Geoscience Reference
In-Depth Information
2
Evolution of Rainfall-Runoff
Models: Survival of the Fittest?
Everything of importance has been thought of before by someone who did not invent it.
Alfred North Whitehead, 1920
2.1 The Starting Point: The Rational Method
It is worth remembering that rainfall-runoff modelling has a long history and that the first hydrologists
attempting to predict the flows that could be expected from a rainfall event were also thoughtful peo-
ple who had insight into hydrological processes, even if their methods were limited by the data and
computational techniques available to them. We can go back nearly 150 years to the first widely used
rainfall-runoff model, that of the Irish engineer Thomas James Mulvaney (1822-1892), published in
1851 (and reproduced in Loague, 2010). The model was a single simple equation but, even so, manages
to illustrate most of the problems that have made life difficult for hydrological modellers ever since. The
equation was as follows:
Q
p
=
CAR
(2.1)
The Mulvaney equation does not attempt to predict the whole hydrograph but only the hydrograph
peak
Q
p
. This is often all an engineering hydrologist might need to design a bridge or culvert capable
of carrying the estimated peak disch
ar
ge. The input variables are the catchment area,
A
, a maximum
catchment average rainfall intensity,
. Thus, this model
reflects the way in which discharges are expected to increase with area and rainfall intensity in a rational
way. It has become known as the
Rational Method
. In fact, variations on Equation (2.1) have been
published by a variety of authors based on different empirical data sets (see Dooge (1957) for a summary)
and are still in use today (try searching on “peak discharge rational method”).
The scaling parameter
C
reflects the fact that not all the rainfall becomes discharge, but here the method
is not quite so rational since it makes no attempt to separate the different effects of runoff generation and
R
, and an empirical coefficient or parameter,
C
