TEmARESEARCH Glacial rebound and sea-level change in the British Isles Kurt Lambeck Research School of Earth Sciences, The Australian National University, Canberra ACT 2601, Australia ABSTRACT dominates over the rise in sea-level from the meltwater of the distant ice Observations of sea levels around the coastline of the British Isles for sheets, whereas in early Holocene time the past 10,000-15,000 years exhibit a major regional variation and the contributions from the meltwater of provide an important data base for testing models of glacial rebound as the distant ice sheets begins to dom- well as models of the Late Devensian ice sheet. A high-resolution inate. In the late Holocene time, after about 6000 yr BP, it is the crustal rebound rebound model has been developed which is consistent with both the that again is the dominant cause of sea- spatial and temporal patterns of sea-level change and which level change. Further away from the demonstrates that the observations are the result of (i) the glacio- centre of rebound, in NW England (Fig. isostatic crustal rebound in response to the unloading of the ice sheet 2a), the balance between the two con- over Britain and, to a lesser degree, of the ice sheet over Fennoscandia, tributions is primarily in favour of the and (ii) the rise in sea-level from the melting Late Pleistocene ice second contribution except in Latest De- vensian time when the rebound compo- sheets, including the response of the crust to the water loading (the nent dominates. The observations from hydro-isostatic effect). The agreement between model and sites in southern England (Fig. 2b-d) observations is such that there is no need to invoke vertical crustal exhibit less spatial variability and the movements for Great Britain and Ireland of other than glacio-hydro- sea-level change here is controlled isostatic origin. The rebound contributions are important throughout mainly, but not wholly, by the melt- the region and nowhere is it sufficiently small for the sea-level change water from the major ice sheets. to approximate the eustatic sea-level rise. The observational data There has been little quantitative modelling of the rebound of Britain and distribution around the periphery as well as from sites near the centre the associated sea-level fluctuations, of the former ice sheet is sufficient to permit constraints to be despite a number of geophysical, glaci- established on both earth model parameters specifying the mantle ological and geomorphological reasons viscosity and lithospheric thickness and the extent and volume of the for doing so. The rebound models can ice sheet at the time of the last glaciation. Preliminary solutions are provide constraints on (i) the Earth's presented which indicate an upper mantle viscosity of (3-5)1eoPa s, a response to surface loading; (5) the lithospheric thickness of about 100 km or less, and an ice model that ice sheet dimensions and the timing was not confluent with the Scandinavian ice sheet during the last of the retreat of the ice sheets; and (iii) the ages of some of the erosional fea- glaciation and whose maximum thickness over Scotland is unlikely to tures, such as the rock platforms of have exceeded about 1500 m. western Scotland (e.g. Dawson, 1984) or the older elevated beaches of eastern Terra Nova, 3,379-389 and northeastern Scotland (e.g. Firth, 1989), where conventional dating methods have failed. such model- I NTRO D UCTl ON Also, Europe, North America and Antarctica ling is desirable in order to establish Complex temporal and spatial patterns (e.g. Donner, 1970; Cullingford et al., whether sea-level observations from of sea-level change have been recorded 1981). The Scottish results, from sites different sites can be combined to form throughout Great Britain and Ireland near the centre of rebound, exhibit this representative sea-level curves for a during Late Devensian and Holocene spatial variability even within restricted given region. This question, in particu- time and the observations illustrated in areas such as the Forth, Tay, and Moray lar, is addressed in this paper. Fig. 1 are characteristic of this regional Firths of eastern Scotland and this is The solution of the glacial rebound variability. This pattern has been qual- perhaps best illustrated by the shoreline and sea-level problem for the Great Brit- itatively understood in terms of the gradient diagrams of Sissons (1983a) ain region requires a knowledge of the crustal rebound in response to the re- and others. The characteristic temporal Earths rheology (E) and of this history treat of the Late Devensian ice sheet patterns of the Scottish observations are of the global ice sheets (I). This ice sheet over Britain and to the rise in sea-level the combined result of these two con- includes the small but important British resulting from the concomitant melting tributions: in Late Devensian time the ice sheet ZB, as well as the more volumin- of distant major ice sheetsover northern glaao-isostatic rebound contribution ous Fennoscandian ice sheet lF and 379 KURT LAMBECK 40, . I of the various parameters is possible Arnprlor Beaulg Flrlh here (Lambeck, 1991) and that, in con- Uppsr Farth Valley - m Northeastern Scotland . sequence, the observation of sea-level p.. change in the recent past can contribute :I I, to several areas of earth science. 0 FORMU LATlON -10 .*--_.,. .___.-- I The formulation of Nakada and Lam- -LO ' J beck (1987, 1989) is used and the sea- IS 10 J 0 a level equation is written as Al(cp,A:t) = A&(t)+Ap(cp, A:t) Lochpll head +Af(cp,A:t)+A{r-'(cp,A:t) Western &oUand . (1) A{(cp,A:t) is the position of mean sea- level at latitude Q, longitude A and at time t relative to the present position at the same location. The term A&(t) is the equivalent sea-level function (or eu- . ..._._.- -.-_. .- .lo static sea-level) defined as I .a A&(t) = (change in uolume of meltwater)/ IS 10 J 0 10 J 0 C (surface area ofocenns) It includes the time dependence of the Brldge d EPrn Ardyne totality of all ice sheets. The three re- Firth of Tag . Firth of Clyde . maining terms on the right-hand-side of (1) include the contributions, for each of the three ice models IB, IF and f-f separately, from (i) the loading-unload- ._._.--._ ing of the crust by the ice sheets, (ii) the loading-unloading of the crust by the 0 ...~-.- meltwater deposited into or removed '. .. ,- I -10 ,._, from the oceans, and (iii) the gravita- IS 10 I 0 e tional self-attraction of the water and ice that ensures that the ocean surface re- Fig. 1. Observed sea-level heights (with error bars where available, and reduced to mean sea-level) mains an equipotential surface at all and predicted lmls at a number of sites in Scotland. The predicted lmls are based on the Scotland times. These 'corrective terms' are func- rebound model (Table 1)and the dashed lines represent the range of values predicted by the upper and tions of position and time. Their evalua- lower limits for the muntleviscosity. (See Fig. 5 for location map.)(a) Arnprior, upper Forth Valley. tion requires a knowledge of the ice Thedataarefrom Sissonsand Brooks (1971);(b) BridgeofEarth, FirthofTay, nearPerth ineastern models I(cp,A:t), of the earth model E, Scotland. Theobservations arefrom Cullingford et al. (2980) and Paterson et al. (7980)for the two and of the mean geometry (which will oldest data points (c) Beauly Firth, northeastern Scotland. The data are from Firth and Haggart itself be a function of time). The earth (2989)for the Holocene timeandfrom Firth (1989)forLate Devensian time; fd)Lochgilphead, Loch model parameters include the effective Fyne, western Scotland. Data are from Peacock et a1.(1978);(e) Ardyne, Firth of Clyde, western thickness of the lithosphere He as well Scotland. Data arefrom Pencock et a1 (2978); ff)Northern shoreofthe Solway Firth, southwestern as the effective viscosity of the mantle q, Scotland, between Dumfries and Kirkcudbright. Data are from Iardine (1982). where 7 will be a function of earth radius. Furthermore, both Heand qmay exhibit lateral variation. The observation model is the far-field ice sheets 1-1 for Laurentia, whether, in view of the uncertainties as- Antarctica and the BarentsKara Seas sociated with both the € and I models region. In glaciological studies it has and with incomplete data sets for past generally been assumed that E is known positions of sea-level, it is indeed pos- and ice models are constructed using a sible to establish independent improve- formulation relating the forces acting ments on both the € and 1 model on and within the ice sheet and the ice parameters as well as resolve some of rheology. In most geophysical studies it the ambiguities in the observational has been assumed that I is known and data. Preliminary modelling of the re- where AS, = observed sea-level (re- earth models are inferred from the sea- bound of Great Britain has, how- duced to mean sea-level) at location level observations. It may be asked ever, indicated that some separation (cp,A) and at time t; E~ = Observation 380 GLACIAL REBOUND AND SEA-LEVEL CHANGE 10 , I (iii) the lithosphere, of thickness Hp, is 0 0 of high (165 Pa s) viscosity and overlies an upper mantle (extend- -10 . ing to a depth of 650 km) with a viscosity qvmand a lower mantle of -m . viscosity qfm. .XI . The earth model parameters are there- Moreearnbe Bay Avonmoutb Norlhwest England Upper Brlstol Channel fore effective parameters only that de- 40 5 0 0 scribe the average regional response of a b lo the Earth to surface loading on time scales of ld-lo4 years.