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<br />
<br />EPHEMERAL STREAMS
<br />
<br />7
<br />
<br />CHANGES OF WIDTH, DEPTH, VELOCITY, AND LOAD
<br />AT mDIVIDUAL CHANNEL CROSS SECTIONS
<br />
<br />Data for establishing the relation of width, depth,
<br />velocity, and load to discharge were obtained from twq
<br />sources: our own wading measurements and gaging
<br />station records. Although there are several gaging
<br />stations in central New :Vlexico on streams that are
<br />essentially ephemeral, the stations command basins of
<br />considerable size. Thus, our \\~ading measurements
<br />provide data not otherwise available and also extend
<br />considerably the rauges of the several hydraulic var- r
<br />iables studied. The gaging station records used for
<br />comparison with the data from smaller ephemeral
<br />streams are for the Rio Galisteo at Domingo (drainage
<br />area about 670 square miles) and Rio Puerco near
<br />Cabezon (drainage area 360 square miles.)
<br />Figure 6 shows the relation of width, depth, and veloc-
<br />ity to discharge at the gaging station on the Rio Galisteo
<br />at Domingo. Figure 7 shows the similar graphs for the
<br />gaging station on the Rio Puerco near Cabezon. When
<br />graphs of this kind were first presented by Leopold and
<br />Maddock (1953) the scatter of points was poorly under-
<br />stood. Wolman (1954a) showed that in a stream where
<br />bed scour and fill are minor, the scatter of points is
<br />markedly reduced if the successive measurements are
<br />made at identically the same cross section. Clarifica-
<br />tion of this matter is important in that the scatter need
<br />not be attributed to lack of adjustment between the
<br />channel and the imposed load and discharge,
<br />More scatter of points occurs on the at-a-station
<br />curves for streams having sandy or silty beds which are
<br />easily eroded than for streams flowing in gravelly chan-
<br />nels. Except for the effect of varying position of meas-
<br />urement, the remaining scatter apparently is caused by
<br />relatively rapid adjustment of channel shape to changes
<br />in suspended-load concentration. These changes in
<br />concentration result from the varying location, in-
<br />tensity, or other characteristics of storms and the con-
<br />sequent varying amount of erosion on the watershed
<br />lands.
<br />Data obtained from measurements of flash flow in
<br />small ephemeral streams are plotted in the graphs of
<br />figure 8, which show variation of width, depth, and
<br />velocity with changing discharge at each cross section,
<br />The same figure includes the lines representing the data
<br />from the two gaging stations discussed earlier as typical
<br />of the large ephemeral streams in central New .\Iexico,
<br />''>lIen one sees the wide, flat-bottomed, sandy ehan-
<br />nels charaeteristic of the ephemeral streams in central
<br />)I' ew :\fexico, he might obtain the impression that even
<br />at very low discharges the water flows over the full
<br />width of the channel. Actually, as shown in figure 8,
<br />wid th of the flowing water increases progressively with
<br />discharge in a, quite uniform manner. The rate of
<br />
<br />increase is about the sa.me as for midwestern perennial
<br />rivers, Values of b in the equation relating width, w,
<br />to discharge, Q,
<br />
<br />w=aQ'
<br />
<br />at a given cross section range from .09 to .44, and have a
<br />median of .26, This is the same as the average value of
<br />b for river data studied by Leopold and .\laddock (1953,
<br />p. 9). For a discharge of 100 efs, the width of flowing
<br />water in the various channels measured ranged from
<br />about 30 to 90 feet.
<br />The rate of increase of depth with diseharge at a given
<br />cross section, shown by the slope of the lines, tends to be
<br />generally similar for the several channel cross sections'
<br />measured. The slopes ranged from .61 to .24, with a
<br />median of .33; the slopes represent the values of the
<br />exponent, j, in the equation relating depth, d, to dis-
<br />charge,
<br />
<br />d=cQ'
<br />
<br />For rivers, this exponent has an average value of .40.
<br />The values here are for mean depth, defined as the
<br />quotient of the cross-sectional area of flowing water
<br />divided by the width of flowing water, The available
<br />data are insuffieient to conclude that depth increases
<br />with discharge less rapidly in the ephemeral streams
<br />studied than in rivers, It should be noted that, as in
<br />rivers, the depth in various arroyo channels for a
<br />particular discharge varies consider';bly. For instance
<br />. ,
<br />at a discharge 100 cfs, for which six examples are avail-
<br />able, the depth ranges from 0.25 to 0.8 feet,
<br />Mean velocity (defined as discharge divided by
<br />cross-sectional area) increases with discharge at about
<br />the same rate in both the ephemeral streams and peren-
<br />nial rivers. The median value of m in the equation
<br />relating velocity, V, to discharge,
<br />
<br />v=kQm
<br />
<br />is .32 for the arroyos as eompared with ,34 for rivers
<br />previously studied, At a discharge of 100 ds, mean
<br />velocity in the various channels measured ranged from
<br />2.9 to 5.0 feet per second.
<br />As shown previously (Leopold and y[addoek, 1953,
<br />p.8),
<br />
<br />because
<br />then
<br />and
<br />
<br />Q=wdv
<br />Q=aQ'XcQ'XkQm
<br />b+j+m=l
<br />
<br />Even without weighing or adjustment, the sum of the
<br />respective median values of these three eXJlonents for
<br />arroyo data equals .91. With so few data available
<br />there is no rational way to adjust the median reported
<br />for each exponent. Refinement of these values must
<br />await collection of additional data.
<br />
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