WSP10396

• File Number: 8056
• Description: Drought Preparedness
• State: CO
• Basin: Statewide
• Date: 1/1/1964
• Author: USGS
• Title: General Effects of Drought on Water Resources on the Southwest
• Water Supply Pro - Doc Type: Report/Study

I'Ir;Q318
e -

GENERAL EFFECTS OF DROUGHT ON VVATER RESOURCES

B17

runoff from large areas, Such conclusions are the pur-
pose of a study of fluctuations in regional runoff,
Streamflow records cannot be compared or averaged
by any simple means, Stream basins differ characteris-
tically in their drainage areas, runoff per unit of area,
and streamflow variability. Although many methods
have been utilized to reconcile these characteristic dif-
ferences, none has been fully successful. Use of dis-
charge in terms of cubic feet per second per square
mile (csm) offsets the difference in size of drainage
area and is useful in humid regions, but in the South-
west it has little value because of the rapid, large, and
erratic changes in discharge per square mile, often
within a relatively small area,
The 'Vater Resources Review 1 compares streamflow
records in terms of the percentage variation of the flow
of each stream from its own median. Difference in
streamflow variability, brought out in the discussion of
the frequency-distribution curves for the Virgin and
San <iabriel Rivers (p. B15), is shown in the maps of
the 'Water Resources Heview by dotted areas, having
discharges in the lower quartile of the range of flows,
and by crosshatched areas, having discharges in the
upper quartile, Thus the area of the Virgin River
would have been shown as dotted, whereas that of the
San Gabriel would not have been designated by a spe-
cial pattern,
The method used in this report to compare stream-
flow records is roughly that used in the Water Resources
Review, but allowance is made for the streamflow vari-
ability of each basin. By measuring the variability of
each basin and adjusting for it, runoff from all basins
is put on the same basis,
STREAMFLOW VARIABILITY
Streamflow variability has been defined and com-
pute~ in several ways by hydrologists, notably by Gal-
ton m England in 1875, Gherardelli in Italy in 1934
Contagne in France in 1935 as cited by Wing (1950);
and Lane and Lei (1950) in the United States. The com-
putation of variability was made by Lane and Lei
directly from flow-duration curves similar to the
frequeney-distribution curves shown on figure 3. Each
nnt.ura~ stream l~as its own individual curve, the slope of
wInch ]s determmed by characteristics of the basin and
the time pattern of precipitation on it. Although such
a curve call be drawn on the basis of a relatively short
record, the frequency distribution, like the mean flow,
is Iikel:f to vary within limits that depend on the period
for ,."hleh I~ IS c?mputed, Thus, although the frequen-
cy distributIOn ]s as fixed a characteristic of a stream
as is the mean flow, its determination requires records

I Published monthly, witl} annual water-year summaries, by the- Geological Survey
of tho U.S. Department oflaterior, in collaboration with the Water Resources Branch
of the Canada Department ot Northern Affairs and National Resources.

sufficiently long to represent an adequate sampling of
runoff events.
Streamflow variability is the slope of the frequency-
distribution curve. Lane (1950) has shown how the
slope of the flow-duration curve can be drawn if the
variability is known:

The Rhape of the duration curve can be obtained by drawing
a straight-line duration curve on logarithmic probability paper
with a slope such that the ratio of the discharge exceeded 15.87
pert'ent of the time to the discharge exceeded 50 percent of the
time is equal to the antilogarithm of the variability index
selected.

This plotting is possible because the point at 15.87 per-
cent is one standard deviation from the median flow,
Lane and Lei computed their variability index by
deriving the standard deviation of 10 uniformly spaced
points picked from a flow-duration curve, In this re-
port, the streamflow-variability index for each basin
has been computed as the standard deviation of the
logarithms of yearly runoff. As thus computed, the
variability index (standard deviation) is in logarithmic
units. Logarithms of yearly runoff are used so that
yearly runoff will approximate a normal distribution-
one in which positive and negative deviations from the
mean of the logarithms occur with equal frequency.

STREAMFLOW EXPRESSED IN UNITS OF STANDARD
DEVIATION

The studies of regional runoff are based upon the
records of 85 stream-gaging stations distributed
throughout the Southwest. Of these, the records of
25 cover the period 1904-53 and 60 cover the period
1930.-:53. The locations of the 85 gaging stations, and
the areas tributary to them, are shown in figure 4. The
observed annual runoff in the period of record, adjusted
for this report where necessary (and possible) for stor-
age and diversions, is given in table 1.
The variability index was computed for each station.
As the index based on one period usually differs some-
what from that based on a different period, the indexes
for the 25 long-record stations were computed both for
the period 1904-53 and for the period 1930-53. Table
2 gives these indexes; those based on the period 1930-53
are listed in ascending order of magnitude. Although
there are notable exceptions to the rule, streamflow
variability tends to be of similar magnitude for streams
in the same region, In general, the streams in Utah
and Colorado have the lowest indexes, those of Arizona,
New Mexico, and Texas are somewhat higher, and those
in California are highest.
Of the 85 stations listed in table 1, 12 have records
. continuous for the period 1904-53, For 13 others it was
possible to complete records for 1904-53 by estimating
ruuoff for some years. The yearly runoff in logarithmic
standard-deviation units for the 25 stations was com-