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

ent makes the graph a straight line on logarithmic
paper, Furthermore, the slope of this line is a measure
of the concavity of the profile.
Hack demonstrated for several streams in the
Shenandoah Valley that the rate of decrease of bed-
material size in the downstream direction is related to
the degree of profle concavity. The greater rates of
pnrticle-size decrease downstream afe associated with
the more concave profiles.
The relation of channel characteristics to the longi-
tudinal profiles of streams was discussed in an initial
way by Leopold and Maddock (1953). They stated
that under most conditions in a river there is a tendency
for channel roughness to be conservative and to change
downstream less rapidly than some of the other
hydraulic variables. They say (1953, p. 51) that "the
suspended load and its change downstream character-
istic of natural rivers require a particular rate of increase
of velocity and depth downstream, Under the condi-
tions of a nearly constant roughness, to provide the
required velocity-depth relations, slope must generally
decrease downstream; it is for this reason that the
longitudinal profile of nearly all natural streams
carrying sediment is concave to the sky."
The data presented in the present paper provide some
indication of how the channel factors are related to the
changing size of bed material, or more specifically, how
the idea expressed by Leopold and .\raddock can be
integrated with the later work of Hack to provide a
more nearly complete picture of the interaction of geo-
logic and hydraulic factors.
The hydraulic variables slope and roughness can be
related to the other factors in an approximate way by
considering a Manning-type equation,

disl
v=1.5 -,-
n

in which d is mean depth (approximately equal to
hydraulic radius), 8 is slope, and n' is a roughness factor,
It is necessary in our data to use the slope of the stream
bed as an approximation to the slope of the energy grade
line, Let n' be the corresponding roughness pammeter.
If these factors are expressed as functions of discharge
in the form used by Wolman (1954a)

s=tQ'
n'=rQ'

and substituting the function of discharge (equations
7 -12) for each variable, then

25

kQm= l,5(cQ)!f(tQ)l'
rQ'

it follows that

m=H+tz--y

If the downstream change of width is related to dis-
charge as woe Q" (shown to he a characteristic of all
streams studied), because b+J+m=l, then m+J=O.5.
Thus, when m increases, f decreases.
The equation

m=H+tz--y

is represented graphically by the lines in figure 22,
assuming that m+J=O.5. The average relations of the
hydraulic variables as fnnctions of Q in the downstream
direction give values of }=.4 and m=.l. For the

"0.2

...0.1

o

-,1

" -.2
o
,
.

~ -.3

oJ EXPLANATION
a.
0 -,'
~ I EpIlemEral streams, N. Mex.
if)
~
0 ..5 2 Kansas-Republican Rivers, Kans.
w
e: 3 Yellowstone-Missouri Riven
Z
'"
I -,6 4 TombigbeeRiver, Miss.
'-'
~ 5 Maumee River, Ind.
0
w -.7
I- 6 Brandywine Creek, Pa.
'"
co
",' -.8 7 Watts Branch, Md.
BAssumed average lor
-.9 perennial rivers
Note: b
.l.0 In relation wa:Q,
h assumed equal to 0.5

-1.1

-1.2
o .1 .2 .3 .4 .5 .6

r. RATE OF CHANGE DF DEPTH. IN "<Of

.5 .4 .3 .2 .1 0
m, RATE OF CHANGE OF VELOCITY, IN va;Qm

FIGURE 22.- Downstreo.m relations oC depth, velocity, slope, and roughness expressed
as values of exponents in equations relating these factors to discha.rge.