Geoscience Reference
In-Depth Information
particles in a river's load lead to a reduction in the median
grain size downstream, a particular discharge needs less
of a channel slope to mobilize the same sediment load.
As a result, the channel gradients decrease over time, by
deposition of sediment in lower reaches and downcutting
in upper reaches, so as to maintain the graded river.
The relationships discussed can be expressed in terms
of a process-response systems diagram of an alluvial
channel system (
Figure 1.9
).
The attributes and variables
are in the boxes in the usual manner, with arrows showing
the direction of the influence, whether one-way or
reversible. The plus and minus signs show direct (positive)
and inverse (negative) relationships respectively.
However, controls can change rapidly, leading to
changes in the landscape element at such rapid rates that
the changes can be measured. Thus modern approaches
to studying environmental systems involve recording
change in the field by experiments, by analysing the
large amounts of data by computers, by constructing
mathematical models of the landscape, and by simulating
landscape processes by numerical methods.
For purposes of simulation and numerical modelling,
it is necessary to express the relationships which control
the shape of long profiles of rivers as mathematical
equations. Hack (1957) proposed an empirical relation-
ship to explain the slope of a river channel:
(a)
Steady state equilibrium
Steady time
(b)
Dynamic equilibrium
Cyclic time
Source: After Chorley et al. (1984)
upon the time scale being used. This can be illustrated by
reference to fluvial geomorphology. Rivers usually have
long profiles which are concave in shape and show a fining
of sediment size downstream. The median grain size
normally decreases as a result of the attrition and abrasion
of particles in bed load and suspended load. It is also usual
for stream discharge to increase downstream as the
catchment area of the stream increases with distance from
the source.
The explanation of these downstream relationships in
rivers is that the river channel is evolving so that its
discharge and sediment load remain in equilibrium. Over
short time scales of hundreds of years, i.e. over
graded
time
, a 'hydraulic geometry' approach can be used to
explain how a river maintains its equilibrium. Particular
discharges and channel gradients have the potential to
mobilize particular sediment sizes. As a result of this,
downstream fining of bed load and suspended load
occurs, and the river achieves equilibrium, maintaining a
constant long profile.
However, changes in median grain size and channel
gradient with increasing discharge are related to each
other not in terms of simple cause and effect but by much
more complex feedback relationships. Over long time
scales it is preferable to apply the 'slope evolution' model
to rivers over the 'hydraulic geometry' model, especially
over time scales of hundreds of thousands of years, i.e. over
cyclic time
. This approach highlights the decrease in grain
size downstream as the cause of changing (i.e. reduced)
gradients downstream. As attrition and abrasion of
= 6·03
10
-5
[
d/A
]
0·6
where
= channel slope,
A
= catchment area and
d
=
median grain size. A more general form of this relation-
ship without the exponents is given below:
Td/Q
is proportional to,
= channel slope,
d
= median grain
size,
T
= downcutting rate and
Q
= bankfull discharge.
The addition of term
T
for the downcutting rate in this
equation is necessary in order to reflect the resistance to
erosion of the channel. Rock type or
lithology
is critical
to the evolution of the long profiles of rivers, because of
the different rates of downcutting over different rocks.
Along the river Wharfe a more easily eroded rock like
shale gives a more gently concave profile as the slope is
reduced more quickly. Sandstone has a moderately
concave profile, whilst limestone shows most resistance
and has a steeply concave profile. Thus rivers like the
Wharfe which cross several different rock types from
source to mouth will have variations in channel slope
along their course as a result of the rocks over which
they flow.
