Geoscience Reference
In-Depth Information
0
P
2.5
3.8
20
40
60
17.6
30
20
78.7
10
0
y
−
10
4
0
2
6
8
10
2 4 6 8
Time (days)
Fig. 12.23 Observed (circles) and simulated (solid line) flood hydrographs (in mm d
−
1
) on the Cache River at
Forman, Illinois, resulting from a 103 mm storm over four days in March 1943. The simulation was
carried out with the first two terms of the Volterra series (12.46); thus the total hydrograph is the sum
of the first-order (linear) response (dashed line) and of the second-order response (dash-dotted line).
(After Diskin and Boneh, 1973.)
12.3.2
Nonlinear runoff routing
This method of transforming rainfall into basin streamflow has mostly made use of
concentrated storage elements, and is therefore also referred to as storage routing. In
most cases the nonlinear storage function was assumed to be of the power type,
K
n
y
m
S
=
(12.48)
where
K
n
and
m
(
1) are adjustable parameters; in this form the storage function can
be considered a generalization of Equation (12.25). After substitution of (12.48) in the
lumped equation of continuity (12.26) (or (1.10) or (7.11)) one obtains
=
K
n
d
(
y
m
)
dt
x
=
y
+
(12.49)
In what follows a few examples are presented of past attempts to include this type of
nonlinearity in the catchment response behavior.
Horton (1941) was the first to use this approach; he proposed that flood hydrographs
can be considered the result of a triangular “virtual channel inflow graph” produced by
rainfall on the adjoining land, which is then routed through nonlinear channel storage by
means of Equation (12.49). Horton (1936; 1937) estimated the parameters of the storage
function (12.48) from quasi-steady open channel flow considerations. From analysis of
a large number of flood events on different rivers, he showed that during a recession
the channel storage behaves nearly the same as if the entire volume were concentrated
in a single reservoir; but during rising stages it behaves as a reservoir of somewhat
