lower Clyde River. The data from Ardyne are illustrated by the solid circles with error bars and the numbered points are discussed in the text. All elevations are with respect to MSL. The estimated sea-level curve is also shown. (b) Sea-level evidence for the Firth of Lome and Loch Fyne regions. The Lower Fyne curve is given by Dawson er al. (1988b), the Oban-Lorne curve is from Synge (1977), the Lochgilphead observations (with error bars) are from Peacock et al. (1977) and the open circle corresponds to the rock barnacles at Oban (Gray 1974).

(Peacock et al. 1977) (see Fig. 9b for location), where the evidence is similar to that obtained by Peacock et al. (1978) for Ardyne in the Clyde Firth. Fig. 8(b) illustrates this result and here also the evidence points to a rapid fall in sea-level I I II 1 up to about 12 000 yr BP followed by a period of at least 70 6O so lo00 yr during which sea-level remained at an approximately constant level. Dawson et al. (198%) give a sea-level curve Figure 9. (a) Elevations (OD) of the Main Postglacial Shoreline for for the lower Fyne region that is presumed to incorporate the Inner Hebrides and Western Highlands. Numbers in italics refer to locations as follow(1) Scarba, (2) Oronsay, (3) Oban, (4) Loch the Lochlgilphead data and only the Holocene part of this Fyne. (b) Same as (a) but for the Main Rock Platform. (1) Ardyne, curve is shown in Fig. 8(b). Near Oban, barnacles of a (2) Dumbarton, (3) Lochgilphead, (4) Firth of Lome, (5) species that normally lives in the intertidal zone have been Ardnamurchan, (6) Moidart. found at 20mOD (Fig. 8b) with an age of about 12 000 yr BP (Gray 1974). 14 m OD near the heads of the inner sea lochs (Gray 1974). Elsewhere, the only information is from the rock The appropriate reference level for these features is the platforms and the shingle beach ridges. The latter are height of modern deposits which in some instances may be believed to correspond to the Main Postglacial shoreline of up to 3m above the MHWS tide level (e.g. Sissons & eastern Scotland and reach a maximum elevation of about Dawson 1981). Fig. 9(a) illustrates the isobases for this 972 K. Lambeck shoreline based on the work of Gray (1974) for the Firth of Lorn and Mull; of Dawson (1984) for Jura, Islay and Scarba; of Jardine (1978) for Oronsay; Synge & Stephens (1966) for Iona, Kintyre and Loch Etive; and the mean Clyde Firth result discussed above. In Wester Ross this shoreline feature is found at about 9 m near Applecross and at about 7 m OD between Loch Gairloch and Little Loch Brook (Sissons & Dawson 1981). All shingle beach deposits have been reduced to mean sea-level assuming a formation height at MHWS + 2 m for the exposed outer coast sites and MHWS + 1 m for the protected inner coast sites. Of the rock platforms only the low rock platforms, the 1 1 (Redkirk, Annan) I Main Rock Platform of Gray (1974), ranging in elevation -8 from 0-10mOD are used. They are particularly well 1412108 6 4 2 0 defined around the Firth of Lorne and the west coast of Jura but they have also been identified in Arran, Kintyre and the Firth of Clyde and as far north as Ardnamurchan and Moidart (Dawson 1984, 1988; Gray 1978). The spatial variation of the platform elevations forms a relatively simple pattern (Fig. 9b) with the highest values occurring along the inner sea lochs of the Highlands and decreasing with distance from the centre of maximum glaciation, and it is usually assumed that they correspond to the same erosion event(s). Different ages have been attributed to this feature at various times but the present consensus seems to be that West Solway Firth it formed or was reshaped during the Loch Lomond Stadia1 (Wigtown Bay & Luce Bay) by periglacial rock erosion (Dawson 1984, 1989). Within the -8 Clyde Firth the platforms occur at between 5 and 10 m OD 141210 8 6 4 2 0 (Gray 1978), consistent with the minimum sea-level time (~1000years BP) recorded at Ardyne in the time interval 11 500-10 000 yr BP. Figure 10. Age-height relations of sea-level indicators and The association of the platform with the relative lowstand estimated sea-level curves, all reduced to MSL, for southwest during the Loch Lomond Interstadial at 11 000-10 500 yr BP Scotland. (a) East Solway Firth near Annan and Redkirk point, (b) is therefore plausible and accepted here, either as a time of the west Solway Firth near Luce Bay and Wigtown. formation or as a time of re-occupation and re-shaping of an older feature. The High Rock Platforms form a less coherent pattern and the consensus is that they are a result data points are given by Jardine (1975) for the Girvan area of shaping by successive glacial events, possibly of on the south coast of Ayr and these indicate that mean pre-Devensian age, with the latest modifications having sea-level here was at about 2m between 9400 and occurred at 13 500-13 000 yr BP when the ice front stood at 8400 yr BP. the western edge of the Highlands. Because of the considerable uncertainty in their interpretation these England and Wales shorelines are not considered here as appropriate for constraining models of Late Devensian rebound. The palaeo sea-level evidence for England and Wales is confined mainly to river estuaries, shallow bays and low-lying coastal plains where sediments and organic Southwest Scotland materials deposited in tidal flat or lagoonal environments This region includes Southern Ayr and the coastal regions of have been preserved. The most complete examination of the Wigtown, Kirkcudbright and Dumfries along the Solway evidence for northwestern England is by Tooley (1978). The Firth (see Fig. 5.3 for locations). Elevated shorelines have preliminary model predictions in Fig. 21 of Part I, indicate not been identified in the region (Jardine 1971) and as the that considerable spatial variation in sea-level response is coastal area was generally ice free soon after 14000yrBP predicted for this area and that it may not be appropriate to (Fig. 2a), the absence of such features, if confirmed, places combine all data into a single sea-level curve. Sufficient sea-level as being near or below the present level at that information exists to construct sea-level curves for three time. The oldest indicators of sea-level occur in the upper localities within the region: Morecambe, the Ribble reaches of the firth and span a time interval of 12 290 f 250 Estuary, and Formby. Fig. 11 illustrates the results. to 10300f 185yrBP (Bishop & Coope 1977) and suggest Following Tooley, all heights are assumed to correspond to that mean sea-level in this period was at -3 to -4m below the MHWS level and have been reduced to MSL in this the present level. The Holocene evidence has been figure. Height errors ranging from f 1 m to f2m have been examined by Jardine (1975) for the eastern Solway near adopted and the minor oscillations noted by Tooley have Annan, and for Wigtown Bay and Luce Bay in the western been ignored. A partial sea-level curve for a fourth region, Solway Firth. Fig. 10 illustrates the results, including the the Duddon Estuary near Millom, has been inferred from a pre-Holocene result for the eastern Solway region. Four few data points in Tooley (1978) and from the mainly Glaciai reborrnd of the British Isles-I1 973

0

-5 0 ,I ,I,# 4b ,I cd - ,I,I 2 -10 ,I -10 ,I,1 e, .>,* ,I,I cd 4 -15 -15 . 1'1

-20 . Morecambe Bay Ribble Estuary (northwest England) (northwest England) -20 8 ' ' ' ' . ' . ' I t ' -25 -25' . 10' 8 6 4 2 0 10 8 6 4 2 0

e, .L S -15 . 4 t

1, -20 . Formby '* Millom (northwest England) (northwest England) . -25 1 10' 8 6 4 2 0 time (x1OOO years BP) Figure 11. Sea-levels for northwest England. (a) Morecambe, (b) Ribble Estuary, (c) Formby, (d) Duddon Estuary, Millom. In (d) rn refers to molluscs which are considered not to be in their growth position but to define an upper limit to sea level. P refers to peat samples at a level near the MHWS level with P-T referring to results from Tooley. Wand C are wood and charcoal samples which also define an upper limit to MSL. mollusc and wood fragment results by Andrews, King Lk observed height-age relationships, with all heights reduced Stuiver (1973). The shell data have come from dune and to MSL. Further south, in the Fenlands of East Anglia, shingle ridge deposits and because they do not appear to be unconsolidated sediments have been deposited in lagoonal, in their growth position they are assumed to define upper perimarine and tidal flat environments that extend over an limits to sea-level. Fig. ll(d) illustrates these results but area of nearly 5000 km'. The sea-level information, in the generally they do not provide useful constraints on past form of peats intercalated between lagoonal and tidal flat sea-levels. [The discovery of a spoon in the same strata as sands and clays, has been examined in detail most recently these shells (Tooley, private communication) highlights the by Shennan (1986). It includes data from Devoy's (1982) uncertainty of this data.] analysis of sea-level in southern England as well as the Tooley (1978) (see also Gaunt & Tooley 1974) discusses Chapel Point data included in Tooley (1978). Shennan's evidence from northeastern England, mainly from the estimates of MHWS have been reduced to MSL and his Humber Estuary in an area between Spurn Head, Hessle error bounds have been adopted (Fig. 12b). Predicted and Brigg. Four points from Chapel Point in this sea-levels through the region based on the preliminary compilation are also found in Shennan's (1986) data set for model (Fig. 21 of Part I) exhibit some spatial variability the Fenlands and are included below. The evidence is of across the region, but this generally lies within the range of several types; peats, wood fragments within estuarine and the adopted error bounds and the single curve is assumed to saltmarsh clays, and molluscs, and they generally constrain be representative of a location near the geographic centre of only the limits to sea-level height. Fig. 12(a) summarizes the the various data points. 974 K. Lambeck

. . . . I His data includes observations from the Fenlands and -2 . Norfolk and these have been included in the above- discussed sea-level curves. The remaining data points fall 4- into three regions within each of which the predicted spatial h . variability is smaller than the accuracy estimates for the $ -6 reduced mean sea-levels. These are the Essex coast, mainly 4 . I -8 from the Blackwater and Colne River estuaries, the Thames 0 .e -10 . r' Estuary as far upstream as London, and the eastern section 3 of the Channel coast between Margate and Weymouth. The . e: -12 evidence is from a variety of peats that are indicative of -14 . Humber Estuary changes from freshwater to marine-brackish environments. t "' (northeastern England) , Fig. 13 illustrates the mean sea-level curves for the three -16 ' . I 8 6 4 2 0 localities. All heights have been reduced to mean sea-level and the corrections given by Devoy for consolidation and , . .~~-. compaction of the peats and underlying sediments have been applied. The data from Devoy is in two parts. For the first (Devoy 1982, Table 3) the evidence is from peats that are assumed to have formed near the MHWS tide level. For the second (Devoy's Table 4) the dated horizons cannot be reliably related to this reference and they provide mainly upper limit estimates of the sea-level curve but they are useful for the interval 10000-8000yrBP for which no information would otherwise be available from this region. Sea-level information for the western sector of the Channel coast is given by Heyworth & Kidson (1982) and is (East Anglia) based on freshwater-estuarine transition peats and in situ tree roots and stumps. Fig. 13(d) illustrates the resulting 6 4 2 0 mean sea-level curve for this part of the coastline. Another important collection of data points is given by Heyworth & Kidson (1982) for the Bristol Channel and Wales where the information is similar to that from the western Channel 4 coast. From Fig. 21 of Part I it would appear inappropriate to group all Bristol Channel observations into a single Yare Valley sea-level curve and instead curves for three localities have been constructed, for Bridgwater Bay, Swansea Bay (Port Waveney Valley Talbot, Fig. 3 of Part I), and the upper Bristol Channel (Fig. 14). For Wales, much of the evidence comes from the submerged forest beds near Borth (Heyworth & Kidson -16 1982) and this is the only locality in Wales for which it is Norfolk possible to construct a sea-level curve for middle and late -20 Holocene time (Fig. 14d). The tree-stump data is based on 8 6 4 2 0 the assumption that the trees have been killed by rising time (~1000years BP) groundwater associated with a rise of sea-level, although the Figure 12. Sea-levels for (a) the Humber Estuary in northeast relationship is not straightforward, particularly if there has England including the Chapel Point data, (b) the MSL curve for the also been significant coastal erosion (e.g. Tooley 1986). Fenlands from Shennan (1986), (c) the Norfolk coast from three Despite this reservation, these observations are assumed different locations. here to be indicative of an upper limit to the sea-level curve.

The Norfolk coast has provided more localized environ- ments for the preservation of Holocene sea-level indicators. French Atlantic Coast Evidence from the northern coast between Brancaster and To complement the observations from southern England, Cley is discussed by Funnel1 & Pearson (1989), observations sites where sea-level is relatively insensitive to the changing from the Yare estuary included in Devoy's (1982) British ice sheet but more strongly dependent on the compilation, and the data from the Waveney Valley has changes in the global ice sheets through the equivalent been examined by A. M. Alderton (Shennan 1987). Fig. sea-level function, observations from the French Atlantic 12(c) illustrates the results for the three localities, all coast are also considered. Ters (1986) has compiled reduced to MSL. The observations are consistent with each observational evidence from locations along the entire other within their errors and the range of spatial variability Atlantic coast of France and estimated a single sea-level predicted across the region for the past 7000yr (cf. Fig. 21 curve, but analogous to the predictions in Fig. 21 of Part I, of Part I). some spatial variability in sea-level response can be An important source of information on sea-level change expected through the spatial dependence of the water-load in southeastern England is provided by Devoy (1979, 1982). term and through the variable distances of the sites from the Glacial rebound of the British Isles-II 975

J 0- .-----$--$-- h. --- -- p -5 . ,.,.I-:.f- - I p'I, 3 -lo ; :; Table 4 -15 . Mersea (Essex) Thames Estuary -20 t . . * -9n I . . * 4,. I -50 10 8 6 4 2 0 10 8 6 4 2 0

-20 ,+' : 1, 1, Channel Coast -25 Channel Coast . (eastern sector) s: &,, (western sector) 1 -30 -30 ' 10 8 6 4 2 0 10 8 6 4 2 0 time (x1OOO years BP) time (~1000years BP) Figure 13. Sea-levels for (a) Mersea on the Essex coast, (b) Thames Estuary, (c) the eastern sector of the English Channel coast from Margate to Weymouth and (d) the western sector of the Channel coast from west of Weymouth to Cornwall.

fb) Upper Bristol .Channel . ' . . . (southwest England) -2 .

-4.

-6 .

-30 -8 . Swansea Bay . (Wales)

-10 "'-I 1 10 8 6 4 2 0 10 8 6 4 2 0

(c).. 0 I J a*-- -5 ' 'I- 0. ,'% ' -5 . - -10 . ,&$ A -10 . 2 -15 . @ :I 0 I(: -15 . -20 . :: 3 I' ;; -20 . -25 Bridgwater -25 . v (southwest England) I -30 ' 1 -30' ' . . ' 10 8 6 4 2 0 10 8 6 4 2 0 time (xlOc0 years BP) time (x1ooO years BP) Figure 14. Sea-levels for (a) Swansea Bay, south Wales, (b) the upper Britsol Channel near Avonmouth, (c) Bridgwater (Somerset), (d) Cardigan Bay, mainly from Borth Bog and the Dovey Estuary but including single data points from Newport and Newquay. 976 K. Lambeck

(4 5 I 'I assumed to be a function of depth) and certain ice model parameters. The local ice model is assumed known except 0- for the possibility of a constant scale parameter 0"" to be applied in space and time to the height of the British ice h -5 -5 1 sheet. The predicted sea-levels for most sites are not > strongly dependent on the Fennoscandian ice sheet, and 3 g -10 - without including sea-level data from northern European OY sites it is not possible to solve for a similar parameter BFEN. An earlier study using such sites indicated that B""" = 1 (Lambeck, Johnston & Nakada 1990) and this value is adopted here. Also, a time-dependent equivalent sea-level correction Sg'(t) is introduced to allow for any inadequacies in the models of the distant ice sheets. The observation equation then becomes (cf. eq. 6 of Part I) ACo(qpI A, t) + 4%A, t) 0 = Ag'(t) + Sg'(t)

-E -10 + B"" ACBR(q,A, t) -v 3 -20 + ACFEN(q,I, t) + ACf-'(q, I, t) + SC" W I = ACpredicted (1) 0 -30 .2 t.."" where A&, = observed sea-level reduced to MSL, at location -50 Manche 81 Calvados (q,A) and at time t. m E() = estimate of the observation error. -60 -' 10 8 6 4 2 0 Ag' = equivalent sea-level function for the totality of the ice sheets. Sg' = correction term to Ag'. p"" = scale parameter for the British ice sheet. ACnR = predicted first-order contribution to sea-level change from the ice- and water-load. Terms of the British ice sheet for specified earth model parameters. ACFEN= predicted contribution to sea-level change from the ice- and water-load terms of the -15 . Fennoscandian ice sheet. Cotes-du-Nord A CCf = predicted contribution to sea-level change from 1 -20' . ' . 1 the water- and ice-load terms of the distant ice 10 8 6 4 2 0 sheets of Laurentia, Barents Sea and Antarctica time (~1000years BP) Stw= second-order corrections to the total water-load Figure 15. Sea-level curves for the France Atlantic coast at (a) Pas terms arising from (1) the dependence of the de Calais, (b) Manche & Calvados and (c) CBtes-du-Nord. water-load term on sea-level change itself, and (2) the time dependence of the ocean function (see Fennoscandian ice sheet. The data has, therefore, been Part I). The full formulation for this term as grouped to construct regional curves for three locations: developed by Johnson (1993) is used here. Pas-de-Calais, Manche and Calvados, and CGtes-du-Nord. The observations in each area of a diverse nature and the An iterative procedure has been adopted to solve for the relation of the sample positions to the tidal range are not various parameters, the He, r] defining the A< functions, always known with precision so that many of the B"" and Sg'(t). In the first iteration predictions are made observations represent lower limits only. Fig. 15 illustrates for the three sea-level terms AC"", AtFEN,AC'-' for earth the three mean sea-level curves. The high-frequency model parameters covering a wide range of values. oscillations in sea-level proposed by Ters have been ignored. Predictions for each earth model k(k = 1 * * . K) within this range are made for each instant of time at every site where 4 AN IMPROVED REBOUND MODEL sea-level has been observed for a total of M(m = 1 . . . M) observations. The corrective terms Sg' and SC" are initially set to zero and for each model k the corresponding A strategy for parameter estimation a,"" value is estimated that minimises the quantity The parameters to be determined from the observations of sea-level include both the effective earth model parameters (the lithospheric thickness He and the mantle viscosity r] Glacial rebound of the British Isles-I1 977 where dm)is the standard deviation of the mth observation. For each earth model k the @"" value is established that gives the minimum solution variance and a search is then conducted through the earth model space to determine those parameters that give an overall minimum variance. Once this minimum variance solution is established, the second-iteration correction terms Sc" are computed only for those earth models in the neighbourhood of this first-iteration minimum because of the substantial computing requirements for these terms and because these corrections .I are relatively small. The solution of (1) for H,, q, p"" and E the correction vector 6r(t)is then repeated for the subset of earth models and the new minimum variance solution is sought.

Earth model parameters 0.5 0.7 0.9 1.1 1.3 1.5 In the first series of calculations the earth model comprises a lithosphere (layer l), a combined upper mantle and PBR transition zone down to a depth of 670km (layer 2) of Figure 16. The variance function u: for three three-layer earth viscosity q2 and a lower mantle (layer 3) of viscosity q,,. models with different q2 values and H, = 80 km as a function of the (This is the three-layered model of Table 1.) The ice-height scale parameter, B"". viscoelastic lithosphere is assumed to have a high viscosity (lo2' Pa s) and its effective thickness He is to be determined from the comparison of the observations with the predicted instance. Two local minima are identified in the q2- He sea-levels. The preliminary calculations (Part I) indicated parameter space, one near q2 = 2-3 X lo2' Pa s, and the that the predicted sea-levels are relatively insensitive to the second near 4 X 102"Pas. This example provides a good choice of qImand the initial search will be for He and q2 for illustration of the frequently encountered existence of two qIm= 1.3 x Pa s (see below) with the search conducted solutions in viscous relaxation problems with one solution within the range corresponding to an early stage of relaxation of a process with a long time-constant and the other corresponding to the (50 I He 5 100) km, (10'" 5 q25 5 X lo2') Pa s. (3) late stage of relaxation of a short time-constant viscous Figure 16 illustrates a typical result for the first-iteration model (e.g. O'Connell 1971). In the absence of any other solutions for a subset of the K earth models and they indicate information the higher viscosity solution would be the that while some trade off occurs between the earth- preferred one in this case. However, for the Scotland data, and ice-model parameters a separation of q2 and @"" where the dominant contribution to sea-level change at the appears feasible. This is further illustrated in Fig. 17 which sites near the centre of loading comes from the local summarizes the minimum variances and associated p"" for rebound, this higher viscosity mantle model does not predict the parameters within the earth model space defined by (3). well the considerable spatial and temporal variability The results are for three observational data sets: (1) the observed and this solution is now excluded (Fig. 17b). The observations from sites outside the former ice sheet margins combined data set (Fig. 17c) also excludes the higher value in England, Wales and France; (2) the observations from and a well-defined optimum solution space is defined by the sites within the formerly glaciated areas of Scotland and = 3 contour and indicates earth parameters that lie in the northwest England; and (3) the combined data set. The first range (60 5 He 5 75) km and (3 x lo2" 5 q25 5 x lo2")Pa s. data set (Fig. 17a) has no resolving power for @"" (see Part The overall minimum variance is (1.58)2 whereas the I) and this parameter has been set to unity in the first expected value from a perfect model and realistic estimates of observation variances would be unity and it appears that there is some room for model improvement unless the observational occurrences have been systematically Table 1. Definition of the multilayered earth models. CMB refers to the core-mantle boundary. underestimated. The statistics of the minimum variance solution 'three-layer Five-layer (He = 65 km, q2= 4 x 102"Pa s) are summarized in Fig. 18 in terms of the degree of correlation between the M observed and predicted sea-levels (Fig. 18a) and in terms of Layer 1 0-HQ HQ =80 krn the histogram of the residuals E~)(eq. 1) (Fig. 18b) and Layer 2 Hp -670 Hp -200 although some of the individual observational errors are large, there does appear to be a high degree of consistency Layer 3 670-CMB 200-400 between the model predictions and the observations of sea-level change. At this stage no attempt has been made to Layer 4 400-670 solve for the correction 85;e(t) to the equivalent sea-level function and a first estimate of it is given as the weighted Layer 5 670-CMB mean of the residuals E~,for each epoch t. This function is 978 K. Lambeck

England &Wales earth model dependent although this dependence is slight for solutions about the minimum variance solution. In the second iteration the correction term cwis evaluated and included in the solution of (1) for parameters in the neighbourhood of the first-iteration solution. Also, the first-iteration estimated of bf'"(r)is now included, and the solution is illustrated in Figs 17(d) and 18(c, d). The resulting minimum variance occurs for

He = 65-70 km (4a) and r], = (4-4.5)102" Pa s. (4b) Neither the inclusion of the second-order terms nor the introduction of the equivalent sea-level correction term significantly affects the solution for the earth model parameters, at least for the British rebound problem, and it appears reasonable to ignore these second-order terms in any further preliminary exploration of the full range of possible earth model parameters although these terms have been included in the five-layer solutions discussed below. Further iterations of the solution of (1) also are not required. In the solutions of the sea-level equations discussed here

I I I, I I 1 I the response of the mantle to loading has been assumed to l(Pl 231 IOU 235 be fully non-adiabatic in the sense that any particle En+nd, Wales & Sro(l.nd displaced to a new depth in a medium of depth-dependent density retains its original density and thereby experiences a buoyancy force. It has been pointed out by Cathles (1975) and Fjeldskaar & Cathles (1984) that adiabatic models may be more appropriate when the mantle is chemically homogeneous or at phase transition boundaries. In these models the displaced particles blend with the material at their new depth and experience no buoyancy. Recently adiabatic solutions have been developed by P. Johnston so that it has been possible to estimate the effect of this assumption on the model parameters. Generally the differences between the two models as applied to the British ice load are relatively small, essentially because the surface load is composed largely of high wavenumber terms whose corresponding viscoelastic Love numbers differ little for either the adiabatic or non-adiabatic assumption. Further- more, the two models lead to results that are nearly linearly proportional to each other and, for this region at least, a direct trade off occurs between the degree of adiabaticity assumed and the scale factor /3 for the ice sheet. Both the adiabatic and non-adiabatic solutions lead to the same viscosities but not the same 0, with the latter leading to an underestimation of the ice height by about 10 per cent (Lambeck 1993b). Thus, in the following solutions, only the

I 1 I I I, I I non-adiabatic models are considered in the discussion of the lP 2 3 5 I l(P1 235 earth parameters.

rli(P8 s) It has previously been established (Part I) that the sea-level predictions for the British Isles are not strongly Figure 17. The variance function as a function of earth u: dependent on the properties of the lower mantle because of parameters qz (the combined upper mantle and transition zone viscosity) and H, for the first iteration solution (a-c) and the the relatively small dimensions of the ice load. However, the three-layered model. (a) The England, Wales and northern France response to the water load, occurring with dimensions equal data set only, (b) the Scotland data set only, and (c) the combined to those of the Atlantic Ocean, does stress the lower mantle data set. In (c) the B dependence on v2 and H, is shown by the to a certain degree and some dependence of the sea-level dashed lines. In (d) the results for the second-iteration solution are response to qI,,, can be anticipated. Fig. 19 illustrates the shown for the combined observational data set. All solutions variance factor u', as a function of both r]* and qIm for correspond to the fully non-adiabatic models. He = 80 km and the result confirms the weak dependence of Glacial rebound of the British Isles-11 979

observed sea level (m) observed-predicted sea level (m)

r. . 're 40 80 -pv .-'. . -2 20 U 8 [ 60 B 0: -B 4g -20 0' 40 . 6#7?- ',a. p =0.949 20 -40.' .,' . , A$red =- 0.16 + 1.013 A{ob, / -60 observed sea level (m) observed-predicted sea level (m)

Figure 18. Statistical evaluation of the minimum variance solutions for (a, b) the first iteration solution and (c, d) the second iteration solution for the three-layered earth model. In (a) and (c) the observed sea-levels are plotted as functions of the predicted values and the (unweighted) best fit linear trend is shown. In (b) and (d) the histograms are of the residuals E,, of eq. (1).

the rebound on qlm, with the smallest value occurring for

qIm= 1.3 x Pas. (4c) Although the resolving power of this data set for the lower mantle viscosity is poor, models with qlm5 4 x lo2' Pas appear to be excluded and there is strong support for models in which the mantle viscosity increases substantially across the 670 km boundary, consistent with previous studies of the crustal rebound in other areas (Lambeck & Nakada 1990; Lambeck el al. 1990). How this increase in viscosity is distributed with depth below 670 km cannot, however, be resolved with the present data. 3- - 10 The estimates (4) for the mantle response are effective parameters that describe the response of the Earth's surface- to-glacial unloading on a time scale and surface-load scale I I 1 I I that is characteristic of the British ice sheet, but it remains to be demonstrated that this simple three-layered rheologi- cal model does in fact give the best representation of the upper mantle response. Therefore, an additional class of model is considered comprising five mantle layers (Table 1). Fig. 20 illustrates the first-iteration results for this model 980 K. Lambeck

7 7 q4=3x1020 Pa s ?'p7Xl@O Pa s 5-

7(3'7(4

I 8 1 2 3 57 1 2 3 5 7 10 0 4 x 10 r 1 10 W q4=10x1#* Pas 7(4=5x1020 Pas 2 7- 7-

n3w4

1 2 3 5 7 10 q3 (~1020Pa s)

Figure 20. Minimum variance solutions for the second-iteration five-layered earth model as a function of the viscosities (q2,11) for the two upper mantle layers and the viscosity q4 for the transition zone from 400 to 670 km equal to (a) 3 X 10'" Pa s. (b) 5 X 102"Pas, (c) 7 X 10'" Pa S, (d) 10" Pas. The other earth model parameters are He = 80 km, qlm= 5 x 10" Pa s.

with H, = 80 km and in which the upper mantle comprises r], = q3= q4 = 5 x lo2"Pa s yield only a slightly larger three layers; the lithosphere, a second layer which extends minimum variance. Fig. 2lfa) illustrates the solution from the base of the lithosphere to 200 km with viscosity r]', variance for those models for which r], = q3 and it confirms and a third from 200 km to 400 km with viscosity q3. The that any increase in viscosity from the upper mantle to transition zone down to 670 km forms the fourth layer of transition zone is either zero or very small. Similar results viscosity q4. The lower mantle viscosity in this example is are illustrated in Fig. 21(b) for Q,~= 102'Pas and equal to 5 x 10" Pas for all models, near the lower limit H, = 80 km and the conclusion is the same as before, that permitted by the earlier solution (Fig. 19). Only the range of there is no compelling evidence fm substantial layering in models in which the viscosity in any layer (other than the the mantle viscosity above 670km. Nor do the results lithosphere) is less than or equal to that of the layer below it support mantle models with a significant inversion of (Table 1) are considered at this stage. The variances are viscosity across the 400 km boundary (Fig. 21b). plotted as functions of r]' and q3 for discrete values of v4 The pattern of the isovariance curves does not suggest that corresponding to the viscosity of the transition zone between models with low-viscosity channels (small r]' values) below 400 and 670 km depth, and for each q4 value the minimum the base of the lithosphere down to a depth of 200km, variance occurs only when r], = q3. The overall minimum except possibly if both q3 and q4 are substantially increased. variance for the H, = 80 km solutions occurs for r], = q3 = However, even in this case, the results in Fig. 20(d) suggest 4.5 x 10'" Pa s and q4 = 7 x 102"Pa s suggesting that there that the smallest variance for such models will be greater may be a small increase in viscosity between the upper than that found for solutions without such a channel. This is mantle and transition zone although solutions with further illustrated in Fig. 21(c) for models in which q3 = v4 Glacial rebound of the British Isles-II 981

100

70 /

50

30

hm 20 a" 2s Wx 10 N F 7

5

3

2

I I I I I I I 23 5 7 10 20 30 3 q3=(q4)(x1020 Pa s)

Figure 21. Minimum variance solutions for the second-iteration multilayered earth model with HI = 80 km and (a) q2 = q3, qlm = 5 x lo2' Pas, (b) q2 = q3, q,,,,= 10'' Pas and (c) with q3 = q4, qlm= 5 x 10" Pa s. and in which the viscosity q2 of the uppermost mantle layer rebound amplitude, although the minimum variance is from the base of the lithosphere to 200 km depth is allowed increased. These @ estimates are for the so-called fully to be as low as 10" Pa s and the observations do not support non-adiabatic models. Fully adiabatic models yield estimates mantle models with very low viscosities for the uppermost that are about 5 per cent smaller and largely within the mantle. uncertainty estimate of this parameter. The estimated correction 6c(t) to the equivalent sea-level function (eq. 1) from the second-iteration solution Ice model parameters is illustrated in Fig. 22 and indicates that after about While the solutions for earth model parameters, at least in 6000yrBP, a rise of about 2m in equivalent sea-level the case of the British rebound, are not significantly affected occurred; that sufficient glacial melting continued after this by the inclusion of the second-iteration corrective term in time over the next 1500 to 1000 years to raise sea-level eq. (l),the estimate of the scale factor p"" for the British globally by about 2m. This result is consistent with earlier ice sheet is, and the inclusion of these terms results in a analyses of Late Holocene sea-levels in both the Australian lowering of the total ice thickness required (compare Figs region and the northwestern European region (Nakada & 17c and d). The solution for the minimum variance Lambeck 1988; Lambeck et af. 1990) and lends support to three-layer earth model points to p"" = 1.02 f 0.04 (Fig. glacial models in which the Antarctic ice sheet continued to 17d) and indicates that the maximum ice thickness is add meltwater to the oceans after the complete melting of unlikely to have exceeded about 1500m over central the northern ice sheets. Before 6000 yr BP the equivalent Scotland, wholly consistent with the geomorphological sea-level corrections change sign, indicating a more complex evidence (Section 2). Some trade off between this parameter melting model than the relatively uniform melting rates and the earth-model parameters does occur (Fig. 17d), with adopted for the ARC and ANT ice models (see Part I). increased lithospheric thickness estimates leading to greater While the accuracy estimates of these corrective terms for p"" values being required in order to produce a comparable earlier times are relatively low, the Sr(t)function points to 982 K. Lambeck

in the second regional solution the earth parameters (4) have been adopted and local p values are estimated independently for each of the four subregions. Of these solutions only the Moray and Solway yield p"" estimates that are significantly different from the combined solution (Table 2). In particular, the Moray solution suggests a need to increase the ice load by about 17 per cent over northern Scotland, while the Solway solution points to a decrease in the ice heights by about 7 per cent over northwest England. These regional solutions are discussed further below.

5 DISCUSSION 15 10 5 0 time (x1OOO years BP) A comparison of observations and predictions of sea-level Figure 22. The corrective term 6T'(t) to the nominal equivalent change sea-level function Ar(f). Intervals in which the gradient of this function is positive indicate times of more rapid global melting than The comparison of the predicted sea-levels with the assumed in the nominal melting model. observed levels can be affected in several ways, including the time series of sea-level change at characteristic sites a faster global melting rate in the interval before about (Fig. 23), as isobases of the mean sea-level for specific 11 000 yr BP than assumed (that part of the function for epochs (Fig. 24), and as height-distance diagrams of past which the gradient of is positive) and to a slower melting mean sea-level surfaces relative to their present levels (Fig. rate at the time of the Loch Lomond Stadial, suggesting that 25). For the Forth and Tay firths of eastern Scotland the the residual global ice sheets expanded in the interval 11 000 predicted isobases for mean sea-level at the time of to 10500yrBP so as to lower sea-level by about 3-4m. formation of the principal shorelines (Fig. 24) can be However, the correction at 10500yrBP is based almost compared with the observed isobases in Fig. 4 with the entirely on the nominal date given for the Late Interglacial proviso that the latter correspond to the shoreline-formation Buried shoreline and Main Rock Platform of Scotland, and heights (mainly the MHWS level which is typically at 2-3 m without a firmer basis for this age it would be premature to above MSL throughout the region). The generally interpret this anomaly in the equivalent sea-level function in satisfactory agreement between the two is also evident in the terms of a global sea-level response. A similar examination sea-level gradient plots for the major shorelines along the of the sea-level evidence along the coasts of Norway and southern shore of the Firth of Forth (Fig. 25a), except that southern Sweden is warranted. the predicted gradients for the older East Fife 6 and Main Perth Shorelines are somewhat steeper than observed. Regional models Along the northern shore of the Tay Firth the observed and predicted gradients are consistent (Fig. 25b) although the Generally, agreement between observations and predictions predicted heights for the East Fife 6 Shoreline lie below the based on the above optimum models (4) with p"" = 1.02 is observed heights. This, together with the Forth result, satisfactory, but some significant discrepancies occur, most suggests that the ice load should be increased to the north or notably for sites in the Beauly Firth of northeastern northwest of the Firth of Tay. Scotland (Fig. 23c), which point to either a regional The regional solution for the Moray-Beauly region variation in the earth response or to local departures of the indicated a need to increase the ice load in this region (Fig. ice load from that assumed in the model. To examine these 23c) and Fig. 24(b) illustrates the sea-level isobases over alternative interpretations, the observational data base for northern Scotland based on the best-fitting local /3 value of Scotland and northwestern England has been divided into j3 = 1.20. The predicted isobases in the region trend in a four subregions: (1) southeastern Scotland, comprising nearly easterly direction, whereas the observed trend is east primarily the Forth and Tay estuaries and valleys, (2) of northeast (compare Fig. 24b with 6) and this points to a northeastern Scotland with the sites occurring in the Moray, need to place the additional ice volume over the region of Inverness and Beauly firths, (3) the Argyll region of western Ross & Cromarty to the northwest of Beauly (see Fig. 3 of Scotland including the Clyde Estuary and Inner Hebrides, I for location map). This conclusion is reinforced by the and (4) the Solway Firth of southwestern Scotland and the limited evidence from Wester Ross (in the area of Malvaig, Morecambe Bay area of northwest England. In a first Fig. 3 of Part I) where the model predicts Late Glacial calculation, effective earth and ice parameters for the shorelines that are near or below present mean sea-level three-layer model are estimated independently for each (Fig. 24b), whereas the rock platforms attributed to a Late subregion. Glacial origin, Sissons & Dawson (1981), occurs at heights However, the resulting q2 and He all lie within the range of 20-30 m. Thus, a considerably greater ice load is required of values defined by the overall solution (4) and a strong in the northern region of Scotland unless the Wester Ross case for lateral variation in earth response cannot be made rock platform pre-dates the last glacial event. The particularly as the solutions for both the Moray and Solway predictions for the Main Postglacial event in this region are regions are not well constrained by the relatively small generally consistent with the observed levels reported by numbers of observations available for these regions. Hence, Sissons & Dawson (1981). Further north, in Orkney and the Glacial rebound of the British Isles-11 983

Glencarse & Bridge of Earn Arnprior Beauly Firth Firth of Tay Forth River lnverness 40 30

- 10 .. 16 14 12 10 8 6 4 15 10 S 0 16 14 12 10 8 6 4 2

s Lochgilphead Loch Fyne

Morecambe Bay Thames Estuary -20 Lancashire 1 16 M -10 1 -25 .- 15 10 5 0 10- 8 6 4 2 0 10 8 6 4 2 0 (9) 01

T/ 1 -20 - I Fenlands -25 - Bridgwater Bay East Anglia 1 f Bristal Channel -15 1 -30 8 6 4 2 0 1086420 time (x1ooO years BP) -time (x1ooO years BP) time (x1ooO years BP)

Figure 23. Predicted and observed sea-levels at selected sites in Scotland and England. The predictions are based on the earth model parameters defined by (4) and on the local /3 factors (Table 2). For the Beauly Firth the prediction based on the global /3 value is also shown (broken line).

Outer Hebrides, the model predicts sea-levels that are observed and predicted sea-level curves for Lochgilphead below the present level throughout Late Devensian and and the Clyde Firth is also satisfactory (Fig. 23d) and the Holocene time, consistent with an absence of observed association of the Main Rock Platform with sea-level at highstands in the region as well as with sea-levels at 10500yrBP leads to a consistent model (Fig. 25d). The 8000-5000 yr BP in the Outer Hebrides being several metres older and higher rock platforms of western Scotland at below present levels (Binns 1972; Ritchie 1985). heights of up to 50 m OD are predicted to occur only during For the west coast of Scotland the agreement between the earliest stages of deglaciation, at about 16 000 yr BP 984 K. Lambeck

Table 2. Regional solutions for pBRand corresponding minimum For the sites in Wales, southern England and the French variances for the earth model defined by (4). For the southern Channel coast (Fig. 25), the predicted sea-levels are England, Wales and northern France solution, the PBR value has generally consistent with observations, although at a number been set to unity. of sites the observations lie above the predicted level. This is the case, for example, for the result at Borth Bog in Region PR Variance Cardigan Bay (Fig. 25) where the tree stumps may define a level above MHWS tide as suggested by Tooley (1979). For the Thames Estuary the discrepancy is greatest for Devoy's Au data 1.03 2.14 (1982) Table 4 results which define mainly upper limits to the sea-level curve. Thus the discrepancies noted for Forth-Tay 1 .oo 0.96 southern England may reflect the different nature of the observational data as much as limitations of the model Moray Beady 1.20 0.74 predictions, and no systematic pattern of the differences for the region as a whole occurs. Western Scotland 1.03 1.52

Solway and NW England 0.96 1.78 Mantle rheology

Southern England, Wales, France 1 .00 1.36 The effective parameters for the mantle below the Great Britain region are defined by the results (4) for the (e.g. Fig. 23d), when the region is believed to have still been three-layer earth model as ice covered and by the time the Inner Hebrides became ice free the predicted isobases are significantly lower than the He = 65-70 km observed heights. The model, therefore, supports the r], = (4-4.5)102" Pa s interpretation that these high-level platforms pre-date the last glacial cycle. 4 x lo2' Pa s < qIm< 2 x lo2' Pa s In neither eastern nor northeastern Scotland do the where r], represents the average viscosity for the mantle models predict the short-duration oscillations in sea-level as between the base of the lithosphere and the 670 km seismic defined by the buried shorelines between about 10200 and discontinuity. These values are effective parameters that are 8700yrBP. If the fluctuations are the results of the Loch representative of the mantle response to load cycles Lomond Advance then the ice volumes involved must have operating on the order of 104yr. The associated stress and been greater than adopted and its duration and timing must strain-rate fields have not been evaluated at this stage, but be different from what is usually assumed. During the simple order-of-magnitude calculations for the mantle above advance, renewed crustal loading will produce an apparent 670 km suggest deviatoric stresses and strain rates of the rise in sea-level at a site such as Arnprior near the advance's order of 1 MPa and (2-5)10-16 s-' respectively and maximum limit (Fig. 17) but this would be expected to have considerably smaller values at greater depths. occurred somewhat earlier than the age of 10200yrBP Tests with multilayered models have shown that: (1) there attributed to the highest of the buried beaches. Also, if the is no significant change in viscosity from the upper mantle to other buried beaches are attributed to the Loch Lomond the transition zone (Figs 20 and 21) and, (2) there is no Advance then the ice retreat would have occurred strong evidence for viscosity layering in the upper mantle, non-uniformly and more slowly until after 8700 yr BP, the including a low-viscosity layer immediately below the age of the Low Buried Beach. Generally, neither the lithosphere (Fig. 20). The absence of a marked viscosity observational constraints nor the numerical resolution of the gradient above 670 km is perhaps not an obvious conclusion present rebound model are adequate to examine in detail in view of the many variables that can be expected to affect the relative sea-level response to the Loch Lomond the creep strength (i.e. viscosity) of the mantle materials. In Advance. particular, because garnet appears to have a considerable Agreement between observations and predictions for the higher creep strength than either olivine or spinel (Karat0 northern England sites is typified by the comparison for 1989), it has sometimes been argued that the transition zone Morecambe (Fig. 23e). In this region the Main Postglacial could be expected to possess a significantly higher viscosity zero contour isobase for mean sea-level is predicted to pass (Spada et al. 1992), but the result of these rebound through Morecambe Bay and small highstands at about inversions suggests instead that the creep strength of this 6000 yr BP are predicted for sites such as the Esk or Duddon layer as a whole is controlled by the weaker spinel phase Estuaries to the north (Fig. 24a). The predictions for these such that the effective viscosity at ambient temperatures and localities suggest that sea-level should have reached its pressures is not significantly different from that of the present level earlier than observed although the observa- predominantly olivine mantle above 400 km depth. Another tional data base (Andrews et al. 1973) is unsatisfactory for factor that could produce a strong depth dependence of this region (see Fig. 1ld). To the south, at Southport and viscosity is the mantle temperature, but the inferred near Formby, agreement between observations and predictions is constancy of viscosity with depth suggests that, if this is an again satisfactory. Also, the gradient of the Main Postglacial important mechanism, then the ratio of temperature to shoreline from the Solway Firth to north of Morecambe Bay melting point temperature does not change significantly with is predicted to be about 0.04 m km-l which agrees well with depth in the mantle beneath the British Isles. the observed gradient of 0.03 m km-' for raised beaches The solution for the earth model parameters based on the reported by Walker (1966). British Isles data agrees well with that previously Glacial rebound of the British Isles-II 985 15 000 years BP

6 000 years BP

Figure 24. Contours of the predicted constant relative mean sea-level over northern Great Britain based on the earth model defined by (4) and (a) the global p"" value, and (b) for northern Scotland based on the p value from the northeastern Scotland regional solution. determined from the Fennoscandian rebound using the same ARC model discussed in Part I). Because the Fennoscan- approach although in the latter case only three-layered dian ice sheet is considerably larger than the British ice mantle models were considered (Lambeck et al. 1990). In sheet the depth dependence of the mantle response to the that study relative sea-level observations were used from loading is different in the two cases so that the similar result sites either near the centre of rebound or well outside the for q2 lends further support to models of nearly constant former ice margin so that the model results were not viscosity profiles between the base of the lithosphere and the strongly dependent on limitations of the ice model used (the 670 km boundary. 986 15 OOO years BP 13 500 years BP \ \ \ -100

10 500 years BP 6 OOO years BP

c- / I' I' -20 - \ 'I\

Figure 24. (Continued.) (b)

Amprior Kincardie Leith bbar Stkling Aberlady

Firth of Forth (south side) lo t Tay Firth (north side) n[ I,,. 1 . " .. 0 20 40 60 80 100 120 -20 0 20 40 60 80 distance (km) distance (h) (d115 I I Western Scotland TT

0-. -_ k3g upper Sound Oh Moray & Beady firths cyuy , (Jmf of Jura _- -10 -5 0 5 10 15 20 25 -20 0 20 40 60 80 100 120 distance (km) distance (km) Figure 25. Predicted'(continu0us lines) and observed (broken lines and error bars) for some of the major shorelines (reduced to MSL) observed in Scotland. Glacial rebound of the British Isles-I1 987

The effective viscosity q2 obtained for both the borderland, Geol. J., 8, 207-224. Fennoscandian and British regions is higher by a factor of Bowen, D. Q. & Sykes, G. A,, 1988. Correlation of marine events about 2 than that obtained from analyses of sea-level change and glaciations on the northeast Atlantic Margin, Trans. R. along the Australian margin. In the last example, the SOC. Lond., B318, 619-665. departures from the eustatic sea-level change is primarily a Bowen, D. Q., Rose, J., McCabe, A. M. & Sutherland, D. G., result of the response of the mantle to the water loading and 1986. Correlation of Quaternary glaciations in England, Ireland, Scotland and Wales, Quat. Sci. Rev., 5, 299-340. to a transport of material between oceanic mantle and Boyd, W. E., 1986. Short Communication: A late Devensian continental mantle. The value of (2-3)102"Pa s obtained shoreline position in north Ayrshire, Scot. J. Geol., 22, (Lambeck & Nakada 1990) can, therefore, be interpreted as 412-416. some average of the two mantle regions and the difference Browne, M. A. E., 1980. Late-Devensian marine limits and the between this and the European value can be attributed to pattern of deglaciation of the Strathearn area, Tayside, Scot. J. lateral variation in mantle structure (Nakada & Lambeck Geol., 16, 221-230. 1991). Such variations in upper mantle viscosity are Browne, M. A. E., Graham, D. K. & Gregory, D. M., 1984. generally consistent with observations of lateral variations in Quaternary esturine deposits in the Grangemouth area, seismic shear wave velocities (e.g. Woodhouse & Dziewon- Scotland, Br. geol. Surv., 16, 13. ski 1984; Tanimoto 1990a,b; Romanowitz 1990) and seismic Browne, M. A. E., McMillan, A. A. & Graham, D. K., 1983. A late-Devensian marine and non-marine sequence near Dum- wave attenuation. barton, Strathclyde, Scot J. Geol., 19, 229-234. 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