Geoscience Reference
In-Depth Information
Fig. 12.9 In the applicatication of the
rational method to calculate the
peak flow, the duration of the
design storm is taken as the time of
concentration, or
D
=
t
c
.Ifthe
duration were shorter, so that
D
<
t
c
, only part of the catchment
would contribute to the runoff; on
the other hand if a longer duration
were assumed, so that
D
>
t
c
, the
design rainfall rate, derived from
available intensity-duration
information (e.g. Figure 3.16),
might be too small for the adopted
design return period
T
r
.
x
y
t
c
D
t
x
y
t
c
D
t
x
y
D=t
c
t
Linear translation with the time-area method
The rational method provides only the peak discharge rate, and over the years attempts
have been made to broaden the approach, in order to allow a more complete description
of the entire hydrograph including its rise and subsequent recession. This was done, for
instance by Hawken and Ross (1921), who considered the effects of the drainage area
shape and of the time variation of the storm rainfall. The effects of the shape of the
drainage area and of the drainage net were accounted for by the introduction of the time-
area(-concentration) function, or time-area diagram, which represents the distribution
of the travel times in the basin to the outlet. This function is obtained by first establishing
a travel time for each point in the basin, and by then sketching isochrones, which are lines
connecting points of equal travel time. The time-area function
A
r
=
A
r
(
t
) is a plot of the
relative areas (as fractions of the total basin area) between different isochrones (equally
spaced in time), against their respective travel times; thus it is the density function of
the travel times to the outlet (Figure 12.10). In this approach, the time variation of the
rainfall input was accounted for by a procedure, which, as pointed out by Nash (1958),
was in fact a numerical convolution operation.
Just like in the standard version of the Rational Method, the basic assumption is that
the entire catchment is equivalent with a plane on which the rainfall is transported to
the outlet by translation. Because the system is linear, the transformation mechanism
is that of a linear kinematic channel as formulated in Chapter 5. Since it is normalized,
