Geoscience Reference
In-Depth Information
the precipitation into steamflow. In general, the response function is derived by routing
a lumped rainfall excess input through a number of elements of storage and translation,
which are patterned after the different processes as described in Chapters 2-10; therefore,
such methods might, in a certain sense, be considered physically based. One of the main
advantages of these methods is, that the resulting response functions usually require only
few parameters; this makes them more general and also easier to calibrate. On the down-
side, however, since their computational scale is so large, the correspondence with the
actual physical processes is not always clear. Indeed, as the computational scale becomes
much larger than the variability scales of the basin, the parameters gradually lose their
original physical meaning. Because of this ambiguity, these types of parameterizations
have also been called conceptual models (see Dooge, 1973).
Linear translatory transport: the Rational Method
This is probably the earliest attempt to relate precipitation with the resulting runoff
from a catchment. Evidently (Dooge, 1957), the method was pioneered already some
150 years ago by Mulvany (1850) in Ireland, but versions of it are still being used today
in the design of small drainage structures. The underlying concept of the method is that
each catchment has a (constant)
time of concentration
,
t
c
, which is the time needed for
the water to flow from the most distant point of the catchment to the outlet. The peak
discharge rate
Q
p
takes place when the entire catchment area
A
contributes to the outflow,
and this occurs at the time
t
0. Thus for a mean
input intensity
I
(rainfall or snowmelt) over that period, the peak rate of flow is
=
t
c
after the onset of the rain at
t
=
Q
p
=
CIA
(12.18)
or, in input-output notation,
y
p
=
x
(12.19)
in which
y
p
=
CI
. The symbol
C
denotes the
runoff coefficient, that is the fraction of the input resulting in direct storm runoff (see also
Section 9.5.2). Note again that if
Q
p
is in m
3
s
−
1
,
I
in (mm h
−
1
) and
A
in km
2
, Equation
(12.18) should be written as
Q
p
/
A
, such that [
y
p
]
=
[L
/
T], and
x
=
Q
p
=
0
.
278
CIA
(12.20)
In principle, (12.18) (or (12.20)) should be applicable to drainage basins of any size, but in
engineering practice its use is normally restricted to small catchments with
A
15 km
2
.
In its standard form the Rational Method can be applied as follows. The size of the
drainage area
A
can be readily measured on topographic maps, after determining the
ridge boundary line of the catchment. The value of
C
can be estimated from a knowledge
of the surface conditions of the catchment by means of Table 12.2. For example, in urban
areas a commonly used value is
C
≤
8. The determination of the design input intensity,
I
, is probably the most difficult aspect in practice. Consider the case of rainfall input,
so that
I
=
0
.
P
. First the duration of the design storm
D
is to be estimated; this is usually
assumed to be equal to the time of concentration
t
c
, that is
D
=
=
t
c
. Several empirical
