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

16

PHYSIOGRAPHIC AND HYDRAULIC STUDIES OF RIVERS

INTERRELATION OF DRAINAGE NET AND HYDRAULIC
FACTORS

RELATION OF STREAM ORDER TO STREAM NUMBER,
STREAM LENGTH, AND DRAINAGE AREA

The quantitative description of drainage nets devel-
oped by Horton (1945) related stream order to the
number, average length, and average slope of strcams
in a drainage basin. Our purpose in this scction is to
show how this useful tool may be extended to include
the hydraulic as well as drainage-net characteristics.
All the data required for the Horton type of drainage-
net description can be obtained from maps. As maps
of several different scales were required for our mvn
analysis, some explanation of the procedure is in order.
Figure 12 presents planimetric maps of a sample area
near t.he city of Santa Fe, The map on the right, which
shows the drainagc net in a typical watershed about
9 miles long by 2 miles wide, was compiled from plani-
met.ric maps made by t.he Soil Conservation Service
from aerial photographs at an original scale of 2 inches
to t.he mile. The left map shows in more detail the
drainage net. in one small t.ributary which for purposes
of this report we will refer to M Arroyo Caliente. This
map was made by pace and compass after a planetable
traverse had been run for control. Each tribut.ary rill
was paced out to its farthest upstream extension in
order that the map would include all recognizable
channels.
The orders of various channels in the basin of Arrovo
Caliente are indicated by numbers appearing in the
upper part of the left map of figure 12, A small
unbranched tributary is labeled "order 1," and the
strcanl receiving that tributary is labeled "order 2.!1
All streams of orders 3, 4, and 5 are labeled with appro-
priate numbers near their respective mouths.
On the right map of figure 12, the little basin called
Arroyo Caliente is one of the minor tributaries which
even on t.his small-scale map appears to be unbranched
like the trihutary just west of it. If only this map
were available, one would conclude that Arroyo Caliente
is a first-order stream. This points up an important
qualification to the Horton scheme of stream-order
classification; namely, that the definition of a first-order
stream depends on the scale of t.he map used. The
first-order stream, by definition, should be the smallest
unbranched channel on the ground. The designation
of which stream is master and \vhich is tributary is
somewhat arbitrary, hut we have followed the guide
suggest.ed by Horton (1945, p. 281).
The largest drainage basin which is included in the
present analysis is that of the Rio Galisteo (fig. 1). At
its mouth this basin drains about 670 square miles,
Such an area contains a very large number of small
tributaries. It was desired to estimate the number of

tributaries of various sizes, their lengths, and other
characteristics. The task of counting and measuring
each individually would be inordinately great but
approximate answers could be obtained by a sampling
process. Arroyo Caliente is one of the samples used.
The detailed map of Arroyo Caliente was used to
determine t.he number, the average length, and average
drainage area of each order of stream in its basin. At
its mouth, Arroyo Caliente is of fifth order.
The Arroyo de los Frijoles basin shown in small scale
at the right in figure 12 was used as another sample and
similar measure,ments were made. The small, Ull-
hranched tributaries on this 1 mile to 2 inch map, of
which Arroyo Caliente is one, would be designated
order 1, in accordance with the definition of stream
order, The detailed study of Arroyo Caliente showed,
however, that on the ground this tributary which had
appeared unbranched ,vas, in reality, composed of a
drainage network of still smaller tributaries. Arroyo
CaJient.c and ot.her channels which appeared as order 1
on the right-hand map are, on the average, actually of
5th order. Thus the true order of any stream dcter-
mined from the right-hand map of figure 12 is increased
by adding 4, so that an order 1 stream on that map
becomes order 1 +4, or 5.
This provides a way of combining maps of different
seales to carry the numbering of stream order from one
map to the other. It can be seen in the plot of st.ream
length against stream order (left graph of figure 13)
that this relation in stream orders 1 t.o 5 (average values
of Arroyo Caliente) fits well with data from the small-
scale maps after the values of stream order were
adjusted as described above.
Similarly, t.his principle was used to obtain the esti-
mate of the number of streams of each order in an 11 t.h
order basin in the area studied, as shown in the right
diagram in figure 13. An actual count of the number of
streams of highest order was made. From the small-
scale maps the order of the Rio Galisteo at its mout.h
(fig. 1) was determined to be 7, which when adjusted
by 4, indicates the true order of 11. Because this is the
only stream of order 11 in the area studied, the graph
must go through the value of 1 on the ordinate scale at.
an abscissa value of 11. The mean relation \vas dra\\'l1
for the numbers of st.reams of highest. orders and ext.rap-
olated to determine the number of streams of order 5,
the smallest tributaries shown on the small-scale map.
The graph of number of streams of orders 1 to 5 in the
Arroyo Caliente basin which included only one stream
of order 5 was superimposed on the graph determined
from the 2 inches to 1 mile map and placed so that the
points representing order 5 coincided, By extending
the graph to order 1, the number of 1st order tributaries
in the 11th order basin could be estimated.