Geoscience Reference
In-Depth Information
7
STREAMFLOW ROUTING
Also called flood routing and channel routing, this is one of the classical problems in
applied hydrology. The word
routing
refers in general to the mathematical procedure
of tracking or following water movement from one place to another; as such, the word
also includes the description of the conversion of precipitation into various subsurface
and surface runoff phenomena. However,
streamflow routing
refers specifically to the
description of the behavior of a flood wave as it moves along in a well-defined open
channel. In practical terms, the problem consists of the determination of the discharge
hydrograph
Q
Q
(
t
) at a given point along a stream, from a known hydrograph fur-
ther up- or downstream and from a knowledge of the physical characteristics of the
channel. The wave may be the result of inflows into the channel following various
events such as heavy rainfall, snowmelt, failure or overtopping of natural or artificial
dams due to landslides or earthquakes, tidal interactions and releases from artificial
reservoirs.
Over the years different methods have evolved. The more fundamental approaches
are based on hydraulic theory of open channel flow and consist of ad-hoc solutions of
some form of the complete shallow water equations by numerical techniques on digital
computer. A detailed treatment of such techniques is beyond the scope of this topic and
good reviews of available methods to solve the complete Saint Venant equations have
been presented by, among others, Liggett and Cunge (1975) and others in Mahmood
and Yevjevich (1975), Cunge
et al
. (1980), and Montes (1998). When accuracy is of
primary concern, a good numerical technique with the complete shallow water equations
should be the method of choice. However, to use any of the available numerical codes,
it is essential to have a thorough understanding of the underlying fluid mechanical
principles.
Some crucial aspects of the routing problem can be clarified by analytical solution
and inspection of simplified formulations that are applicable in certain special situations.
Simplified approaches can also be adequate, and sometimes even preferable for planning
and preliminary design purposes. In this chapter major attention is given to one such
scheme, the Muskingum method; it was developed, in principle, by means of the lumped
kinematic approach and has been found to yield good results under a wide range of
conditions of practical interest in natural rivers. It also has some theoretical ramifications,
which are relevant for a deeper understanding of the complete shallow water equations.
First, however, the behavior is considered of the shallow water equations for the two
extremes of momentum transfer, namely under dynamic and kinematic conditions, in
the case of large waves.
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