FLOOD01888

• County: Statewide
• Title: River Hydraulics
• Date: 10/15/1993
• Prepared By: US Army Corps of Engineers
• Floodplain - Doc Type: Educational/Technical/Reference Information

EM 1110-2.1416
15 Oct 93

Tr = hydrograph time of rise
So = equilibrium energy slope (or bottom slope for
channel of regular cross section)
Uo = average velocity
do = average flow depth
g = acceleration of gravity

b. Data requirements. These depend on the nature
of the method and are described in the sections which
follow and in Appendix D. In general, hydraulic models
require channel geometry, boundary roughness, the initial
state of the water in the channel, and an upstream flow
hydrograph.

(1) An upstream boundary condition with its time
variation, such as a discharge or depth hydrograph, must
be specified, as must be the tributary inflows or oulflows.
In the special case of supercritical flow at the upstream
end of the reach, both depth and discharge must be given
to a dynamic wave model.

(2) With the dynamic wave and diffusion models,
either a depth or discharge hydrograph is required at the
downstream end. In the special case of supercritical flow
at the outlet (dynamic wave model), no downstream
boundary condition can be given.

(3) No downstream condition can be given to the
kinematic wave model, nor to any of the hydrologic
models, as they all employ "marching" solutions, pro-
gressing from upstream to downstream.

5-16. Musklngum-Cunge Model

While the origin of this model is the Muskingum method.
a hydrologic technique, its theoretical basis and applica-
tion, typically to a large number of subreaches, suggest
that its classification be as a hydraulic method. As such,
it is a subset of the diffusion approach; the additional
assumption, linearization about normal depth at the local
discharge, leads 10 problems with accuracy at low values
of bottom slope and precludes analysis of flows in which
backwater effects play a role. Its advantages over the
diffusion approach are not known at this time; compari-
sons might prove it to be a more robust model.

5-17. Hydrologic Routing Schemes

Hydrologic routing focuses on the study reach as a
whole; there is still need for two equations 10 solve for
the two related variables, water surface elevation and
discharge, even if these are required at just one location.

5-30

The principle of mass conservation supplies one of the
required equations but, instead of applying the momen-
tum equation in the interior of the flow. a different the0-
retical or empirical relation provides the second equation.
A summary discussion is presented below.

e

a. Average-lag methods. Two significant features of
flood hydrographs have long been observed in many
rivers. Reflecting the wave-like character of flood
behavior, hydrographs at successive stations are displaced
in time; peaks, for example, occur later at each succes-
sive downstream station. In other words, downstream
hydrographs lag upstream hydrographs. The second
observation is that, usually, hydrograph peaks exhibit
subsidence; that is, a decrease in peak value with dis-
tance downstream if there is no significant tributary
inflow.

(1) Such behavior is observed in the results of the
so-called average-lag methods, empirical techniques
based on averages of inflow hydrograph values lagged in
time. Averages of groups of hydrograph values are
always less than the largest of the group unless all mem-
bers of the group are equal; in particular, the average of
values in the vicinity of the peak will be less than the
peak itself. Ffe!:dom in choosing the time spacing of
points on the inflow hydrograph, the number of points 10
inclode in the average, the weighting coefficients defin-
ing too average, the number and length of subreaches to
which to successively apply the technique, and the travel
time for the hydrograph in each subreach; i.e., the
amount of time to lag the hydrograph, often provides
enough flexibility 10 allow a match of lagged average
reach-oulflow hydrographs with observed ones in a cali-
bration event. Many years of familiarity with a reach of
river and with the observed hydrographs can facilitate
choosing the parameters of such a method for a reason-
ably good fit of computed and measured hydrographs,
but satisfactory routing under different circumstances
would have to be considered fortuitous. There are many
ways in which hydrograph values can be averaged and
lagged. There is no theoretical reason to favor one over
another.

e

b. Progressive average-lag method. This technique
as found in EM 1110-2-1408 also known as Straddle-
Stagger (U.S. Army Corps of Engineers 19903), is the
most empirical of these methods. It provides hydro-
graphs which exhibit subsidence and time lag, and these
can often be made 10 match observed hydrographs
through adjustment of the arithmetic parameters of the
method.

e