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Glaciology of the British Isles Ice Sheet during the last glacial cycle: form, flow, streams and lobes
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Quaternary Science Reviews 25 (2006) 3359–3390
Glaciology of the British Isles Ice Sheet during the last glacial cycle: form, flow, streams and lobes Geoffrey Boulton, Magnus Hagdorn School of Geosciences, University of Edinburgh, Grant Institute, Kings Buildings, Edinburgh EH9 3JW, UK Received 12 January 2006; accepted 29 October 2006
Abstract The last ice sheet over the British Isles, together with other mid-latitude Pleistocene ice sheets, and in contrast to the modern ice sheets of Greenland and Antarctica, had a relatively low profile, low summit elevation and extensive, elongated lobes at its margin. A thermomechanically coupled numerical ice sheet model, driven by a proxy climate, has been used to explore the properties that would have permitted these characteristics to develop. The approach, the key to quantitative palaeoglaciology, is to determine the boundary conditions that permit the simulated ice sheet to mimic the evolution of the real ice sheet through the last glacial cycle. Simulations show how a British ice sheet may have been confluent with a Scandinavian ice sheet during some parts of its history and how unforced periodic and asynchronous oscillations could occur in different parts of its margins. Marginal lobes are a reflection of streaming within the ice sheet. Such streams can be ephemeral, dynamic streams located because of ice sheet properties, or fixed streams whose location is determined by bed properties. The simulations that best satisfy constraints of extent, elevation and relative sea levels are those with major fixed streams that strongly draw down the ice sheet surface. In these, the core upland areas of the ice sheet were cold based at the Last Glacial Maximum, basal streaming velocities were between 500 and 1000 ma1 compared with surface velocities of 10–50 ma1 in interstream zones, shear stresses were as low as 15–25 kPa in streams compared with 70–110 kPa in upland areas and 60–84% of the ice flux was delivered to the margin via streams. r 2006 Elsevier Ltd. All rights reserved.
1. Introduction Ice sheets are by far the largest and climatically most influential part of the global glacier mass. Understanding about them is derived from two sources:
modern ice sheets whose current properties can be measured and modelled, but whose bed cannot be directly observed, and whose time-dependent variations have only been studied for about 50 years; from the evidence left by Pleistocene ice sheets, whose properties cannot be directly measured but whose beds can be directly observed and some of whose longer-term variations can be inferred from geological evidence.
In this article, we use numerical ice sheet modelling and geological evidence to explore relationships between ice Corresponding author.
E-mail address: [email protected] (G. Boulton). 0277-3791/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.quascirev.2006.10.013
sheet form, ice streaming and marginal lobe formation using the ice sheet that covered the Britain Isles during the latter part of the last glacial cycle as the subject of modelling. This is done for three reasons: because it helps us better to understand why and where different types of ice streams form and how lobes are generated; because there are longstanding problems in understanding the form and flow of the last glaciation ice sheet over the British Isles; and in order to infer glaciological properties such as dynamic structure in time and space, velocities and shear stresses. Our approach is one that we believe to be central to palaeoglaciology. We simply ask how we need to adjust the boundary conditions and forcing functions for ice sheet models in order to cause the modelled ice sheet to behave in ways that mimic the geologically deduced real ice sheet. The boundary conditions are fundamental ice sheet/Earth properties, and forcing functions reflect climate/ice sheet interactions. Together they represent logical deductions from geological data about glaciological properties of the palaeo-ice sheet through the medium of the model.
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2. Ice sheet form, ice streams and the problem of ice lobes
2.2. Possible mechanisms
2.1. The problem
By the 1960s, it was beginning to be understood (e.g. Bauer, 1961) that ice sheets were not radially symmetrical in the distribution of their dynamic properties, but that fast ice streams flowed through them. These play a massive role in ice sheet dynamic behaviour, discharging as much as 85% of the mass in the case of Antarctica, even though comprising a relatively small proportion of its area. Major lobes at the terrestrial margin of an ice sheet on a flat bed can only be caused by such streams, which are increasingly recognised as ubiquitous attributes of Pleistocene as well as modern ice sheets (e.g. Boulton et al., 2001). (Valley glaciers are naturally lobate, being prevented from spreading laterally by confining mountain walls.) Elongate lobes imply relatively low longitudinal slopes and relatively high lateral slopes, and, therefore, require a mechanism that permits longitudinal gravity spreading but prevents lateral spreading. The Earth’s two current ice sheets offer no direct analogies. The Greenland ice sheet margin is lobate only where ice flows towards the margin through valleys in the flanking mountains, or on a very large scale in subsidiary ice ridges such as that of NW Greenland. The Antarctic margin calves almost exclusively into deep water. It has been argued on stratigraphic grounds (e.g. Clayton et al., 1985), that some lobes, such as those at the southern margin of the LGM Laurentide ice sheet, are the product of surges, but this in itself does not account for the contrast between their longitudinal and transverse slopes. Ice sheet lobes on a flat bed must reflect areas where relatively fast streams intersect the glacier margin and project it further forward than elsewhere, against the common effect of ablation. Easier movement in them is most likely to result from either:
Early theories of ice sheet form and flow assumed ice sheets to be slowly flowing, quasi-radial domes (Nye, 1951) in which the velocity of flow was a function of radial distance from the flow divide. This view was reflected in early attempts to model former ice sheets (e.g. Boulton et al., 1977; Sugden, 1977) and some modern ones (e.g. Marshall et al., 2002). These models, however, are unable to explain the highly lobate forms of some parts of former ice sheet margins, such as those characteristic of the margins of Last Glacial Maximum (LGM) ice sheets: for example, the Baltic lobe associated with the later stages of the LGM European ice sheet (e.g. Houmark-Nielsen, 2004), the lobes of the LGM British Isles ice sheet along the east coast of England and in the southern Irish Sea (Fig. 1), and the lobes at the southern margin of the Laurentide ice sheet (e.g. Clayton et al., 1985).
Fig. 1. Recent reconstructions of the maximum extent of the Last Glacial Maximum (Late Devensian) ice sheet over the British Isles, showing the uncertainties associated with currently submarine evidence (1—Bowen et al., 2002; 2—Hall, 1997; 3—Balson and Jeffrey, 1991; 4—Scourse and Furze, 2001). Lines marked 5 show the extent of readvances in the Irish Sea Basin (Ireland—Synge, 1977; Isle of Man—Dackombe and Thomas, 1991; Cumbria—Huddart, 1991). 6—possible western margin of the Scandinavian ice sheet at the LGM (Hall, 1997).
a contrast between basal melting along the stream, reducing friction and facilitating easy movement, and basal freezing on its flanks associated with high ice/bed friction; or a contrast between a zone of soft subglacial sediment along the stream in which the sediment either deforms or permits easy sliding because of its low surface roughness, compared with flanks directly underlain by higher friction rock, or frozen rock or sediment, to which the ice adheres.
If differential spreading occurs, either where there are longitudinal carpets of deformable subglacial sediment with a flanking rock bed, or zones of basal melting flanked by basal freezing, such zones would offer a low friction, low shear stress path for longitudinal flow. Lateral spreading would be inhibited by the higher friction along the flanks. The two mechanisms, of sediment deformation or basal melting, reflect quite different controls. The first
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depends upon a geological property of the bed. The second is a dynamic property of the ice sheet. In the latter case, Hulton and Mineter (2000) showed that streaming could develop as a dynamic feature of an ice sheet without any local change in the topography or composition of the bed. They suggested that streaming was a way in which the ice sheet flow system adjusted to the mass balance and temperature regime. Boulton et al. (2003) showed that if the bed of the European ice sheet was arbitrarily changed to a flat plain, other than in the mountain area needed to nucleate the ice sheet, ice streams still developed over the flat plain. Modern Antarctic ice streams are characterised by low friction and low slopes compared with flanking ice, with inferred shear stresses along them of the order of o20 kPa (Alley and Whillans, 1991) compared with shear stresses in flanking ice of the order of 100 kPa. Miller et al. (2002) have shown that low-slope flow of the Laurentide ice sheet along the sediment-floored fjords of east Baffin Island took place under shear stresses as low as 2–7 kPa, which must reflect almost liquefied sediments under almost zero effective stresses. 3. Problems of reconstructing and explaining a British ice sheet We will go on to suggest that ice sheet form and thickness in an ice sheet such as that of the British Isles during the LGM are intimately related to fast ice streams, which can be the only cause of ice lobes on a low relief bed, and ice that is relatively ‘‘soft’’ compared with Glen’s flow law (e.g. Paterson, 1994, Chapter 5), or with a particularly slippery bed. We first review geological evidence of thickness, extent and ice lobes in the LGM British Isles ice sheet. 3.1. Thickness and extent Early attempts to reconstruct the extent of a British ice sheet at the LGM assumed that it was confluent with the contemporary Scandinavian ice sheet in the North Sea and stretched to the edge of the continental shelf 200 km west of Scotland (Geikie, 1878, 1894; Valentin, 1957). The first attempt to model the form and flow of the ice sheet using contemporary glaciological theory (Boulton et al., 1977) suggested that the summit of the ice sheet, over the Grampian Highlands of Scotland, had an elevation relative to the modern land surface of over 1800 m, sufficient to cover the highest mountain summits with several hundred metres of ice (Fig. 2a). However, Lambeck (1993, 1995) used a geophysical model of lithosphere/asthenosphere properties to invert relative sea level data around the British Isles from the period of deglaciation to infer the magnitude and distribution of the ice sheet load at the LGM, and concluded that there had been a maximum ice thickness of 1300–1400 m over the Grampians and about 1100 m over the Northern
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Highlands. He also concluded (Lambeck, 1995) that the ice sheet at the LGM was not confluent with the Scandinavian ice sheet in the North Sea, and that it only extended for a short distance of about 50–100 km beyond the modern eastern coastline of NE Britain. Ballantyne et al. (1998), demonstrated the existence of weathering ‘‘trimlines’’ in NW Scotland, where glacially eroded surfaces at lower elevations gave way to weathered rock surfaces and ‘‘frost debris’’ at higher elevations. They suggested that these trimlines marked the upper surface of the ice sheet during the LGM, from which they deduced an ice thickness over the Northern Highlands during the LGM similar to that inferred by Lambeck. However, it is well established that ice well below the melting point adheres to its bed, and accomplishes very little if any erosion (Goldthwait, 1960; Holdsworth, 1974), because the adhesive strength of an ice/rock interface at temperatures well below the melting point is significantly greater than typical basal shear stresses (Jellinek, 1959). However, sliding can occur at temperatures lower than the ambient pressure melting point (Shreve, 1984; Echelmayer and Wang, 1987) and can locally abrade bedrock (Atkins et al., 2002). Thus although we would not expect a sharp erosion/ no erosion interface at the point where the temperature of basal ice falls below the melting point, we would expect a rapid fall-off in erosion rates as temperatures fall well below this level. It is possible, therefore, that the observed trimline represents a thermal transition from temperate or just sub-temperate ice below to much colder ice above. Stone et al. (1998) used cosmogenic exposure dating, using 10 Be and 26Al, to infer the exposure age of the rock surfaces, and to examine whether the 26Al/10Be ratio could indicate contrasting multi-stage exposure histories above and below the trimline. Unfortunately, they were ‘‘unable to preclude the possibility that the weathering limits mark a former englacial boundary between passive cold-based ice on mountain summits and erosive, warm-based ice at lower elevations’’, with the consequence that the trimline does not provide an unequivocal constraint on ice surface elevation. The glaciological reconstruction of Boulton et al. (1977) had assumed a constant basal shear stress of 100 kPa (effectively an assumed yield strength for ice), and also that the ice sheet was confluent with Scandinavian ice in the North Sea. In a subsequent model (Boulton et al., 1991) the basal shear stress was adjusted, in a way broadly consistent with emerging evidence of much greater variation in basal shear stresses in modern ice sheets, with prescribed values of 70 kPa over the land areas and 30 kPa over the sea areas, assuming that deformation in soft marine sediments areas would restrict basal friction to relatively low values. Its purpose was to explore whether an ice sheet model could fit the emerging evidence (Ballantyne and Sutherland, 1987) of a relatively low ice sheet surface elevation in Easter and Wester Ross in the Northern Highlands of Scotland, and the evidence that the ice sheet was not confluent with Scandinavian ice in the North Sea at the LGM (Stoker
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Fig. 2. (a and b) Earlier models of the British Isles ice sheet at the LGM. Both are inverse models, in which ice sheet form is computed from a prescribed ice sheet margin. (a) The British ice sheet is confluent with a Scandinavian ice sheet. The basal shear stress is assumed everywhere to be 100 kPa (Boulton et al., 1977). (b) An independent British ice sheet (cf Fig. 1). The basal shear stress is taken to be 30 kPa outwith the modern coastline and 70 kPa on the modern land area (Boulton et al., 1991).
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et al., 1985; Sejrup et al., 1987). This generated an ice sheet summit elevation of about 1100–1200 m along an ice ridge through western Scotland and into northern Ireland (Fig. 2b). These models were inverse models. They took the ice sheet margin as given by geological evidence, and merely explored the ice sheet elevation and form consistent with these margins, with a prescribed pattern of basal shear stress and using a simplified calculation of ice sheet thermal properties (Jones, 1978). They were not natural numerical experiments, in which the ice sheet is driven by climate and with a properly posed basal boundary condition, which then examined the extent to which the resultant ice sheet was consistent with other evidence. As we shall show, thermo-mechanically coupled models do not permit the pattern of bed properties assumed by Boulton et al. (1991) readily to generate the desired low-elevations. Sejrup et al. (1994) have argued, from the evidence of radiocarbon dates and amino acid ratios on marine shells above and below till strata in the Northern North Sea, that the British Isles and Scandinavian ice sheets were not confluent at the LGM, but that ice from Scandinavia and Scotland were confluent in the area between 29,000 and 24,000 radiocarbon years before present. The two ice sheets then parted, but re-advanced during the LGM to a maximum about 17,000 years ago, but for only a relatively small distance beyond their respective mainland areas. Clark et al. (2004) are sceptical of this hypothesis of early North Sea confluence in view of the radiocarbon ages from Scotland, collated in Boulton et al. (1991) from bone, peat and plant detritus and U-series ages on speleothems, which indicate ice-free conditions close to the centres of ice accumulation in Scotland at the time that North Sea confluence is said to have occurred. Sutherland and Walker (1984) had suggested that the LGM ice sheet did not extend further than the northern tip of the Outer Hebrides (reconstruction 1 in Fig. 1). However, evidence of seismostratigraphy (Peacock et al., 1992; Stoker et al., 1985) suggested that the LGM ice sheet extended close to the continental shelf edge to the west of Scotland (reconstruction 2 in Fig. 1), which is also consistent with trimline and cosmogenic isotope dating (Stone and Ballantyne, 2006). Von Weymarn (1979) and Peacock (1991) had demonstrated that the Outer Hebrides were not glaciated by mainland ice, but had been covered by an independent dome during the LGM. This was supported by the trimline data of Ballantyne et al. (1998). 3.2. Ice lobes Two major ice lobes, on very low relief beds, protruded from the southern margin of the British ice sheet at the LGM (Fig. 1): one down the east coast of England (Balson and Jeffrey, 1991), and one in the southern Irish Sea and Celtic Sea, between SW England/Wales and SE Ireland, although its extent is a matter of debate. Some (Bowen et al., 1986; Eyles and McCabe, 1989) have suggested a
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limit in St. Georges Channel (see Fig. 3 for locations referred to in the text), between SW Wales and SE Ireland (reconstruction 1, Fig. 1), whilst others (Scourse and Furze, 2001; Hiemstra et al., 2006) have suggested a limit some 150 km south west of the Scilly Isles (reconstruction 4, Fig. 1). The glaciological reconstruction of Boulton et al. (1977) was unable to account for the lobe on the east coast of England, but they suggested that it could represent a surge of the ice sheet margin (Fig. 2a), whilst Boulton et al. (1991) produced a reconstruction, which they recognised as unlikely, of the lobe as a semi-independent ice dome (Fig. 2b). If we discount the marginal ice dome hypothesis, and in the absence of significant lateral topographical constraints, lobes at the margin must be a consequence of local fast streaming in the ice sheet. Fast streaming flow may be ephemeral on a short timescale, or sustained for relatively long time periods, although the distinction may simply be one of response time. The former are referred to as surges, the latter as ice streams. The period of any cyclical behaviour is likely to be scale dependent for both of the most likely mechanisms, which are: (a) The accumulation of ice in the catchment area of the ice stream is unable to sustain the flux within it. Fast streaming is most likely to be sustained for longer periods in ice sheets with large drainage areas compared with valley glaciers. Fast streaming in valley glaciers that are not outlet drainage glaciers for ice sheets will only be sustained for short period surges. (b) For longer timescales, Clarke et al. (1977) identified a ‘‘creep instability’’ in a glacier in which fast flow exhausts replenishment, causing the profile to flatten and velocity to fall, such that the glacier bed freezes, leading to high basal friction, permitting the profile to build up, producing basal melting, friction reduction and fast flow, and repetition of the cycle. McAyeal (1993) suggested that such a ‘‘binge-purge’’ cycle in a Laurentide ice stream flowing through the Hudson strait could account for Heinrich layers in the North Atlantic.
4. The ice sheet model 4.1. Approach Rather than use the inverse approach that has hitherto been used to create glaciological models of the British Isles ice sheet, we now use a model that is driven by a proxy climate function. Our approach is to ask how we need to adjust ice sheet boundary conditions and climate forcing functions in order to match, in broad terms, some of the principal known characteristics of the ice sheet over the British Isles, including the major ice lobes. We regard this as a fundamental approach of ‘‘palaeoglaciology’’, inferring glaciological properties of the ice sheet from glacial
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Fig. 3. Locations referred to in the text.
geology through the intermediary of a numerical ice sheet model that, as far as possible, represents current glaciological understanding. Whereas early glacial geologists (e.g. Geikie, 1894; Charlesworth, 1957) believed that most of the geological impacts of ice sheets during the last glacial period reflected processes at the glacial maximum, we believe that they reflect cumulative, transient processes, and, therefore, that understanding the behaviour of an ice sheet requires simulation through the whole of the glacial cycle. Ideally we would like the ice sheet model to be driven by a general circulation climate model on a spherical Earth. However, our objective is to simulate high-resolution behaviour of the ice sheet over the British Isles through the whole of the last glacial cycle, using grid spacings of 5–10 km and time steps of 6 months in order to capture the annual mass balance cycle. Thus, although the model could be used on a spherical Earth, and could be coupled to a full climate model, the computing time required for a single run would be excessive when we wish to undertake multiple simulations to explore the effect of different boundary conditions, including climate forcing. We have, therefore,
opted for a planar Earth segment restricted to the British Isles (sometimes including Europe) and a series of ice sheet surface climate proxies. This restricted model domain has the further disadvantage that the isostatic component of sea level change is entirely accommodated within the domain, and therefore over-estimates its contribution. However, it was clear that the choice had to be made to restrict the domain in order to fulfil the objectives of the simulation experiments. 4.2. The model The core of the model is a coupled ice sheet/Earth model. The evolution of ice sheet form is determined using the continuity equation: qH ¼ rH ð¯vHÞ þ M S, (1) qt where rH is the two-dimensional horizontal gradient, H the ice thickness, v¯ the vertically averaged velocity, M the mass balance (accumulation minus surface melting rate) and S the melting rate at the base of the ice column.
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The shallow ice approximation is used (Hutter, 1983) so that horizontal shear stresses can be approximated by txzðzÞ ¼ ri gðH þ h zÞ
qðH þ hÞ , qx
tyzðzÞ ¼ ri gðH þ h zÞ
qðH þ hÞ , qy
(2)
where h is the bedrock elevation, ri the density of ice and g the gravitational acceleration. Strain rates of ice are related to the stress tensor by tij ; _ij ¼ AðT n Þtðn1Þ n
i; j ¼ x; y; z,
(3)
where tn is the effective shear stress defined by the second invariant of the stress tensor, n the flow law exponent and A the temperature dependent flow law coefficient (Paterson, 1994). T is the absolute temperature corrected for the dependence of the melting point on pressure. The horizontal velocity vector is found by vertical integration of the flow law (Eq. (3)): vðzÞ vðhÞ ¼ 2ðri gÞn ðrðH þ hÞrðH þ hÞÞðn1Þ=2 r Z z ðH þ hÞ AðT n ÞðH þ h zÞn dz.
ð4Þ
h
Integrating Eq. (4) from the ice base to the surface gives the vertically averaged velocity v¯ . The temperature evolution of the ice sheet is described by qT k q2 T F ¼ vrT þ , qt ri cp qz2 ri cp
(5)
where T is the absolute temperature, k is the thermal conductivity, cp is the specific heat capacity and F is the heat generated due to friction. Here v is the 3-dimensional, 3-component ice velocity. The z component is calculated using the horizontal velocities together with the incompressibility condition and the surface mass balance and basal melt rates. Thus heat is transferred by both diffusion and advection (first and second term of the RHS of Eq. (5), respectively). A shortcoming of the model is the absence of longitudinal stresses. It is assumes that the stress balance is hydrostatic. This is a reasonable approximation for a low slope bed, and given the smoothing of our topographic model, is applicable in most areas of our study. An area where such stresses can be important is in the case of ice streams. Thus, although we believe that our model is likely to represent well the initiation, location and magnitude of streaming, it may miss some of their detailed features and may marginally under-estimate velocities and the pulling power of streams at low shear stresses. The evolution of the ice sheet is strongly coupled to the isostatic response of the Earth. We use the standard Earth model of an elastic plate with a relaxing asthenosphere (Le Meur and Huybrechts, 1996). It incorporates an elastic lithosphere (defined by the flexural rigidity, D; and thickness H), which determines the geometry of deforma-
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tion, and a fluid, non-viscous asthenosphere of density ra, which determines the time-dependence of the isostatic response. The simplest way to account for the latter is to estimate a time-constant and assume that the rate of response is proportional to the difference between the loaded equilibrium h0w (where h0 is the unloaded equilibrium topography and w is the downward deflection due to the load q of a thin plastic plate of thickness H and flexural rigidity D) and the current profile h, and inversely proportional to the time constant: dh 1 ¼ ðh h0 þ wÞ. dt t
(6)
The present topography is assumed to be the initial unloaded topography h0. The downward deflection can be written as (Le Meur and Huybrechts, 1996) Dr4H w þ ra gw ¼ g,
(7)
where rH is the horizontal gradient operator and g is the gravitational acceleration. The solution of (7) involves a linear combination of Kelvin functions (see Lambeck and Nakiboglu, 1980 for details). The Earth model used here does not include effects due to changes of the gravitational field. However, changes of the ocean load are included through a global sea level change term. A sophisticated spherical, self-gravitating visco-elastic Earth model has been coupled to a dynamic ice sheet (Le Meur and Huybrechts, 1996) but the associated computational effort does not allow us to run the large number of experiments required to explore the parameter space. However, Le Meur and Huybrechts (1996) find that the relaxing halfspace/elastic lithosphere model is an acceptable approximation for the time scales being studied here. Tarasov and Peltier (2002) solve the complete sea level equation using a self-gravitating spherical Earth model together with ice sheet histories obtained through inverting relative sea level observations. They compute relative sea level predictions off-line, after they have simulated the ice sheet. This approach improves the relative sea level predictions but does not significantly affect ice sheet dynamics. The resultant sea level change, Dz is a function of geographic position (l, j), time t, and is dependent on the changes of ice distribution and the Earth’s response function. The topography or bathymetry at some time t is related to the present day surface elevation and relative sea level change by hðl; j; tÞ ¼ hðl; j; t0 Þ Dzðl; j; tÞ.
(8)
Sea level change can be expressed as the sum of each ice sheet’s contribution to sea level change: DBðl; j; tÞ ¼
SDBi ðl; j; tÞ i2ficesheetsg
¼ DBa ðl; j; tÞ
þ DBFenn ðl; j; tÞ þ DBBrit ðl; j; tÞ,
ð9Þ
where DBFenn and DBBrit are the contributions due to the European and British ice sheets and DBa is the sum of the
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contributions due to all the other ice sheets. Global sea levels are indirectly derived from the SPECMAP experiment (Fig. 4c) (Goodess et al., 2000). The initial bedrock topography is taken from the ETOPO5 and GTOPO30 datasets projected onto an Albers Equal Area Conic projection with a 10 and 5 km resolution. The numerical ice sheet model has been developed from that of Payne and Dongelmans (1997) and is now publicly available from the GLIMMER web page (http://glimmer.forge.nesc.ac.uk/). The domain chosen for modelling proved in practice to have been too small such that the ice sheet was frequently and arbitrarily stopped by the eastern boundary of the model domain. It is a drawback in several simulations, although in practice the effect is small as the ice sheet terminates close to its natural margin. 4.3. Boundary conditions In our application, the model is constrained by the following boundary conditions:
temperature and mass balance on the ice sheet surface; ice flow properties in the body of the ice sheet; properties of the ice/bed interface; lithosphere flexure; and calving conditions at the marine margin.
global average sea level [m]
temperature [degC]
Equilibrium line altitude variation [m]
The Earth model and the calving law together with their parameters are taken as fixed, whilst the others are taken as free parameters that are adjusted to establish the parameter space within which a modelled British Isles ice sheet approximately fits the geological constraints.
Tðl; j; z; tÞ ¼ a þ bcðll0 Þ þ dz þ DTðtÞ,
0
where a, b, c and l0 ¼ 44:951N are parameters defining the temperature at sea level, d is the lapse rate and DTðtÞ is the time dependent, linear perturbation of the temperature field. The parameters of (10) are fixed by fitting to a temperature model derived from the Greenland ice sheet record (Johnsen et al., 1995). This is based on the approach used by Boulton et al. (1995). We regard this as providing a good proxy for the likely tempo and relative amplitude of palaeotemperature fluctuation over Britain during the last glacial cycle, but a poor match for their absolute magnitudes. This has been derived from a correlation (Boulton and Thompson, in preperation) with palaeotemperature inferences from the continuous pollen record from central France (Guiot et al., 1989), adjusted by the evidence of Coleopteran paleotemperatures from central England for the LGM and the Lateglacial periods (Atkinson et al., 1987). Fig. 4b shows the pattern of assumed temperature change through the last glacial cycle at the standard latitude (central England). We have varied the temperature level by increments, of +8, +5, 5 and 10 1C compared with 0 1C as the mean annual temperature estimate of Atkinson et al. (1987) at the LGM in central England. We find that ice sheet form and flow are sensitive to changes in surface temperature through the effect of temperature on the ice flow law. The lapse rate is kept constant at 0.006 1C m1.
b
zELA ¼ a þ bl þ cl2 þ DzELA . 0
c
-50 -100 -140
(10)
4.3.2. Mass balance and continentality Mass balance is parameterised as a vertical variation above and below the equilibrium line altitude (ELA). Two parameters control the shape of the mass balance M: Mmax is the maximum mass balance value that can be reached and zmax is the vertical distance above the ELA at which the maximum mass balance is reached. The ELA is parameterised in relation to latitude by
a
0
4.3.1. Ice sheet surface temperature The temperature field as a function of the geographic location (l, j), elevation above sea level z and time t, is approximated by
-120
-100
-80 -60 time [ka]
-40
-20
0
Fig. 4. (a–c) Time-dependent input functions. (a) Magnitude of fluctuation of the equilibrium line altitude through the glacial cycle used to drive the ice sheet model. (b) Pattern of mean annual temperature change through the glacial cycle used to drive the model. It is adjusted according to the assumed value of mean annual temperature in central England at the LGM. (c) The prescribed pattern of global sea level change through the glacial cycle derived from Goodess et al. (2000).
(11)
The mass balance can then be defined in terms of Mmax and zmax as 8 2 < 2M z z forz pzmax ; M max max zmax zmax Mðz Þ ¼ :M forz 4zmax ; max (12) where zn is the vertical distance above the ELA. Our central estimate uses a vertical mass balance gradient typical of the ice cap Vatnajo¨kull in Iceland. This is a maritime setting in the south and a more continental setting in the north that seems likely to be a good model for the British Isles during the glacial period. In the extreme
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maritime case, Mmax is 3 and 0.5 ma1 in the extreme continental case. We found that a strong continentality gradient was required over the British Isles if the ice sheet was to be prevented from extending across the North Sea. These parameters also agree well with the mass balance curves described by Kuhn (1984). The mass balance curves together with the continentality functions are combined to yield one mass balance gradient with a continentality parameter, c. The continentality parameter is defined for each grid point, ranging between 0 for an extreme maritime climate and 1 for an extreme continental climate, so that the mass balance is defined as M ¼ cM cont þ ð1 cÞM mar .
(13)
The ELA is thus determined both as function of latitude and of continentality. The form of the overall ELA driver, given by the parameters in Eq. (11), is derived from the form of the ELA driver required to simulate the LGM fluctuation of the European ice sheet, whose tempo of marginal fluctution is better understood than that of the British Isles ice sheet (Boulton et al., 2001). This driver is also used to simulate the Scandinavian ice sheet in Section 6.2. The absolute magnitude of ELA depression over Britain is that required to drive the ice sheet to the known LGM margin (Fig. 4a). The current ELA elevation is assumed to be the same as the modern ‘‘snowline’’, estimated by Manley (1949) as about 1600 m over the northern Grampians, 1800 m over the Lake District and 1900 m in north Wales. 4.3.3. Ice flow parameters The parameter A in the flow law for polycrystalline ice (3) depends on factors such as temperature, crystal size and orientation, and ice impurities, experimentally shown to follow the Arrhenius equation:
AðT Þ ¼ faeðQÞ=RT ,
(14)
where a is a temperature-independent material constant, Q is the activation energy for creep and R is the universal gas constant (Paterson, 1994). f is a tuning parameter that reflects ice history and accounts for impurities and the progressive development of anisotropic fabrics, and needs to be adjusted to account for the form of modern (Payne, 1999) and former ice sheets (Peltier et al., 2000). It was found that the thickness and extent of the ice sheet is sensitive to the ice softness parameter f, and that large values at the high end of the range f ¼ 3220 are required, irrespective of the temperature and mass balance driver, if the ice sheet is to achieve the combination of large extent and limited surface elevation. This suggests that strong fabric development and possibly high debris content must have been characteristic of the ice sheet. 4.3.4. The basal boundary There is strong coupling between mechanical and thermal processes at the glacier bed. If the ice/bed contact is frozen, no decollement occurs, if unfrozen, decollement
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is assumed to be switched on, either by sliding, subglacial sediment deformation or both. The rate of decollement is dependent on water pressure at the ice/bed interface, but the latter is dependent on the efficiency of the subglacial drainage system, which remains a largely unsolved problem. Empirical sliding laws normally take the form ub ¼ atpb N q ,
(15)
where ub and tb are the horizontal basal velocity and shear stress respectively, and p, q and a are parameters (Paterson, 1994). Since, in the absence of a generally accepted drainage theory, effective pressure is unknown, and p is uncertain, we parameterise a decollement relationship by ub ¼ tb tb ,
(16)
in which tb is a decollement parameter that can be used to reflect physical drivers, such as basal melt rate or drainage rate. We have explored the impact of a wide range of basal traction conditions. We have used a range of tb, from 0.005 to 0.05 ma1 Pa1, which fits a range of modern conditions from easy to relatively stiff decollement. 4.3.5. Lithosphere properties We have followed Le Meur and Huybrechts (1996) in using constant values of lithosphere flexural rigidity of 2.4 1024 and an asthenosphere time constant of 4000 years. These values give isostatic behaviour analogous to that inferred by Lambeck (1993) for the British ice sheet using an inverse model. The geothermal heat flux is held constant at 0.042 W m2, a value characteristic of modern Europe (Hurtig et al., 1992). We have also explored the impact of successive glacial periods on the initial geothermal flux, and established that they have a small effect compared with other parameters. 4.3.6. Calving condition at marine margins Iceberg calving enters the continuity Eq. (1) as another mass balance term. Of the ice thickness, 20% is lost due the calving when the ice reaches a water depth of 500 m. Calving only occurs in cells that have at least one boundary with the ocean. 5. Influence of boundary conditions on ice sheet simulations Large numbers of simulations have been made to explore the effect of varying boundary conditions on ice sheet behaviour. Our targets are to simulate independent ice sheets over the British Isles as shown in Fig. 1, and ice sheet confluence in the North Sea as shown in Fig. 2a. It was found that for the prescribed pattern of temperature variation shown in Fig. 4b, the temporal ELA variation in Fig. 4a and the maritime-continental transitions shown in Fig. 5a were required to generate an independent ice sheet over the British Isles. A much larger or much smaller ELA depression produced ice sheets that were significantly larger or smaller than the target ice sheet. The form of the
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Fig. 5. (a–c) Patterns of transition between continental and maritime conditions given by changes in the ELA for (a) an independent British Isles ice sheet; and (b) a confluent British Isles and European ice sheet (Fig. 10). The purple colour on the left shows the extreme maritime zone and the brown colours on the right the extreme continental zone, and the intervening transition zone. (c) The latitudinal variation in relative ELA values across the transition zones shown in (a) and (b) compared to the ELA in the continental condition.
modelled ice sheet was sensitively dependent on the nature of the west–east gradient of maritime to continental conditions. The geographical variation in the magnitude of ELA lowering in Fig. 5a, which produces highly continental conditions over eastern England, is important in limiting the southward extent of the ice sheet in eastern England. A less abrupt transition between maritime and continental conditions failed to create the correct contrasts in western and eastern marginal extents. The marginally more maritime conditions on the east coast of Britain in Fig. 5b compared with Fig. 5a are sufficient, together with the same ELA driver (Fig. 4a) to
extend the British Isles ice sheet far enough to the east to create a North Sea confluence. Also in this case, a very strong W–E gradient across Scandinavia is important to prevent the eastern margin of the European ice sheet extending too far to the south (although we do not show the eastern margin in figures presented here). Consequently, the ELA driver in Fig. 4a was used in all the simulations described below. Similarly, lithosphere flexural properties, the geothermal flux, the marine boundary condition and the pattern but not the magnitude of temperature fluctuation were held constant in all simulations.
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
Within this framework, the key determinants of the extent, form, flow and thermal regime of the ice sheet were:
the value of the decollement parameter, tb at the basal boundary (Eq. (15)) and its spatial variation; the value of the flow law parameter f, which determines ice softness (Eq. (14)); the ice sheet surface temperature.
All combinations of these boundary conditions were used to generate forward simulations of ice sheet behaviour through the glacial cycle. Although a small ice sheet was generated over Britain during isotope stage 4, the period of 72–60 ka, this was insignificant compared with the ice sheet generated between 25 and 14 ka. We have, therefore, concentrated on this latter period. In the following sections we describe the main features of model behaviour for different sets of boundary conditions, and comment on their relevance to geological history.
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valleys in creating lobes. However, although modelled extent matches reality reasonably well, the LGM surface elevation of over 2250 m far exceeds the elevation suggested by geomorphological or relative sea level constraints (ca Fig. 16). Figs. 7–9 show a comparison of LGM time-slices for simulations with different key boundary conditions. Figs. 7a and 9a shows the simulation discussed above, compared in Fig. 7b and 9b with a simulation in which the mean annual temperature has been everywhere increased by 5 1C. The effect is to decrease the surface elevation to just less than 2000 m, dramatically reduce the extent of the divide area of basal freezing, reduce transverse velocity contrasts and make the ice sheet marginally less extensive. In contrast, Figs. 7c and 9c show a simulation in which the basal decollement parameter (tb) has been increased by a factor of 10 (see Section 7), dramatically changing the ice sheet structure, with strong streaming and extreme thermal contrasts between streams and inter-stream areas, although this has a lesser effect on peak ice elevation, which is reduced to just above 2000 m.
6. A uniform stiff bed condition 6.2. Modelling North Sea confluence 6.1. A British Isles Ice Sheet In these simulations we have assumed that the basal decollement parameter is everywhere given by tb ¼ 0:005 ma1 Pa1 , equivalent to assuming a universal rigid rock bed with sliding. Fig. 6 shows time slices for a simulation in which the flow law parameter f ¼ 3, and the LGM central England mean annual temperature is taken to be 0 1C. Ice sheet elevations in all figures are related to the modern, relaxed, topography. The ice sheet nucleates in the western Highlands, but its growth is rapidly outpaced by Grampian ice. There are cold basal temperatures over upland areas but basal melting under thicker ice in some of the major troughs (Fig. 6a2), leading to faster flow streams in these zones (Fig. 6a3), with the streams bi-furcating down-ice. Growth of the ice sheet is accompanied by slight migration of the main NE–SW ice divide towards the SE, and its extension into Ireland (Figs. 6b–c). The evolving thermal and velocity structure is one of cold basal conditions in upland areas, with temperate conditions under major upland troughs (although note that troughs less than 5 km in width are not resolved). Cold bed fingers extend outwards from upland zones into the lowlands, where they are zones of relatively low velocity separating warmer, faster flow zones. For example in Fig. 6a2–3, the Welsh Mountains have cold bed conditions, and similar conditions in the southern Pennines, the Yorkshire Moors and Lincolnshire Wolds also create cold zones in downstream lowlands. Overall, thickness, thermal regime and velocity vary radially, with concentric zonation disrupted by some transverse variation in thermal and velocity structure. There are no major ice streams, no major marginal lobes and the steep ice sheet profile minimises the effect of
The continental-maritime ELA transition was then changed from that in Fig. 5a–b, to investigate how initially independent ice sheets over the British Isles and Scandinavia might evolve to become confluent and then separate and decay. Our primary concern is to understand confluence-related processes in the North Sea, rather than to match specific geological constraints such as ice thickness or stream and lobe creation. If we accept the view of Sejrup et al. (1994) this could be taken as a simulation of glacial events in the North Sea region between about 29 and 24 ka. Alternatively, the simulation could be taken as reflecting conditions during the Saalian or Elsterian glaciations, when such confluence certainly occurred. The results are shown in Fig. 10. In this case model time should not be taken as a particular time before present. Strong growth of ice over south west Norway occurs by 25 ka (Fig. 10a) followed by ice sheet nucleation and growth over Scotland (Fig. 10b), by which time a welldeveloped ice stream had formed at the head of the Norwegian Channel because of its greater depth and warmer basal ice. Sea levels in the North Sea generally had been drawn down by the global lowering of sea level (Fig. 4c). By 20 ka (Fig. 10c), the ice divide over Scotland had extended into Ireland, the Norwegian Channel ice stream had extended and was flowing towards the north– west, and strong ice streams were flowing from Sognefjord, Hardangerfjord and the fjords of the Trondheim region onto the continental shelf. By 20 ka, and much more by 19 ka (Fig. 10d), ice was spilling over the western flank of the Norwegian Channel, and beginning to advance into the central-northern North Sea, where it was confluent with ice from Scotland by 18.5 ka (Fig. 10e), forming a low saddle,
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Fig. 6. (a–d) Time slices of the modelled growth of an ice sheet over the Britain Isles for a uniformly ‘‘stiff’’ bed condition. The simulation is driven by the temperature, mass balance and ELA conditions shown in Figs. 4 and 5. The basal decollement parameter tb ¼ 0:005, the flow law parameter f ¼ 3, and the LGM standard mean annual temperature (T) is taken to be 0 1C. (a1–d1) show the surface form. (a2–d2) show basal velocities, with red areas as high velocities and white with zero velocities, and generally frozen bed conditions. (a) ¼ 22; (b) ¼ 20; (c) ¼ 18; d ¼ 17 ka. The LGM condition (17 ka) is compared with other simulations in Figs. 7–9.
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Fig. 7. (a–j) Examples of simulations of ice sheet form for LGM time slices, for the decollement parameter (t0), the flow law parameter (f), and the standard temperature (T) as follows. Bed conditions: (a–b) all ‘‘stiff’’, tb ¼ 0:005; (c–d) all ‘‘slippery’’, tb ¼ 0:05; (e–j) ‘‘slippery patches’’ (see Fig. 13), tb ¼ 0:05 with tb ¼ 0:005 elsewhere. Ice flow parameters: (a–f) f ¼ 3; g–j) f ¼ 10. Standard temperature: a,c,e,g, T ¼ 0 1C; b,d,f,h,i, T ¼ +5 1C; j, T ¼ +8 1C.
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Fig. 8. (a–j) Examples of simulations of basal temperatures for LGM time slices, for the decollement parameter (tb), the flow law parameter (f), and the standard temperature (T) as follows. Bed conditions: (a–b) all ‘‘stiff’’, tb ¼ 0:005; (c–d) all ‘‘slippery’’, tb ¼ 0:05; (e–j) ‘‘slippery patches’’ (see Fig. 13), tb ¼ 0:05 with tb ¼ 0:005 elsewhere. Ice flow parameters: (a–f) f ¼ 3; (g–j) f ¼ 10. Standard temperature: a,c,e,g, T ¼ 0 1C; b,d,f,h,i, T ¼ +5 1C; j, T ¼ +8 1C. Melting point temperatures are shown in red, sub-melting point temperatures in white.
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Fig. 9. (a–j) Examples of simulations of basal velocities for LGM time slices for the decollement parameter (tb), the flow law parameter (f), and the standard temperature (T) as follows. Bed conditions: (a–b) all ‘‘stiff’’, tb ¼ 0:005; (c–d) all ‘‘slippery’’, tb ¼ 0:05; (e–j) ‘‘slippery patches’’ (see Fig. 13), tb ¼ 0:05 with tb ¼ 0:005 elsewhere. Ice flow parameters: (a–f) f ¼ 3; (g–j) f ¼ 10. Standard temperature: a,c,e,g, T ¼ 0 1C; b,d,f,h,i, T ¼ +5 1C; j, T ¼ +8 1C. High velocities shown in red and frozen bed areas with zero velocities in white.
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Fig. 10. (a–f) A simulation of the growth to confluence between a British Isles and Scandinavian ice sheet in the central North Sea. Boundary conditions are the same as in Fig. 6, with the domain extended to cover the whole area of the European ice sheet, the continentality pattern as shown in Fig. 5b to ensure confluence. Colours show surface velocities and arrows the flow vectors. Red shows high velocities, blue shows low velocities. Note the ice divide areas with low (blue-turquoise) velocities and the evolution of the Norwegian channel ice stream.
leading to divergence of ice to both north and south from the saddle. This then evolved into a Scotland–Norway ice ridge by the glacial maximum at 17.5 ka. The development of this saddle and the succeeding ridge blocked flow from the head of the Norwegian Channel, deflecting ice from the Skaggerak towards the south west, such that it ceased to
flow in a stream. The downstream part of the Norwegian channel continued to be a conduit for an ice stream, but one that was largely fed from the Sognefjord area of SW Norway. We are highly sceptical of the reconstruction by Sejrup et al. (2000), which shows an ice stream along the whole
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length of the Norwegian Channel at the maximum extent of a confluent North Sea ice sheet, and which demands an implausible pattern of flow and of divide geometry. In their reconstruction, the head of the ice stream lies in the Skaggerak and flows all the way along the Norwegian Channel to the continental shelf edge, a distance of some 800 km, at a time when the SW margin of the ice sheet was a mere 200 km south of the head of the Skaggerak, which necessitates a very highly asymmetric ice sheet profile, and without any mountains to prop-up one flank of the ice sheet. We are unable to simulate such a stream even by extreme adjustments of slipperiness and mass balance parameters. We suggest rather that the zone of streaming in the Skaggerak–Norwegian Channel was time transgressive in the way shown in Fig. 10. During ice sheet growth, the ice divide over northern Britain migrates in a south easterly direction, and whilst relative sea levels are low in the central North Sea, they rise in the vicinity of the growing ice sheet due to isostasy. Although we do not show the simulation of decay, the pattern is essentially a reversal of build up, with the difference that relative sea levels are higher and the rate of decay is faster. This points to a way of explaining how a Sejrup et al. (1994) North Sea ice sheet could have developed and collapsed before the LGM. If calving were more powerful in the isostatically high sea levels that developed as the ice sheet expanded, it might produce a negative feedback, causing the North Sea part of the ice sheet to collapse. We remain sceptical, however, that Scottish ice could have been a contributor to a North Sea ice sheet in the period between 30 and 24 ka in view of apparently contemporary non-glacial conditions in central Scotland (Boulton et al., 1991). 7. A uniform soft bed condition 7.1. Boundary conditions In these simulations the ELA driver is held constant. We have, however, assumed that the bed is everywhere softer, with the basal decollement parameter uniformly an order of magnitude larger than in Section 6, with tb ¼ 0:05 ma1 Pa1 . We have then explored the effect of varying the standard temperature and the flow law parameter f.
such as those in the Irish Sea, and the fast streams draining from west to east through the Pennines down the Tyne and Tees valleys (Fig. 11d2–3), others are unrelated to topography. Moreover, the streams in topographic depressions lose their strength from time to time, and streams unrelated to topography die and are replaced by others in different locations. Fig. 12a–c shows time–distance diagrams of the fluctuations of the ice sheet margin and the basal thermal regime along transects through the ice sheet (see Fig. 12d for locations). Fig. 12a and b show longitudinal transects in the Irish Sea and off the east coast of Britain, respectively. Prior to and after the glacial maximum, they show strong unforced oscillations of the margin, particularly strongly in the Irish Sea area. The two major Irish Sea oscillations between 22.5 and 19 ka show clearly that rapid advances of the margin of the order of 50–100 km/100 years are associated with warm bed conditions in the outermost 100–150 km, followed by cessation of advance. Subsequent retreats of the order of 50 km, are associated with a rapid change to warm bed conditions. This occurs as a consequence of a ‘‘creep instability’ (ca Clarke et al., 1977). Warming of the bed leads to fast decollement, this creates strong cold ice advection from the interior into the marginal zone, so that freezing, no-decollement, conditions develop. The flow velocity, therefore, decreases and the margin retreats. This dynamic behaviour occurs all around the ice sheet. It involves the development of ephemeral streams, stream switching, and local readvances which are not coeval along different parts of the ice sheet margin and which are smaller where the flowline length is smaller (shorter readvances on transect C compared with transect A) and where the ice sheet calves into deep water (compare the western with the eastern end of transect B). This behaviour can be regarded as surging, and reflects internal, unforced dynamic oscillation. Although at any one time, the area of the ice sheet bed that is undergoing erosion/transport/deposition is small (assuming that these processes are significant only during phases of decollement), the frequent shifts of the locations of streaming ensure that a large part of the bed does suffer strong erosion, although the rates of erosion vary greatly in time and space. This could explain why in some glaciated regions, discrete lineation sets are superimposed one upon another (Boulton and Clark, 1990).
7.2. The nature of the ice sheet—dynamic streaming 7.3. The match with geology Fig. 11 shows time slices for a simulation in which the flow law parameter f ¼ 3, and the LGM central England mean annual temperature is taken to be 0 1C. There is a strong contrast with the previous simulations. There are well-defined marginal lobes located along topographic depressions, well defined linear zones of basal melting flanked by frozen bed zones, and fast streams located along the axes of basal melting. Although some of the zones of melting and streaming lie along topographic depressions,
The extent of the ice sheet fits relatively well with geological evidence. The lobe structure at the southern margin of the ice sheet at the LGM (Fig. 11) matches well with those identified geologically, in the Irish Sea, the Cheshire Plain, west of the Lincoln Wolds, east of the Wolds and west of the Dogger Bank, and into the Wash and northern east Anglian regions. The fit is less good in Wales, where there is an unglaciated re-entrant in the lee of
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Boulton et al. (1991). However, thermal-mechanical coupling prevents this, as generalised fast flow draws down cold ice from the ice sheet summit area, which slows the flow and steepens the ice sheet. The creep instability, therefore, restrains the development of a low ice sheet slope, and, therefore, of a low summit elevation. Consequently, a large decollement factor (tb) over a wide area of the bed is not a strategy for reducing ice sheet thickness unless the surface temperature is very high, because of the restraining effect of enhanced cold ice advection. This thermal-mechanical forward model demonstrates that the low summit elevation inverse model shown in Fig. 2b (Boulton et al., 1991), which assumes a
the North Wales mountains, and in southern Ireland, where the ice sheet is less extensive than indicated by geology (Fig. 1). The model generates a ridge over northern Ireland. It also generates a cold-based ridge west of the Lake District and into the Cheshire basin (a possible though unlikely feature), and another over the Island of Skye in western Scotland, although it does not create a separate dome over the outer Hebrides. The peak ice sheet elevation of just over 2000 m is, however, far in excess of that assumed from geological constraints. We had assumed that ‘‘softening’’ the basal boundary would lower the mean slope and therefore the summit elevation of the ice sheet as was done by
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Fig. 11. (a–d) Time slices of the modelled growth of an ice sheet over the Britain Isles for a uniformly ‘‘slippery’’ bed condition. The simulation is driven by the temperature, mass balance and ELA conditions shown in Figs. 4 and 5a. The basal decollement parameter tb ¼ 0:05, the flow law parameter f ¼ 3, and the LGM standard mean annual temperature (T) is taken to be 0 1C. (a1–d1) show the surface form. (a2–d2) show the area of where basal temperatures are at the melting point in red and below the melting point in blue. (a3–d3) show basal velocities, with red areas as high velocities and white frozen bed areas with zero velocities. (a) ¼ 22; (b) ¼ 20; (c) ¼ 18; (d) ¼ 17 ka. The LGM condition (17 ka) is compared with other simulations in Figs. 7–9.
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390 348°
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Fig. 11. (Continued)
uniformly low shear stress in all current sea areas about Britain, is not a satisfactory explanation of a low summit elevation. 7.4. Influence of temperature Simulations in which the mean surface temperature is increased by 5 1C cause a lowering of the surface, through its effect on ice flow, with a summit elevation of about 1750 m (Fig. 7d), although with a much less lobate margin which falls far short of the southern margin of the real ice sheet. Basal melting is much more general in the outer part of the ice sheet (Fig. 8d) and associated with broader
marginal zones of relatively high velocity (Fig. 9d). A major contrast is the failure to generate unforced oscillations of the margin. This is because the higher ice sheet surface temperature is sufficient to diminish the cooling effect of cold ice advection from the interior and therefore largely suppresses the dynamic effects of creep instability. 7.5. Influence of the flow law parameter Increasing the flow law parameter from f ¼ 3 to f ¼ 10 produces output intermediate between the two above simulations in terms of ice thickness, extent, stream and lobe structure. The dynamic oscillations have a smaller
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
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Fig. 12. (a–d) Time-distance transects across the modelled ice sheet for a simulation with everywhere a ‘‘slippery’’ bed ðtb ¼ 0:05Þ, a flow law parameter f ¼ 3, a standard temperature of T ¼ 0 1C, using the climatic drivers as in Figs. 4 and 5a. Melting point temperatures are shown in red and brown and submelting point temperatures in blue. (a) Longitudinal transect down the Irish Sea basin. (b) Transect down the east coast of Britain. (c) Transect across Scotland. (d) Locations of transects.
amplitude but a higher frequency, because of the higher rate at which cold ice from the interior is advected towards the margin. 8. Simulating the effect of spatially varying basal boundary conditions 8.1. Boundary conditions In view of the very low ice sheet slopes (and shear stresses) that have been deduced for soft-bed zones of ice sheets (e.g. Miller et al., 2002; Mathews, 1974), implying
much easier local decollement, we have applied a decollement parameter of tb ¼ 0:05 ma1 Pa1 to restricted areas of the bed where soft sediments may play an important role, but with a value of tb ¼ 0:005 ma1 Pa1 for other areas. Most of the softest sediment basins occur in the offshore zone. Unfortunately, geological evidence of their precise nature and extent at glacial horizons is poor. We have assigned the easy decollement parameter to the areas shown in Fig. 13: to the Irish Sea and southern North Sea where major lobes occurred, to the sea area off the Forth valley, which has widespread evidence of strong ice drawdown, and to the shelf troughs of the Moray Firth
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
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are in ice sheet thickness (Fig. 7e–j), basal thermal regime (Fig. 8e–j) and basal velocity structure (Fig. 9e–j). Warmer simulations generate ice sheets with lower surface elevations, more restricted zones of basal freezing in the core of the ice sheet and different velocity distributions. They show lower velocities in the major ice streams and higher velocities in the inter-stream zones compared with colder simulations. This occurs because of the greater concentration of flow in the fixed streams in the colder cases. The concentration of flow in major fixed streams suppresses the creep instability shown in Fig. 12. Funnelling into these streams of flanking, warmer ice offsets the cold ice advection effect from the divide area, so that fast flow does not automatically create a negative feedback, and the stream is maintained. Large fixed streams therefore draw down the ice sheet surface more effectively than a ubiquitous ‘‘slippery bed’’. We suggest that bed-controlled localised streaming may be the vital process leading to a low surface elevation rather than the ubiquitous soft bed condition used by Boulton et al. (1991).
61
8.3. Modelled ice sheet evolution
britain2.10km.nc 0.00ka
Fig. 13. Locations of assumed ‘‘slippery’’ patches of bed where the decollement parameter is taken as tb ¼ 0:05, in contrast to all other areas of the bed, where there is a stiff bed condition given by tb ¼ 0:005.
and north and south of the Hebrides, which could have had a strong influence on ice in the Highlands of Scotland. We could also have chosen other marine trough areas such as the Firth of Clyde and Solway Firth. They are all troughs in which fine-grained sediments were or could have been present during the Late Weichselian. As before, the climate driver and other boundary conditions are held constant, and the effect examined of varying mean annual temperature between limits of 5 and +8 1C compared with the central England standard of 0 1C at the LGM. The flow law parameter f has been varied between 3 and 20.
The simulations of the series in Figs. 7e–j fit well with geology in terms of extent, but of these, Figs. 7h–j bring down the ice sheet surface closest to the trimline elevation in the northern Highlands, if this is regarded as a marking the maximum LGM ice sheet surface elevation. The large fixed streams play a crucial role in this regard. All three are characterised by a large flow law parameter, and a relatively high standard LGM temperature. The modelled evolution of the ice sheet is illustrated in Fig. 14, by a sequence of time slices for the simulation in Fig. 7i. We summarise below the behaviour of the model during ice sheet growth and decay, and go on to compare these results with features of ice sheet behaviour inferred from geological evidence. Initiation—Fig. 14a
8.2. Ice sheet form and structure
Figs. 7–9, e–j, show examples of the variation in form, thermal regime and basal velocity for simulated LGM ice sheets with spatially varying basal boundary conditions. The effect of fixed slippery patches is to fix the locations of major ice streams, although smaller, slower and ephemeral dynamic ice streams continue to exist between them. The extent of the LGM ice sheet and the general form of the margin are similar in all simulations. The contrasts
The initiation and early growth of the ice sheet occurs from centres in the NW Highlands. The principal flow divide then migrates rapidly eastward to the Grampians as the ice sheet expands beyond the Scottish coast. The prescription of a fast decollement zone covering the whole Moray Firth sector tends to distort the ice sheet and extend it further to the east than would otherwise have occurred. Elsewhere, strong streams develop without the assumption of a locally slippery bed. In the SW sector, there is strong flow down the Firth of Lorne, down valleys in the southern Highlands, and from the SE Highlands towards the Tay and Forth. In the west, there is strong westward flow south of Skye into the head of the assumed soft bed axis south of the Hebrides (Fig. 13), whilst north of Skye, significant streams develop in Wester Ross and northern Torridon.
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
Highland valleys that are sufficiently wide to be resolved by modelling are occupied by warm-based ice whilst higher areas are cold-based.
the Antrim coast flowing SW. These flows are deflected around the Merrick mountain area of SW Scotland, which is able to be a local flow centre. None of these streams is pre-determined by the assumption of a soft bed. The prescribed soft bed axis south of the Hebrides draws down ice strongly from western Scotland, drawing ice towards it in a westerly direction from the Firth of Lorne, over Mull and Islay. The northern Hebridean soft bed axis draws down ice from Torridon and the northern Highlands. The effect of these two zones of drawdown is to cause mainland-derived ice to be deflected around the outer Hebrides, which starts to develop into an independent dome. The ice sheet reaches
Growth 2—Fig. 14b
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Fig. 14. (a–e) Time slices of the modelled growth and decay of an ice sheet over the Britain Isles for the pattern of bed conditions shown in Fig. 13. The simulation is driven by the temperature, mass balance and ELA conditions shown in Figs. 4 and 5a. The flow law parameter f ¼ 10, and the LGM standard mean annual temperature (T) is taken to be 5 1C. (a1–d1) show the surface form. (a2–d2) show the area of where basal temperatures are at the melting in red and below the melting point in blue. (a3–d3) show basal velocities, with red areas as high velocities and white frozen bed areas with zero velocities. (a) ¼ 22; (b) ¼ 20; (c) ¼ 17; (d) ¼ 16 ka. The LGM condition (17 ka) is compared with other simulations in Fig. 7–9.
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390 0°
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the continental shelf edge west of Scotland by this stage. Off eastern Scotland, apart from the Moray Firth stream, which may or may not prove to have been a reality, a strong stream develops in the Firth of Forth, largely fed from the Strathmore area. The Lammermuir–Cheviot hills cause ice to be deflected around them, producing locally strong flanking streams. A stream begins to develop near the ice sheet margin along the east coast of England, largely fed by ice deflected towards the SE by the Pennines. LGM—Fig. 14c
There is a strong contrast between the LGM simulations with a colder temperature driver (Figs. 7–9, e–g), which
shows more extensive cold-bed conditions and numerous dynamic streams in addition to the fixed streams, with those driven by warmer temperatures (Figs. 7–9, f, h–j), dominated by the fixed streams and almost no ‘‘dynamic’’ streaming. A major ridge has developed over Ireland. A major ice stream has developed in the Irish Sea, as a consequence of the prescribed soft bed, and fed by confluent flows from northwest England, southern Scotland and eastern Ireland. Some simulations show the stream reaching as far as the Scilly Isles. Ice flows eastward down the Tyne valley to contribute to the major east coast ice stream, and ice flows eastwards down more southerly cross-Pennine valleys to contribute to the stream that flows strongly between the
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
Yorkshire Moors and Pennines. Ice flows from the Lancashire Plain and the Lake District to penetrate as a major lobe into the Cheshire Basin. Cold basal ice occurs along much of the ice sheet margin, which would have facilitated the incorporation of basal debris by freezing-on, and the development of extensive stagnation terrain (e.g. Boulton, 1972). At no time during ice sheet growth or the LGM was isostatic crustal depression at or beyond the ice margin sufficient to offset global sea level lowering to produce relative sea levels higher than present.
9. Comparison with geological evidence Although we have little direct evidence of the climate properties that drove the evolution of the British ice sheet, the available evidence and the strong constraints on climate that ice sheet extent and elevation impose, suggest that our climate drivers are appropriate: a typical North Atlantic vertical mass balance gradient, relatively high mean annual temperatures at the LGM, and a strong W–E gradient of continentality. Moreover, the best-fit simulations for extent (Fig. 7c–j) and for elevation (Fig. 7h–j) produce generally repetitive patterns of glacial evolution. There are four major uncertainties:
Were ice streams restricted to fixed, lobe-generating streams whose locations were determined by bed properties (Fig. 9f, h–j), or did more ephemeral streams also occur, that were a reflection of internal dynamic changes (Fig. 9c–e, g)? Did unforced, asynchronous oscillations of the ice sheet margins and of thermal and flow regimes occur as shown in Fig. 12? How extensive were the zones of basal freezing in the core area of the ice sheet? How serious is our failure to bring down the modelled ice sheet surface to match the levels suggested by Ballantyne et al. (1998) based on the weathering trimlines in the northern Highlands and Hebrides? (See Section 10).
The simulations demonstrate the glaciological probability of a major stream and lobe in the southern Irish Sea/ Celtic Sea, and the credibility of the concept (e.g. Mitchell & Orme, 1967; Scourse & Furze, 2001) that a lobe extending to or beyond the Scilly Islands could be consistent with the LGM ice margins on land in SE Ireland and SW Wales. They also show that a powerful ice stream down the east coast of England could readily be created by ice draining in an easterly direction through the Pennines and from SE Scotland and demonstrate a tendency for the stream to bifurcate at its head, with one sub-lobe penetrating the Wash embayment and one between the coast of east Anglia and the Dogger Bank, as has been suggested by the reconstructions of Straw (1991) in the Wash Basin and Balson and Jeffrey (1991) in
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the offshore zone. The scepticism of Boulton et al. (1977; 1991) about the glaciological credibility of this lobe appears to have been unfounded. The patterns of topographically and dynamically controlled fast flow shown in Figs. 9 and 14 show remarkable similarities to the patterns of flow inferred from studies of indicator erratic dispersal by workers such as Walden et al. (1992) around the northern Irish Sea and SW Scotland, by Raistrick (1926) in the Pennines and eastern England, by Everest et al. (2005) in the Tweed valley in SE Scotland, with ice streaming around the Cheviot Hills. The model supports the interpretation of localised ‘‘trains’’ in which the erratic flux was particularly strong along zones of fast, streaming flow. The effect of the modelled streams passing north and west of the Hebrides (Fig. 9) in drawing down ice and creating the dome over the outer Hebrides (Fig. 7) is consistent with the geological evidence of an ice dome or ridge, reflected by easterly and south-easterly directed striations in the east and westerly directed striations in the west of the islands (Peacock, 1991). In Ireland, the best fit LGM simulations, (apart from Fig. 7–9a,b and e which generate too great a glacial mass) show an ice sheet margin lying further to the north than indicated by geology. Correcting this probably requires a much stronger local depression of the ELA than we have used, implying more highly maritime conditions. Clark and Meehan (2001) have created a new interpretation of the LGM distribution of ice flow and divides in central Ireland based on the identification of overlapping ice flow sets inferred from the pattern of ribbed moraine. They identify three sequential ice sheet phases. The first reflects southwesterly flow from SW Scotland, which we simulate (Fig. 14b); the second, which they presume to represent the maximum, with a N–S divide in eastern Ireland, is one we come close to simulating in Fig. 7–9e–h; and a final ice sheet phase when the divide migrates towards the NW, which we do not succeed in simulating. We are confident that the model could be fine-tuned to adapt to this data by adjusted the climate or decollement parameters. The model readily creates a major fixed ice stream in the Irish Sea. It is consistent with the evidence of Scourse and Furze (2001a,b) that the LGM ice sheet reached the latitude of the Scilly Islands (Fig. 1) and that deforming bed conditions were associated with a major ice stream in the Irish Sea (O´ Cofaigh and Evans, 2001a,b). The simulations (Fig. 12) that create major 50–100 km readvances of the margin of the Irish Sea ice stream is consistent with McCabe’s (1996) suggestion of rhythmic readvances of the ice sheet margin in the Irish Sea basin, and the sedimentary evidence of readvances presented by Evans and O´ Cofaigh (2003). Evidence of readvances during overall retreat of an Irish Sea ice stream (Fig. 1) may reflect such unforced oscillations rather than climatically-forced events. Evans and O´ Cofaigh (2003) have described localised tectonic thickening of till and associated sediments in successive belts, 30–50 km apart, lying parallel
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and near to the margin of the ice stream in south and SE Ireland. They then use Boulton’s (1996a) deforming bed theory, which relates variations in till thickness to fluctuations of the ice sheet, to deduce oscillations of an Irish Sea ice stream margin during retreat, which they suggest would have occurred on scales that are similar to the unforced oscillations of the margin shown in Fig. 12a. Although such re-loading events might be thought capable of generating the short-term relative sea levels above modern sea level argued for by Eyles and McCabe (1989), our simulations do not show this. Whether the entirely unforced ‘‘dynamic streams’’ that are predicted by the model existed must depend upon further geological investigation. There is strong evidence from the West Antarctic Ice Sheet that ice streams can be ephemeral, with one major stream having shut down about 150 years ago (Retzlaff and Bentley, 1993). Boulton et al. (2001) have suggested that fast flow in the major last glaciation ice streams in southern Finland has turned on and off, with one of them having a lifetime of some 200 years. Our simulations are able to create dynamic streams, such as those for example shown in Fig. 11 column 3, that have lifetimes of the order of 150–800 years. Although the grid size in our simulations is no smaller than 5 km, such that relatively narrow highland valleys are unresolved, the existence of warm basal patches along major valleys in our smoothed topography in highland areas that are otherwise cold based (e.g. Fig. 14), suggests that basal melting along valleys and their flanks will be much more widespread than appears (this issue is addressed further in Section 10). We expect that melting will occur along the floors and sides of most of such valleys even when mountain summits and plateau tops are subject to cold bed conditions. This contrast explains why highland valleys with signs of strong glacial erosion can co-exist with un-eroded higher mountain areas only a short distance away, such as occurs in the Cairngorms, where Tertiary weathering residues survive on plateau tops (e.g. Hall and Sugden, 1987). The simulation of a cold basal zone at the LGM ice margin in Fig. 14, with its potential to freeze-in large quantities of basal debris to create substantial areas of supraglacial stagnation topography on retreat (Boulton, 1972), accords well with the widespread presence of such topography near the southern margin of the ice sheet (e.g. Thomas, 1989). 10. Weathering trimlines and the elevation of the ice sheet surface We initially adopted the constraint on ice sheet surface elevation suggested by the work of Ballantyne et al. (1998) on the weathering trimline in the northern Highlands and the Hebrides of Scotland. It is, however, very difficult in our simulations to depress the ice sheet surface elevation to elevation of the trimline. Indeed, our models also throw doubt on the validity of the approach of Boulton et al. (1991) which did produce a model with a surface elevation
that matched the trimline. This leaves us with two options, to change ice sheet flow parameters to extreme values, for which we can find little physical justification, or to question whether the weathering trimlines do reflect the LGM ice surface, or whether they reflect a thermal interface within the ice sheet. A major problem is that of spatial resolution. We have used a maximum resolution of 5 km in modelling. Whereas this resolves parts of such valleys as the Great Glen, the Firth of Lorne and some western sea lochs, with widths in excess of 5–10 km, it fails to resolve the widths of many Highland valleys, which are typically less than 5 km. Highland topography is therefore a smoothed representation, with smoothed elevations that rarely exceed 500 m, intermediate between the elevations of peaks, typically around 1000 m, and the valleys. The barrier to increasing resolution to about 1 km, is that the steep valley-margin slopes which would then appear would require us to relax the small slope approximation that most modern models assume, and to incorporate longitudinal stresses in the model; a step currently beyond our computational resources. The principal effect of modelling at this high resolution would be to create small scale streaming of flow along Highland valleys, increasing the flow velocities along the valleys and reducing them along intervening interfluves (this would occur in addition to the streaming already modelled along wider valleys and troughs). We have tried to illustrate this effect in the following way. Typical interfluve widths in the NW Highlands are of the order of 4–8 km compared with valley widths of the order of 1–3 km. We assume that valley streaming would draw down a large proportion of the flow along interfluves, and, therefore, that valley flux would be at least 2–4 times greater than in our model. This would also apply in the sea areas further west, in the trough of the Sound of Raasay, east of Skye, for example. This would not decrease the slope of the ice surface (it would tend to increase it) but it would significantly warm the ice along valleys and troughs, without incurring the cold ice advection problem. We have, therefore, used a 2D, flowline version of the model along a valley/trough profile driven by the same temperature, ice softness and bed slipperiness functions as in the model shown in Fig. 14 and increased the valley flux by increasing the mass balance on the ice sheet surface by factors of between 2 and 4. Fig. 15 shows the effect of this approximately along the line of transect C (Fig. 12d) but with the elevation of nearby, approximately W–E trending valleys projected onto the line of section. The ice surface elevation and thermal regime are shown for 2D models using a standard temperature of 0 1C and standard mass balance in model 1, and +5 1C and 1.3 standard mass balance in model 2. Whereas the smoothed 3D simulation is associated with relatively widespread basal-freezing conditions in upland areas (e.g. Fig. 14, column 2), the valley streaming model shows how the elevation of the interface between temperate and sub-melting point ice is significantly increased, and the
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Fig. 15. Form of the two-dimensional, flowline model of the ice sheet at the LGM along transect B (Fig. 12d), designed to illustrate the effect of streaming along narrow highland valleys. The dashed lines show the elevation of the interface between ice below the melting point and underlying ice at the melting point. Model 1 is driven by a standard temperature of 0 1C and standard mass balance. Model 2 is driven by a standard temperature of +5 1C and 1.3 standard mass balance. The heavy line shows valley floor profiles on the land area and smoothed representations of the continental shelf. The heavy vertical lines show typical summit elevations of the highest peaks in each area, which tend to carry the evidence of weathering trimlines. The smoothed topography used in the 3D model lies between the valley profiles and the elevations of peaks.
frozen bed area much reduced. Moreover, all models show a maximum elevation of the freezing boundary that is time transgressive. Whilst recognising the simplifications inherent in this approach it does show that an interpretation of the weathering trimline as a transition zone between temperate ice and overlying ice below the melting point is plausible. We do not expect the transition simply to take place where overlying ice falls below the melting point, but within some sub-melting point temperature range, as the adhesive strength of the ice-rock interface is increasingly able to resist the shearing force that tends to disrupt the interface, and as we expect some liquid water to survive at the interface at sub-melting point temperatures. Stone et al. (1998) measured the 26Al/10Be ratio on rocks above the weathering trimline, which showed no evidence of prolonged cover by passive ice. However, our modelled duration of ice cover at elevations above the weathering trimline are of the order of 3–5 ka, which would not be enough to create a significantly observable impact on the 26 Al/10Be ratio. 11. Relative sea level constraints We have used forward models of a coupled ice sheet/ Earth system forced by imposed climatic parameters in which the ice sheet/Earth response is determined by climatic and physical ice sheet parameters. Deflection of the lithosphere as a consequence of differential ice and water loading and the changing volume of ocean water as a consequence of global glacier volume growth and decay
determine the pattern of relative sea level change. The capacity of a model to reproduce the observed pattern of change is an effective means of testing model compatibility with the sea level record. Fig. 16 compares modelled with observed relative sea levels (Shennan, pers. commun., 2000; see also Shennan and Horton, 2002) for the model in Fig. 14. The fit is good, but it does not imply that the modelled magnitude and distribution of ice loading in time and space is a unique solution, but merely that it satisfies the constraints. This is quite a different approach from those taken by Lambeck (e.g. Lambeck et al., 1998) or Peltier (e.g. Peltier et al., 2002) to deduce the loading history of the last British ice sheet. They use relatively full physical descriptions of the Earth, but the glaciers are simply represented by a load distribution, without any glacier physics. Their inverse models seek to deduce the pattern of loading of the lithosphere in time and space from the recoverable relative sea level history. The maximum spatial resolution of ice sheet form is about 100 km and the inversions necessarily lack any glaciological information apart from this. The approach also suffers from the difficulty that apart from the partially known relative sea level record, neither ice loading history nor Earth properties are known a priori. The evidence of weathering trimlines in the Scottish Highlands, if interpreted as an indicator of the LGM ice surface, constrains at least part of the ice loading history, and Peltier et al. (2002) have used this to adjust Earth properties so that the inversion lowers their previous estimation of ice thickness in the Highlands, in ICE-4G
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Glen x 10, warm, extended LGM Fig. 16. Patterns of relative sea level change at sites around Britain during the Late-Devensian and Holocene. Red lines show relative sea levels simulated by the model in Fig. 14. Circles show measured relative sea levels (supplied by Shennan, 2000).
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basal ice horizontal basal basal melt rate temperature velocity [meter/year] [degree_Celsius] [meter/year] elevation [m]
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Fig. 17. (a–b) Examples of deduced glaciological properties of the ice stream in the Irish Sea basin from the model in Fig. 14: (a) along transect A (Fig. 12d); (b) along transect D (Fig. 12d). The colours in the ice sheet sections show ice below the melting point as turquoise and at the melting point as brown.
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(Peltier, 1998), from about 2 km to about 1 km. It is thus crucial that the significance of the trimline is unequivocally established. Our simulations of relative sea level change, in which relative sea levels lie below modern sea levels during the whole of the deglacial phase in the central and southern Irish Sea are incompatible with the view of Eyles and McCabe (1989) that the so-called ‘‘Irish Sea tills’’ exposed around the shores of the Irish Sea basin represent high deglacial sea-levels. They are, however, compatible with the view of Scourse and Furze (2001) that sea level high-stands in the area are of interglacial age. 12. Deduced glaciological properties Part of the purpose of the simulations presented in this paper is to use the properties of models that match geological evidence as indications of the glaciological properties of the real ice sheet. Not only, therefore, are we able to deduce patterns of time-dependent structural organisation that are compatible with geological data but also to infer quantitative glaciological properties. A strong conclusion of our modelling is the importance of major ice streams in controlling the form and flow of the ice sheet, the pattern of dispersal of indicator erratics and the patterns and rates of erosion, transport and deposition in time and space, which will be discussed in a later article. We are also able to estimate some quantitative properties of the ice sheet. For example, Fig. 17a,b shows calculated properties along transects through the Irish Sea ice stream at the LGM for the simulations shown in Fig. 14. The lines of section are those shown in Fig. 12. Fig. 17a shows a section along the ice stream and Fig. 17b across the stream. Basal velocities along the stream increase to a maximum of about 600 ma1 and then decrease towards the terminus, with the contribution of basal velocity to the total horizontal glacier velocity being greatest where basal melting occurs. This velocity profile is consistent with that required to generate the till thickness variations described by Evans and O´ Cofaigh (2003) and predicted by Boulton, 1996a, b). The transverse section clearly shows the location of the major stream along the axis of the Irish Sea trough, abutting against the Welsh hills to the right and the Irish coast to the left (ca Fig. 9i). It also shows that velocities are highest in the zone where the basal melting rate is highest. Velocities of these magnitudes are common in the streams in all simulations. In areas of basal melting away from the strongly streamed areas, basal velocities in the terminal zones of the LGM ice sheet are in the range 50–200 ma1. In terminal zones of no basal decollement, surface velocities are of the order of 10–50 ma1, more than an order of magnitude less than the surface velocities of adjacent streams. Basal shear stresses vary considerably through the ice sheet, from about 15–25 kPa, 100–200 km from the margin in the Irish Sea stream at the LGM, to 70–110 kPa in the mountainous areas of central Scotland.
The distribution of the ice flux also varies considerably. For the models such as those in Fig. 9a,b, none of the ice flux is delivered via fast streams. For models where basal decollement only occurs in highly localised streams (e.g. Fig. 9c), over 84% of the ice flux is delivered to the margin via fast streams. Where basal decollement takes place both in streams and inter-stream zones, between 75% (in Fig. 9e) and 60% (in Fig. 9j) is delivered via streams.
Acknowledgements This work has benefited from discussions and assistance from Nick Hulton, Tibor Dunai, Kurt Lambeck, Sergei Zatsepin, Roy Thompson and an anonymous referee.
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Peltier, W.R., 1998. Postglacial variations in the level of the sea: implications for climate dynamics and solid earth geophysics. Reviews of Geophysics 36, 603–689. Peltier, W.R., Goldsby, D.L., Kohlstedt, D.L., Tarasov, L., 2000. Ice age ice sheet rheology: constraints on the Last Glacial Maximum form of the Laurentide ice sheet. Annals of Glaciology 30, 163–176. Peltier, W.R., Shennan, I., Drummond, R., Horton, B., 2002. On the postglacial isostatic adjustment of the British Isles and the shallow viscoelastic structure of the Earth. Geophysical Journal International 148B, 443–475. Raistrick, A., 1926. The glaciation of Wensleydale, Swaledale and adjoining parts of the Pennines. Proceedings of the Yorkshire Geological Society 20, 366–410. Retzlaff, R., Bentley, C.R., 1993. Timing of stagnation of Ice Stream C, West Antarctica, from short-pulse radar studies of buried surface crevasses. Journal of Glaciology 39, 553–561. Scourse, J.D., Furze, M.F.A., 2001. A critical review of the glaciomarine model for Irish Sea deglaciation: evidence from southern Britain, the Celtic shelf and adjacent continental slope. Journal of Quaternary Science 16 (5), 419–434. Sejrup, H.P., Aarseth, K.L., Ellsingen, K.L., Reiter, E., Jansen, E., Lovlie, R., Bent, A., Brigham-Grette, J., Larsen, E., Stoker, M.S., 1987. Quaternary Stratigraphy of the Fladen area, central North Sea: a multidisciplinary study. Journal of Quaternary Science 2, 35–58. Sejrup, H.P., Haflidason, H., Aarseth, I., King, E., Forsberg, C.F., Long, D., Rokoengen, K., 1994. Late Weichselian glaciation history of the northern North Sea. Boreas 23, 1–13. Sejrup, H.-P., Larsen, E., Landvok, J., King, E.L., Haflidason, H., Nesje, A., 2000. Quaternary glaciations in southern Fennoscandia: evidence form southwestern Norway and the North Sea region. Quaternary Science Reviews 19, 667–685. Shennan, I., Horton, B., 2002. Holocene land- and sea-level changes in Great Britain. Journal of Quaternary Science 17 (5–6), 511–526.
Shreve, R.L., 1984. Glacier sliding at subfreezing temperatures. Journal of Glaciology 30, 341–347. Stoker, M.S., Long, D., Fyfe, J.A., 1985. The Quaternary succession in the central North Sea. Newsletters on Stratigraphy 14, 119–128. Stone, J.O., Ballantyne, C.K., Fifield, L.K., 1998. Exposure dating and validation of periglacial weathering limits, northwest Scotland. Geology 26 (7), 587–590. Stone, J.O., Ballantyne, C.K., 2006. Dimensions and deglacial chronology of the Outer Hebrides Ice Cap, northwest Scotland: implications of cosmic ray exposure dating. Journal of Quaternary Science 21, 75–84. Straw, A., 1991. Glacial deposits of Lincolnshire and adjoining areas. In: Ehlers, J., Gibbard, P.L., Rose, J. (Eds.), Glacial Deposits in Great Britain and Ireland. Balkema, Rotterdam, pp. 213–221. Sugden, D.E., 1977. Reconstruction of the morphology, dynamics and thermal characteristics of the Laurentide ice sheet at its maximum. Arctic and Alpine Research 9, 27–47. Sutherland, D.G., Walker, M.J.C., 1984. A late devensian ice-free area and possible interglacial site on the Isle of Lewis, Outer Hebrides. Nature 309, 701–703. Synge, F.M., 1977. Records of sea levels during the Late Devensian. Philosophical Transactions of the Royal Society of London 280, 211–228. Tarasov, L., Peltier, W.R., 2002. Greenland glacial history and local geodynamic consequences. Geophysical Journal International 150, 198–229. Thomas, G.S.P., 1989. The late Devensian glaciation along the western margin of the Cheshire–Shropshire lowland. Journal of Quaternary Science 4, 167–181. Valentin, H., 1957. Glazialmorphologische Untersuchungen in Ostengland. Abhandlungen des Goegraphischen Institut der Freien Universita¨t Berlin 4, 1–86. Walden, J., Smith, J.P., Dackombe, R.V., 1992. Mineral magnetic analyses as means of lithostratigraphic correlation and provenance indication of glacial diamicts: inter- and intra-unit variation. Journal of Quaternary Science 7, 257–270.
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Glaciology of the British Isles Ice Sheet during the last glacial cycle: form, flow, streams and lobes Geoffrey Boulton, Magnus Hagdorn School of Geosciences, University of Edinburgh, Grant Institute, Kings Buildings, Edinburgh EH9 3JW, UK Received 12 January 2006; accepted 29 October 2006
Abstract The last ice sheet over the British Isles, together with other mid-latitude Pleistocene ice sheets, and in contrast to the modern ice sheets of Greenland and Antarctica, had a relatively low profile, low summit elevation and extensive, elongated lobes at its margin. A thermomechanically coupled numerical ice sheet model, driven by a proxy climate, has been used to explore the properties that would have permitted these characteristics to develop. The approach, the key to quantitative palaeoglaciology, is to determine the boundary conditions that permit the simulated ice sheet to mimic the evolution of the real ice sheet through the last glacial cycle. Simulations show how a British ice sheet may have been confluent with a Scandinavian ice sheet during some parts of its history and how unforced periodic and asynchronous oscillations could occur in different parts of its margins. Marginal lobes are a reflection of streaming within the ice sheet. Such streams can be ephemeral, dynamic streams located because of ice sheet properties, or fixed streams whose location is determined by bed properties. The simulations that best satisfy constraints of extent, elevation and relative sea levels are those with major fixed streams that strongly draw down the ice sheet surface. In these, the core upland areas of the ice sheet were cold based at the Last Glacial Maximum, basal streaming velocities were between 500 and 1000 ma1 compared with surface velocities of 10–50 ma1 in interstream zones, shear stresses were as low as 15–25 kPa in streams compared with 70–110 kPa in upland areas and 60–84% of the ice flux was delivered to the margin via streams. r 2006 Elsevier Ltd. All rights reserved.
1. Introduction Ice sheets are by far the largest and climatically most influential part of the global glacier mass. Understanding about them is derived from two sources:
modern ice sheets whose current properties can be measured and modelled, but whose bed cannot be directly observed, and whose time-dependent variations have only been studied for about 50 years; from the evidence left by Pleistocene ice sheets, whose properties cannot be directly measured but whose beds can be directly observed and some of whose longer-term variations can be inferred from geological evidence.
In this article, we use numerical ice sheet modelling and geological evidence to explore relationships between ice Corresponding author.
E-mail address: [email protected] (G. Boulton). 0277-3791/$ - see front matter r 2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.quascirev.2006.10.013
sheet form, ice streaming and marginal lobe formation using the ice sheet that covered the Britain Isles during the latter part of the last glacial cycle as the subject of modelling. This is done for three reasons: because it helps us better to understand why and where different types of ice streams form and how lobes are generated; because there are longstanding problems in understanding the form and flow of the last glaciation ice sheet over the British Isles; and in order to infer glaciological properties such as dynamic structure in time and space, velocities and shear stresses. Our approach is one that we believe to be central to palaeoglaciology. We simply ask how we need to adjust the boundary conditions and forcing functions for ice sheet models in order to cause the modelled ice sheet to behave in ways that mimic the geologically deduced real ice sheet. The boundary conditions are fundamental ice sheet/Earth properties, and forcing functions reflect climate/ice sheet interactions. Together they represent logical deductions from geological data about glaciological properties of the palaeo-ice sheet through the medium of the model.
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2. Ice sheet form, ice streams and the problem of ice lobes
2.2. Possible mechanisms
2.1. The problem
By the 1960s, it was beginning to be understood (e.g. Bauer, 1961) that ice sheets were not radially symmetrical in the distribution of their dynamic properties, but that fast ice streams flowed through them. These play a massive role in ice sheet dynamic behaviour, discharging as much as 85% of the mass in the case of Antarctica, even though comprising a relatively small proportion of its area. Major lobes at the terrestrial margin of an ice sheet on a flat bed can only be caused by such streams, which are increasingly recognised as ubiquitous attributes of Pleistocene as well as modern ice sheets (e.g. Boulton et al., 2001). (Valley glaciers are naturally lobate, being prevented from spreading laterally by confining mountain walls.) Elongate lobes imply relatively low longitudinal slopes and relatively high lateral slopes, and, therefore, require a mechanism that permits longitudinal gravity spreading but prevents lateral spreading. The Earth’s two current ice sheets offer no direct analogies. The Greenland ice sheet margin is lobate only where ice flows towards the margin through valleys in the flanking mountains, or on a very large scale in subsidiary ice ridges such as that of NW Greenland. The Antarctic margin calves almost exclusively into deep water. It has been argued on stratigraphic grounds (e.g. Clayton et al., 1985), that some lobes, such as those at the southern margin of the LGM Laurentide ice sheet, are the product of surges, but this in itself does not account for the contrast between their longitudinal and transverse slopes. Ice sheet lobes on a flat bed must reflect areas where relatively fast streams intersect the glacier margin and project it further forward than elsewhere, against the common effect of ablation. Easier movement in them is most likely to result from either:
Early theories of ice sheet form and flow assumed ice sheets to be slowly flowing, quasi-radial domes (Nye, 1951) in which the velocity of flow was a function of radial distance from the flow divide. This view was reflected in early attempts to model former ice sheets (e.g. Boulton et al., 1977; Sugden, 1977) and some modern ones (e.g. Marshall et al., 2002). These models, however, are unable to explain the highly lobate forms of some parts of former ice sheet margins, such as those characteristic of the margins of Last Glacial Maximum (LGM) ice sheets: for example, the Baltic lobe associated with the later stages of the LGM European ice sheet (e.g. Houmark-Nielsen, 2004), the lobes of the LGM British Isles ice sheet along the east coast of England and in the southern Irish Sea (Fig. 1), and the lobes at the southern margin of the Laurentide ice sheet (e.g. Clayton et al., 1985).
Fig. 1. Recent reconstructions of the maximum extent of the Last Glacial Maximum (Late Devensian) ice sheet over the British Isles, showing the uncertainties associated with currently submarine evidence (1—Bowen et al., 2002; 2—Hall, 1997; 3—Balson and Jeffrey, 1991; 4—Scourse and Furze, 2001). Lines marked 5 show the extent of readvances in the Irish Sea Basin (Ireland—Synge, 1977; Isle of Man—Dackombe and Thomas, 1991; Cumbria—Huddart, 1991). 6—possible western margin of the Scandinavian ice sheet at the LGM (Hall, 1997).
a contrast between basal melting along the stream, reducing friction and facilitating easy movement, and basal freezing on its flanks associated with high ice/bed friction; or a contrast between a zone of soft subglacial sediment along the stream in which the sediment either deforms or permits easy sliding because of its low surface roughness, compared with flanks directly underlain by higher friction rock, or frozen rock or sediment, to which the ice adheres.
If differential spreading occurs, either where there are longitudinal carpets of deformable subglacial sediment with a flanking rock bed, or zones of basal melting flanked by basal freezing, such zones would offer a low friction, low shear stress path for longitudinal flow. Lateral spreading would be inhibited by the higher friction along the flanks. The two mechanisms, of sediment deformation or basal melting, reflect quite different controls. The first
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depends upon a geological property of the bed. The second is a dynamic property of the ice sheet. In the latter case, Hulton and Mineter (2000) showed that streaming could develop as a dynamic feature of an ice sheet without any local change in the topography or composition of the bed. They suggested that streaming was a way in which the ice sheet flow system adjusted to the mass balance and temperature regime. Boulton et al. (2003) showed that if the bed of the European ice sheet was arbitrarily changed to a flat plain, other than in the mountain area needed to nucleate the ice sheet, ice streams still developed over the flat plain. Modern Antarctic ice streams are characterised by low friction and low slopes compared with flanking ice, with inferred shear stresses along them of the order of o20 kPa (Alley and Whillans, 1991) compared with shear stresses in flanking ice of the order of 100 kPa. Miller et al. (2002) have shown that low-slope flow of the Laurentide ice sheet along the sediment-floored fjords of east Baffin Island took place under shear stresses as low as 2–7 kPa, which must reflect almost liquefied sediments under almost zero effective stresses. 3. Problems of reconstructing and explaining a British ice sheet We will go on to suggest that ice sheet form and thickness in an ice sheet such as that of the British Isles during the LGM are intimately related to fast ice streams, which can be the only cause of ice lobes on a low relief bed, and ice that is relatively ‘‘soft’’ compared with Glen’s flow law (e.g. Paterson, 1994, Chapter 5), or with a particularly slippery bed. We first review geological evidence of thickness, extent and ice lobes in the LGM British Isles ice sheet. 3.1. Thickness and extent Early attempts to reconstruct the extent of a British ice sheet at the LGM assumed that it was confluent with the contemporary Scandinavian ice sheet in the North Sea and stretched to the edge of the continental shelf 200 km west of Scotland (Geikie, 1878, 1894; Valentin, 1957). The first attempt to model the form and flow of the ice sheet using contemporary glaciological theory (Boulton et al., 1977) suggested that the summit of the ice sheet, over the Grampian Highlands of Scotland, had an elevation relative to the modern land surface of over 1800 m, sufficient to cover the highest mountain summits with several hundred metres of ice (Fig. 2a). However, Lambeck (1993, 1995) used a geophysical model of lithosphere/asthenosphere properties to invert relative sea level data around the British Isles from the period of deglaciation to infer the magnitude and distribution of the ice sheet load at the LGM, and concluded that there had been a maximum ice thickness of 1300–1400 m over the Grampians and about 1100 m over the Northern
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Highlands. He also concluded (Lambeck, 1995) that the ice sheet at the LGM was not confluent with the Scandinavian ice sheet in the North Sea, and that it only extended for a short distance of about 50–100 km beyond the modern eastern coastline of NE Britain. Ballantyne et al. (1998), demonstrated the existence of weathering ‘‘trimlines’’ in NW Scotland, where glacially eroded surfaces at lower elevations gave way to weathered rock surfaces and ‘‘frost debris’’ at higher elevations. They suggested that these trimlines marked the upper surface of the ice sheet during the LGM, from which they deduced an ice thickness over the Northern Highlands during the LGM similar to that inferred by Lambeck. However, it is well established that ice well below the melting point adheres to its bed, and accomplishes very little if any erosion (Goldthwait, 1960; Holdsworth, 1974), because the adhesive strength of an ice/rock interface at temperatures well below the melting point is significantly greater than typical basal shear stresses (Jellinek, 1959). However, sliding can occur at temperatures lower than the ambient pressure melting point (Shreve, 1984; Echelmayer and Wang, 1987) and can locally abrade bedrock (Atkins et al., 2002). Thus although we would not expect a sharp erosion/ no erosion interface at the point where the temperature of basal ice falls below the melting point, we would expect a rapid fall-off in erosion rates as temperatures fall well below this level. It is possible, therefore, that the observed trimline represents a thermal transition from temperate or just sub-temperate ice below to much colder ice above. Stone et al. (1998) used cosmogenic exposure dating, using 10 Be and 26Al, to infer the exposure age of the rock surfaces, and to examine whether the 26Al/10Be ratio could indicate contrasting multi-stage exposure histories above and below the trimline. Unfortunately, they were ‘‘unable to preclude the possibility that the weathering limits mark a former englacial boundary between passive cold-based ice on mountain summits and erosive, warm-based ice at lower elevations’’, with the consequence that the trimline does not provide an unequivocal constraint on ice surface elevation. The glaciological reconstruction of Boulton et al. (1977) had assumed a constant basal shear stress of 100 kPa (effectively an assumed yield strength for ice), and also that the ice sheet was confluent with Scandinavian ice in the North Sea. In a subsequent model (Boulton et al., 1991) the basal shear stress was adjusted, in a way broadly consistent with emerging evidence of much greater variation in basal shear stresses in modern ice sheets, with prescribed values of 70 kPa over the land areas and 30 kPa over the sea areas, assuming that deformation in soft marine sediments areas would restrict basal friction to relatively low values. Its purpose was to explore whether an ice sheet model could fit the emerging evidence (Ballantyne and Sutherland, 1987) of a relatively low ice sheet surface elevation in Easter and Wester Ross in the Northern Highlands of Scotland, and the evidence that the ice sheet was not confluent with Scandinavian ice in the North Sea at the LGM (Stoker
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Fig. 2. (a and b) Earlier models of the British Isles ice sheet at the LGM. Both are inverse models, in which ice sheet form is computed from a prescribed ice sheet margin. (a) The British ice sheet is confluent with a Scandinavian ice sheet. The basal shear stress is assumed everywhere to be 100 kPa (Boulton et al., 1977). (b) An independent British ice sheet (cf Fig. 1). The basal shear stress is taken to be 30 kPa outwith the modern coastline and 70 kPa on the modern land area (Boulton et al., 1991).
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et al., 1985; Sejrup et al., 1987). This generated an ice sheet summit elevation of about 1100–1200 m along an ice ridge through western Scotland and into northern Ireland (Fig. 2b). These models were inverse models. They took the ice sheet margin as given by geological evidence, and merely explored the ice sheet elevation and form consistent with these margins, with a prescribed pattern of basal shear stress and using a simplified calculation of ice sheet thermal properties (Jones, 1978). They were not natural numerical experiments, in which the ice sheet is driven by climate and with a properly posed basal boundary condition, which then examined the extent to which the resultant ice sheet was consistent with other evidence. As we shall show, thermo-mechanically coupled models do not permit the pattern of bed properties assumed by Boulton et al. (1991) readily to generate the desired low-elevations. Sejrup et al. (1994) have argued, from the evidence of radiocarbon dates and amino acid ratios on marine shells above and below till strata in the Northern North Sea, that the British Isles and Scandinavian ice sheets were not confluent at the LGM, but that ice from Scandinavia and Scotland were confluent in the area between 29,000 and 24,000 radiocarbon years before present. The two ice sheets then parted, but re-advanced during the LGM to a maximum about 17,000 years ago, but for only a relatively small distance beyond their respective mainland areas. Clark et al. (2004) are sceptical of this hypothesis of early North Sea confluence in view of the radiocarbon ages from Scotland, collated in Boulton et al. (1991) from bone, peat and plant detritus and U-series ages on speleothems, which indicate ice-free conditions close to the centres of ice accumulation in Scotland at the time that North Sea confluence is said to have occurred. Sutherland and Walker (1984) had suggested that the LGM ice sheet did not extend further than the northern tip of the Outer Hebrides (reconstruction 1 in Fig. 1). However, evidence of seismostratigraphy (Peacock et al., 1992; Stoker et al., 1985) suggested that the LGM ice sheet extended close to the continental shelf edge to the west of Scotland (reconstruction 2 in Fig. 1), which is also consistent with trimline and cosmogenic isotope dating (Stone and Ballantyne, 2006). Von Weymarn (1979) and Peacock (1991) had demonstrated that the Outer Hebrides were not glaciated by mainland ice, but had been covered by an independent dome during the LGM. This was supported by the trimline data of Ballantyne et al. (1998). 3.2. Ice lobes Two major ice lobes, on very low relief beds, protruded from the southern margin of the British ice sheet at the LGM (Fig. 1): one down the east coast of England (Balson and Jeffrey, 1991), and one in the southern Irish Sea and Celtic Sea, between SW England/Wales and SE Ireland, although its extent is a matter of debate. Some (Bowen et al., 1986; Eyles and McCabe, 1989) have suggested a
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limit in St. Georges Channel (see Fig. 3 for locations referred to in the text), between SW Wales and SE Ireland (reconstruction 1, Fig. 1), whilst others (Scourse and Furze, 2001; Hiemstra et al., 2006) have suggested a limit some 150 km south west of the Scilly Isles (reconstruction 4, Fig. 1). The glaciological reconstruction of Boulton et al. (1977) was unable to account for the lobe on the east coast of England, but they suggested that it could represent a surge of the ice sheet margin (Fig. 2a), whilst Boulton et al. (1991) produced a reconstruction, which they recognised as unlikely, of the lobe as a semi-independent ice dome (Fig. 2b). If we discount the marginal ice dome hypothesis, and in the absence of significant lateral topographical constraints, lobes at the margin must be a consequence of local fast streaming in the ice sheet. Fast streaming flow may be ephemeral on a short timescale, or sustained for relatively long time periods, although the distinction may simply be one of response time. The former are referred to as surges, the latter as ice streams. The period of any cyclical behaviour is likely to be scale dependent for both of the most likely mechanisms, which are: (a) The accumulation of ice in the catchment area of the ice stream is unable to sustain the flux within it. Fast streaming is most likely to be sustained for longer periods in ice sheets with large drainage areas compared with valley glaciers. Fast streaming in valley glaciers that are not outlet drainage glaciers for ice sheets will only be sustained for short period surges. (b) For longer timescales, Clarke et al. (1977) identified a ‘‘creep instability’’ in a glacier in which fast flow exhausts replenishment, causing the profile to flatten and velocity to fall, such that the glacier bed freezes, leading to high basal friction, permitting the profile to build up, producing basal melting, friction reduction and fast flow, and repetition of the cycle. McAyeal (1993) suggested that such a ‘‘binge-purge’’ cycle in a Laurentide ice stream flowing through the Hudson strait could account for Heinrich layers in the North Atlantic.
4. The ice sheet model 4.1. Approach Rather than use the inverse approach that has hitherto been used to create glaciological models of the British Isles ice sheet, we now use a model that is driven by a proxy climate function. Our approach is to ask how we need to adjust ice sheet boundary conditions and climate forcing functions in order to match, in broad terms, some of the principal known characteristics of the ice sheet over the British Isles, including the major ice lobes. We regard this as a fundamental approach of ‘‘palaeoglaciology’’, inferring glaciological properties of the ice sheet from glacial
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Fig. 3. Locations referred to in the text.
geology through the intermediary of a numerical ice sheet model that, as far as possible, represents current glaciological understanding. Whereas early glacial geologists (e.g. Geikie, 1894; Charlesworth, 1957) believed that most of the geological impacts of ice sheets during the last glacial period reflected processes at the glacial maximum, we believe that they reflect cumulative, transient processes, and, therefore, that understanding the behaviour of an ice sheet requires simulation through the whole of the glacial cycle. Ideally we would like the ice sheet model to be driven by a general circulation climate model on a spherical Earth. However, our objective is to simulate high-resolution behaviour of the ice sheet over the British Isles through the whole of the last glacial cycle, using grid spacings of 5–10 km and time steps of 6 months in order to capture the annual mass balance cycle. Thus, although the model could be used on a spherical Earth, and could be coupled to a full climate model, the computing time required for a single run would be excessive when we wish to undertake multiple simulations to explore the effect of different boundary conditions, including climate forcing. We have, therefore,
opted for a planar Earth segment restricted to the British Isles (sometimes including Europe) and a series of ice sheet surface climate proxies. This restricted model domain has the further disadvantage that the isostatic component of sea level change is entirely accommodated within the domain, and therefore over-estimates its contribution. However, it was clear that the choice had to be made to restrict the domain in order to fulfil the objectives of the simulation experiments. 4.2. The model The core of the model is a coupled ice sheet/Earth model. The evolution of ice sheet form is determined using the continuity equation: qH ¼ rH ð¯vHÞ þ M S, (1) qt where rH is the two-dimensional horizontal gradient, H the ice thickness, v¯ the vertically averaged velocity, M the mass balance (accumulation minus surface melting rate) and S the melting rate at the base of the ice column.
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The shallow ice approximation is used (Hutter, 1983) so that horizontal shear stresses can be approximated by txzðzÞ ¼ ri gðH þ h zÞ
qðH þ hÞ , qx
tyzðzÞ ¼ ri gðH þ h zÞ
qðH þ hÞ , qy
(2)
where h is the bedrock elevation, ri the density of ice and g the gravitational acceleration. Strain rates of ice are related to the stress tensor by tij ; _ij ¼ AðT n Þtðn1Þ n
i; j ¼ x; y; z,
(3)
where tn is the effective shear stress defined by the second invariant of the stress tensor, n the flow law exponent and A the temperature dependent flow law coefficient (Paterson, 1994). T is the absolute temperature corrected for the dependence of the melting point on pressure. The horizontal velocity vector is found by vertical integration of the flow law (Eq. (3)): vðzÞ vðhÞ ¼ 2ðri gÞn ðrðH þ hÞrðH þ hÞÞðn1Þ=2 r Z z ðH þ hÞ AðT n ÞðH þ h zÞn dz.
ð4Þ
h
Integrating Eq. (4) from the ice base to the surface gives the vertically averaged velocity v¯ . The temperature evolution of the ice sheet is described by qT k q2 T F ¼ vrT þ , qt ri cp qz2 ri cp
(5)
where T is the absolute temperature, k is the thermal conductivity, cp is the specific heat capacity and F is the heat generated due to friction. Here v is the 3-dimensional, 3-component ice velocity. The z component is calculated using the horizontal velocities together with the incompressibility condition and the surface mass balance and basal melt rates. Thus heat is transferred by both diffusion and advection (first and second term of the RHS of Eq. (5), respectively). A shortcoming of the model is the absence of longitudinal stresses. It is assumes that the stress balance is hydrostatic. This is a reasonable approximation for a low slope bed, and given the smoothing of our topographic model, is applicable in most areas of our study. An area where such stresses can be important is in the case of ice streams. Thus, although we believe that our model is likely to represent well the initiation, location and magnitude of streaming, it may miss some of their detailed features and may marginally under-estimate velocities and the pulling power of streams at low shear stresses. The evolution of the ice sheet is strongly coupled to the isostatic response of the Earth. We use the standard Earth model of an elastic plate with a relaxing asthenosphere (Le Meur and Huybrechts, 1996). It incorporates an elastic lithosphere (defined by the flexural rigidity, D; and thickness H), which determines the geometry of deforma-
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tion, and a fluid, non-viscous asthenosphere of density ra, which determines the time-dependence of the isostatic response. The simplest way to account for the latter is to estimate a time-constant and assume that the rate of response is proportional to the difference between the loaded equilibrium h0w (where h0 is the unloaded equilibrium topography and w is the downward deflection due to the load q of a thin plastic plate of thickness H and flexural rigidity D) and the current profile h, and inversely proportional to the time constant: dh 1 ¼ ðh h0 þ wÞ. dt t
(6)
The present topography is assumed to be the initial unloaded topography h0. The downward deflection can be written as (Le Meur and Huybrechts, 1996) Dr4H w þ ra gw ¼ g,
(7)
where rH is the horizontal gradient operator and g is the gravitational acceleration. The solution of (7) involves a linear combination of Kelvin functions (see Lambeck and Nakiboglu, 1980 for details). The Earth model used here does not include effects due to changes of the gravitational field. However, changes of the ocean load are included through a global sea level change term. A sophisticated spherical, self-gravitating visco-elastic Earth model has been coupled to a dynamic ice sheet (Le Meur and Huybrechts, 1996) but the associated computational effort does not allow us to run the large number of experiments required to explore the parameter space. However, Le Meur and Huybrechts (1996) find that the relaxing halfspace/elastic lithosphere model is an acceptable approximation for the time scales being studied here. Tarasov and Peltier (2002) solve the complete sea level equation using a self-gravitating spherical Earth model together with ice sheet histories obtained through inverting relative sea level observations. They compute relative sea level predictions off-line, after they have simulated the ice sheet. This approach improves the relative sea level predictions but does not significantly affect ice sheet dynamics. The resultant sea level change, Dz is a function of geographic position (l, j), time t, and is dependent on the changes of ice distribution and the Earth’s response function. The topography or bathymetry at some time t is related to the present day surface elevation and relative sea level change by hðl; j; tÞ ¼ hðl; j; t0 Þ Dzðl; j; tÞ.
(8)
Sea level change can be expressed as the sum of each ice sheet’s contribution to sea level change: DBðl; j; tÞ ¼
SDBi ðl; j; tÞ i2ficesheetsg
¼ DBa ðl; j; tÞ
þ DBFenn ðl; j; tÞ þ DBBrit ðl; j; tÞ,
ð9Þ
where DBFenn and DBBrit are the contributions due to the European and British ice sheets and DBa is the sum of the
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contributions due to all the other ice sheets. Global sea levels are indirectly derived from the SPECMAP experiment (Fig. 4c) (Goodess et al., 2000). The initial bedrock topography is taken from the ETOPO5 and GTOPO30 datasets projected onto an Albers Equal Area Conic projection with a 10 and 5 km resolution. The numerical ice sheet model has been developed from that of Payne and Dongelmans (1997) and is now publicly available from the GLIMMER web page (http://glimmer.forge.nesc.ac.uk/). The domain chosen for modelling proved in practice to have been too small such that the ice sheet was frequently and arbitrarily stopped by the eastern boundary of the model domain. It is a drawback in several simulations, although in practice the effect is small as the ice sheet terminates close to its natural margin. 4.3. Boundary conditions In our application, the model is constrained by the following boundary conditions:
temperature and mass balance on the ice sheet surface; ice flow properties in the body of the ice sheet; properties of the ice/bed interface; lithosphere flexure; and calving conditions at the marine margin.
global average sea level [m]
temperature [degC]
Equilibrium line altitude variation [m]
The Earth model and the calving law together with their parameters are taken as fixed, whilst the others are taken as free parameters that are adjusted to establish the parameter space within which a modelled British Isles ice sheet approximately fits the geological constraints.
Tðl; j; z; tÞ ¼ a þ bcðll0 Þ þ dz þ DTðtÞ,
0
where a, b, c and l0 ¼ 44:951N are parameters defining the temperature at sea level, d is the lapse rate and DTðtÞ is the time dependent, linear perturbation of the temperature field. The parameters of (10) are fixed by fitting to a temperature model derived from the Greenland ice sheet record (Johnsen et al., 1995). This is based on the approach used by Boulton et al. (1995). We regard this as providing a good proxy for the likely tempo and relative amplitude of palaeotemperature fluctuation over Britain during the last glacial cycle, but a poor match for their absolute magnitudes. This has been derived from a correlation (Boulton and Thompson, in preperation) with palaeotemperature inferences from the continuous pollen record from central France (Guiot et al., 1989), adjusted by the evidence of Coleopteran paleotemperatures from central England for the LGM and the Lateglacial periods (Atkinson et al., 1987). Fig. 4b shows the pattern of assumed temperature change through the last glacial cycle at the standard latitude (central England). We have varied the temperature level by increments, of +8, +5, 5 and 10 1C compared with 0 1C as the mean annual temperature estimate of Atkinson et al. (1987) at the LGM in central England. We find that ice sheet form and flow are sensitive to changes in surface temperature through the effect of temperature on the ice flow law. The lapse rate is kept constant at 0.006 1C m1.
b
zELA ¼ a þ bl þ cl2 þ DzELA . 0
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4.3.2. Mass balance and continentality Mass balance is parameterised as a vertical variation above and below the equilibrium line altitude (ELA). Two parameters control the shape of the mass balance M: Mmax is the maximum mass balance value that can be reached and zmax is the vertical distance above the ELA at which the maximum mass balance is reached. The ELA is parameterised in relation to latitude by
a
0
4.3.1. Ice sheet surface temperature The temperature field as a function of the geographic location (l, j), elevation above sea level z and time t, is approximated by
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Fig. 4. (a–c) Time-dependent input functions. (a) Magnitude of fluctuation of the equilibrium line altitude through the glacial cycle used to drive the ice sheet model. (b) Pattern of mean annual temperature change through the glacial cycle used to drive the model. It is adjusted according to the assumed value of mean annual temperature in central England at the LGM. (c) The prescribed pattern of global sea level change through the glacial cycle derived from Goodess et al. (2000).
(11)
The mass balance can then be defined in terms of Mmax and zmax as 8 2 < 2M z z forz pzmax ; M max max zmax zmax Mðz Þ ¼ :M forz 4zmax ; max (12) where zn is the vertical distance above the ELA. Our central estimate uses a vertical mass balance gradient typical of the ice cap Vatnajo¨kull in Iceland. This is a maritime setting in the south and a more continental setting in the north that seems likely to be a good model for the British Isles during the glacial period. In the extreme
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maritime case, Mmax is 3 and 0.5 ma1 in the extreme continental case. We found that a strong continentality gradient was required over the British Isles if the ice sheet was to be prevented from extending across the North Sea. These parameters also agree well with the mass balance curves described by Kuhn (1984). The mass balance curves together with the continentality functions are combined to yield one mass balance gradient with a continentality parameter, c. The continentality parameter is defined for each grid point, ranging between 0 for an extreme maritime climate and 1 for an extreme continental climate, so that the mass balance is defined as M ¼ cM cont þ ð1 cÞM mar .
(13)
The ELA is thus determined both as function of latitude and of continentality. The form of the overall ELA driver, given by the parameters in Eq. (11), is derived from the form of the ELA driver required to simulate the LGM fluctuation of the European ice sheet, whose tempo of marginal fluctution is better understood than that of the British Isles ice sheet (Boulton et al., 2001). This driver is also used to simulate the Scandinavian ice sheet in Section 6.2. The absolute magnitude of ELA depression over Britain is that required to drive the ice sheet to the known LGM margin (Fig. 4a). The current ELA elevation is assumed to be the same as the modern ‘‘snowline’’, estimated by Manley (1949) as about 1600 m over the northern Grampians, 1800 m over the Lake District and 1900 m in north Wales. 4.3.3. Ice flow parameters The parameter A in the flow law for polycrystalline ice (3) depends on factors such as temperature, crystal size and orientation, and ice impurities, experimentally shown to follow the Arrhenius equation:
AðT Þ ¼ faeðQÞ=RT ,
(14)
where a is a temperature-independent material constant, Q is the activation energy for creep and R is the universal gas constant (Paterson, 1994). f is a tuning parameter that reflects ice history and accounts for impurities and the progressive development of anisotropic fabrics, and needs to be adjusted to account for the form of modern (Payne, 1999) and former ice sheets (Peltier et al., 2000). It was found that the thickness and extent of the ice sheet is sensitive to the ice softness parameter f, and that large values at the high end of the range f ¼ 3220 are required, irrespective of the temperature and mass balance driver, if the ice sheet is to achieve the combination of large extent and limited surface elevation. This suggests that strong fabric development and possibly high debris content must have been characteristic of the ice sheet. 4.3.4. The basal boundary There is strong coupling between mechanical and thermal processes at the glacier bed. If the ice/bed contact is frozen, no decollement occurs, if unfrozen, decollement
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is assumed to be switched on, either by sliding, subglacial sediment deformation or both. The rate of decollement is dependent on water pressure at the ice/bed interface, but the latter is dependent on the efficiency of the subglacial drainage system, which remains a largely unsolved problem. Empirical sliding laws normally take the form ub ¼ atpb N q ,
(15)
where ub and tb are the horizontal basal velocity and shear stress respectively, and p, q and a are parameters (Paterson, 1994). Since, in the absence of a generally accepted drainage theory, effective pressure is unknown, and p is uncertain, we parameterise a decollement relationship by ub ¼ tb tb ,
(16)
in which tb is a decollement parameter that can be used to reflect physical drivers, such as basal melt rate or drainage rate. We have explored the impact of a wide range of basal traction conditions. We have used a range of tb, from 0.005 to 0.05 ma1 Pa1, which fits a range of modern conditions from easy to relatively stiff decollement. 4.3.5. Lithosphere properties We have followed Le Meur and Huybrechts (1996) in using constant values of lithosphere flexural rigidity of 2.4 1024 and an asthenosphere time constant of 4000 years. These values give isostatic behaviour analogous to that inferred by Lambeck (1993) for the British ice sheet using an inverse model. The geothermal heat flux is held constant at 0.042 W m2, a value characteristic of modern Europe (Hurtig et al., 1992). We have also explored the impact of successive glacial periods on the initial geothermal flux, and established that they have a small effect compared with other parameters. 4.3.6. Calving condition at marine margins Iceberg calving enters the continuity Eq. (1) as another mass balance term. Of the ice thickness, 20% is lost due the calving when the ice reaches a water depth of 500 m. Calving only occurs in cells that have at least one boundary with the ocean. 5. Influence of boundary conditions on ice sheet simulations Large numbers of simulations have been made to explore the effect of varying boundary conditions on ice sheet behaviour. Our targets are to simulate independent ice sheets over the British Isles as shown in Fig. 1, and ice sheet confluence in the North Sea as shown in Fig. 2a. It was found that for the prescribed pattern of temperature variation shown in Fig. 4b, the temporal ELA variation in Fig. 4a and the maritime-continental transitions shown in Fig. 5a were required to generate an independent ice sheet over the British Isles. A much larger or much smaller ELA depression produced ice sheets that were significantly larger or smaller than the target ice sheet. The form of the
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Fig. 5. (a–c) Patterns of transition between continental and maritime conditions given by changes in the ELA for (a) an independent British Isles ice sheet; and (b) a confluent British Isles and European ice sheet (Fig. 10). The purple colour on the left shows the extreme maritime zone and the brown colours on the right the extreme continental zone, and the intervening transition zone. (c) The latitudinal variation in relative ELA values across the transition zones shown in (a) and (b) compared to the ELA in the continental condition.
modelled ice sheet was sensitively dependent on the nature of the west–east gradient of maritime to continental conditions. The geographical variation in the magnitude of ELA lowering in Fig. 5a, which produces highly continental conditions over eastern England, is important in limiting the southward extent of the ice sheet in eastern England. A less abrupt transition between maritime and continental conditions failed to create the correct contrasts in western and eastern marginal extents. The marginally more maritime conditions on the east coast of Britain in Fig. 5b compared with Fig. 5a are sufficient, together with the same ELA driver (Fig. 4a) to
extend the British Isles ice sheet far enough to the east to create a North Sea confluence. Also in this case, a very strong W–E gradient across Scandinavia is important to prevent the eastern margin of the European ice sheet extending too far to the south (although we do not show the eastern margin in figures presented here). Consequently, the ELA driver in Fig. 4a was used in all the simulations described below. Similarly, lithosphere flexural properties, the geothermal flux, the marine boundary condition and the pattern but not the magnitude of temperature fluctuation were held constant in all simulations.
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Within this framework, the key determinants of the extent, form, flow and thermal regime of the ice sheet were:
the value of the decollement parameter, tb at the basal boundary (Eq. (15)) and its spatial variation; the value of the flow law parameter f, which determines ice softness (Eq. (14)); the ice sheet surface temperature.
All combinations of these boundary conditions were used to generate forward simulations of ice sheet behaviour through the glacial cycle. Although a small ice sheet was generated over Britain during isotope stage 4, the period of 72–60 ka, this was insignificant compared with the ice sheet generated between 25 and 14 ka. We have, therefore, concentrated on this latter period. In the following sections we describe the main features of model behaviour for different sets of boundary conditions, and comment on their relevance to geological history.
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valleys in creating lobes. However, although modelled extent matches reality reasonably well, the LGM surface elevation of over 2250 m far exceeds the elevation suggested by geomorphological or relative sea level constraints (ca Fig. 16). Figs. 7–9 show a comparison of LGM time-slices for simulations with different key boundary conditions. Figs. 7a and 9a shows the simulation discussed above, compared in Fig. 7b and 9b with a simulation in which the mean annual temperature has been everywhere increased by 5 1C. The effect is to decrease the surface elevation to just less than 2000 m, dramatically reduce the extent of the divide area of basal freezing, reduce transverse velocity contrasts and make the ice sheet marginally less extensive. In contrast, Figs. 7c and 9c show a simulation in which the basal decollement parameter (tb) has been increased by a factor of 10 (see Section 7), dramatically changing the ice sheet structure, with strong streaming and extreme thermal contrasts between streams and inter-stream areas, although this has a lesser effect on peak ice elevation, which is reduced to just above 2000 m.
6. A uniform stiff bed condition 6.2. Modelling North Sea confluence 6.1. A British Isles Ice Sheet In these simulations we have assumed that the basal decollement parameter is everywhere given by tb ¼ 0:005 ma1 Pa1 , equivalent to assuming a universal rigid rock bed with sliding. Fig. 6 shows time slices for a simulation in which the flow law parameter f ¼ 3, and the LGM central England mean annual temperature is taken to be 0 1C. Ice sheet elevations in all figures are related to the modern, relaxed, topography. The ice sheet nucleates in the western Highlands, but its growth is rapidly outpaced by Grampian ice. There are cold basal temperatures over upland areas but basal melting under thicker ice in some of the major troughs (Fig. 6a2), leading to faster flow streams in these zones (Fig. 6a3), with the streams bi-furcating down-ice. Growth of the ice sheet is accompanied by slight migration of the main NE–SW ice divide towards the SE, and its extension into Ireland (Figs. 6b–c). The evolving thermal and velocity structure is one of cold basal conditions in upland areas, with temperate conditions under major upland troughs (although note that troughs less than 5 km in width are not resolved). Cold bed fingers extend outwards from upland zones into the lowlands, where they are zones of relatively low velocity separating warmer, faster flow zones. For example in Fig. 6a2–3, the Welsh Mountains have cold bed conditions, and similar conditions in the southern Pennines, the Yorkshire Moors and Lincolnshire Wolds also create cold zones in downstream lowlands. Overall, thickness, thermal regime and velocity vary radially, with concentric zonation disrupted by some transverse variation in thermal and velocity structure. There are no major ice streams, no major marginal lobes and the steep ice sheet profile minimises the effect of
The continental-maritime ELA transition was then changed from that in Fig. 5a–b, to investigate how initially independent ice sheets over the British Isles and Scandinavia might evolve to become confluent and then separate and decay. Our primary concern is to understand confluence-related processes in the North Sea, rather than to match specific geological constraints such as ice thickness or stream and lobe creation. If we accept the view of Sejrup et al. (1994) this could be taken as a simulation of glacial events in the North Sea region between about 29 and 24 ka. Alternatively, the simulation could be taken as reflecting conditions during the Saalian or Elsterian glaciations, when such confluence certainly occurred. The results are shown in Fig. 10. In this case model time should not be taken as a particular time before present. Strong growth of ice over south west Norway occurs by 25 ka (Fig. 10a) followed by ice sheet nucleation and growth over Scotland (Fig. 10b), by which time a welldeveloped ice stream had formed at the head of the Norwegian Channel because of its greater depth and warmer basal ice. Sea levels in the North Sea generally had been drawn down by the global lowering of sea level (Fig. 4c). By 20 ka (Fig. 10c), the ice divide over Scotland had extended into Ireland, the Norwegian Channel ice stream had extended and was flowing towards the north– west, and strong ice streams were flowing from Sognefjord, Hardangerfjord and the fjords of the Trondheim region onto the continental shelf. By 20 ka, and much more by 19 ka (Fig. 10d), ice was spilling over the western flank of the Norwegian Channel, and beginning to advance into the central-northern North Sea, where it was confluent with ice from Scotland by 18.5 ka (Fig. 10e), forming a low saddle,
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a1
a2
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Fig. 6. (a–d) Time slices of the modelled growth of an ice sheet over the Britain Isles for a uniformly ‘‘stiff’’ bed condition. The simulation is driven by the temperature, mass balance and ELA conditions shown in Figs. 4 and 5. The basal decollement parameter tb ¼ 0:005, the flow law parameter f ¼ 3, and the LGM standard mean annual temperature (T) is taken to be 0 1C. (a1–d1) show the surface form. (a2–d2) show basal velocities, with red areas as high velocities and white with zero velocities, and generally frozen bed conditions. (a) ¼ 22; (b) ¼ 20; (c) ¼ 18; d ¼ 17 ka. The LGM condition (17 ka) is compared with other simulations in Figs. 7–9.
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Fig. 6. (Continued)
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Fig. 7. (a–j) Examples of simulations of ice sheet form for LGM time slices, for the decollement parameter (t0), the flow law parameter (f), and the standard temperature (T) as follows. Bed conditions: (a–b) all ‘‘stiff’’, tb ¼ 0:005; (c–d) all ‘‘slippery’’, tb ¼ 0:05; (e–j) ‘‘slippery patches’’ (see Fig. 13), tb ¼ 0:05 with tb ¼ 0:005 elsewhere. Ice flow parameters: (a–f) f ¼ 3; g–j) f ¼ 10. Standard temperature: a,c,e,g, T ¼ 0 1C; b,d,f,h,i, T ¼ +5 1C; j, T ¼ +8 1C.
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Fig. 8. (a–j) Examples of simulations of basal temperatures for LGM time slices, for the decollement parameter (tb), the flow law parameter (f), and the standard temperature (T) as follows. Bed conditions: (a–b) all ‘‘stiff’’, tb ¼ 0:005; (c–d) all ‘‘slippery’’, tb ¼ 0:05; (e–j) ‘‘slippery patches’’ (see Fig. 13), tb ¼ 0:05 with tb ¼ 0:005 elsewhere. Ice flow parameters: (a–f) f ¼ 3; (g–j) f ¼ 10. Standard temperature: a,c,e,g, T ¼ 0 1C; b,d,f,h,i, T ¼ +5 1C; j, T ¼ +8 1C. Melting point temperatures are shown in red, sub-melting point temperatures in white.
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Fig. 9. (a–j) Examples of simulations of basal velocities for LGM time slices for the decollement parameter (tb), the flow law parameter (f), and the standard temperature (T) as follows. Bed conditions: (a–b) all ‘‘stiff’’, tb ¼ 0:005; (c–d) all ‘‘slippery’’, tb ¼ 0:05; (e–j) ‘‘slippery patches’’ (see Fig. 13), tb ¼ 0:05 with tb ¼ 0:005 elsewhere. Ice flow parameters: (a–f) f ¼ 3; (g–j) f ¼ 10. Standard temperature: a,c,e,g, T ¼ 0 1C; b,d,f,h,i, T ¼ +5 1C; j, T ¼ +8 1C. High velocities shown in red and frozen bed areas with zero velocities in white.
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Fig. 10. (a–f) A simulation of the growth to confluence between a British Isles and Scandinavian ice sheet in the central North Sea. Boundary conditions are the same as in Fig. 6, with the domain extended to cover the whole area of the European ice sheet, the continentality pattern as shown in Fig. 5b to ensure confluence. Colours show surface velocities and arrows the flow vectors. Red shows high velocities, blue shows low velocities. Note the ice divide areas with low (blue-turquoise) velocities and the evolution of the Norwegian channel ice stream.
leading to divergence of ice to both north and south from the saddle. This then evolved into a Scotland–Norway ice ridge by the glacial maximum at 17.5 ka. The development of this saddle and the succeeding ridge blocked flow from the head of the Norwegian Channel, deflecting ice from the Skaggerak towards the south west, such that it ceased to
flow in a stream. The downstream part of the Norwegian channel continued to be a conduit for an ice stream, but one that was largely fed from the Sognefjord area of SW Norway. We are highly sceptical of the reconstruction by Sejrup et al. (2000), which shows an ice stream along the whole
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length of the Norwegian Channel at the maximum extent of a confluent North Sea ice sheet, and which demands an implausible pattern of flow and of divide geometry. In their reconstruction, the head of the ice stream lies in the Skaggerak and flows all the way along the Norwegian Channel to the continental shelf edge, a distance of some 800 km, at a time when the SW margin of the ice sheet was a mere 200 km south of the head of the Skaggerak, which necessitates a very highly asymmetric ice sheet profile, and without any mountains to prop-up one flank of the ice sheet. We are unable to simulate such a stream even by extreme adjustments of slipperiness and mass balance parameters. We suggest rather that the zone of streaming in the Skaggerak–Norwegian Channel was time transgressive in the way shown in Fig. 10. During ice sheet growth, the ice divide over northern Britain migrates in a south easterly direction, and whilst relative sea levels are low in the central North Sea, they rise in the vicinity of the growing ice sheet due to isostasy. Although we do not show the simulation of decay, the pattern is essentially a reversal of build up, with the difference that relative sea levels are higher and the rate of decay is faster. This points to a way of explaining how a Sejrup et al. (1994) North Sea ice sheet could have developed and collapsed before the LGM. If calving were more powerful in the isostatically high sea levels that developed as the ice sheet expanded, it might produce a negative feedback, causing the North Sea part of the ice sheet to collapse. We remain sceptical, however, that Scottish ice could have been a contributor to a North Sea ice sheet in the period between 30 and 24 ka in view of apparently contemporary non-glacial conditions in central Scotland (Boulton et al., 1991). 7. A uniform soft bed condition 7.1. Boundary conditions In these simulations the ELA driver is held constant. We have, however, assumed that the bed is everywhere softer, with the basal decollement parameter uniformly an order of magnitude larger than in Section 6, with tb ¼ 0:05 ma1 Pa1 . We have then explored the effect of varying the standard temperature and the flow law parameter f.
such as those in the Irish Sea, and the fast streams draining from west to east through the Pennines down the Tyne and Tees valleys (Fig. 11d2–3), others are unrelated to topography. Moreover, the streams in topographic depressions lose their strength from time to time, and streams unrelated to topography die and are replaced by others in different locations. Fig. 12a–c shows time–distance diagrams of the fluctuations of the ice sheet margin and the basal thermal regime along transects through the ice sheet (see Fig. 12d for locations). Fig. 12a and b show longitudinal transects in the Irish Sea and off the east coast of Britain, respectively. Prior to and after the glacial maximum, they show strong unforced oscillations of the margin, particularly strongly in the Irish Sea area. The two major Irish Sea oscillations between 22.5 and 19 ka show clearly that rapid advances of the margin of the order of 50–100 km/100 years are associated with warm bed conditions in the outermost 100–150 km, followed by cessation of advance. Subsequent retreats of the order of 50 km, are associated with a rapid change to warm bed conditions. This occurs as a consequence of a ‘‘creep instability’ (ca Clarke et al., 1977). Warming of the bed leads to fast decollement, this creates strong cold ice advection from the interior into the marginal zone, so that freezing, no-decollement, conditions develop. The flow velocity, therefore, decreases and the margin retreats. This dynamic behaviour occurs all around the ice sheet. It involves the development of ephemeral streams, stream switching, and local readvances which are not coeval along different parts of the ice sheet margin and which are smaller where the flowline length is smaller (shorter readvances on transect C compared with transect A) and where the ice sheet calves into deep water (compare the western with the eastern end of transect B). This behaviour can be regarded as surging, and reflects internal, unforced dynamic oscillation. Although at any one time, the area of the ice sheet bed that is undergoing erosion/transport/deposition is small (assuming that these processes are significant only during phases of decollement), the frequent shifts of the locations of streaming ensure that a large part of the bed does suffer strong erosion, although the rates of erosion vary greatly in time and space. This could explain why in some glaciated regions, discrete lineation sets are superimposed one upon another (Boulton and Clark, 1990).
7.2. The nature of the ice sheet—dynamic streaming 7.3. The match with geology Fig. 11 shows time slices for a simulation in which the flow law parameter f ¼ 3, and the LGM central England mean annual temperature is taken to be 0 1C. There is a strong contrast with the previous simulations. There are well-defined marginal lobes located along topographic depressions, well defined linear zones of basal melting flanked by frozen bed zones, and fast streams located along the axes of basal melting. Although some of the zones of melting and streaming lie along topographic depressions,
The extent of the ice sheet fits relatively well with geological evidence. The lobe structure at the southern margin of the ice sheet at the LGM (Fig. 11) matches well with those identified geologically, in the Irish Sea, the Cheshire Plain, west of the Lincoln Wolds, east of the Wolds and west of the Dogger Bank, and into the Wash and northern east Anglian regions. The fit is less good in Wales, where there is an unglaciated re-entrant in the lee of
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
Boulton et al. (1991). However, thermal-mechanical coupling prevents this, as generalised fast flow draws down cold ice from the ice sheet summit area, which slows the flow and steepens the ice sheet. The creep instability, therefore, restrains the development of a low ice sheet slope, and, therefore, of a low summit elevation. Consequently, a large decollement factor (tb) over a wide area of the bed is not a strategy for reducing ice sheet thickness unless the surface temperature is very high, because of the restraining effect of enhanced cold ice advection. This thermal-mechanical forward model demonstrates that the low summit elevation inverse model shown in Fig. 2b (Boulton et al., 1991), which assumes a
the North Wales mountains, and in southern Ireland, where the ice sheet is less extensive than indicated by geology (Fig. 1). The model generates a ridge over northern Ireland. It also generates a cold-based ridge west of the Lake District and into the Cheshire basin (a possible though unlikely feature), and another over the Island of Skye in western Scotland, although it does not create a separate dome over the outer Hebrides. The peak ice sheet elevation of just over 2000 m is, however, far in excess of that assumed from geological constraints. We had assumed that ‘‘softening’’ the basal boundary would lower the mean slope and therefore the summit elevation of the ice sheet as was done by
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Fig. 11. (a–d) Time slices of the modelled growth of an ice sheet over the Britain Isles for a uniformly ‘‘slippery’’ bed condition. The simulation is driven by the temperature, mass balance and ELA conditions shown in Figs. 4 and 5a. The basal decollement parameter tb ¼ 0:05, the flow law parameter f ¼ 3, and the LGM standard mean annual temperature (T) is taken to be 0 1C. (a1–d1) show the surface form. (a2–d2) show the area of where basal temperatures are at the melting point in red and below the melting point in blue. (a3–d3) show basal velocities, with red areas as high velocities and white frozen bed areas with zero velocities. (a) ¼ 22; (b) ¼ 20; (c) ¼ 18; (d) ¼ 17 ka. The LGM condition (17 ka) is compared with other simulations in Figs. 7–9.
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uniformly low shear stress in all current sea areas about Britain, is not a satisfactory explanation of a low summit elevation. 7.4. Influence of temperature Simulations in which the mean surface temperature is increased by 5 1C cause a lowering of the surface, through its effect on ice flow, with a summit elevation of about 1750 m (Fig. 7d), although with a much less lobate margin which falls far short of the southern margin of the real ice sheet. Basal melting is much more general in the outer part of the ice sheet (Fig. 8d) and associated with broader
marginal zones of relatively high velocity (Fig. 9d). A major contrast is the failure to generate unforced oscillations of the margin. This is because the higher ice sheet surface temperature is sufficient to diminish the cooling effect of cold ice advection from the interior and therefore largely suppresses the dynamic effects of creep instability. 7.5. Influence of the flow law parameter Increasing the flow law parameter from f ¼ 3 to f ¼ 10 produces output intermediate between the two above simulations in terms of ice thickness, extent, stream and lobe structure. The dynamic oscillations have a smaller
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
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Fig. 12. (a–d) Time-distance transects across the modelled ice sheet for a simulation with everywhere a ‘‘slippery’’ bed ðtb ¼ 0:05Þ, a flow law parameter f ¼ 3, a standard temperature of T ¼ 0 1C, using the climatic drivers as in Figs. 4 and 5a. Melting point temperatures are shown in red and brown and submelting point temperatures in blue. (a) Longitudinal transect down the Irish Sea basin. (b) Transect down the east coast of Britain. (c) Transect across Scotland. (d) Locations of transects.
amplitude but a higher frequency, because of the higher rate at which cold ice from the interior is advected towards the margin. 8. Simulating the effect of spatially varying basal boundary conditions 8.1. Boundary conditions In view of the very low ice sheet slopes (and shear stresses) that have been deduced for soft-bed zones of ice sheets (e.g. Miller et al., 2002; Mathews, 1974), implying
much easier local decollement, we have applied a decollement parameter of tb ¼ 0:05 ma1 Pa1 to restricted areas of the bed where soft sediments may play an important role, but with a value of tb ¼ 0:005 ma1 Pa1 for other areas. Most of the softest sediment basins occur in the offshore zone. Unfortunately, geological evidence of their precise nature and extent at glacial horizons is poor. We have assigned the easy decollement parameter to the areas shown in Fig. 13: to the Irish Sea and southern North Sea where major lobes occurred, to the sea area off the Forth valley, which has widespread evidence of strong ice drawdown, and to the shelf troughs of the Moray Firth
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
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are in ice sheet thickness (Fig. 7e–j), basal thermal regime (Fig. 8e–j) and basal velocity structure (Fig. 9e–j). Warmer simulations generate ice sheets with lower surface elevations, more restricted zones of basal freezing in the core of the ice sheet and different velocity distributions. They show lower velocities in the major ice streams and higher velocities in the inter-stream zones compared with colder simulations. This occurs because of the greater concentration of flow in the fixed streams in the colder cases. The concentration of flow in major fixed streams suppresses the creep instability shown in Fig. 12. Funnelling into these streams of flanking, warmer ice offsets the cold ice advection effect from the divide area, so that fast flow does not automatically create a negative feedback, and the stream is maintained. Large fixed streams therefore draw down the ice sheet surface more effectively than a ubiquitous ‘‘slippery bed’’. We suggest that bed-controlled localised streaming may be the vital process leading to a low surface elevation rather than the ubiquitous soft bed condition used by Boulton et al. (1991).
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britain2.10km.nc 0.00ka
Fig. 13. Locations of assumed ‘‘slippery’’ patches of bed where the decollement parameter is taken as tb ¼ 0:05, in contrast to all other areas of the bed, where there is a stiff bed condition given by tb ¼ 0:005.
and north and south of the Hebrides, which could have had a strong influence on ice in the Highlands of Scotland. We could also have chosen other marine trough areas such as the Firth of Clyde and Solway Firth. They are all troughs in which fine-grained sediments were or could have been present during the Late Weichselian. As before, the climate driver and other boundary conditions are held constant, and the effect examined of varying mean annual temperature between limits of 5 and +8 1C compared with the central England standard of 0 1C at the LGM. The flow law parameter f has been varied between 3 and 20.
The simulations of the series in Figs. 7e–j fit well with geology in terms of extent, but of these, Figs. 7h–j bring down the ice sheet surface closest to the trimline elevation in the northern Highlands, if this is regarded as a marking the maximum LGM ice sheet surface elevation. The large fixed streams play a crucial role in this regard. All three are characterised by a large flow law parameter, and a relatively high standard LGM temperature. The modelled evolution of the ice sheet is illustrated in Fig. 14, by a sequence of time slices for the simulation in Fig. 7i. We summarise below the behaviour of the model during ice sheet growth and decay, and go on to compare these results with features of ice sheet behaviour inferred from geological evidence. Initiation—Fig. 14a
8.2. Ice sheet form and structure
Figs. 7–9, e–j, show examples of the variation in form, thermal regime and basal velocity for simulated LGM ice sheets with spatially varying basal boundary conditions. The effect of fixed slippery patches is to fix the locations of major ice streams, although smaller, slower and ephemeral dynamic ice streams continue to exist between them. The extent of the LGM ice sheet and the general form of the margin are similar in all simulations. The contrasts
The initiation and early growth of the ice sheet occurs from centres in the NW Highlands. The principal flow divide then migrates rapidly eastward to the Grampians as the ice sheet expands beyond the Scottish coast. The prescription of a fast decollement zone covering the whole Moray Firth sector tends to distort the ice sheet and extend it further to the east than would otherwise have occurred. Elsewhere, strong streams develop without the assumption of a locally slippery bed. In the SW sector, there is strong flow down the Firth of Lorne, down valleys in the southern Highlands, and from the SE Highlands towards the Tay and Forth. In the west, there is strong westward flow south of Skye into the head of the assumed soft bed axis south of the Hebrides (Fig. 13), whilst north of Skye, significant streams develop in Wester Ross and northern Torridon.
ARTICLE IN PRESS G. Boulton, M. Hagdorn / Quaternary Science Reviews 25 (2006) 3359–3390
Highland valleys that are sufficiently wide to be resolved by modelling are occupied by warm-based ice whilst higher areas are cold-based.
the Antrim coast flowing SW. These flows are deflected around the Merrick mountain area of SW Scotland, which is able to be a local flow centre. None of these streams is pre-determined by the assumption of a soft bed. The prescribed soft bed axis south of the Hebrides draws down ice strongly from western Scotland, drawing ice towards it in a westerly direction from the Firth of Lorne, over Mull and Islay. The northern Hebridean soft bed axis draws down ice from Torridon and the northern Highlands. The effect of these two zones of drawdown is to cause mainland-derived ice to be deflected around the outer Hebrides, which starts to develop into an independent dome. The ice sheet reaches
Growth 2—Fig. 14b
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the continental shelf edge west of Scotland by this stage. Off eastern Scotland, apart from the Moray Firth stream, which may or may not prove to have been a reality, a strong stream develops in the Firth of Forth, largely fed from the Strathmore area. The Lammermuir–Cheviot hills cause ice to be deflected around them, producing locally strong flanking streams. A stream begins to develop near the ice sheet margin along the east coast of England, largely fed by ice deflected towards the SE by the Pennines. LGM—Fig. 14c
There is a strong contrast between the LGM simulations with a colder temperature driver (Figs. 7–9, e–g), which
shows more extensive cold-bed conditions and numerous dynamic streams in addition to the fixed streams, with those driven by warmer temperatures (Figs. 7–9, f, h–j), dominated by the fixed streams and almost no ‘‘dynamic’’ streaming. A major ridge has developed over Ireland. A major ice stream has developed in the Irish Sea, as a consequence of the prescribed soft bed, and fed by confluent flows from northwest England, southern Scotland and eastern Ireland. Some simulations show the stream reaching as far as the Scilly Isles. Ice flows eastward down the Tyne valley to contribute to the major east coast ice stream, and ice flows eastwards down more southerly cross-Pennine valleys to contribute to the stream that flows strongly between the
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Yorkshire Moors and Pennines. Ice flows from the Lancashire Plain and the Lake District to penetrate as a major lobe into the Cheshire Basin. Cold basal ice occurs along much of the ice sheet margin, which would have facilitated the incorporation of basal debris by freezing-on, and the development of extensive stagnation terrain (e.g. Boulton, 1972). At no time during ice sheet growth or the LGM was isostatic crustal depression at or beyond the ice margin sufficient to offset global sea level lowering to produce relative sea levels higher than present.
9. Comparison with geological evidence Although we have little direct evidence of the climate properties that drove the evolution of the British ice sheet, the available evidence and the strong constraints on climate that ice sheet extent and elevation impose, suggest that our climate drivers are appropriate: a typical North Atlantic vertical mass balance gradient, relatively high mean annual temperatures at the LGM, and a strong W–E gradient of continentality. Moreover, the best-fit simulations for extent (Fig. 7c–j) and for elevation (Fig. 7h–j) produce generally repetitive patterns of glacial evolution. There are four major uncertainties:
Were ice streams restricted to fixed, lobe-generating streams whose locations were determined by bed properties (Fig. 9f, h–j), or did more ephemeral streams also occur, that were a reflection of internal dynamic changes (Fig. 9c–e, g)? Did unforced, asynchronous oscillations of the ice sheet margins and of thermal and flow regimes occur as shown in Fig. 12? How extensive were the zones of basal freezing in the core area of the ice sheet? How serious is our failure to bring down the modelled ice sheet surface to match the levels suggested by Ballantyne et al. (1998) based on the weathering trimlines in the northern Highlands and Hebrides? (See Section 10).
The simulations demonstrate the glaciological probability of a major stream and lobe in the southern Irish Sea/ Celtic Sea, and the credibility of the concept (e.g. Mitchell & Orme, 1967; Scourse & Furze, 2001) that a lobe extending to or beyond the Scilly Islands could be consistent with the LGM ice margins on land in SE Ireland and SW Wales. They also show that a powerful ice stream down the east coast of England could readily be created by ice draining in an easterly direction through the Pennines and from SE Scotland and demonstrate a tendency for the stream to bifurcate at its head, with one sub-lobe penetrating the Wash embayment and one between the coast of east Anglia and the Dogger Bank, as has been suggested by the reconstructions of Straw (1991) in the Wash Basin and Balson and Jeffrey (1991) in
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the offshore zone. The scepticism of Boulton et al. (1977; 1991) about the glaciological credibility of this lobe appears to have been unfounded. The patterns of topographically and dynamically controlled fast flow shown in Figs. 9 and 14 show remarkable similarities to the patterns of flow inferred from studies of indicator erratic dispersal by workers such as Walden et al. (1992) around the northern Irish Sea and SW Scotland, by Raistrick (1926) in the Pennines and eastern England, by Everest et al. (2005) in the Tweed valley in SE Scotland, with ice streaming around the Cheviot Hills. The model supports the interpretation of localised ‘‘trains’’ in which the erratic flux was particularly strong along zones of fast, streaming flow. The effect of the modelled streams passing north and west of the Hebrides (Fig. 9) in drawing down ice and creating the dome over the outer Hebrides (Fig. 7) is consistent with the geological evidence of an ice dome or ridge, reflected by easterly and south-easterly directed striations in the east and westerly directed striations in the west of the islands (Peacock, 1991). In Ireland, the best fit LGM simulations, (apart from Fig. 7–9a,b and e which generate too great a glacial mass) show an ice sheet margin lying further to the north than indicated by geology. Correcting this probably requires a much stronger local depression of the ELA than we have used, implying more highly maritime conditions. Clark and Meehan (2001) have created a new interpretation of the LGM distribution of ice flow and divides in central Ireland based on the identification of overlapping ice flow sets inferred from the pattern of ribbed moraine. They identify three sequential ice sheet phases. The first reflects southwesterly flow from SW Scotland, which we simulate (Fig. 14b); the second, which they presume to represent the maximum, with a N–S divide in eastern Ireland, is one we come close to simulating in Fig. 7–9e–h; and a final ice sheet phase when the divide migrates towards the NW, which we do not succeed in simulating. We are confident that the model could be fine-tuned to adapt to this data by adjusted the climate or decollement parameters. The model readily creates a major fixed ice stream in the Irish Sea. It is consistent with the evidence of Scourse and Furze (2001a,b) that the LGM ice sheet reached the latitude of the Scilly Islands (Fig. 1) and that deforming bed conditions were associated with a major ice stream in the Irish Sea (O´ Cofaigh and Evans, 2001a,b). The simulations (Fig. 12) that create major 50–100 km readvances of the margin of the Irish Sea ice stream is consistent with McCabe’s (1996) suggestion of rhythmic readvances of the ice sheet margin in the Irish Sea basin, and the sedimentary evidence of readvances presented by Evans and O´ Cofaigh (2003). Evidence of readvances during overall retreat of an Irish Sea ice stream (Fig. 1) may reflect such unforced oscillations rather than climatically-forced events. Evans and O´ Cofaigh (2003) have described localised tectonic thickening of till and associated sediments in successive belts, 30–50 km apart, lying parallel
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and near to the margin of the ice stream in south and SE Ireland. They then use Boulton’s (1996a) deforming bed theory, which relates variations in till thickness to fluctuations of the ice sheet, to deduce oscillations of an Irish Sea ice stream margin during retreat, which they suggest would have occurred on scales that are similar to the unforced oscillations of the margin shown in Fig. 12a. Although such re-loading events might be thought capable of generating the short-term relative sea levels above modern sea level argued for by Eyles and McCabe (1989), our simulations do not show this. Whether the entirely unforced ‘‘dynamic streams’’ that are predicted by the model existed must depend upon further geological investigation. There is strong evidence from the West Antarctic Ice Sheet that ice streams can be ephemeral, with one major stream having shut down about 150 years ago (Retzlaff and Bentley, 1993). Boulton et al. (2001) have suggested that fast flow in the major last glaciation ice streams in southern Finland has turned on and off, with one of them having a lifetime of some 200 years. Our simulations are able to create dynamic streams, such as those for example shown in Fig. 11 column 3, that have lifetimes of the order of 150–800 years. Although the grid size in our simulations is no smaller than 5 km, such that relatively narrow highland valleys are unresolved, the existence of warm basal patches along major valleys in our smoothed topography in highland areas that are otherwise cold based (e.g. Fig. 14), suggests that basal melting along valleys and their flanks will be much more widespread than appears (this issue is addressed further in Section 10). We expect that melting will occur along the floors and sides of most of such valleys even when mountain summits and plateau tops are subject to cold bed conditions. This contrast explains why highland valleys with signs of strong glacial erosion can co-exist with un-eroded higher mountain areas only a short distance away, such as occurs in the Cairngorms, where Tertiary weathering residues survive on plateau tops (e.g. Hall and Sugden, 1987). The simulation of a cold basal zone at the LGM ice margin in Fig. 14, with its potential to freeze-in large quantities of basal debris to create substantial areas of supraglacial stagnation topography on retreat (Boulton, 1972), accords well with the widespread presence of such topography near the southern margin of the ice sheet (e.g. Thomas, 1989). 10. Weathering trimlines and the elevation of the ice sheet surface We initially adopted the constraint on ice sheet surface elevation suggested by the work of Ballantyne et al. (1998) on the weathering trimline in the northern Highlands and the Hebrides of Scotland. It is, however, very difficult in our simulations to depress the ice sheet surface elevation to elevation of the trimline. Indeed, our models also throw doubt on the validity of the approach of Boulton et al. (1991) which did produce a model with a surface elevation
that matched the trimline. This leaves us with two options, to change ice sheet flow parameters to extreme values, for which we can find little physical justification, or to question whether the weathering trimlines do reflect the LGM ice surface, or whether they reflect a thermal interface within the ice sheet. A major problem is that of spatial resolution. We have used a maximum resolution of 5 km in modelling. Whereas this resolves parts of such valleys as the Great Glen, the Firth of Lorne and some western sea lochs, with widths in excess of 5–10 km, it fails to resolve the widths of many Highland valleys, which are typically less than 5 km. Highland topography is therefore a smoothed representation, with smoothed elevations that rarely exceed 500 m, intermediate between the elevations of peaks, typically around 1000 m, and the valleys. The barrier to increasing resolution to about 1 km, is that the steep valley-margin slopes which would then appear would require us to relax the small slope approximation that most modern models assume, and to incorporate longitudinal stresses in the model; a step currently beyond our computational resources. The principal effect of modelling at this high resolution would be to create small scale streaming of flow along Highland valleys, increasing the flow velocities along the valleys and reducing them along intervening interfluves (this would occur in addition to the streaming already modelled along wider valleys and troughs). We have tried to illustrate this effect in the following way. Typical interfluve widths in the NW Highlands are of the order of 4–8 km compared with valley widths of the order of 1–3 km. We assume that valley streaming would draw down a large proportion of the flow along interfluves, and, therefore, that valley flux would be at least 2–4 times greater than in our model. This would also apply in the sea areas further west, in the trough of the Sound of Raasay, east of Skye, for example. This would not decrease the slope of the ice surface (it would tend to increase it) but it would significantly warm the ice along valleys and troughs, without incurring the cold ice advection problem. We have, therefore, used a 2D, flowline version of the model along a valley/trough profile driven by the same temperature, ice softness and bed slipperiness functions as in the model shown in Fig. 14 and increased the valley flux by increasing the mass balance on the ice sheet surface by factors of between 2 and 4. Fig. 15 shows the effect of this approximately along the line of transect C (Fig. 12d) but with the elevation of nearby, approximately W–E trending valleys projected onto the line of section. The ice surface elevation and thermal regime are shown for 2D models using a standard temperature of 0 1C and standard mass balance in model 1, and +5 1C and 1.3 standard mass balance in model 2. Whereas the smoothed 3D simulation is associated with relatively widespread basal-freezing conditions in upland areas (e.g. Fig. 14, column 2), the valley streaming model shows how the elevation of the interface between temperate and sub-melting point ice is significantly increased, and the
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Fig. 15. Form of the two-dimensional, flowline model of the ice sheet at the LGM along transect B (Fig. 12d), designed to illustrate the effect of streaming along narrow highland valleys. The dashed lines show the elevation of the interface between ice below the melting point and underlying ice at the melting point. Model 1 is driven by a standard temperature of 0 1C and standard mass balance. Model 2 is driven by a standard temperature of +5 1C and 1.3 standard mass balance. The heavy line shows valley floor profiles on the land area and smoothed representations of the continental shelf. The heavy vertical lines show typical summit elevations of the highest peaks in each area, which tend to carry the evidence of weathering trimlines. The smoothed topography used in the 3D model lies between the valley profiles and the elevations of peaks.
frozen bed area much reduced. Moreover, all models show a maximum elevation of the freezing boundary that is time transgressive. Whilst recognising the simplifications inherent in this approach it does show that an interpretation of the weathering trimline as a transition zone between temperate ice and overlying ice below the melting point is plausible. We do not expect the transition simply to take place where overlying ice falls below the melting point, but within some sub-melting point temperature range, as the adhesive strength of the ice-rock interface is increasingly able to resist the shearing force that tends to disrupt the interface, and as we expect some liquid water to survive at the interface at sub-melting point temperatures. Stone et al. (1998) measured the 26Al/10Be ratio on rocks above the weathering trimline, which showed no evidence of prolonged cover by passive ice. However, our modelled duration of ice cover at elevations above the weathering trimline are of the order of 3–5 ka, which would not be enough to create a significantly observable impact on the 26 Al/10Be ratio. 11. Relative sea level constraints We have used forward models of a coupled ice sheet/ Earth system forced by imposed climatic parameters in which the ice sheet/Earth response is determined by climatic and physical ice sheet parameters. Deflection of the lithosphere as a consequence of differential ice and water loading and the changing volume of ocean water as a consequence of global glacier volume growth and decay
determine the pattern of relative sea level change. The capacity of a model to reproduce the observed pattern of change is an effective means of testing model compatibility with the sea level record. Fig. 16 compares modelled with observed relative sea levels (Shennan, pers. commun., 2000; see also Shennan and Horton, 2002) for the model in Fig. 14. The fit is good, but it does not imply that the modelled magnitude and distribution of ice loading in time and space is a unique solution, but merely that it satisfies the constraints. This is quite a different approach from those taken by Lambeck (e.g. Lambeck et al., 1998) or Peltier (e.g. Peltier et al., 2002) to deduce the loading history of the last British ice sheet. They use relatively full physical descriptions of the Earth, but the glaciers are simply represented by a load distribution, without any glacier physics. Their inverse models seek to deduce the pattern of loading of the lithosphere in time and space from the recoverable relative sea level history. The maximum spatial resolution of ice sheet form is about 100 km and the inversions necessarily lack any glaciological information apart from this. The approach also suffers from the difficulty that apart from the partially known relative sea level record, neither ice loading history nor Earth properties are known a priori. The evidence of weathering trimlines in the Scottish Highlands, if interpreted as an indicator of the LGM ice surface, constrains at least part of the ice loading history, and Peltier et al. (2002) have used this to adjust Earth properties so that the inversion lowers their previous estimation of ice thickness in the Highlands, in ICE-4G
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(Peltier, 1998), from about 2 km to about 1 km. It is thus crucial that the significance of the trimline is unequivocally established. Our simulations of relative sea level change, in which relative sea levels lie below modern sea levels during the whole of the deglacial phase in the central and southern Irish Sea are incompatible with the view of Eyles and McCabe (1989) that the so-called ‘‘Irish Sea tills’’ exposed around the shores of the Irish Sea basin represent high deglacial sea-levels. They are, however, compatible with the view of Scourse and Furze (2001) that sea level high-stands in the area are of interglacial age. 12. Deduced glaciological properties Part of the purpose of the simulations presented in this paper is to use the properties of models that match geological evidence as indications of the glaciological properties of the real ice sheet. Not only, therefore, are we able to deduce patterns of time-dependent structural organisation that are compatible with geological data but also to infer quantitative glaciological properties. A strong conclusion of our modelling is the importance of major ice streams in controlling the form and flow of the ice sheet, the pattern of dispersal of indicator erratics and the patterns and rates of erosion, transport and deposition in time and space, which will be discussed in a later article. We are also able to estimate some quantitative properties of the ice sheet. For example, Fig. 17a,b shows calculated properties along transects through the Irish Sea ice stream at the LGM for the simulations shown in Fig. 14. The lines of section are those shown in Fig. 12. Fig. 17a shows a section along the ice stream and Fig. 17b across the stream. Basal velocities along the stream increase to a maximum of about 600 ma1 and then decrease towards the terminus, with the contribution of basal velocity to the total horizontal glacier velocity being greatest where basal melting occurs. This velocity profile is consistent with that required to generate the till thickness variations described by Evans and O´ Cofaigh (2003) and predicted by Boulton, 1996a, b). The transverse section clearly shows the location of the major stream along the axis of the Irish Sea trough, abutting against the Welsh hills to the right and the Irish coast to the left (ca Fig. 9i). It also shows that velocities are highest in the zone where the basal melting rate is highest. Velocities of these magnitudes are common in the streams in all simulations. In areas of basal melting away from the strongly streamed areas, basal velocities in the terminal zones of the LGM ice sheet are in the range 50–200 ma1. In terminal zones of no basal decollement, surface velocities are of the order of 10–50 ma1, more than an order of magnitude less than the surface velocities of adjacent streams. Basal shear stresses vary considerably through the ice sheet, from about 15–25 kPa, 100–200 km from the margin in the Irish Sea stream at the LGM, to 70–110 kPa in the mountainous areas of central Scotland.
The distribution of the ice flux also varies considerably. For the models such as those in Fig. 9a,b, none of the ice flux is delivered via fast streams. For models where basal decollement only occurs in highly localised streams (e.g. Fig. 9c), over 84% of the ice flux is delivered to the margin via fast streams. Where basal decollement takes place both in streams and inter-stream zones, between 75% (in Fig. 9e) and 60% (in Fig. 9j) is delivered via streams.
Acknowledgements This work has benefited from discussions and assistance from Nick Hulton, Tibor Dunai, Kurt Lambeck, Sergei Zatsepin, Roy Thompson and an anonymous referee.
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