Geoscience Reference
In-Depth Information
distribution of the antecedent precipitation. This means that
Q
(
t
) need not be a unique
function of time. Over smaller catchments, when the precipitation can be assumed to be
sufficiently uniform, this may not be a problem. However, for larger basins it is not easy
to define a unique base flow function from experimental data. This difficulty of non-
uniqueness is aggravated by the fact that also the time reference, that is
t
0, is almost
impossible to define. Indeed, in the case of a long-term streamflow record with base
flow episodically interrupted by stormflow events resulting from precipitation, it is not
a simple matter to identify the start of each base flow episode. In the past, this difficulty
of non-uniqueness and uncertainty in time origin has been avoided mainly in two ways,
namely by assuming that the low-flow recession hydrograph can be represented as an
exponential decay or some other a priori adopted function, or by casting the recession
hydrograph in differential form.
=
10.6.2
Average base flow recession as an exponential decay process
Whenever the time dependence of the flow rate in a river can be assumed to be an
exponential decay process, this can be written in the following form
Q
=
Q
0
exp(
−
t
/
K
)
(10.153)
where
Q
0
is the flow rate at
t
0, and
K
is a constant, representing a characteristic
storage delay in the watershed; both can be considered as parameters to be determined
from observations. An important feature of Equation (10.153), and the main reason for
its wide usage in practice is that, if (10.153) truly describes the flow, the value of
K
,as
determined by regression or other techniques, should be totally insensitive to the choice
of the time reference,
t
=
0. This means that in a semi-logarithmic plot of
Q
versus
t
,
it should be possible to identify a base flow recession graphically, as the (straight) lower
envelope of a number of tail end sections of low flow recession hydrographs, after shifting
them horizontally until the best coincidence is obtained; the value of
=
K
−
1
is obtained
−
from the slope of that envelope.
Early representations of base flow by an exponential decay function have been
reviewed by Hall (1968). In Barnes's (1939; 1959) approach, which is often quoted,
the total recession hydrograph in a stream channel was assumed to be the sum of three
exponential decay functions, namely the contribution by surface runoff, the contribu-
tion by interflow, and the contribution by the groundwater outflow from the watershed;
eventually, after surface runoff and interflow are depleted, the recession consists only
of ground water drainage. Some other examples of the wide practical application of
Equation (10.153) in characterizing base flows can be found in the studies by Laurenson
(1961), Feldman (1981) and Dias and Kan (1999), among many others.
Equation (10.153) is essentially in the form of (10.115), (10.116), and also the first
term of (10.143), that is the first harmonic of the solution of the linearized Boussinesq
equation. It is, of course, also the response of a lumped linear storage element, as used
in the hydrologic systems approach (see Section 12.2.2). The fact that (10.153) has the
same exponential form as these physically based expressions of Section 10.4 provides a
strong indication that the storage delay constant
K
can be expected to depend on the soil
