Dissertation 2011sm

To What Extent is Evidence from the
Last Stadial a Proxy for the Long-Term
Pattern of Glaciation in Scotland?
Barnaby Bedford,
Geography (BSc Hons.),
University of Edinburgh.
Expected Graduation 2011
Supervisor: Professor David Sugden
Word Count: 11,784

II
Declaration of Originality
I hereby declare that this dissertation has been composed by me and is based on my own
work.
Signature: Date:
Barnaby Bedford

IV
Abstract
Quaternary glaciations have exerted a considerable erosive force across the Scottish landscape.
Numerous studies have attempted to reconstruct the extent and dynamics of the most recent ice
mass, that of the Loch Lomond Stadial (ca. 12.9-11.5ka BP) from a varied catalogue of geological
and geomorphological data. This research aimed to assess the extent to which the ice cap that
covered western Scotland at this time represents the long-term pattern of glaciation and more
importantly erosion. A recent empirically-validated numerical reconstruction by Golledge and
others (2009) provided ice thickness, basal temperature and basal velocity for the calculation of
basal shear stress across Scotland which could broadly be used here to infer the likely distribution
of erosion during the Loch Lomond Stadial. The modelled data was compared to data relating to
valley morphology extracted from a DTM along Glen Lyon, Western Grampian Highlands. A long-
profile allowed the assessment of longitudinal variations in basal shear stress relative to
overdeepend rock basins – a direct result of increased erosion at a glacier bed. 25 valley cross-
profiles were extracted and a general power law used to determine the shape and width-depth
relationship at various stages along the glen that could then be compared to data from the ice sheet
model. It was found that the macro-scale geomorphological evidence supports multiple styles of
glaciation. These styles have variously occurred during entire stadials or at certain times during the
growth and decay of larger ice sheets. The orientation of the preglacial topography appears to play
an important role in determining ice flow conditions and hence the spatial and temporal pattern of
erosion at the ice-bed interface. Future research could incorporate cosmogenic nuclide exposure
dating and model data for the more expansive Main Late Devensian ice sheet to allow a more
holistic approach to assessing the importance of a single style of glaciation on valley morphology.

VI
Acknowledgements
My utmost thanks go to Professor David Sugden for his guidance throughout the project and
to Dr Nicholas Golledge (Antarctic Research Centre, Victoria, NZ) for providing data crucial
to this research and for discussions in the early stages of data manipulation. Professor
Andrew Dugmore and Dr Nicholas Hulton must also receive thanks for their direction at
various stages.
Thanks go to the InterMAP Technologies for granting access to NEXTMap Britain DTM tiles,
British Geological Survey (BGS) for access to geological data and to the National Library of
Scotland (NLS) for assistance in the purchase of loch bathymetric images and in the
distribution of loch bathymetric data on behalf of the Scottish Environmental Protection
Agency (SEPA). I am grateful to Frank Pattyn (Université libre de Bruxelles) and Wim Van
Huele (AGIV, Belgium) for making the GPL program used herein publicly available,
improving the quality of results considerably.

VIII
Table of Contents
1. Introduction
• 1.1 The Loch Lomond Stadial in Scotland……………………………………………... 1
• 1.2 Palaeoglacialogical reconstructions in determining landscape evolution ……… 4
2. Scientific Basis
• 2.1 Landscape evolution under glaciers and ice sheets………………………………. 7
• 2.2 500m-Resolution Scottish Ice Sheet Model……………………………………….. 10
• 2.3 Study Area Selection………………………………………………………………… 11
• 2.4 Study Area – Glen Lyon…………………………………………………………….. 12
• 2.5 Arising Questions……………………………………………………………………. 14
• 2.6 Multiple Hypotheses………………………………………………………………… 15
3. Approach and Methodology
• 3.1 Integration of bathymetrical survey data with the Digital Terrain Model……….. 17
• 3.2 Ice Sheet Model Data Manipulation……………………………………………….. 18
• 3.3 Long-Profile Analysis………………………………………………………………… 18
• 3.4 Morphometric Analysis……………………………………………………………...
Cross-Profile Extrapolation………………………………………………………
Geometric Assessment…………………………………………………………..
19
19
19
• 3.5 Other Methods………………………………………………………………………. 21
4. Results
• 4.1 Mapped results………………………………………………………………………. 23
• 4.2 Long-Profile………………………………………………………………………….. 23
• 4.3 Valley Cross-Profiles
b values…………………………………………………………………………...
Form Ratio (FR)…………………………………………………………………..
26
27
28
• 4.4 Depositional Features………………………………………………………………. 30

IX
5. Discussion
• 5.1 Loch Lyon: evidence for a Glen Lyon valley glacier?.......................................... 33
• 5.2 Beyond the LLS limits……………………………………………………………….. 35
• 5.3 Micro- and meso-scale evidence…………………………………………………… 36
• 5.4 The preglacial valley network in focussing erosion……………………………….. 37
• 5.5 Alternative Explanations…………………………………………………………….. 38
• 5.6 Methodological Limitations…………………………………………………………. 40
• 5.7 Implications and Future Research………………………………………………….. 43
6. Conclusion……………………………………………………….…..………………………... 45
7. References……………………………………………………………………………………... 47
Appendix I – Sample GPL Output……………………………………………………………... 53
Appendix II – Valley Cross-Profile Data………………………………………………………. 54
Appendix III – Long-Profile Geological Data………………………………………………….. 55
Appendix IV – ISM Limitations………………………………………………………………….. 56

X
List of Figures
1 Empirical Loch Lomond Stadial and Last Glacial Maximum limits………………………… 2
2.1 Schematic diagram to show development of parabolic trough form………………………. 8
2.2 Schematic diagrams to show overdeepening relative to valley tributaries………………… 9
2.3 Simulated ice surface relative to LLS limits and the distribution of basal sliding across
model domain…………………………………………………………………………………..
11
2.4 Study area………………………………………………………………………………………. 13
3 Transect locations relative to empirical and modelled LLS limits………………………….. 19
4.1a Calculated basal shear stress across model domain…………………………………………. 24
4.1b Calculated basal shear stress in study area…………………………………………………… 24
4.2a FR values relative to longitudinal variations in basal shear stress………………………….. 25
4.2b A values relative to longitudinal variations in basal shear stress…………………………… 25
4.2c b values relative to longitudinal variations in basal shear stress……………………………. 25
4.2d River long-profile adjusted for bathymetric data relative to simulated ice thickness and
main ice tributaries……………………………………………………………………………..
25
4.3 Example transects cross-profiles ………………………..……………………………………. 27
4.4 b-FR diagram…………………………………………………………………………………… 29
4.5 Photographs showing sediment deposits in valley bottom and on valley sides…………… 30
5.1 Ice accumulation area for Loch Lyon within Glen Lyon……………………………………. 34
5.2 Bedrock geology along transects for high medium and low glacial erosion scenarios…… 39
Tables
4 Statistical descriptions of valley morphology coefficients from Glen Lyon………………. 26
5 Changes in main valley morphology down valley of the Glen Daimh tributary………… 35

1
1. Introduction
The Quaternary has been a period of unsettled climate with Pleistocene (ca. 2,588,000-11.5ka BP)
glaciations terminating in the Holocene interglacial (ca. 11.5ka BP – present) which has been
characterised by varying degrees of paraglacial activity in formerly glaciated areas throughout the
northern hemisphere (Ballantyne, 2008; Bradwell et al, 2008). During the Pleistocene ice masses
covered many upland continental regions eroding landscapes from preglacial forms which had
themselves been subject to paraglacial activity since the preceding glaciations of the Neogene
(Ballantyne, 2010). The evidence provided by the final period of renewed cooling before ice masses
in mid-latitudes disappeared – the Younger Dryas (Loch Lomond Stadial in Britain) – has typically
been used to make inferences regarding the scale and dynamics of ice masses during this period
alone. In this paper a method is used for testing how much the likely dynamics and behaviour of the
Loch Lomond Stadial (LLS) ice cap match valley morphology – a representation of the long-term
pattern of glacial erosion – and hence how much such inferences can be used to explain this long-
term trend in Scotland.
1.1 The Loch Lomond Stadial in Scotland
The Loch Lomond Stadial, a period of renewed cooling in the Northern Hemisphere at the close of
the last glacial cycle, began at around 12.7 ka BP and terminated around 11.5 ka BP (Simpson, 1933;
Bjork et al, 1998; Lowe et al, 2008). Among the various explanations for such an event, the most
widely accepted is the notion of a catastrophic disruption to the North Atlantic Thermohaline
circulation. This may have resulted from an influx of freshwater from beneath the Laurentide ice
sheet, decreasing sea surface salinity causing a reduction or even terminating the of production of
North Atlantic Deep Water – reducing the northward transfer of heat from tropical latitudes (Firestone
et. al., 2007; Broeker et. al., 1989; Teller, 1990). Ultimately, the southerly movement of the Northern
Polar Front increased the extent of sea ice in the North Atlantic ocean, cooling the region prompting
the development of an ice cap land system centred on the western Highlands (Figure 1) (Payne and
Sugden, 1990; Clapperton, 1997; Golledge, 2007a).

2
As freshwater concentrations in the North Atlantic surface waters faded, North Atlantic Deep Water
formation was revived, drawing warm tropical waters northwards once again (Broeker et al, 1989).
Subsequently, the Polar Front retreated northwards leading to warming atmospheric temperatures and
increasing aridity across northern Europe; a return to the less seasonal climate typical of the
interstadial preceding the LLS by ca. 11ka (Denton et. al., 2005; Ballantyne, 2008; Benn et al, 1992;
Golledge, 2010). This mechanism for regenerated warming likely explains the brevity and intensity of
Figure 1 Loch Lomond Stadial limits (black line) according to Clark et al (2004). Red dotted line
shows known terrestrial and marine LGM limits joined to form coherent ice sheet after
Ballantyne et al (1998), Clark et al (2004) and Ballantyne (2010).

3
the LLS relative to stadials driven more dominantly by Milankovitch-scale forcings, an important
factor when considering the thermal regime of such a briefly present ice mass (Hubbard et al, 2009;
Golledge, 2010).
Due to its brevity, the LLS ice cap may represent an intermediary phase of other, larger ice caps and
ice sheets to have affected Scotland. The Main Late Devensian (MLD) British-Irish ice sheet (BIIS),
reaching maximum extents during the Last Glacial Maximum (LGM) covered a large portion of
Scotland, Ireland, northern England and Wales (Figure 1) (Ballantyne et al, 1998; Clark et al, 2004;
Evans et al, 2005; Ballantyne, 2008, 2010). The margins of this ice sheet are expected to have
dynamically fluctuated in response to the oscillating climate throughout the last glacial cycle (ca. 31-
11.5ka BP). Bradwell et al (2008) concluded that Older Dryas (ca. 14ka BP) ice caps were
considerably thicker and more extensive than during the LLS and that a sizeable ice cap with
fluctuating margins relative to the climatic changes shown in palaeoclimatic records likely existed in
parts of Scotland to some degree for much of the this period. Rapid retreat phases interrupted growth
phases where temperatures warmed to ensue rapid mass loss through marine-terminating ice streams
(Hubbard et al, 2009). Previous suggestions that the LLS did little in the scheme of shaping the
bedrock landscape relative to earlier ice masses may be appropriate where dynamic ice regularly (in
geological time) manipulates the earth surface. In this paper the scale of erosion is less relevant than
the overall pattern.
It is not confirmed whether ice from the MLD glaciation survived the lateglacial interstadial to aid in
the rapid development of a Scottish ice cap at the inception of the LLS (Sugden, 1980; Sutherland,
1984). Increasing evidence from the suggests that MLD ice in ‘favourable locations’ may have
remained (Clapperton, 1997; Bradwell et al, 2008, Hubbard et al, 2009; Ballantyne, 2010). The
hysteresis known to occur in glacier growth cycles would aid in explaining the lag of deglaciation
behind an end to initial ice build up as temperatures warmed at the end of the Main Late Devensian
into the interstadial (Oerlemans, 1982; Hulton and Sugden, 1997; Ballantyne, 2008).
In terms of the suggested LLS ice cap it is thought that dynamic behaviour was only effective at ice
margins, focussed in outlet glaciers where resultant basal shear stresses were high or where
deformable sediments promoted sliding (Thorp, 1986; Clarke, 2005; Golledge et al, 2009; Golledge,
2010) At the margins of many outlet glaciers, particularly in the north of Scotland, sedimentological
and geomorphological evidence suggest significant dynamic behaviour. Towards the ice cap centre,
it is thought that ice flowed predominantly through ice deformation – creep – and so landforms and
sediments formed during earlier glaciations were subject to limited modification by LLS ice, possibly
areas of landform preservation (Sugden, 1968; Golledge 2006, 2007b, 2010).

4
It is considered that the latter stages of the stadial were characterised by a phase of rapid ice thinning
and active retreat with few existing landforms supporting the idea of ice stagnation or in situ decay
(Benn et al, 1992; Golledge, 2010; Murray-Gray, 1997). Deglaciation is thought to have occurred in
two main phases, with the first retreat phase being prompted by reduced precipitation following the
ice cap maximum. A number of periods of active recession, stillstands and minor re-advances are
thought to have occurred before climate warming initiated a final phase of active retreat (Murray-
Gray, 1997; Golledge and Hubbard, 2005; Benn et al, 1992). The increased temperatures and aridity
during this period likely led to increased basal meltwater flux at the ice-bed interface, leading to
enhanced basal motion giving outlet glaciers more dynamic behaviour in the final stages of the
stadial (Benn et al, 1992; Golledge, 2010) which in turn likely led to enhanced modification of
sediments and landforms in marginal areas, resulting in the final distribution of moraines and
sediment sequences described in many of the papers discussed below.
Geomorpholgocial evidence can sometimes be confusing and is subject to interpretation by the
observer, sometimes leading to differences in opinion. For example the four different estimated ice
surface altitudes for the LLS ice cap from Thomspson (1972), Horsfield (1983), Thorp (1984) and
Golledge and Hubbard (2005) are based on evidence from the same area within the Grampian
Highlands. GIS-based numerical models shed greatest light on the dynamics and behaviour of former
ice masses since they are able to draw upon a wide range of datasets, incorporating numerous
techniques to deduce various glaciological parameters which can then be related to field evidence
(Napieralski et al, 2007).
1.2 Palaeoglacialogical reconstructions in determining landscape evolution
Over the past century there has been a great deal of interest in attempting to reconstruct, both
theoretically and numerically, an LLS ice cap which agrees with the palaeoclimate derived from
various environmental proxies, and the physical constraints determined through geomorphological
and geological fieldwork throughout Scotland. An increasing understanding of glacial processes and
an ever more complete catalogue of dated glacial landforms for specific stadials, gives the
opportunity for more advanced ice sheet models (ISM) to be developed, incorporating more
processes and more accurate boundary conditions to ultimately to more accurately simulate this
stadial (Glasser and Bennet, 2004). Evaluating the extent to which the inferences made from
palaeoglaciological reconstructions are consistent with landscape features and the long-term pattern
of glaciation can aid in refining General Circulation Models and ideas about landscape evolution
under different climates in order to better predict future climate change and to understand landscape

5
evolution under different climates (Benn and Lukas, 2006; Golledge et al, 2008; Lukas and Bradwell,
2010).
Traditionally, geologic and geomorphic records have been used to infer the glacial processes beneath
past ice masses, such as Sugden (1977, 1978) using contemporary ice masses as analogues in
combining landforms features with glacial theory to explain post-glacial landscapes in North
America. Thorp (1986), Finlayson (2006), Horsfield (1983) and Sissons (1979) used features of the
Scottish landscape to theorise the characteristics of parts of an LLS ice cap, assuming certain glacial
processes with regard to specific glacial landforms.
Now that an extensive record of the LLS ice margin has been documented (summarised by Clark et al
2004 – Figure 1), ISM’s can been used to iteratively reconstruct the main West Highland glacier
complex and known satellite ice fields to fit empirical limits. Recent three-dimensional LLS ice sheet
model outputs have been used to quantify the dynamics and behaviour of ice in such reconstructed
ice caps and to determine how they are likely to have varied spatially and temporally (Hubbard,
1999; Golledge et al, 2008; Golledge et al, 2009).

7
2. Scientific Basis
2.1 Landscape evolution under glaciers and ice sheets
Glacial erosional and depositional processes act to modify landscapes and following deglaciation a
variety of geomorphological evidence can be observed on the micro-, meso-, and macro-scale
(Glasser and Bennett, 2004). Most relevant to this paper is the macro-scale evidence explained
below.
When a glacier occupies a fluvial (preglacial) valley it is theorised that valley form evolves through
erosion such that ice flow becomes more efficient (Sugden and John, 1976: 179). In theory any initial
V-shaped (fluvial) channel undergoes deepening and valley-side erosion such that it becomes more
U-shaped in cross-section (Harbor, 1989). In practice it is considered unlikely that an infinitely steep
U-shape could develop and so a parabola may be more appropriate as an equilibrium form resulting
from extensive glacial erosion, illustrated in Figure 2.1 (Graf, 1970; Li et al, 2001a; Hirano and
Aniya, 1988; Li et al, 2005; Harbor and Wheeler, 1992; Harbor, 1995; Fabel et al, 2004). Long-
profile and cross-profile assessments, as well as modelling works by Harbor (1988, 1992, 1995)
support the idea that development of parabolic profiles from V-shaped profiles requires greater
erosion in the valley-bottom and along the lower valley sides compared with higher up the valley
sides. This results in the average valley depth increasing, with a much broader valley bottom and
steeper valley sides. Reynaud (1973) highlighted the importance of the V-shape in determining the
pattern of erosion by an ice mass due to the pressure distribution at the bed (Figure 2.1). Rock
strength is likely to be important in establishing a maximum slope which can be maintained and
therefore limits the development of a true parabola in places even where glacial erosion has worked
to sufficiently improve efficiency of ice flow (Pippan, 1965; Sugden and John, 1976: 182).

8
Anderson et al (2006) wrote that glacial occupation of valleys results in a distinct stepped long-valley
profile due to down-cutting by glacial erosion on a scale much greater than fluvial erosion. In
temperate glaciers the greatest erosion is likely to occur beneath the ice surface expression of the
Equilibrium Line Altitude (ELA). Ice thickness and basal flow are likely to reach a combined optimum
here which determines the greatest ice discharge, allowing more rapid erosion than elsewhere along
a glaciers profile. Also expected is a flattening of the valley floor down valley of the ELA and
steepening of it upvalley (as shown in Figure 2.2 (Penck, 1905; Sugden and John, 1976: 181). Where
confluent ice from, for example hanging valleys, joins an ice mass in a valley the ice volume similarly
increases. This leads to elevated pressure at the base, subsequent increases in basal temperatures,
water pressures, sliding and hence increased erosion (McGregor et al, 2000). This can be expressed
as a rock basin immediately down valley of a tributary, forming a stepped profile (as in Figure 2.2
inset) (Li et al, 2001; Anderson et al, 2006).
Figure 2.1 Evolution of a parabolic glacial trough cross-profile following
extensive glacial excavation through abrasion and plucking of the valley
sides and bottom. The theoretical shear stress (after Reynaud, 1973)
demonstrates the likely pattern of erosion acting on a fluvial channel,
focussing on the lower-valley sides and hence trending towards a parabola.

9
Benn (1997) noted that glacial troughs in Scotland typically have parabolic profiles and down valley
variations in the amount of erosion have in some instances resulted in ‘overdeepened basins’ close to
theoretical ELA’s (Sugden and John, 1976: 181). Although the Scottish landscape the result of
successive glacial cycles acting to reinforce the erosive work of previous ice masses, it could be
argued that the spatial pattern of erosion characteristic of the most recent stadial would be reflected
in an erosion signal in any valley affected by the appropriate stadial ice mass (Sugden, 1968; Glasser,
1995). Any valley is unlikely to be in a true equilibrium form and paraglacial processes in interstadial
periods would act to adjust the valley form back to the fluvial form suitable in unglaciated conditions,
meaning that any glacier should have to erode bedrock in order to trend towards a more efficient
channel for ice flow (Ballantyne, 2007).
A’
A
Fluvial Long-Profile
Glacial Long-Profile
A
A’
Figure 2.2 Schematic diagrams showing the concept of overdeepening in
glacial troughs under steady-state conditions as a result of abrasion
underneath the glacier sole (as in c) as ice flows from A to A’. Greatest ice
thickness and ice velocities would be expected down valley of tributaries (a &
b) and beneath the ELA (c), causing the stepped profile shown in b]. c] relates
to boxed area in b] and shows exaggerated valley deepening beneath ELA
with simplified ice flow vectors. After Boulton (1974, p76) and Anderson et al
(2006).
ELA
a]
b]
c]

10
Sugden (1978) tested the hypothesis that “landscapes of glacial erosion are related primarily to the
basal thermal regime of the ice sheet”, an idea also explored by Glasser (1995), Harbor (1988, 1995),
Wilch and Hughes (2000) and Glasser and Siegert (2002). Since the spatial variation in temperatures
at the ice-bed contact are directly linked to the distribution of water at the bed, this parameter
determines the local variation in basal sliding. It is known that where ice slides along its bed the
likelihood of erosion increases significantly (Clark, 2005). In this sense, studies based on the spatial
variation in basal temperatures of former ice caps can likely be used to analyse and explain the
spatial variations in glacial erosion described by the geomorphological record in post-glacial
environments.
Sugden (1968) detailed the importance of the preglacial topography in determining the location of ice
accumulation, direction of flow and the focussing of erosion. Assuming that each ice mass covering a
given area has the same pattern of basal temperatures then the selectivity of glacial erosion should
encourage the consistent scouring of troughs and preservation of peaks and plateaux in successive
glaciations, developing a clear erosion signal. Payne and Sugden (1990) identified the changes likely
to occur as ice flow becomes increasingly independent of topography as ice masses grow from corrie
glaciers through to ice sheets.
2.2 500m-Resolution Scottish Ice Sheet Model
Golledge et al. (2008) presented an empirically validated numerical simulation of the West Highland
ice cap shown in Ballantyne (1997), enabling the prediction of the dynamics and behaviour of the
developing ice sheet throughout a model run simulating the full length of the LLS. The latest iteration
of the three-dimensional, time-dependent coupled ice flow-climate model, developed in Hubbard et
al (2006), used by Golledge et al (2008, 2009) allows derivation of parameters including ice
thickness, basal temperatures and ice surface and bed velocities across the model domain, allowing
the calculation of patterns of basal shear stress (with some limitations). Such data allows the spatial
and temporal analysis of glacier dynamics across the ice cap, which fits well to the empirical limits at
a specific point in the model run representing the ice cap maxima.
It was found that the reconstructed ice sheet best fit empirical limits at a time slice representing 2500
model years (representing an early LLS ice maximum at about ~12.5ka BP as the start of the model
run represents 15ka BP during the lateglacial) (Golledge et al, 2008). This time period corresponds to
just after the coldest period of the Younger Dryas stadial where the model run begins at the onset of
LLS glaciation in Scotland ca. 12.5ka BP (Golledge et al, 2008; Golledge et al, 2010). Considering

11
that this ‘optimum fit’ timeslice fits well with empirical limits, it is could be assumed that at the time
that those landforms marking the maximum ice limits were formed, the former ice sheet exhibited
similar characteristics as are predicted by the ISM.
Modelled data relating to the optimum fit timeslice was provided to the author by Nicholas Golledge
(of Golledge et al, 2009) in raster format. Bed temperature and velocity, surface temperature and
velocity, proportion of the ice predicted to be sliding, ice surface altitude, and ice thickness data
were provided.
2.3 Study Area Selection
From the model data, marginal areas of the ice cap appear to be most appropriate since the outlet
glaciers in glacial troughs are predicted to have hosted thick, warm, fast-flowing ice. In much of the
central area of the ice sheet ice deformation appears to dominate, likely giving a weak erosion signal
and making any efforts to identify an LLS erosion signal difficult. Figure 2.3 shows that particularly in
the south-western portion of the ice sheet basal flow dominated in outlet glaciers. Although these
troughs likely experienced the greatest amount of erosion during the LLS the presence of lochs and
Figure 2.3 ISM data for the entire model domain. a] shows the surface ice extent at 2500-model years with
empirical LLS limits for reference and b] shows the speed-up of basal ice predicted at ice margins relative to
increasing basal temperatures. Red colours indicate highest rates of basal flow and dark blue areas indicate
stable cold-based ice. Lighter shades show intermediate areas.

12
fjord-like sea inlets under current sea level mean that any assessment of valley morphology in such
valley networks would rely on digital terrain models built entirely from bathymetrical data (not
widely available), limiting the available literature that describes geomorphological evidence in these
locations and making field checking of results largely impossible. Eastern inland areas were deemed
more appropriate, firstly due to the more sparse concentration of lochs and secondly because of the
large amount of research which has previously been done in this region due to its accessibility,
allowing this study to use the wealth of previously collected evidence. After analysis of both literature
and maps, Glen Lyon was chosen for its remoteness, rurality (limiting anthropogenic influences on
the landscape) and importantly its location relative to proposed ice domes in both the LLS and LGM.
2.4 Study Area – Glen Lyon
Glen Lyon is situated in the western Highlands of Scotland, at its source just south of Rannoch Moor
which is regarded as one of a possible two main ice accumulation and distribution centres for the LLS
ice cap (Figure 2.4) (Golledge et al, 2008). This area is considered as part of the south-eastern sector
of the LLS ice cap and various studies support the proposition of it being occupied by a dynamic
outlet glacier of the LLS ice cap throughout much of the LLS (see below). The valley, the longest in
the Highlands (>40km), is now sparsely populated and characterised by heather and grassland with
few forested areas. Although two artificial water bodies, Loch Lyon and the Stronuich reservoir lay in
Glen Lyon the availability of bathymetric data for Loch Lyon from before the hydroelectric scheme
and the small extent of Stronuich Reservoir mean that these do not pose such a hindrance to this
study.

13
Figure 2.4 Study area with locations mentioned in text.
Six principle authors have previously directly addressed the LLS glaciation of Glen Lyon: Thompson
(1972), Horsfield (1983), Thorp (1986, 1991), Golledge and Hubbard (2005) and Golledge (2006,
2007b). These studies used an array of landforms, particularly moraines, drift, erratics and striae
throughout the study area and further afield to argue for various LLS ice configurations. Thompson
(1972) concluded that a valley-glacier occupied the glen, supplied with ice accumulating in the
corries and high valleys surrounding the glen. Thompson (1972) found evidence that suggests there
were three main ice accumulation areas contributing ice to the glen: the high mountains west of Glen
Lyon; the southern side of the valley east of Loch Lyon (Coire Loaghain); and Glen Daimh. Thompson
(1972) proposed that ice in high corries and adjoining valleys on the northern side of the glen
blocked ice flowing from Rannoch Moor, yet this is contested by Golledge and Hubbard (2005).
Horsfield (1983) agreed with the limits detailed by Charlesworth (1955) in his ‘Highland Readvance’
theory but favoured the idea of an ice cap centred on the Etive and Nevis mountains that had a
maximum surface altitude much higher (>1000m) and therefore steeply sloping towards its margins

14
than the has since been suggested (Golledge and Hubbard, 2005). [Horsfield, 1983 was not available
directly therefore only comments on the paper from other studies could be used].
Thorp (1984, 1986, 1991), working mostly in the area to the north of Glen Lyon suggested the
presence of an LLS age mountain icefield in the western Grampians and developed his own
calculations of basal shear stresses in the area. His reconstruction was based on a distributed ice
network flowing around moderate to high peaks with a low maximum surface altitude (~750m),
giving a gentle surface. [Similarly, Thorp, 1984 was not available directly thus only comments on the
paper from other studies could be used – later, more detailed work by this author was of great use].
Golledge and Hubbard (2005), by summarising work by the above authors an undertaking their own
field studies and using the ISM discussed above (Hubbard, 1999) determined their own conclusions
as a combination of the previous suggestions. Most significant is the idea of an LLS ice cap with
transfluent ice flowing obliquely across Glen Lyon from Rannoch Moor to the northwest.
Golledge (2007b) assessed the sedimentological evidence for LLS glaciation in upper Glen Lyon and
the area to the west (from Loch Lomond north to Loch Tulla – Figure 2.4). He concluded that much of
the landscape is palimpsest and evidence can be ascribed to the work of the MLD ice sheet rather
than the LLS ice cap.
Glen Lyon was almost certainly not developed from a preglacial fluvial valley in a single stadial,
especially not the short (~1,400 years) LLS (Glasser and Hall, 1997). This assumption forms the basis
of this research since the method used relies on the consensus view of repeated glaciations in
Scotland.
2.5 Arising Questions
1. Do areas of high modelled basal shear stress correlate with areas where valley
morphology suggests greatest glacial erosion in repeated cycles and hence is valley
morphology explained by evidence from the LLS or does it relate to a different style
of glaciation?
2. Does the preglacial valley network and location of ice tributaries fit with areas
where valley morphology suggests greatest glacial erosion?

15
2.6 Multiple Hypotheses
The predicted patterns of basal shear stress along the valley will correlate with valley morphology to
advocate greatest erosion beneath the ELA and a decrease up and down valley of this. The least
erosion will be seen to have occurred close to the valley head and close to the snout where minimal
basal sliding and decreasing ice thickness respectively reduce ice discharge leading to less erosion.
The pattern of erosion under ice sheets preceding the LLS will mimic that of the LLS. The distribution
of major ice tributaries to the Glen Lyon glacier will have created locally elevated basal shear stresses
and have lead to valley deepening, expressed as overdeepened rock basins in the long-profile.

17
3. Approach and Methodology
Golledge et al.’s (2009) ISM fits well with empirical evidence and agrees largely with other
reconstructions, hence the dynamics and behaviour which lead to the development of ice likely
relate to those active during the LLS to some degree. Thus it was possible to compare valley
morphology with simulated ice behaviour and dynamics using GIS techniques. By assuming that
erosion is broadly proportionate to ice discharge, basal shear stress could be calculated from the ISM
data and the relationship between this and mathematically calculated valley morphology parameters
could be assessed.
3.1 Integration of bathymetrical survey data with the Digital Terrain Model
Since the NEXTMap DTM (courtesy of InterMAP Technologies) gave water surface altitudes for Loch
Lyon, data from the bathymetric Scottish loch survey of 1902 (provided by the NLS on behalf of
SEPA) was used to interpolate a coherent surface under Loch Lyon in the DTM to give a
representation of the overdeepened bedrock surface beneath the water to aid in the analysis of all
areas of the glen. In ArcGIS software ordinary kriging with an exponential semivariogram model
produced the smoothest surface that could then be spliced into the DTM.
The bathymetrical survey did not include height information for beyond natural loch shoreline so it
was necessary to extrapolate a surface from the average change in altitude between the last loch
isobath (340m) and a point beyond the Loch Lyon Dam at Pubil. This gave me an average decrease
in elevation of 0.6667m for every 100m in the down-valley direction for 3.9km. These data could be
combined with the present-day loch shore coordinates provided by NLS to give a coherent bed
surface likely to reflect the bed profile present at the end of the LLS. A similar extrapolation was
carried out to remove the expression of the Stronuich Reservoir from the DTM.
The DTM is 2m resolution in the horizontal direction and 1.25m in the vertical, apart from over Loch
Lyon where the resolution is 17.2m cell size based on the minimum distance between data points.
This can be considered high resolution, adding important precision to the below analyses
(Napieralski et al, 2007, Goodenough et al, 2009).

18
3.2 Ice Sheet Model Data Manipulation
Subglacial processes are important since they “determine the large-scale behaviour of glaciers and
ice sheets” (Clarke, 2005). In an effort to quantify erosion power at the ice-bed interface both basal
shear stress and a relative ‘erosion potential’ were calculated from the ISM output (Clarke, 2005).
The erosion potential calculation used (Equation 1) incorporates basal velocity (Vb) and ice thickness
(H) to determine the likely areas where glacial erosion would be focussed (Jamieson et al, 2008).
Erodibility (f) had to be ignored (so f = 1) in the calculations (as in Golledge et al, 2009) due to
difficulties in estimating rock erodibility coefficients from the available data (Hooke and Rohrer,
1977; Annandale, 2005). Lithology was also ignored by Li et al (2001) where they suggest that
lithology has greatest effects on micro-landforms and not the overall valley cross-sectional shape,
something contested by Harbor (1995). Erosion potential units are arbitrary.
Basal shear stress was calculated to test whether a similar pattern of erosion would be expected when
incorporating slightly different parameters. Basal shear stress is a function of ice density (917kg/m-3
),
acceleration due to gravity (9.8m/s2
), ice thickness and the ice surface slope (Jamieson et al, 2005).
(1) Erosion potential
E = – f | Vb | H
(2) Basal Shear Stress
!b = ".g.h.sina
The resulting basal shear stress units are in millibar yet the units are largely arbitrary and relative due
to the lack of sufficiently accurate predictions of basal thermal conditions.
After calculation of these parameters from data layers within the GIS, the overall patterns given by the
different parameters were the same and hence basal shear stress was chosen for graphical
representation. Since both relate so closely, they are both discussed as basal shear stress in the
remainder of the report since neither offers clear advantages in accuracy over the other.
3.3 Long-Profile Analysis
In order to assess the relationship between predicted erosion patterns and landforms suggestive of
significant removal of material from the valley bottom, a long valley profile was extracted from the
modified DTM. Sinks in the DTM were filled to form a hydrologically consistent surface and
Hydrology functions within ArcMap’s Spatial Analyst Tools were implemented in order to extract the
stream network and ultimately sample altitudes along the main river channel. The extrapolated
profile was also used to sample basal shear stress data from the DTM.

19
3.4 Morphometric Analysis
Cross-Profile Extrapolation
25 transects were extracted from the DTM perpendicular to the valley to calculate cross-profile
morphology (Figure 3). Transects were placed such that hanging valleys, corries and other connecting
valley segments were avoided, taking profiles only where coherent valley sides of similar height were
present on both sides; allowing full geometric assessment of trough form. Spacing between transects
was thus decided by topography rather than a set interval. Initially the issue of ‘where does a valley
end and a hill begin?’ arose due to the complexities of topography in this area of the Scottish
Highlands. Thompson (1972) stated that it is difficult to identify ice limits in Glen Lyon since the ice
surface altitude meant that all but the highest peaks, for example Meall Ghaordaidh and Stuchd an
Lochain, were overwhelmed by ice. Thus, transects were drawn from one peak or break in slope to
another on the opposite side of the valley. Once transects were extracted they were edited to divide
each transect into points spaced 5m apart.
Figure 3 Transect locations relative to modelled and empirical LLS limits.
Geometric Assessment
Such a geometric assessment of valley morphology does not appear to have been employed to assess
systematic changes in valley cross sections longitudinally along valleys affected by ice sheets and ice
caps. Rather than evaluating the usefulness of geometric power models in calculating valley form,
here I use the most appropriate and versatile model to quantitatively assess the macro-scale evidence
for ice dynamics relative to those predicted by the ISM.

20
Svensson (1959) was the first to propose the use of a power law (Equation 3) to numerically represent
valley form.
(3) Original power Law
y = a x b
Where y is valley depth, x is distance from the valley centre (origin, x, y = 0) and a and b are
constants relating to the slope of the curve. Solving this original power law involves the fitting of a
curve to the logarithmic transform of the observed cross-profile data (Doornkamp and King, 1971),
which Pattyn and Huele (1998) suggest is problematic for two main reasons. The first is that this law
is highly sensitive to the selection of the origin in the valley bottom that all other points are
considered relative to. The second is in the bias given to points closest to the origin in developing a
best-fit curve when the equation is in its logarithmic transform (Li et al, 2001a). Further this original
power law can only be reliably used to analyse cross-profile data from a single valley side since
Equation 3 can only use positive values, necessitating an assumption of valley symmetry or the
implementation of two separate analyses for each valley side that are not directly comparable
(Harbor and Wheeler, 1992; Pattyn and Huele, 1998).
Due to these problems the general power law (GPL), developed by Pattyn and Huele (1998) based on
the original power law introduced by Svensson (1959), was chosen for the morphological analyses.
This method is based on the fitting of a curve to the actual valley cross-profile data through a series of
x, y coordinates along a transect as a function of the distance (x) or elevation (y) from the origin (x0,
y0 in Equation 4), avoiding the logarithmic transform of the data. The resultant curve describes the
form of the true cross-profile data rather than the form of a logarithmic trough. The GPL is presented
as:
(4) General Power Law
y – y0 = a | x – x0 | b
y0 and x0 are the coordinates of the origin and a is the slope. The equation can be solved using a
general least-squares method allowing better curve-fitting to trough cross-sections, treating the entire
cross-section at once rather than a single side. This allowing comparison of different cross sections
along the valley not relative to one another but relative to basal shear stress. First, each coordinate
along the cross-profile gives a measurement vector (x, y coordinate). The coordinates of the origin
and the slope act as unknowns whilst exponent b is considered as a known value through iteratively
repeating the least squares analysis for a large number of different b values until a best-fit can be
found. The benefit of this method over the original power law is that it allows a more dynamic fitting

21
of curves to the data in order to produce a better fit through continual adjustment of the unknown
values until a curve of b value where with the lowest Root Mean Squared error (RMSE) is found.
Since this method implements a large number of iterations to find the most suitable curve the
software ‘GPL’ developed by Pattyn and Huele (1998) proved infinitely useful in the rapid calculation
of valley cross-profile form. From the software’s simple output one is able to easily assess the
closeness of the cross-profile to a parabola (b = 2.0) as well as plot the coordinates of the fitted curve
(new-y) (See Appendix I for sample output file). The GPL is intended for bedrock channels and hence
any major sediment accumulations should be removed (Harbor and Wheeler, 1992). For the most
part this could not be achieved since sediment depths could not be determined. Small irregularities
were however removed from the transect cross-profiles yet where more pronounced valley-side the
protrusions were found it was not possible to determine whether they represented glacio-fluvial
sediment accumulations or bedrock features. Data points outlining these features were given lower
importance than others in the GPL. In Figure 2.1 the fluvial profile has a b value of 1.0 whereas the
parabolic profile has a b value of 2.0.
By calculating the Form Ratios (FR) as proposed by Graf (1970), a more complete representation of
overall valley form can be established when compared with data from the GPL (Hirano and Aniya,
1988). FR essentially involves the comparison of trough depth (D) and the width at the top of the
section (Wt):
(5) Form ratio
FR = D / Wt
3.5 Other Methods
Previous to and following the above procedures the glen was visited in order to gain a better
understanding of the orientation of hills, valleys and the interpreted evidence for ice flow during the
LLS. Checking of the chosen transect locations in the field was also necessary to ensure sufficient
coverage. These excursions were not an attempt to remap features already identified by others but a
means to ensure personal agreement with the proposed ice limits and configuration of likely
tributaries to the Lyon ice glacier.
For discussion of the bedrock geology a 50m resolution bedrock geology dataset (on behalf of BGS)
were also incorporated into the GIS to allow further relationships to be explored.

23
4. Results
4.1 Mapped results
The modelled data shows that basal shear stress is broadly greatest in the centre of valleys (Figure
4.1a). Figure 4.1b shows the areas along Glen Lyon in which the model simulates ice to be flowing in
from other catchments, most notably from Rannoch Moor between Beinn a’ Chreachain and Meall
Buidhe (see Figure 2.4) and from Glen Daimh. A more precise description of the basal shear stress
fluctuations is shown in Figure 4.2a, b and c since Figures 4.1a and b are only of use for
demonstrating the variations away from the main valley centreline. Much lower basal shear stresses
are shown to be predicted on peaks, especially in marginal areas. The model predicts higher basal
shear stresses in the centre, particularly along the Highland boundary fault than would immediately
be expected.
4.2 Long-Profile
After extraction of the present-day river long profile from the adjusted DTM there is a clear gently
sloping ground surface (~ -5m/km) (Figure 4.2). An overly deep basin can be seen at ~6km from the
valley-head where the unflooded Loch Lyon shoreline begins. The loch can be seen to be deeper at
the up-valley end, suggesting that the erosion that brought about such a landform decreased
gradually with distance from the deepest point. The loch’s location matches with the location of a
peak in basal shear stress close to 8km.
Some areas where the steady valley gradient is punctuated with steeper sections up valley of rock
basins, coinciding with main valley tributaries, notably at around 14-15, 25-27, 32-34 and 43-44km
in Figure 4.1d. The drop in ground elevation approximately 47km from the valley head denotes
where Glen Lyon joins with the Tay valley, a considerably larger valley. This principally confirms that
the ice volume increases are likely to occur in the vicinity of tributaries and are associated with
increases in erosion vertically downwards. Increases in ice thickness and basal shear stress relate to
the location of tributaries at approximately 11-12, 13-14, 23-24 and 25-27km from the valley head,
providing evidence for this contention.

24
Figure4.1a]BasalshearstressacrossmodelledScottishLLSicecap.Boxedareashowninb.
b]showsbasalshearstressacrossGlenLyonareawithclearchannel(highbasalshearstress)
alongthecentreoftheGlen.Placesmentionedintextalsoshown.
a]b]

25
Figure 4.2 Subplots showing: a] The form ratio, b] A value and c] b value for each cross
section profile relative to basal shear stress (scale same in a] and b] as c] for basal shear stress)
extracted from the ISM along the present-day river; d] and ice surface altitude relative to bed
long-profile interpolated to incorporate loch bathymetry data, and main tributaries to the
valley as identified by Thompson (1972) and through personal field work. Equilibrium Line
Altitude (ELA) suggested by Golledge (2007a). Transects named 1-25 from left to right on
figure.

26
4.3 Valley Cross-Profiles (Full valley cross-profile dataset in Appendix II)
The key statistical descriptions given in Table 4 and the general trends shown in Figure 4.1
demonstrate the variation in valley cross-profile morphology found using the GPL. The exact same
trends for A as b values can be seen in Figure 4.1b and c only inverse due to their derivation from
similar parameters (correlation between the two calculated as rp = -0.995 significant at the 99%
level). This can be used to state that whatever processes determine b values have the opposite effect
on A values. Hence I will here only discuss the b values since these relate most usefully to the curve
of the line fitted to the extracted data (Harbor and Wheeler, 1992). A similar approach was used by Li
et al (2001a).
Table 4 Statistical descriptions of valley morphology coefficients from Glen Lyon.
b values
The maximum and minimum b values demonstrate the range of overall cross-profile shapes from
roughly V-shaped (0.71- ~1.5) to roughly U-shaped (~1.5-2.06). The mean here shows that in general
the glen does not exhibit the clear curved valley side profiles expected of glacial troughs. In six main
places the b value approaches or exceeds 2.0 suggesting significant glacial erosion and preservation
of valley form since deglaciation. Four of these values relate to transects taken within the LLS ice
limits. Transects 9, 10 and 11 are taken in the area between Stronuich reservoir and the Glen Daimh
confluence where the valley narrows and changes direction until the confluence, possibly increasing
the erosion potential, in particular upon the outside of the bend (reflected in the slightly steeper
valley side on the southern valley side in Figure 4.2 – Transect 10). This, as shown in Figure 1.2 (main
valley map with basal shear) and Figure 4.1 relates to an area of increasing basal shear stress. The
increased b value at Transect 15 does not specifically correlate with a peak in basal shear stress yet
its location relative to the Glen Daimh ice tributary and a significant drop in the valley-bottom
altitude suggests the influence of the increased ice volume on erosion under different basal
conditions than predicted.
Interestingly, there is a drop in b values in the immediate vicinity of the Glen Daimh tributary
(transects 12, 13, 14) where there is a notable peak in modelled basal shear stress following a small
decrease. Ice thickness decreases between this tributary and the previous one probably as a result of
A b a Width (m) Height (m) FR
Mean -3.450 1.3468 0.298 0.1630
Maximum 1.1 2.06 3.00 4080 0.2355
Minimum -8.1 0.71 0.00 0.0884

27
the increasing valley width, allowing ice to spread laterally across the valley, decreasing basal shear
stress.
Transect 24
Transect 10
Transect 17
Figure 4.3 Example transects to show key characteristics mentioned in the text.

28
Although b values vary in some respects relative to basal shear stress (Figure 4.2c) the relationship
appears to be complicated by some other factor not clear here. In places (such as up until 8km from
valley-head) the two datasets correlate positively, yet at other points (such as from 11-16km) where
there is a marked increase in basal shear stress b values continue to fall until the general trend in
basal shear stress climbs again at 16km showing weak negative correlation (rs = -0.295).
The scale of fluctuations in b decreases between the modelled and empirical LLS limits (empirical
limits ~8km further down valley from the modelled limits according to Thompson (1972)), alongside
complete reversals in the trend at each transect. Essentially this results in b values more consistently
close to 2.0 (a parabolic form) yet the average b value is still only 1.48 (semi-parabolic) in this area.
Form Ratio (FR)
Relative to other studies, the form ratios calculated for the glen are low, with a maximum of just over
0.2 where other valleys have exhibited FR’s closer to 1.0. Nevertheless, there is a notable increase in
FR values beyond the LLS limits. The fluctuations down valley indicate the diverse influences on
valley form. Thompson (1972) notes that close to the ‘mouth’ of the valley, there is deep gorging
where the valley becomes narrow (higher FR), possibly a reflection on the bedrock geology (Appendix
III) where the deeper Appin and Grampian strata become exposed in a similar location (Cummins
and Shackleton (1955). The narrowing may also relate to the retention or return to the linear fluvial
morphology, as suggested by Transect 24 (Figure 4.2). Down valley narrowing of the valley could
have lead to increased stream power and hence rapid incision leading to headward knick-point
propagation following a drop in base level since final deglaciation (Reinhardt et al, 2007; Korup and
Schlunegger, 2007).

29
Hirano and Aniya (1988) highlighted the importance of comparing b and FR values to assess the
relationship between deepening and widening of the valley. In some areas b increases whilst FR
decreases and in others the opposite can be seen to occur (Figure 4.1a and c). Moreover, the internal
fluctuations in each dataset are not uniform which has led to scatter within the b-FR diagram (Figure
4.3). This possibly relates to the differing relative amounts of erosion through different styles (be it
from valley glacier, ice sheet, fluvial or general hillslope) that has affected each area within the glen.
There is significant correlation between b and FR at the 95% level of 0.419 and the b-FR relationship.
Both show larger and more infrequent changes in the upper glen and an increase in the average
values down valley which suggests more parabolic, deep-rather-than-wide cross-profiles beyond the
LLS limits (population of grey-centred data points in the upper right of Figure 4.3) – suggesting greater
alpine style glaciation in this area. Possibly inferring a greater mix in the styles of erosion in the upper
glen.
Figure 4.4 b-FR diagram showing important relationship between valley side shape and changes
in deepening versus widening. Positive trend shows correlation between cross-profiles with
semi- and true-parabolas and deep rather than wide sections. Scatter may be explained by
differing styles of glacial erosion, proceeding hillslope adjustments and sediment deposition.

30
4.4 Depositional features
Transect profiles show that areas
away from the reservoirs generally
show a significant fluvial plain in
the valley bottom ranging from
~0.3km to >1km width and up to
approximately 30m in depth
according to the valley profiles
predicted by the GPL (e.g. Figure
4.2 – Transect 17 and Figure
4.4a). River incision appears to
have been on the order of 0.5 –
3m into this medium, not
changing uniformly down valley.
Two main fluvial terraces outwith
the LLS limits are present along
much of the valley bottom, with
the higher one approximately 3m
above the current shallow river
bed (Main Holocene Terrace –
Ballantyne, 2008) and the lower
one closer to 1m above. Within
the LLS limits a single terrace is
present, with a height of
approximately 2.5-3m. Personal
field research indicated that in places significant valley-side deposits are present, hiding the true
bedrock form. For example, Figure 4.4b shows talus slopes suggesting a very steep rock slope
beneath the sediment, which has accumulated down slope of the outcrop. At the base of the steep
hillslopes on the northern valley side adjacent to Loch Lyon, there is widespread evidence of mass
movements in the regolith layer where and even deeply cut freshly exposed sections do not reveal
bedrock, indicating a deep surficial sediment layer.
Although this and a widespread surface layer of peat influences the valley cross profiles and their
associated b and FR values, such deposits could not uniformly be removed due to variation at every
stage along the valley. It is possible that a significant depth of sediment is present in some cases,
where generally smooth valley sides intersect the flat valley-bottom with a sharp change in angle.
Figure 4.5 Photographic evidence for depositional features on a] the
fluvial plain at the Glen Daimh tributary; b] the valley sides at the
eastern end of Loch Lyon looking north.
a]
b]

31
This post-glacial fill is not representative of the true bedrock valley morphology. According to the
long profile Transect 17 is in the locality of a rock basin which may explain the significant valley-
bottom infilling. Other transects, such as the post-glacial fluvial system, act to return the stepped long
profile to the smooth profile characteristic of fluvial systems.
For detailed discussion on depositional features mapped by others see the following section.

33
5. Discussion
5.1 Loch Lyon: evidence for a Glen Lyon valley glacier?
The peak in basal shear stress predicted at ~8km from the valley head is likely due to the
convergence of ice at the upper end of Loch Lyon (Figure 5.1). Even if ice were only sourced from
within Glen Lyon, for example if the Lyon glacier were not connected to a larger ice cap, then this
concentration of ice flow may explain the closer to parabolic cross-profiles in part of this area (Figure
4.2c). It may in part explain the considerable overdeepening which must have occurred to produce
Loch Lyon. In fact, Thomspon (1972) suggested that ice flowing from Rannoch Moor (Figure 1) may
have been blocked by the hills at the western end of Glen Lyon and ice within the upper reaches of
the glen may have been sourced largely from within it (Figure 5.1). The oblique (south-easterly) ice
flow direction put forward by Horsfield (1983) and Golledge and Hubbard (2005) during the LLS
cannot easily explain the location of Loch Lyon. Hence, the idea of topographically constrained
convergent ice flowing from within the Lyon catchment seems more appropriate, especially since the
slopes within this catchment are generally north facing which fits well with evidence for lingering or
early ice mass formation at the start or end of the preceding interstadial (Bradwell et al, 2008;
Golledge, 2007b, 2010). A similar explanation was drawn for the overdeepening found in Yosemite
Valley by Macgregor et al (2000). This suggestion complicates the contention that the morphological
evidence in the contemporary glen can be explained by the most recent glaciation.
The proposed location of the LLS ELA over Glen Lyon at 550m means a surface expression around
23km from the valley head given the modelled ice surface profile (Figure 4.2d) (Golledge, 2007a).
Theoretically the ELA should correspond with the area of greatest erosion along the valley due to it
likely being the area of greatest ice discharge (Sugden and John, 1976: 183; MacGregor, 2000). In the
case of Glen Lyon this would appear to be around the location of the loch (where Figure 4.2c shows
elevated b values and a deep rock basin in Figure 4.2d) yet for the loch to be the area of highest
erosion one would expect the ELA to be somewhat higher, at around 780m, possibly in a significantly
warmer or dryer climate (Li et al, 2001). Interestingly, a firn line altitude of between 7-800m was
proposed by Sissons (1979), giving possible backing to this proposal. This is further evidence for a
valley-glacier style of glaciation in some stadial when the large ice cap centred on the high
mountains of the Western Highlands may not have occupied Glen Lyon.

34
The ice dome proposed to have lain on the hills at the northwest of Figure 5.1 during the Main Late
Devensian could also provide a suitable explanation (Thorp, 1987). The lack of well-defined trimlines
in the Glen (likely due to LLS ice covering all but the highest peaks – Figure 4.1b) does not allow for
an accurate general LLS ice surface altitude to be developed without extrapolation from Invervar to
known ice surface heights from Rannoch Moor, a distance of >15km between the two means that
such an estimate may be imprecise (Figure 2.4). Kuhle (1988) highlighted the importance of glacier
geometry in determining ELA from geomorphological evidence (Golledge and Hubbard, 2005).
Where a more gentle ice surface profile is assumed the ELA appears further up-valley, hence
explaining the location, but not orientation of Loch Lyon, especially due to the proposed obliquity of
ice flow, meaning flow parallel to upper Loch Lyon only occurred during active retreat. Golledge and
Hubbard (2005) used a range of ice marginal features and erratic locations to constrain the upper
limits of the LLS ice cap in Glen Lyon, arguing for a steep ice margin and an ice surface altitude of
>900m. These contrasting proposals likely go some way to explaining the large-scale morphological
evidence for LLS glaciation in the Glen. If in numerous stadials transfluent ice from distant ice domes
entered the Glen from the northwest and flowed in a south-easterly direction during intermediate
phases (high ice volume) and only flowed parallel to the valley long-profile during early and late
Figure 5.1 Limits to the upper Lyon catchment contributing ice directly to the Loch
Lyon area from within the glen only. Vectors show ice flow from Rannoch Moor ice
accumulation zone and dashed line indicates the mountains which blocked this ice
flow according to Thompson (1972).

35
phases of glaciation then the location of Loch Lyon and the varied cross-profile morphology can
explain a common trend in Scottish glaciations (Payne and Sugden, 1990).
5.2 Beyond the LLS limits
Whilst some issues with the reliability of form ratios calculated here may have arisen due to the
absence of trim lines in much of the valley (Graf, 1970), the change in trend of b and FR values
beyond the LLS limits (Table 5 and Figure 4.2a and c) may reflect the theoretical increase in basal
erosion further from the accumulation area of any glacier occupying the glen – not only the LLS ice
cap. Relating Glen Lyon to allometric fluvial principles (stream order), as proposed by Graf (1970),
could explain the slight step change in b and FR values beyond the modelled ice limit, since it is likely
that the ice entering Glen Lyon from Glen Daimh (increasing stream order) explains the change rather
than evidence actually relating to the LLS ice cap. Figure 4.1b shows the extensive area which given
the proposed southwesterly flow direction would contribute to the ice entering Glen Lyon at this
confluence (Table 5). Although ice discharge does not increase continually down valley as in fluvial
systems, the punctuated increases in basal shear stress and the presence of rock basins in this study
further confirms ice tributaries as a reason for increased basal erosion in glacial valleys (Penck, 1905;
Sugden and John, 1976: 181; Anderson et al, 2006).
The idea of the elevated FR values reflecting deeper, narrower valley cross-profiles at the mouth of the
glen being used to infer a more common valley-glacier configuration this far down valley may be
unjustified. Should the long-term pattern of glaciation be defined by more expansive ice cover in the
upper reaches of the glen and topographically constrained ice streams in the lower reaches, then one
would expect broadly different topography in general and much higher FR values than were found.
According to Hirano and Aniya’s (1988) work, the low FR values given in Table 5 (and Figure 4.3)
suggest a relationship between valley depth and width more likely to relate to ice sheet erosion (Li et
al, 2001a). The slightly higher b values in the down valley area do however suggest more focussed
erosion in the valley bottom, still representative of a valley glacier style of erosion not appropriate to
that of the MLD ice sheet at full extent, but possibly during growth or decay (Kleman et al, 2008).
Hall and Glasser (2003) found that despite the assumption that much of the topography of Scotland
can be described as a the product of selective linear erosion, basal sliding and hence rapid erosion
may not have simply occurred in glacial troughs (as in valley glaciers and icefields) but may have
Above tributary Below tributary
Average b 1.279 1.406
Average FR 0.144 0.182
Table 5 Changes in main valley morphology down valley of the Glen
Daimh tributary

36
extended up to valley heads, particularly in glaciations predating the Late Devensian – possibly
explaining the limited number of transects with exhibiting deep parabolic forms (high b and FR)
(Sugden, 1968; Stokes and Clarke, 1999; Hall and Glasser, 2003). Figure 4.1b shows the low basal
shear stresses expected on peaks during the LLS, possibly giving ruling out widespread erosion during
this stadial. Nonetheless, this conflicting evidence suggests varied styles of glaciation acting on
different timescales, as was found by Finlayson (2006) in an area north of Glen Lyon and supported
by the work of Hubbard et al (2009).
5.3 Micro- and meso-scale evidence
The smaller scale sedimentological features, as mapped by Thompson (1972), Golledge (2006,
2007b) and Hubbard and Golledge (2005) seem to reflect the flow characteristics inferred by other
studies reflecting the work of the LLS ice cap. This does not come as a surprise since any surface
obstructions to flow made of easily deformable sediments or (rocks) from preceding stadials would be
removed by renewed glacial activity (Sugden and John, 1976: 185). Golledge and Hubbard (2005)
used the orientation of moraines along the base of the southern valley as evidence for their support
for oblique ice flow (Horfield, 1983) rather than flow parallel to the valley long-profile in a valley-
type glaciation as proposed by Thompson (1972).
Golledge (2007b) mapped glacial deposits in a significant portion of the upper glen and highlighted
that here, and in the area immediately to the west (Rannoch Moor and Bridge of Orchy), mapping of
such features has previously brought about a number of conclusions regarding glaciation at different
stages in the Pleistocene. Some infer the dominant effects of the Last Glacial Maximum ice sheet
(Hinxman et al, 1923), the Main Late Devensian glaciation (Sissons, 1965), and a highland readvance
or LLS ice cap (Charlesworth, 1955; Thompson, 1972; Horsfield, 1983; Thorp, 1986, 1991).
Importantly Golledge (2007b) makes clear the case that evidence is varied. Scouring and deep
significant erosional forms relating to specific glaciations are present in some areas where preserved
sediment sequences are present in others, not always where one would expect dynamic behaviour
and subsequent sediment disturbance to be at a minimum.
According to Clark et al (2004) and Golledge (pers. comm. 2010) one would expect slopes outwith
the LLS limits to exhibit evidence of more periglacial activity (scree), yet their earlier exposure than
slopes exposed during glacial erosion within the LLS limits will mean that they may be more
extensively vegetated mature features extending high against the source rockwalls, whereas those
features created since LLS deglaciation are still active. To some degree the active nature of slopes can

37
be seen in Figure 4.4b (within LLS limits). The slopes are however greatly varied and often shallow
gradients throughout the area lend limited support to this claim.
Although the scale and location of fluvial terraces are not directly relevant to the answering of the
research questions posed herein, they do emphasise the importance of rates of paraglacial activity
and morphological adjustments to isostatic uplift on the preservation of the valley forms seen
immediately following deglaciation (Shennan et al, 2005; Ballantyne, 2008). Furthermore, they
highlight the difficulties in determining the exact morphology of glacial valleys formed by former ice
masses (see Figure 4.3 – Transect 17).
The varied evidence used by these authors likely suggests that a range of different glaciological
conditions have led to the depositional features which, although mostly relating to deglaciation,
begin to explain the contrasting evidence provided by the morphological assessment detailed herein
(Glasser and Bennet, 2004).
5.4 The preglacial valley network in focussing erosion
The meanders in Glen Lyon are an initial indication of the importance of the preglacial valley
network in guiding ice flow since there is no reason for ice to meander, unlike water (Sugden and
John, 1976: 185). From the overdeepenings of the long-profile shown in the Figure 4.2d and the
correlation between tributaries and locations of higher b and FR values it seems likely that the
location of ice tributaries plays a huge role in determining the areas of elevated ice discharge after the
ELA and in determining the macro-scale valley morphology (Thorp, 1987). These overdeepenings are
much more distinct and reliable than changes in morphology related solely to distance from the
valley head or other vague parameters, suggesting that at least in the case of the long-profile the
location of tributaries is the dominant factor in its form development over successive glacial cycles
since this does not change vastly whereas the extent or basal thermal conditions may vary greatly.
Despite the valley network determining the broad direction and location of major ice accumulations,
it could actually be that the differing glacial conditions lead to different focussing of erosion in each
stadial – not lending itself to the preservation of the parabolic trough form (Nicolas Hulton pers.
comm. 2011). For example, if Thompson (1972) and Horsfield (1983) are both correct in their
different inferences of styles of glaciation at some point in growth cycles of Late Devensian ice
masses, then erosion maxima would likely range from close to Loch Lyon (Thompson) to the area
around the Glen Daimh confluence (Horsfield), an idea supported by Golledge (2007a). In any case,
the trends shown in the cross-profile morphology may be better explained by basal shear stress

38
calculations for a modelled MLD ISM, such as that in Hubbard et al (2009). The higher basal shear
stresses in the MLD ice sheet at full extent would likely have occurred much closer to the east coast,
where marine-terminating outlet glaciers would be prevalent, although the model simulation shown
in Figure 4.1a suggests that the depth of ice in central regions creates highest basal shear stresses
since basal temperatures are not incorporated into these calculations. The LGM model in Hubbard et
al (2009) predicts that for a high percentage of time during the MLD central areas of Scotland would
experience temperatures below the pressure melting point – increasing the likelihood of landform
preservation, as in the LLS (Golledge, 2006, 2007b). This may lend to the suggestion that valleys in
central Scotland (eg. Glen Lyon) were largely eroded during phases of limited erosion during longer
stadials than the LLS, rather than under full ice sheet conditions. Hubbard et al (2009) suggest that ice
caps similar in extent to the LLS may have been prevalent before the Tolsta Interstadial which
preceded the LGM BIIS ice growth phase. A similar conclusion was made by Kleman et al (2008)
when attempting to explain the distribution of landscape features across Fennoscandia where they
found that a full Fennoscandian Ice Sheet, known to have occupied the subcontinent for a significant
proportion of the Pleistocene would not explain the deep gorging seen in central areas since a similar
distribution of basal sliding and hence basal temperatures as shown in Figure 2.3b (creep-dominated
central areas) would be expected.
5.5 Alternative Explanations
The complex distribution of different valley morphologies could well be a result of the underlying
bedrock geology since Burbank et al (1996) concluded that slopes are more related to rock type than
large-scale geomorphic processes. Variations in lithology were not incorporated into the basal shear
stress calculation due to associated complexities, possibly leading to overestimations of basal shear
stress (Augustinus, 1992; Annadale, 2005) and so a more basic visual interpretation must be made.
There are 3 main strata underlying the Glen: Ben Lawers calcareous schists, Ben Lui garnetiferous
schists and Ben Eagach graphitic schists (Appendix III and Cummins and Shackleton, 1955). There are
also some metalimestone layers and rocks from the Carn Mairg Quartzite group, primarily in the form
of quartzite and psammite close to the valley head and gritty psammite close to Invervar. Analysis of
the correlation between different rock types and the variation in valley morphology (Appendix III)
does not help to explain the long-profile form as well as do the location of ice tributaries. Three
example transects were selected from the b-FR diagram to represent areas of high, moderate and low
level glacial modification (Figures 5.2a, b, and c respectively). The high and moderate scenarios do
show some consistency in that the high scenario is dominated by semipelite and the moderate
scenario is largely consists of quartz. The relationship is however inconsistent and other transects, for
example Transect 7 (Figure 5.2c) and other cases of high, moderate and low b and FR values do not

39
a]
b]
c]
Figure 5.2 Bedrock geology along profiles a] Transect 17 (HIGH); b] Transect
4 (MOD); and c] Transect 7 (LOW). It does not provide a clear explanation of
breaks in slope nor overall valley morphology since each transect has very
different geology.

40
show reliable correlation with bedrock geology as would be expected (Sugden and John, 1976: 181;
Goodenough et al, 2009). It would be expected that areas dominated by quartz would have the
highest b and FR values (closest to deep, narrow parabolic form) since steeper slopes would be
maintained relative to other lithologies (Sugden and John, 1976: 182). On a larger scale the variations
in bedrock geology might be visible, for example across Scotland more generally. The hard
metamorphic rocks in Glen Lyon are likely not as easily affected by glacial erosion as much weaker
rocks elsewhere.
Harbor (1995) states that although valleys theoretically trend towards parabolic cross-sections, the
complexities in erosion and hillslope processes during glaciation can produce a variety of cross-
sectional forms. Moreover, Harbor’s (1995) modelling experiments showed that a small amount of
post-glacial fill of sediment into a valley bottom given certain erodibility characteristics of the
dominant lithologies could lead to valley-side slopes more representative of fluvial erosion than
glacial erosion. Such factors may mean that cross profiles identified here as fluvial forms (such as
Transect 4 and 17) may in fact exhibit bedrock channels closer to parabolic form (Harbor and
Wheeler, 1992). Whether the ‘evidence’ left by the last stadial should include valley-side deposits
which may or may not relate to the LLS or paraglacial activity is an important consideration since it
may have a significant influence on the interpreted pattern of erosion related to the predicted basal
shear stress in studies such as this.
5.6 Methodological Limitations
A number of factors prove the ISM data used to derive ice behaviour and dynamics to be possibly
erroneous. These are detailed more fully in Appendix IV so as not to draw attention away from the
key questions addressed in this study but the two key factors will be discussed here. Firstly the issue
that the modelled ice cap predicts the snout to be 8km further upvalley than empirical evidence
suggests may have led to miscalculations of basal shear stress since 3 major ice tributaries were
significant during the LLS were not seen to contribute ice to Glen Lyon in the ISM. Such
miscalculations may have led to the misinterpretation of valley morphology parameters in relation to
basal shear stress (Golledge et al, 2010).
Second is the issue of model resolution. The modelled ice sheet was ‘grown’ on the same high
resolution NEXTMap DTM as is used here, yet the ice cap which develops has a resolution of 500m.
Since the model was intended to demonstrate ice-cap wide changes dynamics and behaviour it fits its
purpose well, however, for the smaller-scale study presented in this paper the information given is
limited. The basic simulated pattern is possibly sufficient, especially considering that during

41
calculations of basal shear stress each cell in the DTM was included in calculations relative to the
overlying ice thickness and ice flow rasters, providing estimated basal shear stress on a scale relative
to the resolution of the DTM. This may still have introduced a miss-representation of basal shear
stress and not allowed for accurate variations to be properly calculated.
In a hypothetical situation the basal thermal conditions under the ice masses of any two stadials
lasting the same amount of time, even with similar maximum extents, are likely to vary since the ice
originates from different climatic scenarios and the second ice mass must build on a more
geomorphologically developed landscape after already being affected by the previous stadial and
interglacial (N.Hulton pers. comm. 2011). Thus, the basic spatial pattern of basal thermal conditions
of any similarly sized and oriented ice masses is all that could be definitively compared.
Unfortunately, the lack of preservation of sedimentological evidence from stadials similar in length to
the LLS after excavation during the MLD glaciation and subsequent reworking of sediment and further
erosion during the lateglacial and LLS means that such a direct comparison of spatial patterns cannot
be made. Realistically even the hypothetical situation is unlikely. Even the simplest assumption here
is unlikely since two stadials are unlikely to last the same amount of time. This could result in the
greater evolution of the basal thermal regime during the longer stadial, giving rise to warmer basal
temperatures and more extensive basal erosion (Clark, 2005).
The majority of evidence used to determine the empirical limits, ice surface altitude and gradient and
flow directions during the LLS by authors such as Thompson (1972) comes largely from the
sedimentological record and the expected ice configurations from the existing valley network. As
with other eastern outlet glaciers (western outlet glaciers mostly drained into sea lochs with fjord-like
morphologies, providing pinning points which stabilised ice margins and maintained more consistent
erosion patterns (Greene, 1992)) the empirical LLS ice margin in Glen Lyon, close to Invervar (Figure
2.4) is only a maximum limit, this is unlikely to be representative of the ice margin over the 1,400
years of the LLS which may have been any distance further upvalley (Golledge, 2007b). Timings of
the various stages in the ice caps growth cycle are disputed (Clapperton, 1997; Murray-Gray, 1997).
Typically ISM’s and various dating proxies agree on an early to mid-stadial ice volume maximum
(12.7-12.5 ka), although varve records contest such an early maximum, suggesting a later peak
(~11.9 ka) in the area close to Glen Roy (Palmer et al, 2010; Palmer, 2008). If the maximum
conditions represented by the ISM data were only reached close to the end of the LLS then the
relationships found in the data may be built on false assumptions. In such a way, Golledge (2007b)
argues that the majority of the (limited) work done by the LLS ice cap is likely to have occurred
during the warm period which accompanied deglaciation, with flow mechanisms being limited to
certain areas, during limited time periods (Sugden, 1970).

42
The dynamic nature of mid-latitude ice masses and the range of climatic conditions which have
caused the glaciations in Scotland mean that the end member of glacial erosion, the parabolic cross-
profile in an overdeepened trough, is often not mathematically visible even if to the naked eye a clear
glacial signature can be observed. The complexities brought to light when attempting to numerically
constrain the extent to which a valley is parabolic likely explains the number of propsed laws to
describe cross-profiles mathematically and the debates among relevant authors over these (Li et al,
2001b). Nevertheless, for the purposes of this study the rapid and clear representations given by the
GPL provides suitable data for broad comparison.
The data presented herein does show considerable agreement with the long-term pattern of glaciation
in Glen Lyon, if only a result of the valley configuration. This is, however unlikely to reflect the long-
term trend in Scotland since each valley configuration bears hugely different conditions for
accumulation and flow, and different regions experience significantly contrasting climates (Benn and
Ballantyne, 2005; Golledge, 2007a, 2010; Finlayson, 2006; Lukas and Bradwell, 2010).
Research by Glasser and Hall (1997) and Hall and Glasser (2003) may provide important insights into
the explanation of the results explained here insofar as it highlights the significance of expansive pre-
Late Devensian glaciations in shaping the Scottish landscape. The MLD ice sheet may be the most
recent such ice mass to cover much of Scotland, replacing informative surficial deposits from
previous stadials, but its dynamics and behaviour do not explain the long-term trend (Kleman, 1992).
Nor does the evidence from the most recent stadial, since this smaller ice cap landsystem is unlikely
to be representative of the long-term pattern of glaciation in Scotland. Preglacial valley networks,
appear to be the most informative in assessing the intricacies of common ice mass accumulations and
their dynamics and behaviour (Payne and Sugden, 1990).
5.7 Implications and Future Research
Although somewhat outdated, I feel that the Whalley et al.’s (1989) statement still applies to many
palaeoglacial research projects. They identified the need for a more holistic approach to glaciological
research. If a wide range of evidence is incorporated, most easily in a GIS, then hidden relationships
may come to light not previously visible from a more limited number of datasets (Napieralski et al,
2007). An understanding of such factors as thermal regime, the size of an ice mass, and topography is
critical for future model simulations which requires small-scale analysis of these complexities (such
as with my study) to allow a more global synthesis of glacial process change over time to be made.

43
The range of interpretations possible from evidence found throughout Scotland for Pleistocene ice
masses demonstrates the ambiguity in determining the origin and relevance of glacial geomorphic
features. An emerging theme in the literature seems to be that since the advent of techniques such as
seismic stratigraphy to explore beneath sediment, and dating techniques such as cosmogenic nuclide
dating the extensive nature of many former ice masses has been realised, possibly ruling out the
limited ice extents proposed in the past (eg. Dix and Duck, 2000; Glasser and Bennet, 2004;
Golledge et al, 2007; Bradwell et al 2008; Lukas and Bradwell, 2010). To this end, cosmogenic
exposure dating would likely serve to identify the true LLS limits in Glen Lyon, aiding in the
determination of the extent to which modeled dynamics and behaviour of the LLS ice cap are
representative of the pattern of erosion in the long-term. Ideally, surface exposure ages could be
calculated through cosmogenic nuclide dating (most usefully with 10
Be and 26
Al) to constrain erosion
ages of different sections of the valley in order to more accurately map the spatial and temporal
patterns of erosion. This would provide information on a timescale suitable to assess the differences
between inherited nuclides from the penultimate interstadial and the exact ages accumulated since
final deglaciation (Ballantyne, 2010; Li et al, 2005; Fabel et al, 2004).
Comparison of the BIIS model data from Hubbard et al (2009) with the data from Golledge et al
(2009) used here would allow more detailed comparison of the likely flow conditions which
prevailed across Scotland throughout the Late Glacial period and improve the strength of conclusions
made here.

45
6. Conclusion
The hypotheses set out above are to a great extent proved correct. Whilst improvements could be
made, especially with respect to increasing the size of the study area and incorporating more
accurate and varied datasets, this research has helped in further determining the dominant styles of
glaciation to cause large-scale erosion in Scotland’s recent geological history. Inferences made match
largely with those made previously by other authors yet this approach provides a unique insight into
the relevance of the most recent stadial.
I have been able to draw four main conclusions:
1. Glen Lyon exhibits macro-scale geomorphological evidence suggesting its formation under
varied styles of glaciation.
2. The morphology of Glen Lyon is best explained by the configuration of ice tributaries which
act to increase basal erosion since they likely determine the pattern of basal temperatures and
hence basal sliding in any ice mass which terminates within the glen.
3. During each stadial, although exhibiting different styles of glaciation and thermal conditions,
ice masses affecting Glen Lyon selectively erode a trough and preserve peaks.
4. Modelled basal shear stresses and hence erosion potential are highest in the base of valleys
across Scotland. The limited extent of the LLS ice cap likely represents a limited extent in the
growth cycle (during growth and decay) of more extensive ice sheets which force similar
basal thermal regimes as predicted here. The macro-scale evidence in central areas of
Scotland likely reflects similar basal conditions as in Glen Lyon but the majority of erosion
likely happened during limited extents of large ice masses, present for longer periods than the
LLS.

47
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