FLOOD06431

• County: Statewide
• Basin: Statewide
• Title: Estimating Design-Flood Discharches for Streams in Iowa Using Drainage-Basin and Channel-Geometry Characteristics
• Date: 1/1/1993
• Prepared For: Iowa City
• Prepared By: USGS
• Floodplain - Doc Type: Educational/Technical/Reference Information

APPLICATION AND RELIABILITY
OF FLOOD-ESTIMATION
METHODS

The regression equations developed in this
study for both the drainage-basin and
channel-geometry flood-estimation methods
apply only to streams in Iowa where peak
streamflow is not affected substantially by
stream regulation, diversion, or other human
activities. The drainage-basin method does not
apply to basins in urban areas unless the effects
of urbanization on surface-water runoff are
negligible. The channel-geometry method does
not apply to channels that have been altered
substantially from their stabilized conditions by
human activities, as outlined in Appendix C.

Limitations and Accuracy of
Equations

The applicability and accuracy of the
drainage-basin and channel..geometry flood-
estimation methods depend on whether the
drainage-basin or channel-geometry character-
istics measured for a stream site are within the
range of the characteristic values used to
develop the regression equations. The
acceptable range for each of the drainage-basin
characteristics used to develop the statewide
equations (table 2) are tabulated as maximum
and minimum values in table 6. Likewise, the
acceptable range for each of the channel-
geometry characteristics used to develop the
statewide and regional equations (tables 3-5)
also are tabulated as maximum and minimum
values in table 6. The applicability of the
drainage-basin and channel-geometry
equations is unknown when the characteristic
values associated with a strearn site are outside
of the acceptable ranges.

The standard errors of estimate and average
standard errors of prediction listed in tables 2-5
are indexes of the expected accuracy of the
regression-equation estimates in that they
provide measures of the differ,mce between the
regression estimate and the Pearson Type-III
estimate for a design-flood recurrence interval.
If all assumptions for applying regression
techniques are met, the difference between the
regression estimate and the Pearson Type-III
estimate for a design-flood recurrence interval

will be within one standard error approximately
two-thirds of the time.

The standard error of estimate is a measure
of the distribution of the observed annual-peak
discharges about the regression surface
(Jacques and Lorenz, 1988, p. 17). The average
standard error of prediction includes the error of
the regression equation as well as the scatter
about the equation (Hardison, 1971, p. C228).
Although the standard error of estimate of the
regression gives an approximation of the
standard error of peak discharges, the average
standard error of prediction provides more
precision in the expected accuracy with which
estimates of peak discharges can be made. The
average standard error of prediction is
estimated by taking the square root of the
PRESS statistic mean. Because the standard
errors of estimate and average standard errors
of prediction are expressed as logarithms (base
10), they are converted to percentages by
methods described by Hardison (1971, p. C230).

The average standard errors of prediction
for the regression models ranged as follows:
statewide drainage-basin equations, 38.6 to 50.2
percent (table 2); statewide channel-geometry
bankfull equations, 41.0 to 60.4 percent (table
3); statewide channel-geometry active-channel
equations, 61.9 to 68.4 percent (table 3); Region
1 channel-geometry bankfull equations, 33.8 to
48.3 percent (table 4); Region I channel-
geometry active-channel equations, 43.0 to 53.0
percent (table 4); Region II channel-geometry
bankfull equations, 30.3 to 52.1 percent (table
5); and Region II channel-geometry active-
channel equations, 59.7 to 70.0 percent (table 5).

The average equivalent years of record
represents an estimate of the number of years of
actual streamflow record required at a stream
site to achieve an accuracy equivalent to each
respective drainage-basin or channel-geometry
design-flood discharge estimate. The average
equivalent years of record as described by
Hardison (1971, p.C231-C233) is a function of
the standard devia tion and skew of the observed
annual-peak discharges at the gaging stations
analyzed for each respective regression
equation, the accuracy of the regression
equation, and the recurrence interval of the
design flood. The average equivalent years of
record for a design flood with a recurrence

32 ESTIMATING DESIGN.FLOOD DISCHARGES FOR STREAMS IN IOWA