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Chapter Two
Scale and spatial analyses in Geomorphology
Landscape form reflects the interaction of physical processes that operate over a range
of spatial and temporal scales. Consequently, scale studies have been undertaken on many
geomorphic topics, including the way in which river channel form varies in the downstream
direction. For example, research has been performed on issues such as downstream changes in
channel morphology (Leopold et al., 1964; Parker, 1979; Pitlick and Cress, 2002; Wohl and
Wilcox, 2004), bedforms (Richards, 1976; Knighton, 1998; Madej, 2004), sediment
characteristics (Ashworth and Fergurson, 1989, Constantine et al., 2003), bank erosion
processes (Bull, 1979; Lawler, 1992; Abernethy and Rutherford, 1998; Prosser et al., 2001),
stream power (Leece 1997; Knighton, 1999; Reinfelds et al., 2004) and hillslope processes
(Wischmeier and Smith, 1978; Millward and Mersey, 1999; Yair and Raz-Yassif, 2004).
However, scale induced changes within river networks have only been briefly
investigated. This is despite the fact that understanding links between the various scales in a
catchment is becoming increasingly important in river management projects that need to
relate local implementation practices with regional outcomes. Therefore, the aim of this study
is to assess whether changes that occur within a river network are similar to those that have
been observed in the downstream direction of a single channel. This work will contribute to
improving knowledge on the links between the operation of reach and catchment scale
processes and has the potential to provide a framework for stream rehabilitation and the
delineation of habitat types within a network.
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2.1 Scale-dependant spatial variations in fluvial geomorphology
2.1.1 Downstream trends in channel morphology
Early scale related research in fluvial geomorphology began with studies on
downstream variations in discharge and its relation to channel dimensions (Leopold and
Maddock, 1959; Leopold and Wolman, 1960). Since then these interactions have been
expanded upon in great depth within the fluvial geomorphologic literature with a progressive
move away from describing and classifying features to understanding, explaining and
modelling relationships between physical variables (Lane, 1995; Lane and Richards, 1997).
The size and shape of alluvial channels adjust in response to temporal and spatial
variations in discharge and sediment load (Rosgen, 1994; Leopold et al., 1964; Leopold and
Maddock, 1953; Hey et al., 1982; Richards, 1982; and Knighton, 1998) which are, in turn,
controlled by catchment characteristics such as topography, geology, vegetation and landuse.
Topography has an influence on hillslope form and channel slope and, consequently, on the
energy of flows and rate and volume of sediment transport. Geology determines the nature of
sediment supply and the extent of channel confinement while vegetation can both stabilise a
bank and retard channel flows (Thorne, 1990; Nakamura and Swanson, 1993; Abernethy and
Rutherford, 1998). Landuse changes within catchments are complicated and can have both
direct and indirect impacts on fluvial systems (Walker et al. 1992; Brooks and Brierley, 1997;
Brierley et al. 1999; Brierley and Stankoviansky, 2002). The direct impacts include physical
alterations of a stream channel such as dams, weirs and bridges, while indirect impacts
include the effects of alterations within catchments such as changes to vegetation or the
concreting of surfaces.
Generally, discharge, sediment load, topography, geology, vegetation and landuse
exhibit spatial and temporal variations. These variations complicate the way in which stream
morphology changes in the downstream direction. In humid environments rivers typically
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increase their channel dimensions in the downstream direction to accommodate an increasing
discharge (Ferguson, 1986; Schumm, 1988, Knighton, 1998). However, variations in geology,
topography, vegetation and landuse influence the rate of water and sediment delivery to the
stream channel and the erodibility of the channel bed and banks (Reinfelds et al., 2004). This
results in irregular discharge trends and complicates the manner in which channel form
changes downstream. Despite discontinuities along rivers due to inconsistent additions of
water and sediment, however, numerous empirical studies have establishes downstream
relations for channel form (Knighton, 1998).
2.1.2 Downstream hydraulic geometry
One of the most pervasive scale related themes in fluvial geomorphology is that of
downstream hydraulic geometry. Originally proposed by Leopold and Maddock (1953)
downstream hydraulic geometry predicts how channel form and flow varies downstream as a
function of discharge (Ferguson, 1986). Downstream hydraulic geometry relationships as
quantified by Leopold and Maddock (1953) rely on discharge as the controlling variable over
channel width, depth and mean velocity
w=aQb
(1)
d=cQf
(2)
v=kQm
(3)
where Q is bankfull discharge (m3/s), w is channel width, d is flow depth (m) and v is mean
velocity (m/s). Then continuity equation
Q= w.d.v
(4)
requires that b+f+m= 1 and a.c.k= 1. Effectively these equations are descriptive as the
exponents and coefficients vary between rivers systems, highlighting the necessity for further
research (Hey et al, 1982). These relationships take the form of simple power functions with
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discharge as the independent variable and parameters such as width, depth, velocity, slope or
friction as the dependent variable (Knighton, 1998).
In humid environments the basic form of the hydraulic geometry relations indicate that
width, depth and velocity increase with discharge while slope and friction decrease (Parker,
1979; Schumm, 1988; Pitlick and Cress, 2002). This is illustrated by the exponents of
downstream hydraulic geometry relationships listed in Table 2.1. The exponents indicate the
rate at which the dependent variable changes relative to the dependent variable.
Table 2.1: Exponents for downstream hydraulic geometry relations at bankfull discharge. (Modified from
Knighton, 1998. p. 173)
Exponent
Source
Location
b
f
m
Emmett (1975)
Upper Salmon River, Idaho
0.56
0.34
0.12
Charlton et al. (1978)
Britain
0.45
0.40
0.15
Hey and Thorne (1986)
Britain
0.45
0.35
0.20
For channels in dry climates, trends for discharge and stream morphology contradict
those documented for humid environments. Three different trends have been reported through
studies of ephemeral rivers; channel width oscillates in the downstream direction (Thornes,
1976), channel width decreases in the downstream direction (Dunkerley, 1992), and width
increases rapidly and then reaches a consistent asymptotic value of 100-200 m after the
catchment area has exceeded 50 km (Knighton and Nanson, 1997 and Wolman and Gerson,
1978). Tooth (2000) established and compared downstream trends in channel width along
three dryland rivers in arid central Australia. This study concluded that decreases in channel
width in the downstream direction were linear for the smallest river but, for the two larger
rivers discharge showed irregular downstream declines due to geologic discontinuities.
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Statistical characteristics of variability within channel links have received little
attention. In one of the few geomorphic studies into small-scale variability within and
between stream channels, Moody and Troutman (2002) characterised the spatial variability of
channel link length and elevation change. The authors used four separate rivers with over five
orders of magnitude in discharge to identify the variability of water surface width and average
depth. Moody and Troutman (2002) found a level of similarity across five orders of
magnitude when comparing the spatial variability of water surface width and average depth
within a channel link indicating that processes controlling these aspects of channel form vary
independently of scale.
2.1.1 Spatial variability of bedform features
Bedform features are irregularities in the channel bed; they include features from
pebble clusters to undulations in the bed topography. The characteristic reach-scale bedforms
for gravel bed rivers are pool-riffle sequences (Clifford, 1993; Robert, 1997) and these are the
features which are examined in this study. Pools are zones of localised bed scour caused by
flows capable of removing more sediment than is deposited (Buffington, et al, 2002). Riffles
represent zones of hydraulic resistance and may store little or no transient material (Church
and Jones, 1982). These undulations in the channel bed, which also produce variations in
width and depth are deemed critical for maintenance of a heterogenous aquatic habitat
(Thompson and Hoffman, 2001).
The formation and maintenance of these channel bed features has been of considerable
interest to fluvial geomorphologists (Keller, 1971; Church and Jones, 1982; Clifford, 1993;
Heritage and Milan, 2004). As outlined by Clifford (1993) there are three identifiable
processes involved in the formation of pool and riffle sequences. Firstly, an obstacle in the
channel causes local scour of the bed which is then followed by a corresponding deposition of
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scoured material downstream. This deposited material then creates another flow irregularity
further downstream which ultimately results in another zone of scour. It was theorised riffles
are maintained by the selective scour of fine sediment which, results in relatively coarse
material being left exposed (Leopold and Wolman, 1957). More recently the maintenance of
pool riffle sequences has been attributed to spatial and temporal differences in near bed
velocities, caused by the features themselves, which create differences for the entrainment of
bed surface sediments (Clifford, 1993). Past research has shown that riffles tend to have
coarser bed material than their adjacent pools, which suggests that local sorting mechanisms
take place (Keller, 1971; Lisle, 1979; O’Connor et al., 1986). This supports the theory that
pools and riffles are maintained by the local flow regime.
The velocity characteristics of pools and riffles have been studied to a great extent
(Carling, 1991; Clifford and Richards 1992; Robert, 1997). These characteristics are a good
example of the way in which processes operating at the reach scale are spatially and
temporally variable within these features. At low flow velocity gradients tend to be higher
across riffles than across their adjacent pools (Robert, 1997). However, the differences for
near bed velocities between pools and riffles, decrease gradually with increasing flow stage
(Robert, 1997). This is known as the theory of velocity reversal between pool and riffle
features which was first hypothesized by Keller (1971). The hypothesis states that during
events of high flow near bed velocity is greater in pools allowing scour and thus maintenance
of the pool. This theory lends insight to the understanding of the way in which sediment is
transported along pools and riffles, and as a result, also the role of local flow irregularities in
the maintenance of such features. With respect to the theory of velocity reversal, pool-riffle
sequences are seen to be maintained by a form process feedback mechanism (Clifford, 1993).
An inconsistency with the theory was raised by Thompson et al. (1999) as pools have been
documented in having larger cross sectional areas than riffles at high flows. Continuity would
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suggest that as a result of a larger cross sectional area, velocity would be lower in the pool
than the riffle (Richards, 1978; Carling, 1991). Thompson et al. (1999) address this dilemma
through the proposal of a model that relies on the constriction of flow by recirculating
turbulent eddies. The constriction of flow results in a small zone of high velocity at the centre
of pools allowing scour to occur. Diverging flows at the downstream end of the pool results in
deposition of material on what is termed the exit slope of the pool.
Although the processes where by these features are formed and maintained appear to
operate on at the local (reach) scale, their morphological size and spacing is related to channel
width. Thus, characteristics of their morphologies tend to increase in a consistent manner
when related to scale variables, in particular, channel width. The spacing of pool riffle
sequences is generally 5 to 7 channel widths (Keller and Melhorn, 1978; Gregory et al.,
1994). Thus, distance between sequences is determined by the scale of the reach being
studied.
The characteristics of pools and riffles cause local variations in river reach
morphology. This is because riffles tend to have greater width/depth ratios than pools,
indicating that riffles tend to be wide and shallow, where as pools tend to be narrower and
deeper (Knighton, 1998). The local differences of channel form have been shown to have an
impact on overall downstream hydraulic relationships (Richards, 1976). Spatial variations in
bedforms occur at both reach and network scales. Research of such variations between scales
can be used to characterise the evolution of channel bed patterns within a network, therefore
improving our understanding of how river networks behave.
Flow resistance differs between bedform features and is influenced by several factors
including, particle size which controls skin friction, form roughness caused by bed
irregularities including bed forms and pebble clusters and larger scale features of bed
topography, flow obstructions, large woody debris, channel bends and abrupt changes in
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channel geometry (Dingman, 1984). The relative importance of these features is dependent on
the size of the stream. For example, a small pebble cluster would influence the velocity of
flow in a small stream to a greater extent than it would the velocity of flow in a large river.
This is because the pebble cluster protrudes into a greater proportion of the flow in the small
stream and thus increases the effects of bed roughness to a greater extent than it would in a
large river.
The spatial variability of bedform features was examined by Madej (2004) in a
Californian gravel bed river. The aim of this study was to characterise temporal changes in the
spatial structure of the bed topography. The longitudinal pattern of bed elevations was
analyzed to determine whether bedform patterns were random or regular and to establish the
maximum variance or similarity in different parts of the channel. The study also sought to
determine whether temporal variation in bedform patterns was linked to a 12 year flood event.
It was found that where pools were forced (by channel constrictions or woody debris)
bedform patterns demonstrated a random distribution and in reaches where alternate bars
dominated bedform features were more regularly spaced (Madej, 2004). It was also found that
bedform heterogeneity increased with time since disturbance.
2.1.3 Spatial variability of sediment characteristics
Spatial variability of sediment characteristics in river networks results from disparities
in source materials and the downstream fining of sediments. Downstream fining in gravel bed
rivers commonly occurs via two processes; selective sorting of sediment (Ashworth and
Fergurson, 1989, Fergurson and Ashworth, 1991, Fergurson et al., 1996) and the abrasion of
sediment (Schumm and Stevens, 1973). Abrasion studies indicate that it is an important
process where the channel bed is made up of sediments less resistant to erosion processes. As
the bed material in this study is relatively resistant, abrasion is unlikely to be a dominant
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process at this site. (the problem here is that I have a few references stating that
sandstones break up over relatively short distances. Considering that sandstone is a
major parent material for the KR then wouldn’t abrasion be responsible for at least
some of the downstream fining?)
The ability of selective sorting to produce downstream fining depends on differences
in the mobility of fine and coarse grained sediments. Although smaller gravels are less dense
than larger particles they are not necessarily more easily entrained due to the effects of hiding
and protrusion (Ashworth and Fergurson, 1989: and Constantine, 2003). This reduces
differences in the sediment mobility rates of different sized material and has implications for
downstream fining patterns in rivers with longitudinal differences in gravel mobility caused
by variations in shear stress (Constantine, 2003). However, strong trends of downstream
fining are not always apparent. Downstream fining relationships of the Colorado River were
shown to be relatively weak (Pitlick and Cress, 2002). This was attributed to the high supply
of coarse sediments from tributaries and adjacent hillslopes which was suggested to be high
enough to replenish material worn by abrasion.
2.1.4 Spatial variation of channel erosion processes
The spatial zonation of bank erosion processes is not a new concept. Bull (1979)
investigated downstream trends in the relative importance of vertical and lateral erosion on
valley morphology and downstream trends in stream power and sediment supply. Recently,
however, the spatial patterns of channel erosion within river networks have received increased
attention (Lawler, 1992; Prosser et al., 2000; Abernethy and Rutherford, 1998). It has been
theorised (Lawler, 1992) and field-tested (Abernethy and Rutherfurd 1998; Lawler et al,
1999) that there is a spatial zonation of bank erosion processes in river networks. Bank
erosion processes can be segregated into three categories with respect to spatial dominance.
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These categories are; sub-aerial preparation, fluvial entrainment and mass failure. Sub-aerial
activity includes those processes that weaken the bank face such as freeze- thaw activity and
continued wetting and drying of sediments causing slaking among clay particles (Couper and
Maddock, 2001; Couper, 2003). Fluvial entrainment is a process where by, loose bank
sediments are eroded by the stream flow and carried away. Mass failure is a process that
occurs when bank heights reach a threshold where they are no longer sufficiently supported
by the material below and a segment of the bank collapses.
Lawler (1992; 1995) outlines a scale based model that suggests that due to low stream
power in the upper reaches of river basins (as a result of low discharges) and despite steep bed
slopes the available energy for fluid entrainment of bank sediments is limited. In addition
bank heights along these reaches are low, thus limiting the success of mass failure
mechanisms. As a result bank-weathering processes should be the most effective erosion
process. Further, it was shown that bank erosion rates were greatest in the mid-basin section.
Lawler (1992, 1995) theorised that this results from a combination of increased stream power
and erodible bank sediments. In the downstream end of a catchment, however, mass failure
processes come to dominate due to the critical increase in stream bank heights.
Abernethy and Rutherfurd (1998) documented a spatial zonation in the dominance of
the three types of bank erosion along reaches of the Latrobe River (Victoria) and its
tributaries. Sub aerial preparation was the more prevalent process in the upper reaches of the
river whereas bank erosion in the mid-basin reaches was dominated by fluvial entrainment.
Therefore, as catchment area increases and the channel becomes larger, the dominant bank
erosion mechanism can change. Ultimately, therefore, the bank erosion mechanisms exhibit a
clear downstream trend with sub aerial preparation dominating upstream, fluvial erosion midstream and mass failure dominating bank erosion downstream. This shift in dominant bank
erosion mechanism may have significant implications for downstream variations in channel
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form as the volume and frequency of bank erosion is directly related to the dominant bank
erosion process.
2.1.6 Spatial variability of stream power
Leece (1997) and Knighton (1999) demonstrated that downstream changes in stream
power are likely to vary considerably even between streams within a single network largely
due to variations in slope at the profile and local scales. The downstream patterns of change in
channel gradient and stream power are related to the landforms and processes occurring
within river systems (Reinfelds et al., 2004). Stream power, through its relation to sediment
transport, provides a mechanism for predicting variations in broad scale river form and
processes both within and between systems.
The spatial distribution of stream power was examined further by Fonstad (2003) who
investigated whether spatial patterns of energy expenditure (stream power) can be linked with
the distribution of river forms. Fonstad (2003) sought the answer to two driving questions:
How does stream power vary geographically within a mountain stream basin? And, can other
variables besides hydraulic geometry be used to describe stream power so that geographic
variables can be negated? It was found that within the study network, stream power varied
non-linearly in the downstream direction and that the major deviations of observed stream
power from predicted trends were due to stream fragmentation as a consequence of geologic
diversity.
2.1.7 Spatial variation of hillslope processes.
Hillslope processes are central to the behaviour of any river system and are also
controlled by inherent scale components (Pilgrim, 1983, De Boer, 1992, Yair and Razyassif,
2004). For example, it is well known that specific runoff yield decreases with increasing area
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(Yair and Lavee, 1985; El-Huassanin et al. 1993; Van de Giesen et al. 1996; Yair and
Razyassif, 2004). For very large catchments, the trend of decreasing specific runoff yield is
usually attributed to rain-cells being insufficiently large to cover the entire catchment
(Pilgrim, 1983, Yair and Lavee; 1985), as well as variations across the catchment in
precipitation duration and intensity (Cammeraat, 2004). However,
processes also occur
within small catchments to limit the increase in specific runoff with increasing scale
(Cammeraat, 2002; Yair and Raz-Yassif 2004). It has been demonstrated that flow continuity
decreases with increasing area for hillslopes within a small catchments (Yair and Raz-Yassif,
2004). The processes influencing this are the occurrence of short storm events, as a threshold
storm concentration time exists for continuous runoff to occur, and this increases with area. In
addition, the incidence of discontinuous flows on hillslopes results in deposition towards the
bottom of the slope causing the depth of alluvium to increase (Cammeraat, 2002; Yair and
Raz-Yassif, 2004). This in turn This then results in higher infiltration rates and reduced runoff
(Yair and Raz-Yassif, 2004). Understanding of these processes that operate at different scales
on hillslopes allows for the creation of models to predict the way in which processes may
scale up (Kirkby et a., 1996).
2.2 Scale dependent relationships
Numerous geomorphic studies have indicated that many environmental processes are
scale dependent (Sugden and Hamilton, 1971). When dealing with a scale dependant process
it is important to recognise that the scale of measurement influences the observed
magnification of spatial variation, as variables that are homogeneous at one scale may be
heterogeneous when studied at a larger scale. Alternatively, variables may seem regular at one
scale and irregular at another (Atkinson and Tate, 2000). It is, therefore, necessary to examine
the heterogeneity of data as it can reveal much about the structure of the system.
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Hierarchy theory predicts that variance will decrease slowly at scales corresponding to
the hierarchical levels and more rapidly at intermediate scales (O’Neill et al., 1991). For
hierarchically structured landscapes it is theorised that processes affecting patterns will be
isolated at different scales and that the dynamics and patterns present at one scale are the
result of interactions among lower level systems. Therefore, when studying a process it is
important to select an appropriate scale of measurement at which the variation of interest
exists (Atkinson and Tate, 2000).
Issues of scale are particularly relevant to fluvial geomorphologists who identify river
networks as hierarchical systems, with large catchments being comprised of nested sets of
smaller catchments. Form defining processes at each catchment scale operate and interact at
different levels and systems that function at higher-order scales will be an influencing factor
for patterns and processes at lower scale orders (Sugden and Hamilton, 1971). In the case of
river networks, variables that are dependent at higher scales can become independent when
scales are collapsed (Schumm and Lichty, 1965). For example, the geology of a region is
dependant on many factors including tectonic activity and geomorphic processes, but when
the time scale is collapsed these processes are often occurring so slowly that the geology of a
catchment is considered to be an independent variable that controls other processes
functioning within the catchment. This suggests that elements of a system can often become
systems themselves when the scale is reduced (Harvey, 1969). Problems associated with
issues of scale arise when small scale data are extrapolated over larger spatial or temporal
scales (De Boer, 1992; Bloschl and Sivapalan, 1995). For example, linear up-scaling from
small to large catchments is impossible due to the many thresholds and non-linear processes
that are involved at specific scales and that operate between scales (Cammeraat, 2002).
Thus, it is important to understand scale issues within catchments. This would include
identifying the systems that operate at specific spatial scales, analysing the spatial structure
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and function of such systems and developing principles to explain the spatial structure of the
systems at specific scales (Sugden and Hamilton, 1971)
Part of the evolution of modern fluvial geomorphology was the move away from
merely categorising and classifying rivers and river systems towards the understanding of
process operation. As a result, more recent research within fluvial geomorphology has tended
to move from catchment wide investigations to site-specific studies along river reaches,
resulting in a reduction in the spatial and temporal scales of investigation. This move is part
of a general shift toward process-based geomorphic studies (Lane, 1995; Lane and Richards,
1997). Poole (2002) stated that this trend addresses the problem of understanding trans-scale
processes in geomorphology from the lower levels upwards. The advantage of such a
reduction in scale is that it enables fluvial geomorphologists to conduct intensive field studies,
resulting in greater understanding of processes in specific reaches. By collapsing the spatial
scale of studies, researchers are also able to reduce the temporal scale within which they are
working. This is because the smaller the spatial scale, the shorter the reaction time required to
change the controlling variables (Trudgill, 1976). This allows for an increase in predictions
based on physical relationships as opposed to empirical rules (Prosser et al., 2001) and
increases the necessity of better understanding spatial patterns of river morphology, including
channel width, bankfull discharge and the extent of the floodplain. Having reduced the
temporal and spatial scales of research a question has arisen; can studies of river channels that
transcend spatial scales lend insight to understanding longer-term aspects of landform
behaviour and evolution (Lane and Richards, 1997)?
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2.3 Summary and Implications of research
The above review of the literature provides evidence that many aspects of the fluvial
processes are inherently scale dependent. This study addresses several of these processes,
both in the context of a river network and at the reach scale. Although processes of
downstream hydraulic geometry and downstream fining have been extensively studied for
single rivers there is a relative paucity of studies which provide analyses of the way in which
these processes scale up within river networks. To address this gap in the literature several
scales of observation were used to determine the spatial variance of channel morphology and
the potential processes to scale up within a river network context.
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