Reconstructing past glacier dynamics and erosion from glacial geomorphic evidence: Snowdon, North...

JOURNAL O F QUATERNARY SCIENCE (1 989)4 (2) 1 15-1 30 @ Longrnan Group UK Ltd 1989

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Reconstructing past glacier dynamics and erosion from glacial Snowdon, North Wales

geomorphic evidence:

MARTIN SHARP Department of Geography, University of Cambridge, Cambridge CB2 3EN, UK JULIAN A. DOWDESWELL Department of Geography, University College of Wales, Aberystwyth SY23 3DB, UK J . CAMPBELL GEMMELL Christ Church, Oxford, UK

Sharp, M., Dowdeswell I . A . and Cernrnell I Campbell 1989 Reconstructing past glacier dynamics and erosion from glacial geomorphic evidence: Snowdon, North Wales. lourndl of Qudfernary Science, Vol. 4, pp. 1 15-1 30. ISSN 0267-81 79

Received 3 lune 1988 Revised 19 luly 1988

ABSTRACT: Bedrock surfaces exposed around Llyn Llydaw, North Wales demonstrate contrasting styles of erosion beneath a Late Devensian ice sheet and a Loch Lomond Stadial (LLS) valley glacier. Ice sheet erosion involved lee-side fracturing, surface fracture wear ,md abrasive wear, while LLS erosion was primarily by abrasive wear. Preservation of ice sheet erosional features indicates limited rates of erosion during the LLS. Analysis of the geometry and distribution of erosional markings suggests that the low erosional capacity of the LLS glacier was due to a low basal sliding velocity. This prevented the formation of lee-side cavities, reduced the debris flux over the bed and minimised particle-bed contact loads. Reconstructions of the mass balance and geometry of the LLS glacier indicate that most of its balance velocity could be achieved by internal deformation alone. A combination of low subglacial water pressures and an unusually rough substrate explain the low sliding velocities. High bed roughness is due to the absence of leeside cavities and a change in flow orientation between ice sheet and LLS times, which meant that the LLS glacier was in contact with roughness elements which were generated in cavities beneath the ice sheet.

Jourml of Quaternary Science

KEYWORDS: Glacial erosion, glacier dynamics, Loch Lomond Stadial, North Wales.

Introduction

Reconstruction of ice dynamics and erosion at the base of past glaciers from glacial geomorphic evidence requires consideration of several key parameters. The extent and thickness distribution of former glaciers and contact conditions at the ice-rock interface are fundamental. The dimensions of former glaciers can be derived from such evidence as the position and elevation of trimlines and of terminal and lateral moraines. Contact conditions can be inferred from detailed analysis of the geometry of erosional features such as striations and crescentic fractures, and of their distribution in relation to the topography of larger scale glacial bedforms. Information on the mass balance of former glaciers is also required in any dynamic reconstruction, and these data can be obtained from modern analogues. This paper used glacial geomorphic and mass balance data to reconstruct ice dynamics and erosion in the Snowdon area of North Wales, UK (Fig. 1 ), where ice cover in the form of both an ice sheet and a small valley glacier was present at different times in the Late Devensian.

The Snowdon area

The Snowdon area (Fig. 1 ) was selected for study because the

presence of particularly well-preserved glacial erosion features and moraine sequences allows reconstruction of former ice mass dimensions and ice-bed contact conditions (Gray and Lowe, 1982). During mid-nineteenth century mining oper- ations the level of Llyn Llydaw, the lake occupying the glacial trough surrounded by the ‘Snowdon Horseshoe’ (Fig. 11, was lowered by about 4m. As a result, a number of glaciated bedrock hummocks (composed of tuff and ignimbrite) were exposed (Fig. 2), probably for the first time since they were last ice-covered during the Late Devensian, over 10000 years ago. The surfaces of these hummocks display particularly fresh erosional markings, and appear to have experienced two episodes of erosion, associated respectively with ice flows from the south west and from the west (Gray and Lowe, 1982). Striations produced by the earlier ice movement were weathered before the younger set of striations was formed, suggesting that the features developed in two discrete glaciations rather than at different stages of the same glacial event (Gray and Lowe, 1982; Gregory, 1986). Gray and Lowe (1 982) proposed that the older striations were formed when the area was covered by the Devensian ice sheet, and that the younger set was formed during the Loch Lomond Stadial (LLS) (Younger Dryas) when a valley glacier occupied the Snowdon Horseshoe (Gray, 1982). Ice flow direction i s believed to have changed between the two phases because the ice sheet was sufficiently

116 JOURNAL OF QUATERNARY SCIENCE

1 Joints in the bedrock (Fig. 3b) 2 Rock chips removed by fracture of the bedrock surface

(Fig. 3b) 3 Lee-side fracture surfaces (Fig. 3c) 4 Lee-side cavities (defined as areas down-flow of lee-side

fracture surfaces, which lacked striations from the south west - north east phase of flow) (Fig. 3c)

5 The mean orientation of striations related to each of the two phases of flow in each grid square. These were then mapped as an integrated pattern of ice flow across the area (Fig. 4a-b)

6 The orientation of striations on the floor of the lee-side cavities (Fig. 4c).

Figure 1 mapping site and the patterns of ice flow reconstructed for the ice sheet and Loch Lomond Stadia1 valley glacier (after Gray and Lowe, 1982). Contours are in metres.

The Llyn Llydaw basin, showing the location of the

thick to submerge the bedrock topography and flow into the Llanberis Passacross theeasternend oftheCribGoch ridge(Fig. 1). By contrast, the valley glacier was constrained by the bedrock topography to flow eastwards from the Llyn Lydaw basin into Cwm Dyli (Fig. 1).

The bedrock hummocks are streamlined in relation to the ice sheet flow direction, and extensive lee-side fracturing occurred during this phase of erosion (Gray and Lowe, 1982). The ice sheet also eroded its bed by abrasive wear (producing striations) and by contact-induced surface fracture wear (producing crescentic cracks and gouges). By contrast, erosion during the LLS was mainly by abrasive wear, and was insufficient to remove completely striations produced by the ice sheet. This limited LLS erosion i s problematic, since erosion rates beneath contemporary valley glaciers can be on the order of millimetres per year (Drewry, 1986). As the LLS in North Wales may have lasted up to 1000 years (Gray, 19821, much greater amounts of erosion, and complete removal of pre-existing striae, might be expected. The observation that abrasion rates were apparently very low, and that surface fracture wear and lee-side fracturing were suppressed during the LLS, i s thus of considerable glaciological interest. The analyses presented in this paper attempt to explain this apparent anomaly.

Methods

Contact conditions at the former glacier bed are inferred from detailed studies of the geometry and distribution of erosional markings, such as striations and crescentic fractures, and their relationship with the topography of larger scale bedforms. Detailed mapping of the topography and geomorphology of a small (170m') bedrock hummock at the eastern end of Llyn Llydaw was carried out (Fig. 3a). The area was surveyed by laying out a 1 m by 1 m grid, and mapping the location and relative elevation of the corner points of the grid squares with a Wild T2 theodolite and Kern DM102 electro-optical distance meter (Fig. 3a). Elevations were contoured by hand at an interval of 0.2m. The topographic map was then used as the basis for geomorphic mapping. Features mapped included:

To provide a measure of the roughness of the glacier bed parallel to each of the flow directions, we surveyed two detailed elevation profiles across the bedrock (Fig. 5). Points were located at intervals of 0.05 m along these 12.8m long profiles, which were selected to provide the maximum possible profile length given available bedrock exposure. Survey accuracy is k0.003 m for position and f0.005 m for elevation.

The reconstruction of LLS glacier dimensions from glacial geomorphic evidence has already been undertaken by Gray (1982), and the details of the method are presented there. Although there are some difficulties in reconstructing the dimensions of LLS glaciers, particularly in their accumulation areas where evidence is sparse, our field experience broadly supports Gray's reconstruction and we therefore combine it with modern mass balancedata from Nigardsbreen, Norway, in our modelling. The justification for selecting these mass balance data i s given below.

Results

The bedrock hummock is elongated parallel to the ice sheet flow direction (40°/2200) and shows a distinct asymmetry in this direction (Fig. 3a). The south west side of the bump slopes 10" SW, while the north east side slopes 26" NE. The north west side of the bump is, however, higher than the south east side, producing an additional north west - south east asymmetry, with the steepest slopes on the north west side. The amplitude of the hummock is about 2m, and the wavelength about 10m. There are two distinct high points along the ridge on the north west side of the bump (Fig. 3a).

Hummock morphology relates closely to jointing patterns in the bedrock (Fig. 3b). Two main joint sets were identified, aligned at 45"/225" and 140"/320". The long axis of the bump thus lies parallel to the 45" set, and the high ground at the north west margin is located where the spacing of joints in this set is above average. Lee-side fracture surfaces are often associated closely with joints of the 140" set, although some have clearly eroded backwards from an origin at the location of a joint (Fig. 3c). The majority of the rock chips removed by bedrock fracture are also located along joints (Fig. 3b). Bedrock joints thusexerta strong control on the pattern of rock fracture. Their role may have been particularly significant because the two major joint sets are orientated approximately parallel to and normal to the ice sheet flow direction. The change in orientation of flow relative to the joint sets which occurred during the LLS may thus have been a contributory factor to the limited amount of erosion by fracturing during that period.

Striation patterns developed during the ice sheet flow phase indicate flow parallel to the long axis of the bedrock bump, with

RECONSTRUCTING PAST GLACIER DYNAMICS AND EROSION FROM GLACIAL GEOMORPHIC EVIDENCE: SNOWDON, NORTH WALES 117

Figure 2 (a) View ot the bedrock bump mapped in detail in this study. The Loch Lomond Stadia1 glacier flowed directly towards the viewer. (b) Bedrock bump viewed from the north, showing the north-west/ south-east asymmetry.

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cavities do, however, show some striations, usually aligned at around 100"to 12O0(sub-parallel tothelongaxesofthecavities) (Fig. 4c). These striations are aligned almost at right angles to the ice sheet flow direction, but obliquely to the LLS flow direction. Furthermore they show no sign of the red weathering skin found in some ice sheet striations (Gray and Lowe, 1982). We therefore suggest that as ice flowed over the crest of the bump during the LLS, it was channelled into these troughs in the bedrock, setting up a weak secondary flow parallel to their long axes. Although the striations produced by this flow are generally short and relatively shallow, indicating weak ice-rock contact, i t appears that extensive areas of bedrock which were separated from the glacier sole during the ice sheet flow phase were in contact with the sole during the LLS. Although i t is clear that the intensity of striations formed during the LLS decreases as flow passed from the stoss to the lee-side of the bump, we have been unable to find any areas in which there is evidence for extensive ice bedrock separation during the LLS. We thus infer that while 75% or less of the glacier bed was in direct contact with the base of the ice sheet, virtually 100% of the bed was in contact with the base of the LLS glacier. This has considerable implications for the frictional resistance to glacier sliding in the two phases of flow, and for the potential for lee-side fracturing.

Mechanics of glacial erosion SNOWDON - LOCH LOMOND STADIAL

Lee-side fracturing

:::I , , , , , , , 0

0 2 4 6 8 10 12 14 16 Distance (m)

Figure 5 (b) the ice sheet flow direction with cavitation; and (c) the Loch Lomond Stadia1 flow direction.

Bed elevation profiles for (a) the ice sheet flow direction;

slight divergence around its upstream end and stronger conver- gence in its lee (Fig. 4a). Striations related to this phase of flow are not well-preserved on the steep north west side of the bump, where they have been largely obliterated by erosion during the LLS. They are, however, very well exposed on the south east side of the hummock, where they would have been in a lee-side location relative to this later phase of flow. Striations formed during the LLS are aligned obliquely to the long axis of the bump, and they too indicate flow divergence around the bump with a relatively strong convergent flow directed towards 110" on the lee side (Fig. 4b). The density and depth of this set of striations decrease markedly across the crest of the bump (Fig. 61, as flow shifted from a stoss to a lee-side location. There was thus a strong stoss-lee contrast in intensity of erosion during the LLS which resulted in differential preservation of ice sheet striations.

Ice sheet striations are also missing from four broad areas orientated at approximately 1 30"/310" across the bump (Fig. 3c). All these areas are depressions in the bedrock surface downstream from bumps or ridges with well-developed lee-side fracture surfaces. We thus interpret them as the sites of lee-side cavities during the ice sheet flow phase. The floors of these

To understand why lee-side fracturing occurred beneath the ice sheet, but not beneath the LLS glacier, the mechanics of the process are considered. Boulton (1 974) demonstrated that large scale fracturing of subglacial bedrock can be caused by the stresses induced in bedrock by pressure fluctuations which occur as ice moves over bedrock bumps. Lee-side fracturing is favoured because shear stresses are maximised on the down- glacier flanks of bedrock bumps, and because bedrock strength, which depends in part on frictional strength derived from the ice overburden, i s minimised in lee-side areas of low pressure. This is particuarly so when lee-side cavities exist, because the frictional component of strength is zero in cavities. Boulton (1 974) showed that the tendency towards failure can usefully be measured by a 'safety factor' (SF), given by the ratio of rock strength to applied stress, with failure occurring at SF < 1. Boulton gives two equations for the safety factor. When lee-side cavities exist:

SF = T J ( ~ .25qV/X) + (0.188 pigh)) (1 1

With no cavitation, this is modified to:

SF = (7, + (pgh - (1 OqVIX) tan cp))/(3.13qV/h) ( 2 )

here T, is the cohesive strength of bedrock (taken to be 500 kPa), q i s the viscosity of ice (taken as 3.15 x 10'' Pa s-'), V i s the glacier sliding velocity, h i s the wavelength of the bedrock bump (lorn), pi i s the density of ice (900kg m-?, g i s acceleration due to gravity, h i s ice thickness, and tan cp i s a coefficient of internal friction (taken to be 0.7). These equations assume that bedrock bumps have an amplitude to wavelength ratio of 1/4, relatively similar to the shape of the bedrock bumps measured in this study. They permit an assessment of the likelihood of bedrock failure given known conditions of ice thickness and sliding velocity. We therefore need to estimate values for these parameters under both the ice sheet and LLS glacier.


Figure 6 crest of the bedrock bump. Heavy striations on the left of the picture were produced by the Loch Lomond Stadia1 glacier. On the right of the picture, these striations become less well-developed and cut across striations produced by the ice sheet. Note that fractures on the right of the picture are aligned perpendicular to the ice sheet flow direction.

Photograph showing the change in intensity and orientation of striations which occurs across the

Gray’s (1982) reconstruction of the LLS glacier in the Llyn Llydaw basin suggests that the ice surface elevation above the hummock was between 500 and 550m above sea level. As the elevation of the bedrock surface in this area i s around 420m, the ice thickness must have been between 80 and 130m at this time. The elevation of the ice sheet surface is harder to estimate. Gemmell et a/. (1986) have mapped ice sheet striations at elevations of up to 650m on the eastern end of the Crib Goch ridge (Fig. l), and Boulton (1 977) suggested that theelevation of the ice sheet surface in Snowdonia would have been about 800m at a time when the ice sheet margin lay in the vicinity of Glanllynau, some 30km away. The maximum ice sheet reconstruction of Boulton et a / . (1977) indicates a surface elevation to 1400m in this area. A minimum ice sheet thickness of 300400m i s suggested by these studies, and maximum thicknesses may have approached 1000m.

Estimation of sliding velocities is difficult, but we can make progress by using the observation that lee-side cavities developed beneath the ice sheet, but not beneath the LLS glacier. According to the sliding theory of Nye (1969), the magnitude of the pressure fluctuation associated with the flow of linear viscous ice over a bump of wavelength to amplitude ratio of 4/1 is 2AP. where:

AP 5 (1 O-qV/h) (3)

Cavities will develop in the leeof bumps when (AP/p,gh) > 1, so it i s possible to solve equation 3 for the critical sliding velocity at which cavities will form for given values of the ice

thickness (Fig. 7). Cavities will open at a velocity of about 9m yr-’ beneath 100m of ice, while velocities of 35m yr-’ are required beneath 400 m of ice and 88 m yr-’ beneath 1000 m of ice. We therefore conclude that the sliding velocity during the LLS was less than about 10m yr-I, while that beneath the ice sheet was in excess of about 35 m yr-’.

Combining equations 1 and 3, it is possible to calculate the factor of safety for the bedrock bump at the critical velocity for cavity opening under varying ice thicknesses (Fig. 7). At an ice thicknessof l oom thefactorofsafetyisaround 2.5, but itdrops to 1 at a thickness of about 250 m, and is less than one at higher thicknesses. In the absence of cavities, the factor of safety beneath the LLS glacier would have been greater than indicated on Figure 7, while it would have been less than indicated beneath the ice sheet at locations where cavities existed. Given our assumptions about parameter values, too much emphasis should not be placed upon the precise results of this analysis. What is important is the finding that factors of safety for the low ice velocities and ice thicknesses which characterised the LLS would have been significantly higher than thoseassociated with the higher velocities and ice thicknesses of the ice sheet.

This result suggests that lee-side fracturing beneath the LLS glacier was suppressed because the low sliding velocities induced minimal stress concentrations in bedrock and because, in the absence of cavitation, the ice overburden contributed significantly to the rock strength on the lee side of the bump. Beneath the ice sheet, stress concentrations were increased by the higher ice thicknesses and ice velocities, while lee-side rock strength was reduced by the formation of cavities. This allowed fracturing to take place.

122 lOURNAL OF QUATERNARY SCIENCE

70 1

Cri t ical Ice Velocity

(m yr -11

0 100 200 300 400 500 600 700

Ice thickness (ml

Safety Factor a t Cr i t ical

Ice Veloci ty

Figure 7 and the safety factor for lee-side bedrock on the thickness of the overlying ice. Al l calculations assume a bump of 1 Om wavelength and amplitude to wavelength ratio of 114.

Diagram to show the dependence of the critical ice velocity at which lee-side cavities open up

Surface fracture wear

Crescentic cracks and gouges such as those described by Gray and Lowe (1 982) form when the stress concentration induced in bedrock by contact between an entrained clast and the bed i s sufficient to cause crack propagation (Johnson, 1975; Riley, 1982). For given indentor, it i s possible todefine a critical load and flaw size below which cracks will not propagate (Lawn and Evans, 1977). Values for these parameters depend upon indentation hardness and fracture toughness of the bedrock, but are approximately constant for a given rock type. A possible explanation for the limited development of crescentic fractures in the LLS might therefore be that, while the loads imposed on clasts by the ice sheet were large enough to cause crack propagation, those imposed by the LLS glacier were not. This is a testable hypothesis since, according to Drewry (19861, contact loads can be calculated from measurements of the width of striations using the relation:

D = (2u/u, 7~)' Ti (4)

where 2D is striation width, u i s contact load, and uy is yield strength of bedrock. Striation width is thus proportional to contact load, and a reduction in striation width from the ice sheet to LLS flow phases would therefore indicate a reduction in contact load.

To examine this possibility, we have made micrometer measurements of the widths of samples of 25 to 30 striations from each set at five localities on the bedrock hummock (Figs 3a, 8). Modal widths of LLS striations are in the range 0.2 to 0.6mm, while those of ice sheet striations are usually in the range 0.6 to 0.8mm. Maximum widths recorded were 1.6 to 1.8mm for the LLS (but all but one observation was less than 1.2mm) and 2mm for the ice sheet. Thus, although the size distribution of ice sheet striations i s partially truncated at the fine end by the effects of LLS erosion, these measurements suggest that LLS striations are consistently narrower than ice sheet striations. If we assume a yield strength for bedrock of 1 OOMPa, and modal values for D of 0.2mm for the LLS striations and 0.35mm for the ice sheet striations, we obtain modal contact loadsof6.3N fortheLLSand 19.2Nfortheicesheet. Assuming a rock density of 2700kg m-', such contact loads could be developed by the buoyant weight of spherical rock particles of radius 0.045 m and 0.066m respectively. Maximum contact

loads would be 56.5 N for the LLS and 157 N for the ice sheet, equivalent to the buoyant weight of rocks of radius 0.094 m and 0.0131 m.

We do not know the value of the critical load required to cause fracture propagation in the tuffs and ignimbrites of the Llyn Llydaw basin, but Riley (1 982) gives values in the range 1.5 to 33 N for sandstones, limestone and gypsum. Modal contact loads in the LLS were at the lower end of this range and are thus unlikely to have induced fracture, while maximum values may have been sufficient to account for the limited number of crescentic gouges produced during this period (Gray and Lowe, 1982). Modal contact loads for the ice sheet phase would have been more likely to induce fracture than those in the LLS, accounting for the greater number of crescentic gouges orientated in relation to the ice sheet flow direction. We defer discussion of the possible causes of the low LLS contact loads until the next section.

Abrasive wear

There is an observed deficiency of striations of less than 0.4 mm width in the ice sheet set (Fig. 8). This deficiency probably arises because striations in this width range have been removed by LLS abrasion. This information can be used to assess the likely maximum amount of erosion during the CLS, since striation depth (H) is related to width by the relation:

H = D cot 0 ( 5 )

where 8 i s the half angle of the tip of the wearing asperity (Drewry, 1986). If LLS erosion removed striations with a width of up to 0.4mm (D = 0.2mm), then maximum amounts of abrasion of 0.62mm, 0.33mm and 0.17mm are implied by values for 8 of 10, 25 and 45". This suggests that total abrasion during the LLS was probably less than 1 mm in those areas where we measured striations. Greater amounts of abrasion may have occurred on the north west side of the bump where ice sheet striations have been almost obliterated.

To explain these low values for abrasion during the LLS, we refer to the abrasion model of Hallet (1 981) in which the rate of abrasion, A, is given by:

A = a c V , u (6)

RECONSTRUCTING PAST GLACIER DYNAMICS AND EROSION FROM GLACIAL GEOMORPHIC EVIDENCE:

SNOWDON, NORTH WALES 123

4 0 -

30 -

20 -

10 -

0 1

Site 1 Site 2 Site 3 Site 4 1 Site 5' 40

N=25 N=30 N =30 N =30 N=30. 3o

- 4 0' 40' 4 0' 4 0' 4 0'

- - 20 - - - - 10

n l n i n n n 1 in 0

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9 0' N =25

site 2

N =30

Site 3

90' - N=30

0 1 2 0 1 2 0 1 2 0

Striation Width (mm)

Site 4

90' N =30

where c1 is an attritivity coefficient (taken as 5 x 10-"kg J - ' , a value rather lower than that for limestones given by Hallet), c is the concentration of rock fragments in the basal ice of the glacier, V,, is the velocity of entrained particles (taken as equivalent to the sliding velocity, following Hallet (1 981 I ) , and u i s the contact load.

Since we believe that the maximum total abrasion in the LLS was 1 mm and that the modal contact load was 6.3 N then, by assuming a vdlue for the attritivity coetficient, we can solve for thetotal amountofslidingrequired toaccount forthisamount of abrasion with different values for the concentration of debris particles producing the modal contact force. The results are plotted as Fig. 9. The required sliding ranges from 85 km with a debris concentration of 1 clast mpL, to 3.5 km with a concentration of 25 clasts r f 2 . If the LLS lasted 1000 years (Gray, 1982), this would require sliding velocities of less than 85m yr-' (greater if the period of ice cover was less than 1000 years). If, as we have already argued to account for the absence of cavities, the velocity was actually less than 9 ni yr- ' , clast concentrations greater than 10 mpL would be needed to produce the observed abrasion. If the contact load was entirely attributable to the buoyant weight of clahts of radius 0.045 m, such a concentration would be equivalent to a volumetric concentration of 8% or more. Such debris concentrations are commonly found in the basal ice of contemporary valley glaciers (Lawson, 1979; Sharp, 1982; Cemmell, 1985). If the attritivity coefficient had a higher value than we have assumed, we would need to invoke smaller amounts of sliding and lower debris concentrations to explain the observed abrasion.

In reality, it is unlikely that the contact load was entirely due to the buoyant weight of clasts. According to Hallet (1979, 1981) part of the load is also attributable to a pseudo-viscous drag force produced by the flow of ice towards the bed around

Site 5 40

Nl:I

Figure 8 5ites located on Figure 3a

Histograms showing the width of ice sheet and LLS striations at each of the five measurement

the clasts which i s due to basal melting. This component of the load (ud) i s given by:

(7 )

where R i s clast radius, R. i s the transition radius (equivalent to the controlling obstacle size in the sliding theory of Weertman (1 964) and taken to be 0.1 m following Hallet (1 981 I ) , and V, i s

~d = ( 4 r q R J R.' + R') V,

l o o 1 60 01 \ 40

20

0 I 1 I 1 I I 10 15 20 25 30

0 \ 5 I 1 I 1 I I

0 5 10 15 20 25 30

DEBRIS CONCENTRATION (CLASTS M-*)

Figure 9 Diagram to show the amount 01 basal sliding required to produce 1 mm of abrasion in the 1000 years of the Loch Lomond Stadia1 given varying assumptions about the concentration of debris in the basal ice The calculations assume a bedrock attritivity coefficient of 5 x I0 " Kg J ' and a modal particle-bed contact load o f 6 1 N


800 -

1000

100

10

Contact Load 1.0

"1

0.1

0.0 1

0.00 1 0.00 1 0.0 1 0.1 1.0

Part icle Radius [ m l

Figure 10 given a basal melt rate of 0.014m yr - l and ice viscosity of 3.15 x 1O"Pa 5 - l .

Particle-bed contact load as a function of clast radius

the vertical component of ice velocity. Melting due to geo- thermal heating can produce a vertical velocity of about lOmm yr-' (Hallet, 19791, and we estimate that the sliding friction generated by a glacier sliding at 9m yr-' and a basal shear stress of 137 kPa could account for an additional 4mm yr-'. Our shear stress (7) estimate is derived from:

T = f p, g h sin p (8)

where f is a shape factor (Nye, 1965) (0.85 for the Llyn Llydaw basin in the study area), and p is the surface slope angle of the glacier averaged over a distance equivalent to 10 ice thicknesses (measured at the centre-line) about the 525 m surfacecontour (7.6"over 1500m in thiscase, derived from Fig. 4 of Gray's (1 982) reconstruction of glacier dimensions).

We thus assume that V, was about 0.014m yr-', although higher rates may have occurred on the stoss side of the bump where pressure melting and compressive strain may also have occurred. On this assumption we use equation 7 to calculate the contact force associated with clasts of different sizes (Fig. 10). These calculations indicate that, even at the low sliding velocities inferred to have characterised the LLS glacier, the observed modal contact load of 6.3 N can be accounted for by the pseudo-viscous drag exerted on clasts with radius of around 2cm, while the maximum contact load of 56N only requires a clast of radius 3 4 c m .

These results thus suggest a deficiency of large clasts in the debris transported by the LLS glacier, a deficiency which can perhaps be explained by the minimal extent of lee-side fracturing discussed above. We therefore attribute the limited amount of abrasion by the LLS glacier to its low sliding velocity, low englacial debris concentrations (particularly in the coarser size fractions) and low clast-bed contact loads. This explanation is entirely consistent with our explanation for the absence of lee-side fracturing and surface fracture wear, since these also demand low sliding velocities and low clast-bed contact loads. We must, however, try to account for the low sliding velocities. To do this, we have approached the problem from two different perspectives; that of the glacier mass balance, and that of the mechanics of the sliding process.

Mass balance of the Loch Lomond stadia1 glacier

The first approach to accounting for the low sliding velocities which we postulate for the LLS glacier involves estimating the balance velocity of the glacier and an assessment of the extent to which thiscan be accomplished by icedeformation alone. Gray (1 982) estimated that the annual accumulation at the equilibrium line in Snowdonia during the LLS was around 2500- 3000mm yr-' of water equivalent, and that by analogy with modern Norwegian glaciers the mean May-September tem- perature would have been about 3.5"C. This would imply that the mass balance characteristics of the LLS glacier were similar to those of a glacier such as Nigardsbreen in southern Norway today (cf. Sutherland, 1984, Fig. 4). We have therefore used mass balance data from Nigardsbreen (Kasser, 1977) to estimate the mass balance of the LLS glacier (Fig. 11).

-10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 -2 - 1 0 1 2 3 4

BALANCE [ M I

Figure 11 elevation for Nigardsbreen, southern Norway. Source: Kasser (1 977).

Net balance and ablation rate as a function of surface


Gray (1982) estimated that the equilibrium line of the LLS glacier lay at 590m. By setting the point of zero net balance on the net balance versus elevation curve for Nigardsbreen to 590m, we determined values of annual accumulation or ablation for each 50m elevation increment of the LLS glacier. By multiplying these values by the area of the appropriate elevation increment (determined by planimetry from Fig. 4 of Gray (1982)), we calculated total annual accumulation or ablation for each increment. We then summed the accumulation values for areas above the equilibrium line to obtain an estimate of the annual accumulation over the glacier, and summed the ablation values for areas below the equilibrium line to estimate the annual ablation. This calculation indicated an excess of ablation over accumulation, but by lowering the equilibrium Iinealtitudeto570m, wewereable to bringthetwo quantities into balance. The balance flux calculated by this method was 1.46 x l o 6 m3 yr-' (Table 1 ). From Ordnance Survey 1 :25000 maps we calculated the cross sectional area of the valley below the 570m surface contour to be 1.04 x l o 6 m2, and we thus obtained a balance velocity (balance flux/cross sectional area) of 14 m yr-' . The assumption that the glacier was in equilibrium thus sets an upper limit to the sliding velocity of the glacier which is only 5m yr-' greater than our estimate based on the failure to form cavities at the bed. In a growing glacier, the actual flux through the equilibrium line would exceed the balance flux and thus permit a greater contribution to the overall velocity from sliding. A growing glacier would, however, also be likely to be steeper than an equilibrium glacier and it might therefore experience greater shear stresses and rates of internal deformation.

To determine the contribution of sliding to the balance velocity, we calculated the mean velocity due to ice deformation. The surface velocity due to deformation at the centre-line of a glacier i s given by (Paterson, 1981 1:

U = 2A 7" h/(n + 1 ) (9)

where A and n are exponents in Glen's (1 955) flow law for ice. The centre-line ice thickness below the equilibrium line was 170m, and the glacier surface slope averaged over 1500m was 6". With a shape factor of 0.74, equation (8) gives a basal shear stress, 7, of 11 7kPa. Taking n = 3 and A = 5.3 X

s-' kPa- ' (Paterson, 1981), equation 9 gives a velocity of 22.75m yr-'. This would, however, have been the maximum velocity found anywhere in the section, and for comparison with the balance velocity should be reduced to a mean velocity. This was done by using Fig. 6.5 of Paterson (1981) to

reconstruct a transverse surface velocity profile along which points were located at distances Z = 0, 0.5, 1,. . .3 on either side of the centre-line (Z = distance from centre-line/ice thickness at centre-line). The mean velocity due to ice deformation was then estimated as the mean of the velocities at these thirteen points. It was 14.1 m yr-I, virtually the same as the balance velocity. The implication of this must be that, given the reconstructed glacier geometry, ice deformation alone can account for the bulk of the balance velocity, and only a small contribution to the overall velocity i s required from sliding. Mass balance considerations therefore support our contention that the sliding velocity of the LLS glacier was small.

Mechanics of the sliding process

To explain these low sliding velocities, the mechanics of the sliding process are considered. It i s now widely recognised that the glacier sliding velocity (V) i s controlled by the basal shear stress, the effective pressure at the glacier bed and the bed roughness (Nye, 1969; Kamb, 1970, 1987; Iken, 1981 ; Binds- chadler, 1983), but most available sliding laws are empirical in nature. For instance, on the basis of laboratory experiments on theslidingof iceover rocksurfaces, Budd eta/. (1 979) proposed a law which has the form:

(1 0)

Here N is effective pressure (pgh - PJ, P, is subglacial water pressure and K is a constant, the value of which depends upon bed roughness. For ice sliding over rough granite, Budd eta/. (1 979, Fig. 7) found values for K in the range 0.4-1.1 m d-' 100kPa-*. Bindschadler (1983) was able to fit the flow law to flow data for Variegated Glacier, Alaska, in its non-surging state by taking K = 0.2 m d-' 100 kPa-*. If we use this rangeof values for K, and take the value of 137 kPa which we calculated for the basal shear stress at the study site, then we can solve for the values of N which are consistent with sliding velocities of 9m yr-' or less. Even for the lowest value of K, the value of N required to produce such low sliding velocities is greater than the maximum possible given the ice thickness of 150m (2050 kPa compared to a possible maximum of 1324 kPa). From this, we conclude that such low slidingvelocities would only be possible over a very rough bed with subglacial water pressures close to atmospheric pressure.

V = K ( T ~ / N )

Table 1 Distribution of net balance and ablation ratesas a function of elevation for the Loch Lornond stadia1 glacier occupying the Snowdon Horseshoe

Total net Ablation Total Cumulative Elevation range Area Net balance balance rate ablation d i sc harge (m) (m? (m yr-') m' yr-') (m yr-'1 (m3 yr-'1 (m3 yr-')

900-950 76 053 2.32 176 443 0.78 59 321 59 321 850-900 72 431 1.97 142 689 0.91 65 912 125 233

302 762 80&850 155 727 1.62 252 278 1.14 177 529 750-800 273 427 1.28 349 987 1.30 355 455 658 217 700-750 173 834 0.93 161 666 1.53 265 966 924 183 650-700 362 155 0.59 213 671 1.69 612 042 1 536 225 600-650 543 232 0.24 130 376 2.02 1 097 329 2 633 554 550-600 458 126 -0.1 1 -50 393 2.21 1 012 458 3 646 012 500-550 612 042 -0.45 -275 419 2.50 1 530 105 5 176 117 450-500 376 641 -0.80 -301 313 2.86 1 077 193 6 253 310 400-450 331 372 -1.14 -377 764 3.19 1057077 7 310 387 350-400 204 617 - 1.49 -304 879 3.58 732 529 8 042 916 300-350 95 971 -1.84 -176 587 3.84 368 529 8 411 445

B


We know from our observations that the development of lee-side cavities was minimal during the LLS, so we presume that most of the water draining from the glacier passed through a major conduit incised upwards into the ice (Rothlisberger, 1972) rather than through a system of linked subglacial cavities (cf. Walder, 1986; Kamb, 1987). For such a conduit system, the steady state effective pressure (N) i s given by:

Qw = (d2") E4 M3 (w/Ph)"" (T/3N)12 (1 1)

(Kamb, 1987). Here M is the Manning roughness coefficient (0.1 m-lns), w is the tortuosity of the conduit system (31, P h is the hydraulic gradient (0.1 - the surface slope at the equilibrium line), Qw is the meltwater discharge, T is a constant taken from equation 11 of Karnb (1987) which describes the non-linear relationship between ice viscosity and the second strain invariant (94 kPa yr1l3), and E i s a constant equal to piJ/pwg, giving a value of 31 krn. In the latter equation J i s the latent heat of melting and pw is the density of water. Values assumed for M, w and T are those used by Kamb (1987). From data on the ablation - altitude relationship for Nigardsbreen (Fig. 1 l), we estimate that the annual meltwater flux through the 525m contour would have been about 5.18 x 10" m3 yr-' (Table 1). Assuming that most of this water passed through the glacier in a five month ablation season, the mean meltwater discharge at theequilibrium line in summerwould have been approximately 0.4m3 s-'. The steady state effective pressure for such a discharge is 1220 kPA, suggesting that the subglacial water pressure was only about 100kPa. This i s consistent with our earlier assumption that very low water pressures are required to account for the low sliding velocities.

We now need to account for the apparently high bedrock roughness to complete our explanation of the low sliding velocities. It i s widely recognised (Boulton, 1974, 1979) that glaciers produce erosional bedforms which are relatively smooth in the direction of ice flow, but rough transverse to it. In addition, roughness elements tend to be removed from the stoss sides of bumps by the process of abrasion, while they are generated in lee-side locations by the process of bedrock fracture. When cavities exist in the lee of bedforms, roughness created by this process does not contribute to the frictional resistance to glacier sliding because the ice is separated from the bedrock and does not 'see' the roughness. A change in the direction of ice flow over a glacially eroded bedrock surface may, therefore, change the frictional properties of the surface significantly. In this case, a 50" change in flow direction between the ice sheet and the LLS glacier may have resulted in bedforms which were formerly oriented parallel to flow becom- ing oriented oblique to flow, and in ice coming into contact with roughness elements which were generated by fracturing beneath the ice sheet but which were then located in cavities.

To test these hypotheses, we have quantified the roughness properties of the glacier bed in directions parallel to both ice sheet and LLS glacier flowlines. This has been done by performing a spectral analysis on the bed elevation profiles described earlier (Fig. 5). The elevation series were detrended using linear least squares regression techniques, and the residual series were subjected to spectral analysis by the conventional method, which involves calculating the discrete Fourier transform of the autocorrelation function of the series. Nye (1 970) argued that the average shear stress (7) at the base of a temperate glacier sliding in continuous intimate contact with its bed (which is assumed to be wavy only in a direction parallel to flow) depends on the sliding velocity and the spectral power density of the bed profile:

7 = (2qk*'/n) V i d k S(k) W(k) (1 2) 0

90 - 80 - 70 -

SNOWDON - ICE SHEET

1 . 8 . 1

0 0 .02 0.04 0.06 0 .08 0 . 1 0 . 1 2 0 .14 0.16 Frequency

SNOWDON ~ ICE SHEET WITH CAVITIES

70

4 0

30 \ l o 0 4 0 0 . 0 2 0.04 0.06 0.08 0 .1 0 . 1 2 0 .14 0 . 1 6

Frequency

SNOWDON - LOCH LOMOND STADIAL

7 0

30 - 20 -

0 0 . 0 2 0 .04 0.06 0 . 0 8 0 - 1 0 . 1 2 0 .14 0 . 1 6

Frequency

Figure 12 sheet flow direction; (b) the ice sheet flow direction with cavitation; and (c) the Loch Lomond Stadia1 flow direction. Units for frequency are cycles per 0.05m.

Raw power spectra of bed elevation profiles for (a) the ice

where k is the wave number, k* is a constant, the so-called transition wave number, S(k) is the spectral power density and W(k) i s a weighing function equal to k3 (k.' + k2)-'. This weighing function takes account of the fact that glaciers move around bumps of different size by varying combinations of regelation and enhanced plastic flow. The form of the weighing function indicates that large bumps have little influence on the sliding process and that it is therefore appropriate to consider bed roughness at a scale of metres and below.

To determine the total roughness of the bedrock surfaces we derived a relationship between spectral power density and wave number which has the form (Nye, 1969):

S(k) = B k-" (1 3)

we then multiplied this relation by the weighing function and numerically integrated the resulting function. From our know- ledge of the spectral power density of the surfaces, we also computed a dimensionless roughness parameter, 5, which was introduced by Kamb (1 970):

(1 4)

The major limitation of this approach is that we are unable to estimate the spectral power density for wave numbers greater

k2 = (3/4a3) k3 S(k)


1 0 -

Y) 0 0 - a

0 6 -

= 0 4 -

W 3 0

a1

22:: 4 SNOWDON . ICE SHEET

180-

160- 1 4 0 -

p 120- 5 100- g 80 -

60 1 q , , , . , . , , , . , . , . , , , . , , , . , . 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7

W a v e Number

200-1 I \ I

SNOWDON . ICE SHEET WITH CAVITIES

;:#, , . , , , , , , , , , , , . , , , , , . I 0 0 1 0 2 0 3 0 4 0 5 0 6 0 7

0

W a v e Number

C ) SNOWDON LOCH LOMOND STADIAL

o 0 1 0 2 0 3 0 4 0 5 0 6 n 7 W a v ~ NurnhPr

Figure 13 the ice sheet flow direction, (b) the ice sheet flow direction with cavitation, and ( c ) the Loch Lomond Stadia1 flow direction Wave number i s defined as 2 d h cm-'

Weighed power spectra of bed elevation profiles for (a)

than about 0.63cm-', a constraint imposed by the 0.05m spacing of sampling points. As a result, power associated with higher wave numbers i s folded back into the region 0 6 k 0.63, producing an aliasing problem. This i s particularly significant because the form of the weighing function i s such that the aliased power is multiplied by values ofW(k) which are too small, so that we may underestimate the total weighed power of the surface.

Raw and weighed power spectra, together with roughness data for the bedrock surfaces, are plotted as Figs 12, 13 and 14. The ice sheet bed is rougher than the LLS glacier bed over the wavelength ranges 0.14-0.25m and 0.8-5m, while the LLS glacier bed i s rougher over wavelengths ranging from 0.25- 0.8m and longer than 5m. This indicates that: (a) the oblique flow of the LLS glacier over bedforrns produced by the ice sheet increases their apparent wavelength, and (b) there are transverse waveforms with a wavelength of decimetres which are crossed by the LLS ice flow direction but not by the ice sheet flow direction. The short wavelength roughness associated with the ice sheet flow direction appears to be mainly located in areas in the lee of the major bedrock bumps. To demonstrate this, we have twice smoothed the ice sheet bedrock profile

using running medians of 4, 2, 5 and 3 points and then resmoothed it using a running average filter which has the form:

Z(t) = 0 . 2 5 ~ (t - 1) + 0 . 5 ~ (t) + 0 . 2 5 ~ (t + 1) (15)

Here Z(t) i s the smoothed bed and y(t) is the measured bed. We have then subtracted this smoothed profile from the original profile, and plotted the residuals against position on the profile (Fig. 15). There are four major clusters of residuals, all associated with lee-side locations. Spectral analysis of the residual series reveals concentrations of weighed power and roughness in the 0.1-0.1 5 m wavelength range (Fig. 15).

Despite the differences noted above, the relation between spectral density and wave number for both profiles i s S = 61.66k-'.'', giving a total weighed power of 80.23. From this we conclude that the changes in bed geometry associated with the reorientation of ice flow between the ice sheet and LLS flow phases are unlikely to explain the low LLS glacier sliding velocities. We therefore consider the alternative explanation that variations in the extent of subglacial cavitation account for the changes in bed roughness. Since we have already demonstrated that there are concentrations of roughness in the wavelength range,o.l-O.l5m in the lee of those bedrock

a1 SNOWDON - ICE SHEET

O 2il\f 0 . , ~ , . , . , ~ 1 ~ , ' 1 ~ 1 ' , . I ~ I . , ~ , . l

0 0 1 0 2 0 3 0 4 0 5 0 6 0 7 W a v e Number

bl

' 2 1 SNOWDON - ICE SHEET WITH CAVITIES

C)

"1 1 . 0 4

SNOWDON . LOCH LOMOND S T A D I A L n

.^ 0 . 8 -I

, I 1 . 1 . ? ' I ' I . 1 . 1 ' 1 . '

0 0 1 0 2 0 3 0 4 0 5 0 6 0 1 W a v e Number

Figure 14 number for (a) the ice sheet bed profile; (b) the ice sheet bed profile with cavitation; and (c) the Loch Lomond Stadia1 bed profile.

Dimensionless roughness parameter as a function of wave

1 8 -

p 1 6 -

c 1 1 -

w

I

f 1 2 -

4 1 0 -

n 0 8 - f 0 6 -

0 4 -

0 2 - fn

- SNOWDON - ICE SHEET

6 0 SNOWDON - ICE SHEET RESIDUALSERIES

5 0

% 5 4 0

m ? 3 0 2 B 2 0

c

u)

1 0

--7 0 7 . 1 . I . 1 . 1 . I . I . 1 . 1 0

30000

25000

SNOWDON - ICE SHEET RESIDUAL SERIES

n

n w I I T - 0 . 4 . , . , , , . , . , . , . , . #

0 2 4 6 8 10 12 14 16

Dislance (in) 0 0 . 1 0 .2 0 . 3 0 4 0 5 0 6 0 7

Wave Number

Figure 15 (a) Smoothed ice sheet bedrock elevation profile. (b) Residuals from the smoothed profile (raw profile - smoothed profile). (c) Raw power spectrum of the residual series. (d) Weighed power spectrum of the residual series.

obstacles which initiated cavities beneath the icesheet, it seems likely that these roughness elements may have contributed significantly to the drag on the base of the LLS glacier, beneath which cavitation was extremely limited. To test this hypothesis, we used our geomorphic map to reconstruct the extent of cavities along the ice sheet flow line and used linear inter- polation to reconstruct the form of the glacier sole above the cavities (Fig. 5b). We then performed a spectral analysis of the glacier sole by the methods described above (Figs 12b, 13b, 14b).

The effect of cavitation i s to increase roughness at wavelengths of 0.1-0.7 m and greater than 5 m, and to reduce it at wavelengths of 1.7-5m. These changes occur because cavitation effectively elongates the major bedforms, and because some small bumps, which previously appeared as oscillations superimposed on the surface of larger bumps now appear as bumps in their own right (as at the downflow end of the profile depicted in Fig. 5b). The relation between spectral density and wave number is S = 75.86 k- ' '', and the total weighed power is 90.3 1. Surprisingly, therefore, the total roughness of the glacier sole with cavities is greater than that of the bedrock surface. It must, however, be remembered that the glacier was separated from the bedrock along approximately 35% of the length of the profile, and would have experienced no drag at all in those areas. If we reduce the total weighed power accordingly, it drops to 58.7 or 73% of the LLS value. We therefore conclude that changes in the extent of subglacial cavitation between ice sheet and LLS flow phases may have caused a significant increase in bedrock roughness, which could contribute to an explanation of the low LLS glacier sliding velocities.

Conclusions

Glaciated bedrock surfaces exposed around Snowdon show evidence for two phases of ice flow and associated processes of

glacial erosion. The earlier of these phases was probably associated with a Devensian ice sheet, and the more recent with a Loch Lomond Stadia1 valley glacier. Whereas the ice sheet submerged the bedrock topography in the area, the valley glacier was confined by topography and forced to flow in a direction which differed locally from that of the ice sheet by as much as 50". Evidence for ice sheet flow i s provided by the direction of streamlining of the major erosional bedforms, and by the orientation of lee-side fracture surfaces, striations and crescentic fractures. By contrast, the LLS glacier flowed obliquely across pre-existing bedforms, was apparently unable to fracture the bedrock, and only left evidence for its existence in the form of striations which cut across those produced by the ice sheet but do not generally obliterate them. The LLS was thus associated with a different style of glacial erosion to the ice sheet, and with very low erosion rates.

The principal cause of the low erosional capacity of the LLS glacier is believed to be a very low basal sliding velocity. This prevented lee-side cavities from developing beneath the glacier, reduced the flux of basally-entrained debris across the glacier bed and minimised particle-bed contact forces. Lee-side fracturing was suppressed because the safety factor for subglacial bedrock beneath 1OOm of ice was greater than 1. This is because low sliding velocities induced minimal stress concentrations in the bedrock and because, in the absence of cavities, the ice overburden contributed to the frictional component of bedrock strength on the lee-side of bumps. Surface fracture wear was suppressed because contact loads associated with entrained debris were insufficient to cause fracture propagation in bedrock. Low contact loads appear to have resulted from an absence of very large clasts in the debris assemblage (which may be attributed to the lack of lee-side fracturing), and from the low rates of basal melting due to sliding friction. Low basal melting values resulted in only a minor contribution to the contact load from the pseudo-viscous drag associated with the downwards flow of ice around debris particles. Low sliding velocities, low contact loads and probably a relatively low


englacial debris concentration also account for the limited degree of abrasive wear.

Although the LLS glacier must have been sliding over its bed to produce striations, our results indicate that it did so at a very low rate. Consideration of the mass balance of the glacier and the likely rate of flow by internal deformation indicates that most of the balance velocity could have been achieved by internal deformation alone. Modelling of the sliding process indicates that sliding velocities of the magnitude required could only have been achieved over a very rough bedrock surface with subglacial water pressures close to atmospheric. Con- sideration of the steady state effective pressure associated with the likely summer meltwater discharge suggests that water pressures close to atmospheric were indeed likely given the observed ice thicknesses. Anomalously high bedrock rough- nesses are attributed to the absence of cavitation beneath the LLS glacier. This would have brought the glacier sole into contact with roughness elements which were created by lee-side fracturing beneath the ice sheet, but which did not contribute to the drag on the sole of the ice sheet because of their location within cavities. Spectral analysis of bed elevation profiles indicates that this process could account for a 37% increase in roughness between ice sheet and LLS flow phases. We therefore believe that the LLS valley glacier which occupied the Snowdon Horseshoe moved largely by internal deformation with a limited velocity contribution from basal sliding. The resulting contact conditions at the glacier bed resulted in suppression of the processes of lee-side fracturing and surface fracture wear, and in a very low rate of erosion by abrasive wear.

The links demonstrated above between glacier dynamics and the morphology of glacier beds also have more general implications. Bed roughness and the potential for basal cavitation are significant controls on glacier motion, which may be impeded by high roughness and limited cavitation. There are several situations in which glacier beds may appear relatively rough to overlying ice. One is at the beginning of an Ice Age; for example, the earliest Cenozoic ice sheets would have flowed across a pre-glacial topography rather than across streamlined bedrock features, such as roche mountonnees. It is likely that such glacier beds, which may have been covered by considerable depths of weathered regolith, were rougher than those encountered during, for example, the build-up of late Deven- sian ice sheets. Ice flow across them would thus have been impeded, and restricted ice masses with relatively steep surface profiles may as a result have characterised the first late Cenozoic glaciations. Glacier bed roughness may also change at the scale of single glacial episodes within the late Cenozoic. The example of the Snowdon ice masses suggests that bed morphology may be adjusted to ice flows characteristic of full glacial conditions, when ice submerges the bedrock topography. During the early stages of ice build-up, however, and perhaps also during ice decay, patterns of ice flow may be constrained by bed topography, as they were on Snowdon during the LLS. Under such conditions, ice flow may not be conformable with the direction of streamlining of glacial bedforms and bed roughness may therefore be greater than under full glacial conditions. This factor may strongly influence spatial patterns of ice accumulation and wastage, and since i t also influences contact conditions at the glacier bed (and thus rates and mechanisms of glacial erosion) i t may help to explain why large scale glacial erosional bedforms often appear to reflect stable patterns of ice flow associated with ice maximum conditions (Sugden, 1978). Low rates of erosion and the suppression of some erosional processes over rough subglacial substrates demand relatively long periods of stable flow direction to produce well-aligned erosional bedforms. The geo-

morphological interaction between glaciers and their beds is thus seen as a significant control on the dynamics and geometry of ice masses.

Acknowledgments We are grateful to Bryn Hubbard, Evelyn Dowdeswell and David Sexton for assistance with the fieldwork, and to Nick Clifford for assistance with the spectral analysis. Our approach to the analysis of glacier bed roughness closely follows that developed by Bernard Hallet in an unpublished manuscript, and we are grateful to him for making a copy of that manuscript available to us. We thank David Sugden for his constructive review of an earlier draft of the paper.

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