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

interval;

x is the mean of the logarithms
(base 10) of the observed
annual-peak discharges;

k is the standardized Pearson
Type-III deviate for a selected
T-year recurrence interval and
weighted skew coefficient; and

s is the standard deviation of the
logarithms (base 10) of the
observed annual-peak dis-
charges.

Results of the Pearson Type-III flood-
frequency analyses are presented in table 8
(listed as method B17B, at end of this report) for
the 188 streamflow-gaging stations analyzed
using either the drainage-basin or channel-
geometry flood-estimation techniques. Included
in table 8 is information about the type of gage
operated, the effective record length of the gage,
whether a systematic or historical analysis was
perfonned, the observed annual-peak discharge
record (listed as flood period), and the maximum
known flood-peak discharge and its recurrence
interval. An example flood-frequency curve is
shown in figure 3.

DEVELOPMENT OF
MULTIPLE-REGRESSION
EQUATIONS

Multiple linear-regression techniques were
used to independently relate selected drainage-
basin and channel-geometry characteristics to
design-flood discharges having recurrence
intervals of 2, 5, 10, 25, 50, and 100 years. A
general overview of the ordinary least-squares
and weighted least-squares multiple linear-
regression techniques used to develop the
equations is presented in thE' following two
sections. Specific infonnation on the multiple-
regression analyses for either nood-estimation
method is presented in later sections entitled
"Drainage-Basin Characteristic Equations" and
"Channel-Geometry CharacteriMic Equations."

Ordinary Least-Squares Regression

Ordinary least-squares (OLS)
linear-regression techniques were

multiple
used to

develop the initial multiple-regression
equations, or models, for both the drainage-
basin and channel-geometry flood-estimation
methods. In OLS regression, a design-flood
discharge (termed the response variable) is
estimated on the basis of one or more significant
drainage-basin or channel-geometry character-
istics (tenned the explanatory variables) in
which each observation is given an equal
weight. The response variable is assumed to be
a linear function of one or more of the
explanatory variables. Logarithmic transforma-
tions (base 10) were perfonned for both the
response and explanatory variables used in all
of the OLS regression analyses. Data
transformations were used to obtain a more
constant variance of the residuals about the
regression line and to linearize the relation
between the response variable and explanatory
variables. The general form of the OLS regres-
sion equations developed in these analyses is

loglO(QT) = log 10 (C) + bfloglO (X,) + (2)
b210g 10 (X2) +. ,+ bplog '0 (Xp) ,

l
I
j
I

where Qr

is the response variable, the
estimated design-flood discharge,
in cubic feet per second, for a
selected T-year recurrence
interval;

c

is a constant;

b
,

is the regression coefficient for
the ith explanatory variable (i =
1, ... ,p);

x
,

is the value of the ith explanatory
variable, a drainage-basin or
channel-geometry characteristic
(i = 1, ... ,p); and

p

is the total number of
explanatory variables in the
equation.

Equation 2, when untransformed, is
algebraically equivalent to

l
~

QT = C(X,)bl(X2)b2.. (Xp)bp. (3)

6 ESTIMATING DESIGN-FLOOD DISCHARGES FOR STREAMS IN IOWA