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

Calculation of Estimates

Design-flood discharge estimates calculated
using both the drainage-basin and channel-
geometry flood-estimation methods can be
weighted inversely proportional to their
variances to obtain a weighted average that has
a smaller variance than either of their
individual estimates. According to the
Interagency Advisory Committee on Water Data
(IACWD, 1982), the weighted average is
calculated as

QT(db) ISE(eg))2+QT(eg) ISE(db))2
Qr = ,(14)
(dbeg) (SE 12+ (SE )2
(db) (eg)

where QT(dbcg)is the weighted average
design-flood discharge, in cubic
feet per second, for a selected
T-year recurrence interval;

QTldb) is the drainage-basin regression-
equation design-flood discharge,
in cubic feet per second;

SE(cg) is the standard error of estimate,
in log units (base 10), of the
channel-geometry regression
equation (tables 3-5);

QTlcgl is the channel-geometry
regression-equation design-flood
discharge, in cubic feet per
second; and

SE(db) is the standard error of estimate,
in log units (base 10), of the
drainage-basin regression
equation (table 2).

The standard error of estimate (SEldbcgl)' in
log units (base 10), of the weighted average
design-flood discharge estimate QT(dbeg) can be
cal cula ted as

BE (dbcg)

[ (SE(db))2(SE(eg))2J05
(SE(db)12+ (SE(eg)12

(15)

Example ofWeighting--ExampIe 5

Examole 5.--Use the 100-year drainage-
basin and channel-geometry regression
estimates (table 8) to obtain a weighted average,
100-year peak-discharge estimate for the
discontinued Black Hawk Creek at Grundy
Center crest-stage gaging station (station
number 05463090; map number 73, figs. 1 and
2).

The 100-year flood estimate calculated for
this gaging station using the drainage-basin
equation is 7,740 ft3/s (listed as method GISDB
in table 8), and the standard error of estimate,
in log units (base 10), for this equation is 0.198
(table 2). The 100-year flood estimate calculated
for this gaging station using the Region I,
bankfull channel-geometry equation is 8,860
ft3/s (listed as method BFRI in table 8), and the
standard error of estimate, in log units, for this
equation is 0.192 (listed in the first set of
equations in table 4). The weighted average,
100-year flood estimate is calculated using
equation 14 as

QIOO(dbcg)

QIOO(db) (SE(eg))2+QI00(eg) (SE(db))2
ISE(db)12+ ISE(eg))2

7.740(0.19212+8.860(0.19812
(0.198)2+ (0.192)2
= 8,320 fl'ls.

The standard error of estimate for this
weighted average, 100-year peak-discharge
estimate is calculated using equation 15 as

SE(dbcg) =

[ (SE(db))2(SE(eg))2JO.5
2 2'
(SE(db)l + IBE(eg))

[ (0.198)2(0.192)2 JO'5,
(0.19812+ (0.19212
= 0.138 log units or 32.6 percent.

Weighting Design-Flood Discharge
Estimates for Gaged Sites

Weighted design-flood discharges are
estimated for a gaged site based on either the
Pearson Type-III estimate and regression-
equation estimates from both the drainage-

APPLICATION AND RELIABILITY OF FLOOD-ESTIMATION METHODS 35