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

28

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

Other very small ephemeral streams are similar to
the New Mexico example in that the slope of the graph
is relatively small compared with that of Calfpasture
River. Note the line representing the rills developed
on an artificial fill at Perth Amboy, N. J., which was
studied by Schumm,' Although analyses of particle size
on Perth'Amboy streams are not available, Schumm's
report implied that particle size tended to remain more
or less constant or decrease slightly in the downstrcam
direction.
The difference in slope of the lines representing Calf-
pasture River and the New Mexico streams in figure
24 is associated with difference in rates of downstream
change of channel characteristics. It is presumed that
in the ephemeral streams, the small value of z (slope
of the line in the gradient-discharge relation) is related
to the downstream increase in sediment concentration
reported in a previous section of this paper. It is
reasoned that to maintain a quasi-equilibrium with this
increase in sediment concentration downstream, there
must be an accompanying downstream increase of
velocitv Somewhat larger than that which characterizes
norma) rivers. As can bc seen in figure 22, the more
rapid downstream increase in velocity (large value of
m) is provided by a relatively small value of z for any
given value of the rate of change of roughness (value
of V).
In summary, the longitudinal profile of a river is
related to a combination of geologic and hydraulic
factors, These hydraulic factors are, first, the rate of
change of particle size of bed sediment downstream,
which tends to govern the change of channel roughness ;
and second the relative rate of increase of velocity
, ,
downstream, which appears to he controlled by the
rate of change of suspended-sediment concentration
downstream, Other things being equal, the less con-
cave profiles are characterized by greater rates of in-
crease of suspended-sediment concentration do,"vnstream
or by less rapid decrease of bed-particle size in thc
downstream direction.

EQUILIBRIUM IN EPHEMERAL STREAMS

MUTUAL ADJUSTMENT OF HYDRAULIC FACTORS

As has been discussed previously (Mackin, 1948;
Leopold and Maddock, 1953), the factors which may
be considered independent of the channel itsclf arc dis-
charge and quantity of sediment load, and to some
degree, caliber of load. Slope, width, velocity, and
depth are determined by or altered by forces operating
within the channel. In the words of Ruhey (1952, p.
131), the dependent variables "are determined not
separately but jointly"; that is to say, when circum-
stances require or impose a change in one or more of
the factors, the others will hecome adjusted to main-

tain a quasi-equilibrium between forces of erosion and
forces of deposition.
That some of the forces operating within the channel
may be determined by previous history is generally
recognized. There may be a difference in the "de-
grees of freedom" characteristic of the different hy-
draulic situations. As an example, one might consider
a flume with a movable bed. If the sides of the flume
are made of wood or metal so that the width is not
adjustable, there must be an adjustment among all the
remaining variables to a condition of mutual accommo-
dation. The fixed width may be thought of as the
restriction of one degree of freedom in the process of
mutual accommodation.
If a particular valley had been carved during the
Pleistocene bv a relatively large river, and througb
change in c1~ate or other physiographic factors the
valley at present carries only a minor streamlct, it is
likely that the small stream would not be able to rccarve
the valley bed to such an extent t.hat the valley slope is
materiallv altered. In such a circumstance the minor
stream, initially at least, would have to accommodate
itself to the slope of the valley in which it flows.
The organization of a drainage system and the re-
markable adjustment of its various hydraulic factors
have been amply demonstrated. Thesc have been
discussed by several authors, Rubey (1952), Leopold
and Maddock (1953), and in detail by Wohuan (1954a).
The present paper presents further evidence that.
nearly all rivers approach a condition of quasi-equi-
librium which was formerly attributed only to a graded
stream. This postulate implies further that if t,he
degrees of freedom of the hydraulic parameters are.
reduced, the remaining factors tend toward a mutual
accommodation or quasi-equilibrium. It is our purpose
here to demonstrate that this reasoning can be extended
even to a headwater stream in youthful topography as
far as the uppermost tributary rill.
In figure 18 a line has been drawn to represent the
relation between channel slope and channel width for
arroyos of large and moderate size. In the upper left
part of this figure the open squares represent values of
slopc and width of the smallest unbranched rills in the
headwater tributary hasin of Arroyo Caliente. These
rills averaged somewhat less than 1 foot in width.
Gradients were measured by laying a board in the bed of
each rill and determining its slope with a Brunton
compass. The measurements may be considered crude
and the scatter of the points on the graph may be partly
attributed to the method of obtaining the data; never-
theless, the position of those points indicates that the

2 S. Schumm, 1954, Ei'olution of drainage systems on an eroding fill at Perth
Amboy.~. I., Ph. D. thesis, Columbia Unlv.