Non stationarity of basin scale sediment delivery in response to
climate change
T. J. Coulthard1, J. Lewin2 and M. G. Macklin2
1
Geography Department, University of Hull, Hull, HU6 7RX, U.K.
2
Institute of Geography and Earth Sciences, University of Wales, Aberystwyth, SY23 4DB, U.K.
T.Coulthard@hull.ac.uk
http://www.coulthard.org.uk
Abstract
Results from a cellular river basin evolution model (CAESAR) that contains a
detailed multi-grain size sediment transport model, indicate that over longer time
scales (greater than 50 years) the relationship between sediment discharges (Qs) and
water discharges (Qw) is not stable when routed through a prototype catchment. By
modelling how the daily bedload yield from a medium sized river basin (383 km2)
responds to changes in climate over the last 9000 years, high resolution and long term
basin-scale bedload ratings curves can be simulated. These show that quasi linear
relationships can be established between Qs and Qw during stable climatic periods, but
an increase in flood magnitude and frequency over a sustained period (>10 years) can
lead to a very large increase in the amount of sediment delivered for identical sized
floods. Thus different ‘climatic periods’ can produce significantly different
relationships between Qs and Qw. Furthermore, over the 9000 years simulated there is
considerable variation in response, with daily sediment yields for a medium sized
flows (16-32 m3s-1) varying over 8 orders of magnitude. The change in Qs/Qw
relationship is believed to be conditioned by sediment supply and storage, and also by
the ‘context’ of the climate period with respect to previous periods. These results have
important implications for the application of sediment transport formulae, engineering
calculations based on these (e.g. longer term reservoir siltation), and predictions of
how river systems are likely to respond to climate change.
1
Introduction
Understanding the relationship between catchment water and sediment discharges is
important for comprehending how fluvial systems operate. For geomorphologists
controls on the delivery of sediment have numerous implications, from understanding
fluvial landform development to interpreting alluvial stratigraphies. And for
engineers, knowledge of catchment sediment yields are vital, especially for assessing
channel design, stability and sedimentation problems.
Therefore, it is important for both scientists and practitioners to be able to model, and
predict how the amounts of sediment transported from a catchment may respond to
changes in water discharge over a range of time scales. To do this, researchers have
measured catchment sediment yield - the amount of sediment that leaves a catchment
over a measured period of time. This can be related to the size of the catchment and
other factors such as climatic and altidudinal setting (e.g. Milliman and Syvitski,
1992). These records are variable, and changes in sediment yield over time have been
related to changes in land use and land cover (Dearing, 1992) as well as to
fluctuations in climate (Wilby et al., 1997). More detailed studies have directly
related catchment sediment yields (Qs) to catchment water discharge (Qw), and these
are termed sediment ratings curves. The relationship between Qs and Qw is not
straightforward and rarely linear. Typically, there is a hysteresis effect over a flood,
where there are reduced levels of sediment relative to water discharges in the latter
parts of a flood, due to sediment exhaustion. Sediment ratings curves are usually used
to describe suspended sediment to Qw relationships, but bedload ratings curves have
also been developed (Whiting et al., 1999; Emmett and Wolman, 2001; Ryan et al.,
2002; Hayes et al., 2002; Whiting and King, 2003; Ryan et al., 2005). These also
show considerable variation, but do not show the same daily hysteresis effects, though
Moog and Whiting (1998) described a seasonal hysteresis. Both suspended sediment
and bedload ratings curves are characterised by large quantities of scatter, which like
hysteresis effects can be attributed to limitations in sediment supply. However,
empirical models have been developed that use these field data from ratings curves to
predict both suspended sediment and bedload yields from catchments (Barry et al.,
2004). A more sophisticated method is to use sediment transport functions. These
typically measure sediment discharge per unit width, and can therefore incorporate
2
local channel characteristics such as slope, bed material etc. Therefore, they build in
more of the local conditions and thus physics influencing sediment transport at that
point. Sediment transport functions have been extensively developed, but have
encountered difficulties as they tend to perform well on the data with which they were
developed, but less so when applied to different environments. Gomez and Church
(1989) clearly illustrated this point with their comparison of 12 formulae, applied to 8
different data sets. None performed accurately, the Bagnold equation was best, and
only 3 others performed reasonably.
The difficulties found in predicting bedload discharge are perhaps not surprising when
the raw field and laboratory data shows significant variations (Reid et al., 1980; Hoey
and Sutherland, 1991; Ashmore, 1988; Carling et al., 1998). For example, Cudden
and Hoey (2003) measured bedload from two anabranches of a pro-glacial stream and
noted substantial variations in bedload yields. These appear highly non-linear, and
Gomez and Phillips (1999) calculated that most of the non-linearity on 10000 flume
bedload measurements could be described as chaotic. Causes for these irregularities
include the threshold based nature of sediment entrainment and other threshold
dominated processes operating on the bed of heterogeneous gravel-bed rivers, such as
bed armouring and equal mobility. Furthermore, the passage of bedforms (e.g. dunes
and bars) and larger scale features such as sediment waves (Nicholas et al., 1995) can
cause irregularity in at a point bedload yields ranging from 1 to 1000s m3 that may
take seconds to years to pass. Over longer time scales, the impacts of climate or land
cover change may also cause longer lasting perturbations in sediment delivery
(Macklin and Lewin, 1989; Coulthard and Macklin, 2001).
These problems are compounded by the physical difficulties associated in measuring
bedload. Measurements are carried out using active methods (e.g. Helly Smith
samplers, pressure pillows (e.g. Reid et al., 1980), magnetic devices (Tunnicliffe et
al., 2000)) or passive techniques (sediment traps, repeat surveys of channel cut and
fill or lake/reservoir sedimentation rates). Active methods can give temporally high
resolution data (hourly or less) but are demanding in human resources and typically
only span a few hours or days. Passive techniques can provide much longer records,
but with a far coarser temporal resolution, as data points are only collected when traps
3
are emptied or cross sections re-surveyed. Therefore we are limited to either short
high resolution, or longer low resolution records.
Other researchers have looked to the geological record as a longer term recorder of
changes in sediment yield. These demonstrate varying flood-frequency episodes, with
‘wet’ and ‘dry’ periods related to climatic fluctuations on a scale of tens to thousands
of years (e.g. Knox, 1993; Macklin and Lewin, 2003; Macklin et al. 1992; ). Such
timescales are compatible with the likely travel times of bed materials through
catchment systems. However, the resolution of the dating methods used to establish
fluvial chronologies is generally not precise enough to accurately link sediment
response to individual floods. Similarly, the resolution and accuracy of proxies used
to reconstruct palaeo climate records also hampers correlation with a stratigraphy.
Furthermore, the sedimentary record is palimpsest, a record that may have been reworked and erased (Lewin and Macklin, 2003), and is not a straightforward ‘recorder’
being described as a ‘finicky’ by Paola, 2003.
Therefore, we are faced with the reality of having temporally limited data on present
day sediment yields (too short a length of record), and long term records (too coarse a
temporal resolution). As a consequence, it is difficult to apply longer term records to
shorter time scales (e.g. 10’s to 100’s of years) for instance to see how climate change
may effect river systems. Similarly, it could be dangerous to apply present day
process rates to interpret past longer term changes. Therefore, outside of our
comparatively short length record we have little information on whether or how Qs/Qw
relationships may change, and what might control it. Does the amount of sediment
discharged for a given flood change over time, if so by how much, and what may
influence this?
In order to better understand this and how river systems may respond to both
individual floods, as well as longer term shifts in average flood magnitude and
frequency caused by climate changes, ideal data would be hourly water and sediment
discharge data integrated across a river basin and spanning a period of several
thousand years. This is clearly beyond the scope of monitoring studies and
palaeoflood reconstruction techniques. But by using numerical modelling it is
possible to explore the probable roles of changing flood frequency and sediment
4
supply and routing factors on a catchment wide basis. Indeed, previous studies have
modelled non-linear sediment discharges from identical floods on small UK
catchments (Coulthard et al., 1998) and larger abstract landscapes over longer time
scales (De Boer, 2001). They also show how decadal outputs of sediment can vary
significantly between catchments despite having identical drivers (Coulthard et al.,
2005) as well as how thresholds are important for non-linear catchment response
(Tucker, 2004).
In this paper, we use a cellular landscape evolution model CAESAR (Coulthard et al.,
2002) to reconstruct a series of bedload ratings curves based on 9000 year simulation
of daily water and sediment discharges. The results presented here may have
important implications for the management of catchments and some of the concepts
that underpin our current understanding of geomorphology.
Method
The results presented in the paper are based on further analysis of data first presented
in Coulthard et al. (2005), generated using the CAESAR landscape evolution model.
A brief description of the model is provided below, but for a detailed account, readers
are referred to Coulthard et al. (2002) and Van De-Wiel et al. (In Press). CAESAR is
a cellular landscape evolution model (Coulthard, 2001; Willgoose, 2005) that
represents a river catchment with a grid of equally sized square cells (as per a raster
DEM). Each of these cells has properties, or values, for elevation, grain size, water
discharge, flow depth, vegetation cover etc.. For every iteration or time step of the
models operation these values are altered according to equations that describe four
key groups of processes; hydrological, hydraulic, fluvial erosion and deposition, and
slope processes.
The hydrological model is an adaptation of TOPMODEL (Beven and Kirkby, 1979)
and is driven by an hourly rainfall data set. Key parameters within TOPMODEL (m
and K) can be altered to change the hydrograph peak and rate of flood decay, and
these are altered within CAESAR to simulate the effects of land cover change on
catchment hydrology. This provides distributed values of soil saturation levels, and
when a grid cell is saturated, any excess discharge from the hydrological model is
5
treated as surface flow. This model is also dynamic, so wetted areas and thus the
drainage network, can expand and contract during storm events.
Surface discharge from the hydrological model is then fed into the hydraulic
component, where depths, inundation areas and surface water routing are carried out.
Flow depths are calculated for each cell using an adaptation of Mannings equation
(using bed slope) and then routed according to a scanning multiple flow routing
algorithm. This sweeps across the catchment four times (north to south, east to west,
west to east and south to north) routing water to the three cells in front, as per Murray
and Paola (1994), using the slope between the water surface height and the receiving
cells bed elevation. The maximum depth calculated for a cell through each of the four
scans is recorded and taken as the cell flow depth.
Where a cell has a flow depth, fluvial erosion and deposition is carried out. Using
water depth and bed slope between cells, bedload transport for 9 separate grain sizes
(1-256 mm in Phi classes) is calculated using the Einstein-Brown (1950) formulae.
Erosion and deposition of the separate size fractions is implemented through the use
of an active layer system (Hoey and Ferguson, 1994) where a proportion of each
fraction is held in a series of layers that during erosion can be replenished from layers
below, or during deposition displace material to lower layers. Importantly, this system
allows many of the processes associated with heterogeneous bed sediment transport to
be modelled, such as bed armouring and size supply limited entrainment.
Two sets of slope processes are modelled. First, mass movement occurs when a
threshold slope angle is exceeded and secondly, soil creep is calculated according to
local slopes. Importantly, both slope processes are fully integrated within the fluvial
model, which allows the addition of sediment into the fluvial system from a landslide
or eroding river bank, for example.
In summary, CAESAR allows hydrological, hydraulic, fluvial and slope processes to
be simulated over an entire catchment modelling series of individual flood events,
driven by and hourly rainfall record and DEM.
6
The simulations described here were carried out on the upper part of the River Swale,
U.K., the northern tributary of the Yorkshire Ouse system. The modelled catchment
area covers 383 km2 and varies in relief from 514 to 20m A.O.D. The Swale has a
mixed lithology of Carboniferous sandstone, gritstone and limestone, and was
glaciated during the Quaternary, leaving wide steep walled valleys covered with
periglacial and glacial deposits. The catchment was extensively forested (Flemming,
1998) but present day land cover is typically rough grazing on upland moorland, with
pasture on the lower sections and valley floors. The catchment is sufficiently high to
be unaffected by Holocene sea level rise.
The model was applied to a 50 m resolution DEM of the Swale, and was driven by a
proxy climate and land cover data set covering the last 9000 years. The topography of
the Swale catchment 9000 years ago is impossible to reconstruct, so rather than make
crude reconstructions based on limited data, the present day topography was used.
This is not a wholly unreasonable assumption, as field evidence indicates that there
has been less than 2-4 m of vertical channel and valley floor movement over the
Holocene. For such a long simulation, a 9000 year hourly rainfall record was required.
We used a combination of two climatic indices derived from peat bog surface wetness
reconstructions from northern England for the period 6300 cal. BP to present (from
Barber et al., 1994) and from 9000 to 6300 from Scotland (Anderson et al., 1998). A
full description and discussion of this method can be found in Coulthard and Macklin
(2001) and Coulthard et al., (2005). These indices provided climate data in 50 year
steps and were then normalised between 0.75 and 2.25 to create a rainfall index. The
model was then driven by a 10 year hourly rainfall record that is repeated 5 times to
span 50 years, then multiplied by the rainfall index to create 9000 year proxy hourly
rainfall data. For land cover changes, a basic reconstruction of catchment
deforestation constructed from local palynological records were used to change the
‘m’ parameter in the hydrological model.
Results
The simulation generated a time series of 87x106 data points of hourly flow and
sediment discharge. To simplify analysis of the data set, it was divided into 50 year
sections, discharge data were averaged and bedload yields summed to create a daily
7
time series. In effect, we have used the model to generate daily water discharge and
bedload totals for the River Swale over a 9000 year period.
Figure 1 shows the relationship between Qw (water discharge) and Qs (sediment yield)
for three 50 year sections (50-100, 100-150 and 150-200 cal. BP). Despite being
plotted on log-log axis these data demonstrates a significant amount of scatter, with an
interesting increase in variability to up to 8 orders of magnitude around the 15-50
m3/sec Qw. These periods were chosen as they contained very high (150-200 cal. BP),
high (100-150 cal. BP) and medium (50--100 cal. BP) sediment discharges, though
similar patterns of scatter are found in all 50 year sections. When the data is grouped
into log classes according to Qw (1, 2, 4, 8, 16, 32, 64, 128, 256 and 512 respectively)
the standard deviation of the Qs in each bin varied considerably, with a peak in the 1632 m3s-1 group. Using this group from the 150-200 cal. BP section and classing the Qs
into linear bins (incrementing from 0 to 20000 in steps of 1000) the frequency of daily
sediment yield (Qs) to water discharges in the 16-32 m3s-1 group can be plotted as a
power law (Figure 2b). Data from 50 cal. BP period, with far lower sediment yields,
also follows a similar relationship, though smaller bin sizes are required (Figure 2a).
Examining Figure 1, there is also considerable difference in the angle of the
regression lines plotted through the data sets. This suggests that there could be
significant variation in the Qs/Qw relationship during different periods of the model
operation. However, R2 values indicate that the relationship is clearly not significant
due to the large amount of scatter. In order to reduce this scatter and to allow
comparisons in the Qs/Qw relationship between each 50 year section of the simulation,
these data were grouped into log classes as above. When the medians of Qs for each of
these bins were plotted these revealed a good linear relationship as shown in Figure 3.
This good level of fit was found to be consistent for each of the 50 year sections of
data, though it must be remembered that using medians conceals a large amount of
scatter and therefore should only be used as a comparator between individual 50 year
sections.
Linear regression was then carried out for the medians of all 50 year time sections and
the slopes of the regression line are shown as a time series in Figure 4. This indicates
how the angle of the modelled relationship between Qs/Qw changes quite dramatically
8
throughout the simulation as well as following sediment yield and climate input
closely. The standard deviation and median for the 16-32 m3s-1 class were also
calculated and are shown in temporal sequence for all data in Figure 5.
Discussion
(1) Scatter
Figure 1 indicates that there is considerable scatter within the Qs/Qw relationship, and
it is apparent that there is a flow size with substantially more scatter than others (1632 m3s-1). This is not the most frequent class of flow (8-16 m3s-1) and this area of
scatter seems to persist throughout every 50 year section, though for some sections is
less well defined. These results raise two questions: why is there so much scatter in
the Qs and why does there appear to be a flow range that produces substantially more
scatter than any other?
At first the large amounts of scatter may seem to be inappropriate, as CAESAR is
driven by a conventional sediment transport formulation (Einstein and Brown, 1950)
that has no stochastic element. Thus it might be expected that sediment outputs would
follow this relationship. However, within CAESAR this formulae is applied to
individual cells, with sediment transport calculated locally, based upon the flow
depths and bed slopes of each cell. The output presented here, is the product of
erosion and deposition being carried out over thousands of grid cells within the
model. Therefore, by calculating sediment transport on a cell by cell basis, CAESAR
mimics the processes of internal storage and re-mobilisation of sediment that can
operate within real catchments. Furthermore, as CAESAR contains a sophisticated
sediment transport model using several grain sizes, when supply of a certain grain size
is exhausted within a cell, no more of this fraction can be eroded. Thus sediment
supply limitations, such as bed armouring and selective entrainment are incorporated
in each cell. This can generate internal erosional thresholds, so sediment is not eroded
until stream powers are great enough to move the particle itself or to remove the
coarser armour layer above. Therefore, erosion is threshold dominated giving rise to
high variations in sediment delivery. Furthermore, as the model incorporates slope
processes (soil creep and mass movement) material can be added from landslides,
9
which are also threshold controlled, again introducing high variations in sediment
delivery.
Explanations for why one class of mean daily flows produces such high levels of
variability are not straightforward. It is logical to assume that in threshold based
supply limited catchments, small floods will largely generate little sediment yield and
large floods will generally mobilise a substantial volume of material. Therefore the
medium sized flows, that here show most variability, may be close to erosional
thresholds, where there is high potential for variability.
In order to evaluate what might control the variability shown in the model results,
data from similar simulations on two nearby catchments were examined. Figure 6
plots Qs/Qw relationships from the River Swale, as well as the nearby River Nidd (281
km2) and River Wharfe (697 km2). Both exhibit similar patterns of scatter, with the
similar sized Nidd being closest. However, the larger Wharfe catchment shows
greatest variability in a larger flood size class. This suggests that the size of the
catchment or possibly its morphology may be a controlling factor. Possibly it is not
small scale erosional thresholds such as bed armour breaching that influence the
scatter in this way, but larger controls on thresholds, such as valley floor shape and
internal catchment storage. Further research is required into the precise causes of this
behaviour, and it is possible that other factors, for example, grain size and land cover
may strongly influence this.
Figure 2b shows that the distribution of the scatter follows a power law. This indicates
that Qs may vary from 0 to 20 000 m3day-1 for a mean daily flow between 16 and 32
m3s-1. Interestingly, Figure 2a indicates that different climatic periods produce
different power law relationships, showing that whilst the magnitude of scatter may
be different, they both follow similar distributions. Power laws can also be indicative
of systems exhibiting self organised criticality (SOC) though this is not an area we
wish to explore in this paper.
Implications of scatter
The large amounts of scatter (up to 8 orders of magnitude for flows between 16 and
32 m3s-1) suggest that bedload ratings curves are not ideal for predicting sediment
10
discharges. Sediment transport functions that take account of factors such as channel
width, depth and local slopes where the bedload is measured (here the edge of the
DEM) would improve these predictions. But, both will still feel the effects of changes
in sediment supply outlined above and this study highlights some of the difficulties
faced when trying to predict sediment transport. Possibly and alternative method is to
smooth these data, and average it over monthly, annual or even decadal time steps,
much of the scatter would be removed. By using such long measurement intervals we
might then be able to derive generalised relationships between long term flow and
sediment yield data. But such relationships, though statistically less variable would
mask the extremes of response that might be crucial for management strategies.
The clustering of most scatter around a certain flow size may be of great importance
to engineers and practitioners. Akin to the concept of the effective flood (Wolman and
Miller, 1960) is there a size of flood that may be most difficult to account for the extra
levels of uncertainty associated with it? Certainly, these results suggest that this may
be the case, and that such magnitude floods are very common. However, when
reviewing these data presented here, it should be remembered that Figures 1 and 6 do
not represent individual flood totals, they are daily sediment totals compared to daily
discharge averages. Therefore, these data could easily conceal daily/event scale
hysteresis effects. Furthermore, the data for 150-200 years cal. BP represents an
extreme of wetness and the greatest level of variation. Under dryer conditions the
maximum size of variation is far less (e.g. see Figure 2 b) but the amount of scatter
remains very high.
(2) Non stationarity of response
Figures 4 and 5 show how 50 year climatic ‘periods’ produce a different relationship
between Qs/Qw. There is an increase in the gradient of the relationship with increasing
wetness, resulting in a greater Qs for the same Qw in a wetter climate (represented by
an increase in the climate index). In a wetter period in a mid latitude temperate river
basin, it would be anticipated that there would be a higher overall sediment yield, due
to larger floods. But the slope shows how the ratings curve, the Qs/Qw relationship,
changes significantly. In effect the relationship is non-stationary over time.
11
These changes can be explained firstly by morphological changes within the
catchment. Increasing flood size leads to an expansion of the drainage network, that
generates fresh material from expanding stream heads and incision within first order
streams as demonstrated by previous applications of CAESAR (Coulthard et al.,
2002). In a small catchment, it might be expected that all this new material would be
flushed from the system. But within a medium to large sized catchment, such as the
Swale, this material will be deposited and progressively moved downstream as a
series of sediment waves or slugs. This in turn leads to the increase in the Qs/Qw
relationship, as the larger floods have mobilised sediment that is then available for
smaller floods to export. In effect, larger floods or wetter climatic periods loosen or
release large amounts of sediment, increasing the volume of material that could be
transported for smaller flood events. Similarly, changes in the general pattern of flood
events may breach armour layers on the stream bed, which can release sediment as
well as make the channel more vulnerable to incision (Coulthard and Van de Wiel,
2007).
The sudden shift in Qs/Qw could also be explained by changes in the channel pattern.
Significant increases in bedload yield would be consistent with a transformation from
a single thread channel to a braided one. This can be seen in Figure 7, which shows
the channel pattern for two identical size floods at 4500 and 200 years Cal. BP,
corresponding with low and high Qs/Qw relationships. The upper 4500 cal. BP. image
shows a predominantly single channel, with some overbank inundation cutting across
meander bends. The lower 200 cal. BP image shows a widening of the channel in the
upper parts (as an adjustment to increased flows) and a shift in channel pattern to a
multi threaded braided planform. Such behaviour is consistent with field evidence
from similar catchments in the UK (the river South Tyne; Macklin and Lewin, 1989)
that showed dramatic changes in channel pattern and valley floor aggradation. Such a
planform change could also explain increases in scatter and the standard deviation
(Figure 6) during wetter climates, as braided channels can have a far greater
fluctuating bedload yield.
The changes in the Qs/Qw relationship can also be explained by the effects of sediment
recharge and removal. For example, during several hundred years of relatively
constant moderate rainfall events, the river channel armours and adjusts its
12
width/depth ratio’s to accommodate the flow. During this period, in upland areas soil
creep will slowly move soil and sediment to the base of slopes and thus the margins of
streams. Present sediment supply remains the same, but potential supply has
increased. If there is then a wetter climatic period, with more frequent and larger
floods, the relative equilibrium within the channel will be broken and erosion will
start to remove this available material adjacent to channels. This increases the relative
sediment delivery per flood size, as we see in Figure 1.
Implications
These results have significant implications for the application of bedload rating curves
as they show that the Qs/Qw relationship can vary considerably over time. The
modelling results presented here show that there is a double response, as not only will
wetter climate periods increase sediment yields through larger floods, but will also
increase the relative sediment yield for all floods (the Qs/Qw relationship). This is
especially important for design predictions as if, for example, we predict the rates of
sedimentation in a reservoir – or around a structure such as a bridge, based on existing
sediment/bedload ratings curves, these may alter significantly in the future. Therefore
future changes in climate may influence not only the size of future floods, but also the
relative volumes of sediment released. This is especially pertinent given the rapid
present day changes to our climate. For sedimentologists, when interpreting
sequences, the double effect may lead to a large deposit being disproportionately
thick, as there is clearly a far from linear relationship between climate and unit
thickness. Relating both scatter and the Qs/Qw relationship, Figure 6 shows how an
increase in the standard deviation of the 16-32 m3s-1 flood class follows the climate
and sediment yield. This indicates that not only are Qs/Qw values going to change, but
also the variability, which could make engineering decisions and sedimentological
interpretations even harder.
Finally, as changes in the Qs/Qw relationship are influenced by the release of stored
sediment and the renewal of erosional activity in stream heads and adjacent parts of
the channel, then catchment response will be heavily influenced by the previous
patterns of erosion and deposition. Therefore, catchment sediment yields are heavily
contingent on the system history and predictions, and assumptions based upon
bedload ratings curves should take this into account. Preliminary analysis examining
13
how the Qs/Qw relationship varies during the 50 year blocks studied here indicates
that there is significant adjustment over the first 20 years followed by more minor
changes. This suggests that the reaction time to climatic changes of the simulated
River Swale is fairly rapid, but how this timing scales between catchments of different
shapes and morphologies is beyond the scope of this paper and warrants further study.
However, this does give us some indication of how rapidly river systems may respond
to climatic changes.
Conclusions
Catchment modelling of bedload sediment yield for a moderate sized river basin over
the last 9000 years using the CAESAR model suggests that the spatial and temporal
complexities of sediment transport and storage produce markedly non-linear
relationships between water discharge and sediment yield. The yield of any particular
discharge is conditioned by prior events, sediment availability and sediment supply.
This is particularly striking for moderate sized flows (in the case of the modelled
River Swale 16-32 m3s-1) for which daily yields vary over eight orders of magnitude.
For a given flow magnitude, wetter periods also yield more sediment than drier ones,
probably because sediment mobilisation then exceeds critical thresholds, as in the
breaching of bed-armouring, landslide generation or storage activation. The spatial
complexities of larger catchments, in terms of available storage and the temporal
routing of sediment transfers would also appear to make predictions of Qs/Qw
relationships much more variable than in the case of small catchments. Transitions
between ‘wetter’ and ‘drier’ periods also seem liable to particularly uncertain
predictions.
All these uncertainties have serious management implications at times when rapid
climate change and human impacts on sediment yields are much in evidence. There
are no long term data sets available with which to attempt model validation, though
there are no reasons to suppose that the use of a conventional sediment transport
equation, along with their hydrological and process relationships, to model catchment
wide transportation and delivery, is in any general sense invalid. Indeed, it suggests
that ‘site’ transport equations do need to be aggregated with procedures which
incorporate catchment behaviour, if sediment yield variability is to be simulated in an
14
apparently realistic manner. Modelling reveals some interesting characteristics of this
variability which have management consequence at times of rapid environmental
change.
Acknowledgements
We would like to thank Chris Paola, Jim Pizzuto and a third anonymous referee for
their excellent comments and guidance in the preparation of this paper. TJC would
also like to thank the organisers of GBR6 for the opportunity to present this research.
15
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20
0.01
1000000
1000000
1000000
100000
100000
100000
10000
10000
10000
1000
1000
1000
100
100
100
10
10
10
1
1
0.1
0.1
1
10
100
10000.01
0.1
0.1
1
1
10
100
0.01
1000
0.1
0.1
0.01
0.01
0.01
0.001
0.001
0.001
0.0001
0.0001
0.0001
0.00001
0.00001
0.00001
0.000001
0.000001
0.000001
1
10
100
1000
1000000
y = 37.833x + 323.58
R2 = 0.0422
150
100000
100
10000
50
Linear (50)
Daily sediment yield (m3)
1000
100
Linear (150)
Linear (100)
y = 6.4567x - 16.271
R2 = 0.5217
10
1
0.1
y = 2.9363x - 17.33
R2 = 0.306
0.01
0.001
0.0001
0.00001
0.000001
0.01
0.1
1
10
Mean Daily Flow (m 3 sec -1)
100
1000
Figure 1. This illustrates Qw and Qs plotted for 3 50 year sections of the data set, 50100, 100-150 and 150-200 cal. BP. Note, both axis are log scaled. The top three plots
show each data set (50, 100 and 150) plotted separately.
21
10000
150
50
Pow er (150)
1000
Frequency
Pow er (50)
100
y = 235347x -1.9608
R2 = 0.9345
10
50-100 cal. BP
y = 5E+08x -1.9822
R2 = 0.9154
150-200 cal. BP
1
10
100
1000
10000
100000
Daily Bedload Yield (m3)
Figure 2. Power law distribution of bedload yield for (a) time period 150-200 cal. BP
and (b) 50-100 cal. BP.
1400
1800
Median daily sediment yield (m 3)
1200
y = 8.7701x - 71.444
R2 = 0.9406
1850
1900
1000
Linear (1900)
Linear (1850)
800
Linear (1800)
y = 4.7874x - 45.638
R2 = 0.9319
600
400
y = 1.2572x - 2.9453
R2 = 0.9709
200
0
0
20
40
60
80
100
3
120
140
-1
Mean Daily Flow (m s )
Figure 3. Medians of simulated sediment yields for the periods 1800, 1850 and 1900
Cal. BP.
22
2.5
100
100
4.3724x
y = 0.0008e
R2 = 0.4535
Climate
10
Qs/Qw slope
Slope of Qs Qw
2
10
1
Climate proxy
0.01
1.5
1
0.001
0.5
1
climate index 1.5
2
2.5
1
0.1
0.5
Slope of Qs Qw relationship
0.1
0.01
0
0
1000
2000
3000
4000
5000
Years Cal. BP
6000
7000
0.001
9000
8000
100000000
100
100
0.7415
y = 0.0002x
R2 = 0.6475
Sediment yield
10
10000000
Qs/Qw slope
Slope of Qs Qw
10
0.1
0.01
100000
0.001
100
1000
10000
100000
1000000 10000000
1E+08
1
Sediment Yield
10000
0.1
1000
Slope of Qs Qw relationship
Sediment Yield (m3 per 50 yrs)
1000000
1
100
0.01
10
1
0
1000
2000
3000
4000
5000
Years Cal. BP
6000
7000
8000
0.001
9000
Figure 4. Slope of Qs/Qw relationship plotted with the climate driver for the
simulations (top) and the modelled sediment yield (bottom).
23
100000000
10000
Sediment yield
Standard deviation
10000000
1000
1000000
Sediment Yield (m3 per 50 years)
100
100000
10
10000
1
1000
0.1
Standard Deviation and Median
Median of 16-32 flow
class
100
0.01
10
1
0
1000
2000
3000
4000
5000
Years Cal. BP
6000
7000
8000
0.001
9000
Figure 5. Standard deviation and medians of the 16-32 m3s-1 flood class plotted with
the modelled sediment yield
100000
10000
nidd
wharfe
1000
swale
Daily Sediment Yield (m 3)
100
10
1
0.1
0.01
0.001
0.0001
0.00001
0.000001
0.01
0.1
1
10
3
100
1000
-1
Mean Daily Flow (m s )
Figure 6. Qs/Qw plots for the rivers Swale, Wharfe and Nidd.
24
Figure 7. Areas inundated by a 50 m3s-1 flow at 4500 (top) and 200 (bottom) Cal
B.P.
25