Geoscience Reference
In-Depth Information
historical streamflow data; a common predicament
around the world. The Institute of Hydrology in the
UK carried out an extensive study into producing
synthetic unit hydrographs for catchments, based
on factors such as the catchment size, degree of
urbanisation, etc. (NERC, 1975). They produced a
series of multiple regression equations to predict
peak runoff amount, time to peak flow, and the
time to the end of the recession limb based on the
measurable characteristics. Although this has been
carried out relatively successfully it is only applic-
able to the UK as that is where the derivative data
was from. In another climatic area the hydrological
response is likely to be different for a similar
catchment. The UK is a relatively homogeneous
climatic area with a dense network of river flow
gauging, which allowed the study to be carried out.
In areas of the world with great heterogeneity
in climate and sparse river monitoring it would be
extremely difficult to use this approach.
Flow duration curve: step 1
A table is derived that has the frequency, cumulative
frequency (frequency divided by the total number of
observations) and percentage cumulative frequency.
The percentage cumulative frequency is assumed to
equal the percentage of time that the flow is
exceeded. While carrying out the frequency analysis
it is important that a small class (or bin) interval is
used; too large an interval and information will be
lost from the flow duration curve. The method for
choosing the best class interval is essentially through
trial and error. As a general rule you should aim not
to have more than around 10 per cent of your values
within a single class interval. If you have more than
this you start to lose precision in plotting. As shown
in the worked example, it is not essential that the
same interval is used throughout.
Flow duration curve: step 2
The actual flow duration curve is created by plotting
the percentage cumulative frequency on the x-axis
against the mid-point of the class interval on the y-
axis. Where two flow duration curves are presented
on the same axes they need to be standardised for
direct comparison. To do this the values on the
y-axis (mid-point of class interval) are divided by
the average flow for the record length. This makes
the y-axis a percentage of the average flow (see
Figure 6.6).
The presentation of a flow duration curve may
be improved by either plotting on a special type of
graph paper or transforming the data. The type of
graph paper often used has the x-axis transformed in
the form of a known distribution such as the Gumbel
or Log Pearson. A natural log transformation of the
flow values (y-axis) achieves a similar effect, although
this is not necessarily standard practice.
FLOW DURATION CURVES
An understanding of how much water is flowing
down a river is fundamental to hydrology. Of
particular interest for both flood and low flow
hydrology is the question of how representative a
certain flow is. This can be addressed by looking
at the frequency of daily flows and some statistics
that can be derived from the frequency analysis. The
culmination of the frequency analysis is a flow
duration curve which is described below.
Flow duration curves are concerned with the
amount of time a certain flow is exceeded. The data
most commonly used are daily mean flows: the
average flow for each day (note well that this is not
the same as a mean daily flow, which is the average
of a series of daily flows). To derive a flow duration
curve the daily mean flow data are required for
a long period of time, in excess of five years. A
worked example is provided here, using twenty-six
years of data for the upper reaches of the river Wye
in mid-Wales, UK (see pp. 108-109).
Interpreting a flow duration curve
The shape of a flow duration curve can tell a lot
about the hydrological regime of a catchment. In
Figure 6.6 two flow duration curves of contrasting
shape are shown. With the dotted line there is a
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