Geoscience Reference
In-Depth Information
Q
i
+
1
with the upper envelope was probably introduced by Langbein (1938), who applied
it to characterize channel storage recession. It was later extended by Linsley
et al
. (1958)
to characterize also the base flow recession by using the lower envelope.
10.6.3
Base flow decline rate: recession slope analysis
Under conditions when freezing, thawing and snowmelt do not play a role, long-term
streamflow records normally consist of base flow episodes that alternate with episodes
of storm flow resulting from precipitation. In general, except when it is an exponential
function of time, the functional form of the base flow obtained from streamflow data
is sensitive to the choice or definition of
t
0, that is the assumed start of each base
flow episode. This uncertainty in the determination of a consistent time reference can be
avoided by eliminating the time variable
t
from the analysis of the data, and by taking
instead its differential
dt
. This can be done by considering not the hydrograph
Q
(
t
) itself,
but rather its slope as a function of
Q
, as follows
dQ
dt
=
=
f
(
Q
)
(10.155)
where
f
( ) is a function that is characteristic for a given catchment. With actual stream-
flow measurements
Q
i
versus
Q
i
+
1
at successive times
t
apart, this function can be
approximated by
Q
i
+
1
−
f
Q
i
+
1
+
Q
i
Q
i
=
(10.156)
t
2
The rate of decline of groundwater outflow is markedly slower than that of other
streamflow input components, resulting from precipitation related events, such as over-
land runoff or channel storage depletion. Therefore in the application of Equation
(10.155) it can be assumed that base flows represent the smallest
|
dQ
/
dt
|
for a given
Q
(or the largest rate of flow
Q
for a given
|
dQ
/
dt
|
). This means that in any graphical
representation of (
Q
i
−
2 data points, for base flows
the function
f
( ) in (10.155) can be taken as the lower envelope. The main objective of
such a procedure is to capture some characteristics of the ensemble of many recessions,
which cannot possibly be seen or detected by analyzing individual recessions. Indeed,
in a natural catchment, hydrographs and their recessions come in many different shapes
and they can vary greatly from one runoff event to the next. The shape of a hydrograph
depends on many factors, such as the spatial distribution of the initial soil moisture
content, the spatial distribution of the water table levels, and the spatial and temporal
distribution of the prior precipitation events over the catchment. This infinity in possible
outcomes and the large variability and non-uniqueness of shapes is illustrated by the fact
that when one plots daily values of
dQ
Q
i
+
1
)
/
t
data versus (
Q
i
+
Q
i
+
1
)
/
dt
vs
Q
for a natural watershed one obtains a
broad cloud of points. Figure 10.31 shows an example.
Thus the lower envelope is the locus of points for the slowest recession rate
dQ
/
/
dt
;
conversely, it represents also the largest flow rate
Q
for any given recession rate
dQ
dt
.
In principle, this largest flow rate is the one that would be observed (even though this may
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