Geoscience Reference
In-Depth Information
Figure 5.9
A comparison of different routing methods applied to a reach of the River Yarra, Australia (after
Zoppou and O'Neill, 1982).
but it is worth noting that these are theoretical studies, comparing one mathematical description with
another. The problems of parameter estimation and uncertain knowledge of the subsurface geometry and
values of recharge or lateral inflows will often mean that these differences are not so important in real
applications, and that the kinematic wave approximation may be a useful predictive model. This has been
demonstrated, for example, in the study of Zoppou and O'Neill (1982) in a comparison of methods for
routing flood waves on the River Yarra in Australia (Figure 5.9).
5.5.2 Kinematic Wave Models for Surface Runoff
An early exposition of the mathematics of kinematic wave theory by Lighthill and Whitham (1955) used
traffic routing and flow routing in channels as example applications. This work was later developed by
Eagleson (1970) for the case of overland flow routing on hillslopes to predict hydrographs. Eagleson
gave analytical solutions for the case of a constant effective rainfall input. Later Li
et al.
(1975) and
Smith (1980) provided simple numerical solutions that could be used for arbitrary sequences of inputs.
Numerical solutions have been used in a number of catchment rainfall-runoff models based on the infil-
tration excess overland flow runoff mechanism, the most well-known of which are probably KINEROS
(Smith
et al.
, 1995 ) and the US Corps of Engineers model HEC1 (Feldman, 1995). Both of these models
treat a catchment area as a sequence of hillslope segments, bounded by streamlines. Flow is treated as
one-dimensional in the downslope direction. Each hillslope may be represented by a single plane or by
a cascade of planes of different widths and slopes. In fact, as shown in the development of Box 5.7, it
is not difficult to include continuous changes in width and slope in the kinematic wave equations. This
would make analytical solutions difficult, but is not a problem with numerical solutions. Goodrich
et al.
(1991) describe a finite element solution of the kinematic wave equation for overland flow for a catchment
discretisation based on a triangular irregular network (TIN).
The one-dimensional description requires an appropriate function for the storage-discharge relation-
ship. This may be different for overland and channel flows. However, it has been common in surface
water hydrology to use a uniform flow relationship, such as the Manning equation, for both overland and
