FLOOD00408

• County: Statewide
• Title: Techniques of Water-Resources Investigations of the US Geological Survey Regional Analyses of Streamflow Characterictics
• Date: 1/3/1997
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

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TECHNIQUES OF WATER-RESOURCES INVESTIGATIONS

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EXPLANATION

o Plotted point
. Point adjusled
for P

0.1
2S 50 100 300
MEAN ANNUAL
PRECIPITATION, (Pi
IN INCHES

10 100
DRAINAGE AREA, IN SQUARE MILES

1000

1. Graphical analysis of data from table 1.

error of estimate of the regression, signifi-
cance tests of the regression coefficients,
deviations of the individual points from re-
gression, and other information in addition
to the regression equation,

The model commonly used in regional anal-
ysis of flood peaks is of the form

log QRI = log a + b,log X, + b, log X,
+ b3 log X3. . . .

The equation of the graphical relation of fig-
ure 1 is of the above form and is

log Q" = -2.28 + 0.94 log A + 2.25 log P,

where Q" is the 25-year-recurrence-interval
flood in cubic feet per second (cfs), A is drain-
age area in square miles, and P is mean annual
precipitation in inches. Using the same data
in a digital computer produced the following
equation

log Q" = -2.07 + 0.97 log A + 2.11 log P.

Both regression coefficients are highly signifi-
cant, and the standard error of regression is

0.14 log units which corresponds to +38 and .
- 28 percent. Although the coefficients in the
above two regressions are appreciably differ-
ent, the computed values of Q" at a site by the
two equations generally will be within a few
percent of each other.
In a common procedure several regressions
are computed, the first one including all basin
and climatic characteristics considered appli-
cable. A "step-backward" computer program
will make the first computation, eliminate the
least significant variable and recompute the
regression, then continue the elimination
process until only one independent variable
remains. Differences in the standard errors of
the various regressions indicate the degree of
improvement obtained by inclusion of each
independent variable. For examples, see table
6 of Thomas and Benson (1970).
A preferable approach is to carefully select
a few variables having clear physical relation-
ships to the flood peak and to compute the
regression equation and check the regression
coefficients for significance. A computer pro-
gram called "step-forward" regression will

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