FLOOD05589

• County: Statewide
• Community: Statewide
• Stream Name: All
• Basin: Statewide
• Title: Ephemeral Streams Hydraulic Factors and Their Relation to the Drainage Net
• Date: 1/1/1956
• Prepared For: State of Colorado
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

EPHEMERAL STREAMS

Horton (1945, p, 291) which, in his words, "supple-
ment Playfair's law and make it more definite and
more quantitative. They also show that the nice
adjustment goes far beyond the matter of declivities."
The equations listed above merely state the condition
of proportionality; for them to he definitive the con-
stants involved must be determined, In addition to the
values of certain exponents already discussed, data
collected during this investigation established the rela-
tions among order, slope, and width, as will now be
described.
Although channel depth, velocity, and discharge at
a particular cross section ean be measured only when
the stream is flowing, the important hydraulic var-
iables, channel "idth and channel slope, can be esti-
mated even in a dry stream bed. During the many
days when no thunderstorms were occurring in the
area studied, our field work included measurement of
width and slope in the dry channels, The proccdure
used will be described briefly.
The width was defined as width near bankfull stage.
In Eastern United States where the development of
the river flood plain is the rule rather than the excep-
tion, the bankfull width is relatively easy to define and
measure. It is the width which the water surface
would reach when at a stage equal to the level of the
flood plain: In dry arroyos where flood plains are the
exception and alluvial terraces exceedingly common,
it is difficult to point specifically at an elevation which
might be called bankfull. Nevertheless, field inspec-
tion allows fairly consistent estimates of width cor-
responding to an effective or dominant discharge, even
by different observers, The positions on the stream
banks representing the two ends of the cross section
were chosen independently by each of us, and the
recorded widths represent a compromise het\veen our
individual judgments,
Channel slope is somewhat easier to determine,
Although there are local dry pools or deeps resulting
from both definite patterns of flow and random channel
il-regularities, a smooth profile of channel bed drawn
through several points in a reach provides an estimate
of channel slope which is reproducible by successive
measurements. Our procedure was to place the plane-
table in the center of the dry stream bed and take a
series of sights both upstream and down as far as the
stadia rod could be read with a leveled instrument.
In Inost instances this gave a measurement of slope
through a reach of about 600 feet.
'Width and slope were measured at more than 100
channel cross sections. Because of the widespread
geographic distribution of measured cross sections and
because of the lack of adequate maps, we have not

21

determined the order of the streams on which many of
these are located. The graphs of figures 17 and 19

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13

FIGURE l1,-Relation of channel slope to stream order, shOWing the individual
measurements and the mean relation (solid line) derived from other parameters.
~umber beside point is serial1dentitlcation keyed to data in appendix.

were plotted from data on cross sections of streams of
known order. As cxpected, order is related to width
and slope by equations of the type,

O=k log wand O=k log s

The relation between width and slope can be determined
by equating the relations above or by direct plotting
of the data as in figure 18. To represent the relation
in larger streams, a straight line on logarithmic paper
has been drawn through the numbered points (fig. 18).
The equation of this line is

8=O,12w-O.5

This means that for the area studied, channel slope
decreases downstream approximately as the reciprocal
of the square root of channel width. This expresses an
interrelation and does not imply a direct dependence be-
tween these two parameters.
Establishing the relations among width, slope, and
order merely requires collecting and plotting the appro-
priate data. It should be possible to combine those
factors which are most easily and definitively measured,
and t,hereby arrive at approximations of other factors
which are more difficult to measure. Such a scheme
would expand the usefulness of the techniques now
available, An example to illustrate this possibility will
now be cited.