Geoscience Reference
In-Depth Information
Fig. 10.30 Daily discharge data in m
3
s
−
1 measured
during stream flow recessions over a five-year
period on Fall Creek, near Ithaca, NY. The rate
of flow on the
i
th day is plotted against the rate
of flow on the (
i
30
1)th day. The area of this
catchment is 326 km
2
.
+
20
Q
i
10
0
0
10
20
30
Q
i+1
(m
3
s
−
1
)
properties
k
0
and
n
e
, the thickness
D
and the breadth
B
of the riparian aquifers, their
slopes
, and possibly other basin characteristics. This will be further investigated in
Section 10.6.3.
In some applications, the exponential outflow function is represented in a different
form, as
α
Q
0
K
r
Q
n
=
(10.154)
in which
K
r
=
Q
i
/
Q
i
−
1
is the depletion ratio,
n
=
(
t
/
t
) is the number of time intervals
of duration
t
since the start of the recession, when
t
is taken as zero, and
Q
i
is the rate of
flow at the
i
th time interval. Equation (10.154) is derived by assuming that the decrease
in flow rate from any time
t
to time (
t
+
t
) is constant, so that
Q
1
=
Q
0
K
r
,
Q
2
=
Q
0
K
r
, and so on. This shows that (10.154) is just another form of (10.153)
with ln(
K
r
)
Q
1
K
r
=
K
. It also means that, in light of the similarity of (10.153) with
(10.115), (10.116) (and also the first term of (10.143)),
K
r
can be expected to depend on
the same soil, aquifer, and basin characteristics as
K
.
The applicability of (10.153) or (10.154), that is the linearity of the basin for base
flow, can be checked graphically by plotting
Q
i
versus
Q
i
+
1
for available recession flow
data. An example of such data is shown in Figure 10.30. The upper envelope of these
points describes the fastest rate of decrease in flow rate on record; it can therefore be
assumed to be caused by the depletion of channel storage during a storm flow event
and, as will be discussed below, depletion of the steeper hill slopes in the basin. On the
other hand, the lower envelope, which describes the slowest rate of decrease on record,
can be assumed to represent base flow recession, due to the depletion of groundwater
storage in the riparian aquifers. If the base flow recession is truly linear and given by
Equation (10.154),
K
r
must be constant; because
K
r
is the slope of the lower envelope,
it should be a straight line. In the example shown in Figure 10.30, the points do not
quite have a straight line lower envelope, and therefore for this basin the possibility of
a nonlinear base flow regime cannot be excluded. This procedure of plotting
Q
i
versus
=−
t
/
