U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5073

Prepared in cooperation with the Metropolitan St. Louis Sewer District

Estimation of the Magnitude and Frequency of Floods 

in Urban Basins in Missouri
Cover photographs.

Grand Glaize Creek road overflow at 

intersection of Dougherty Road and Big 

Bend Road, near Valley Park, Missouri,

September 14, 2008.

Grand Glaize Creek overflow along 

Dougherty Ferry Road, near Valley Park, 

Missouri, September 14, 2008.

Grand Glaize Creek right overbank 

flow on Big Bend Road, near Valley

Park, Missouri, September 14, 2008.

Grand Glaize Creek along downstream 

side of Big Bend Road bridge, near 

Valley Park, Missouri, September 14, 

2008.
Estimation of the Magnitude and Frequency 

of Floods in Urban Areas in Missouri

By Rodney E. Southard

Prepared in cooperation with Metropolitan St. Louis Sewer District

Scientific Investigations Report 2010–5073

U.S. Department of the Interior

U.S. Geological Survey
U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2010

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Southard, R.E., 2010, Estimating the magnitude and frequency of floods in urban basins in Missouri: U.S. Geological 

Survey Scientific Investigations Report 2010-5073, 27 p. 

ISBN 978–1–4113–2847–1
iii

Contents

Abstract ..........................................................................................................................................................1

Introduction.....................................................................................................................................................1

Background and Problem....................................................................................................................2

Physical Setting.....................................................................................................................................2

Previous Studies ...................................................................................................................................2

Purpose and Scope ..............................................................................................................................3

Data Development .........................................................................................................................................3

Site Selection.........................................................................................................................................3

Flood-Frequency Analyses..................................................................................................................6

Basin Characteristics...........................................................................................................................8

Regionalization....................................................................................................................................11

Estimation Of The Magnitude And Frequency Of Floods ......................................................................11

Definition of Regions ..........................................................................................................................11

Model Development ...........................................................................................................................11

Model Verification and Diagnostics ................................................................................................19

Summary........................................................................................................................................................24

Selected References...................................................................................................................................26

Figures

1–2. Maps showing:

 1. Location of urban areas in and adjacent to Missouri and selected 

urban areas with U.S. Geological Survey streamgages used in this 

study ........................................................................................................................................4

 2. Location of streamgages in and adjacent to Missouri used in this 

study ........................................................................................................................................7

3–6. Graphs showing:

 3. Residuals of the regression equations for estimating the magnitude

 of the (A) 50-, (B) 10-, and (C) 1-percent annual exceedance 

probability flood in relation to drainage area and percent impervious 

 area........................................................................................................................................12

 4. Comparison of observed and estimated peak flows of the 

(A) 50-, (B) 10-, and (C) 1-percent annual exceedance probability 

flood .......................................................................................................................................13

 5. Drainage area and impervious area basin characteristics at 

U.S. Geological Survey streamgages in urban areas in and 

 adjacent to Missouri ...........................................................................................................22

 6. Maximum recorded flood discharges at U.S. Geological Survey 

streamgages in urban areas in and adjacent to Missouri in relation 

to estimated peak flows from the regression equations for the 1- and 

0.2-percent annual exceedance probability flood using 46 percent 

impervious area ...................................................................................................................23
iv

Tables

1. Description of selected streamgages in urban areas in and adjacent 

 to Missouri .....................................................................................................................................5

2. Basin characteristics of streamgages in urban areas in and adjacent 

 to Missouri used in the development of urban regression equations ...............................10

3. Flood-frequency statistics for annual peak flow data from 35 U.S. Geological 

 Survey streamgages in urban areas in and adjacent to Missouri .....................................14

4. Flood discharges at given annual exceeedance probabilities for streamgages 

 in urban areas in and adjacent to Missouri ...........................................................................15

5. Weighted least-squares regression equations for streams in urban areas 

 in Missouri ...................................................................................................................................18

6. Variance of estimated values for U.S. Geological Survey streamgages 

 in urban areas in and adjacent to Missouri ...........................................................................20

7. Accuracy statistics of weighted least-squares regression equations for 

 urban basins in Missouri ...........................................................................................................21

8. Model error variances, Student’s t distribution, and covariance matrices 

 of regression equations for urban basins in Missouri..........................................................21

9. Ranges of basin characteristics used to develop the regression equations 

 for urban basins in Missouri .....................................................................................................22

10. Results of sensitivity analyses presented as percent change in computed 

 flood discharge as a result of a 10- and 20-percent change of the input 

 basin characteristic ...................................................................................................................23

11. Flood discharges at the 1-percent annual exceedence probabilities for 

 rural and urban regression equations at selected U.S. Geological Survey 

 streamgages................................................................................................................................24
v

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

foot (ft) 0.3048 meter (m)

foot per mile (ft/mi) 0.1894 meter per kilometer

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 259.0 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic foot (ft3) 0.02832 cubic meter (m3) 

 Flow Rate

foot per second (ft/s) 0.3048 meter per second (m/s)

cubic foot per second (ft3/s) 0.02832 cubic meter per second (m3/s)

Horizontal coordinate information is referenced to North American Datum of 1983 (NAD 83).

Elevation, as used in the report, refers to the distance above the North American Vertical Datum 

of 1988 (NAVD88).

Conversion Factors and Datums
vi
Abstract 

Streamgage flood-frequency analyses were done for 35 

streamgages on urban streams in and adjacent to Missouri for 

estimation of the magnitude and frequency of floods in urban 

areas of Missouri. A log-Pearson Type-III distribution was 

fitted to the annual series of peak flow data retrieved from the 

U.S. Geological Survey National Water Information System. 

For this report, the flood frequency estimates are expressed 

in terms of percent annual exceedance probabilities of 50, 20, 

10, 4, 2, 1, and 0.2. Of the 35 streamgages, 30 are located in 

Missouri. The remaining five non-Missouri streamgages were 

added to the dataset to improve the range and applicability 

of the regression analyses from the streamgage frequency 

analyses.

Ordinary least-squares was used to determine the best set 

of independent variables for the regression equations. Basin 

characteristics selected for independent variables into the ordinary least-squares regression analyses were based on theoretical relation to flood flows, literature review of possible basin 

characteristics, and the ability to measure the basin characteristics using digital datasets and geographic information system 

technology. Results of the ordinary least-squares were evaluated on the basis of Mallow’s Cp statistic, the adjusted coefficient of determination, and the statistical significance of the 

independent variables. The independent variables of drainage 

area and percent impervious area were determined to be statistically significant and readily determined from existing digital 

datasets. The drainage area variable was computed using the 

best elevation data available, either from a statewide 10-meter 

grid or high-resolution elevation data from urban areas. The 

impervious area variable was computed from the National 

Land Cover Dataset 2001 impervious area dataset. The 

National Land Cover Dataset 2001 impervious area data for 

each basin was compared to historical imagery and 7.5-minute 

topographic maps to verify the national dataset represented 

the urbanization of the basin at the time streamgage data were 

collected. Eight streamgages had less urbanization during the 

period of time streamflow data were collected than was shown 

on the 2001 dataset. The impervious area values for these eight 

urban basins were adjusted downward as much as 23 percent 

to account for the additional urbanization since the streamflow 

data were collected.

Weighted least-squares regression techniques were used 

to determine the final regression equations for the statewide 

urban flood-frequency equations. Weighted least-squares 

techniques improve regression equations by adjusting for 

different and varying lengths in streamflow records. The final 

flood-frequency equations for the 50-, 20-, 10-, 4-, 2-, 1-, and 

0.2-percent annual exceedance probability floods for Missouri provide a technique for estimating peak flows on urban 

streams at gaged and ungaged sites. The applicability of the 

equations is limited by the range in basin characteristics used 

to develop the regression equations. The range in drainage 

area is 0.28 to 189 square miles; range in impervious area is 

2.3 to 46.0 percent. 

Seven of the 35 selected streamgages were used to 

compare the results of the existing rural and urban equations 

to the urban equations presented in this report for the 1-percent annual exceedance probability. Results of the comparison 

indicate that the estimated peak flows for the urban equation in 

this report ranged from 3 to 52 percent higher than the results 

from the rural equations. Comparing the estimated urban peak 

flows from this report to the existing urban equation developed in 1986 indicated the range was 255 percent lower to 10 

percent higher. The overall comparison between the current 

(2010) and 1986 urban equations indicates a reduction in estimated peak flow values for the 1-percent annual exceedance 

probability flood.

Introduction

Hydraulic design of bridges and culverts, the establishment of flood-insurance rates, and the designation of emergency routes require information about the flood characteristics of streams. These characteristics depend substantially on 

upstream basin characteristics. Urban basins are characterized 

by substantial development consisting of streets, highways, 

residential homes, and commercial buildings. This development results in impervious surfaces that limit infiltration of 

precipitation, reduce runoff times, and increase peak flows in 

channels. Rural basins are characterized by agricultural land 

Estimation of the Magnitude and Frequency of Floods in 

Urban Areas in Missouri

By Rodney E. Southard
2 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

use, forests, and natural channels. Regulated streams in rural 

or urban basins are characterized by upstream locks and dams, 

and these streams have unique flow characteristics dependent 

on the operational plans of these structures. Peak flows on 

regulated streams typically are delayed and attenuated compared to unregulated streams.

Estimates of the peak flow flood characteristic for urban 

basins are determined separately from rural basins. The 

increase in impervious area of urban basins and efficient drainage systems results in higher peak flows and decreased basin 

response times compared to rural basins. Peak flow estimates 

are computed using regression equations. The dependent 

variable is derived from frequency analyses of flow data from 

streamgages located in urban basins. The independent variables consist of basin characteristics that describe basin size 

and shape characteristics, land use, and climatic variables.

Background and Problem

Proper design of bridges and culverts, land-use planning, and flood-risk assessments are all dependent on the 

best available estimates of peak flood discharges to minimize 

costs and protect lives and property. There has been a need to 

re-evaluate the current (2010) statewide urban flood frequency 

equations in Missouri for several reasons. First, the last set 

of urban equations (Becker, 1986) was based on streamgages 

with data only through the 1984 water year (October 1 to September 30). Between 1985 and 2008, 24 years of additional 

streamflow data have been collected at selected streamgages. 

Also, 15 streamgages have been established or re-activated in 

the St. Louis area and are available for regression analyses. 

Second, computers and their associated storage and processing capabilities have increased dramatically since 1984. Large 

digital datasets now can be evaluated and processed to more 

accurately define historically recognized basin characteristics and evaluate potentially new characteristics that in the 

past were too computationally intensive to do by hand or 

with earlier computer systems. Third, the field of statistical 

analyses has progressed because of computer capabilities and 

improved methods such as accounting for length of record 

at streamgages and correlation of streamgages on the same 

stream and in similar geographic regions. A fourth reason is to 

define the 0.2-percent annual exceedance probability flood for 

urban basins for risk assessments. Previous studies estimated 

floods only up to the 100-year recurrence interval (1-percent 

annual exceedance probability flood); Becker (1986) and 

other authors of previous flood frequency studies in Missouri expressed flood-frequency estimates in terms of T-year 

discharges, where T is a recurrence interval that indicates the 

average number of years between occurrences of peak discharges of the same or greater magnitude. For these reasons, 

the U.S. Geological Survey (USGS) conducted a study, in 

cooperation with the Metropolitan St. Louis Sewer District, 

to develop and apply a new set of regression equations for 

estimating the magnitude and frequency of floods in urban 

basins in Missouri. 

Physical Setting

The state of Missouri is located in the Midwest region of 

the continental United States with no topographic barriers to 

hinder cold air masses from the northern plains and Canada or 

warm air masses from the Gulf of Mexico. Copious amounts 

of precipitation sometimes are produced as thunderstorms 

develop and re-develop along fronts that separate contrasting 

air masses. For example, thunderstorms on August 12 and 13, 

1982, in the Kansas City area resulted in a 24-hour rainfall 

report of 12.6 inches and widespread flash flooding (Becker 

and Alexander, 1983). Tropical systems from the Gulf of 

Mexico also provide substantial amounts of precipitation as 

they move across the state. Tropical systems typically do not 

have the rainfall intensity as frontal type thunderstorms, but 

they are capable of producing substantial amounts of rainfall 

over large areas. Mean annual rainfall rates vary from 34 

inches in the northwest to 50 inches in the southeast part of the 

state (Missouri Climate Center, 2009).

Physical features within a state or region can affect the 

runoff characteristics of flood flows. Elevation varies from 

about 200 feet above the North American Vertical Datum of 

1988 in the southeast part of Missouri to about 1,700 feet in 

south-central Missouri. Local relief varies from less than about 

30 feet in the southeast part of the state to 500 feet or more in 

central and south-central Missouri. Stream slopes in the southeast part of the state are relatively low, with slopes averaging 

about 1.5 feet per mile. Flash flooding is a concern in other 

urban areas of the state where slopes of 150 feet per mile exist 

(Alexander and Wilson, 1995).

Drainage patterns are sometimes altered in urban areas. 

Stream channels often are straightened and enlarged, and may 

even be routed underground in long culverts or conduits. The 

hydraulic characteristics of streams in urban areas may be 

altered because of constrictions from the numerous road and 

highway crossings of stream channels. Retention ponds in 

urban areas also change the dependent times and magnitudes 

of peak discharges on urban streams (Feaster and Guimaraes, 

2004).

Previous Studies

Spencer and Alexander (1978) documented an investigation to define flood frequency estimates for urban basins in 

Missouri. The study area was St. Louis County and a network of 30 streamgages was established to define the hydrologic characteristics in this region of the state. Data from 

the streamgages were used to develop regression equations 

and nomographs to estimate flood frequencies. Independent 

variables were drainage area and percentage of impervious 

area. Drainage area was computed manually using a mechanical planimeter and USGS 7.5-minute quadrangle topographic 
Data Development 3

maps at a scale of 1:24,000. Macroscopes with scalar reticules 

were used to measure areas of impervious surface from aerial 

photography at a scale of 1:8,400. Standard errors of estimate 

ranged from 15.7 to 17.8 percent for the regression equations. 

The equations were applicable for streams in St. Louis County 

with a drainage area range of 0.8 to 39 square miles and an 

impervious area range of 1 to 32 percent. 

Sauer and others (1983) completed a nationwide study 

of urban basins to estimate selected flood annual exceedance probabilities of 50 to 0.2 percent for ungaged sites. The 

study utilized data from 269 streamgages located in urban 

basins in 56 cities and 31 states. Their work resulted in 

two sets of seven-parameter equations and one set of threeparameter equations. The standard error of estimate for the 

seven-parameter equations ranged from 32 to 49 percent. 

The standard error of estimate for the three-parameter equations ranged from 40 to 52 percent. Common independent 

variables used in the three sets of equations were drainage 

area, basin development factor, and rural discharge. The basin 

development factor variable is an index of urbanization, which 

provides a measure of the efficiency of the drainage system. 

The efficiency of a drainage system is based on the percentage of channel improvements and linings, storm sewers, and 

curb-and-gutter streets. The rural discharge variable is based 

on frequency analyses of peak discharges in rural basins. This 

rural discharge variable is important for explaining geographical variations in runoff from urban areas in different parts of 

the country. 

Becker (1986) is the most recent urban flood frequency 

study applicable for urban basins in Missouri and documented the first statewide urban flood frequency equations 

for Missouri. To develop the regression equations for Missouri 37 USGS streamgages were used; of these 27 were 

located in urban basins, and 10 were located in predominantly 

rural basins. The rural basins were included in the study to 

increase the number of streamgages for statistical analyses, 

and to extend the applicability of the equations developed 

by assuming a minimum of 1 percent of impervious area in 

the rural basins. Streamgage records were extended using a 

rainfall-runoff model and by simulating runoff using long term 

precipitation records. Becker (1986) provided flood-frequency 

estimates from 50 to 1 percent of the flood annual exceedance 

probability with two sets of equations. The first set of equations included the independent variables drainage area and the 

basin development factor from Sauer and others (1983). The 

second set of equations included drainage area and impervious 

area as independent variables. The range of standard errors of 

estimate from these sets of equations was 25.9 to 32.9 percent. 

These equations were applicable for drainage area from 0.28 

to 38.9 square miles, a basin development factor from 0 to 11, 

and percentage of impervious area from 1 to 34. 

Purpose and Scope

The purpose of this report is to document the development and application of regression equations for estimating the magnitude and frequency of floods in urban basins 

in Missouri. The flood frequency estimates for the flood 

annual exceedance probabilities of 50-, 20-, 10-, 4-, 2-, 

1-, and 0.2-percent (recurrence intervals of 2-, 5-, 10-, 

25-, 50-, 100-, and 500-years) were selected for this study. 

The equations were based on data from 35 streamgages in 

urban basins in and adjacent to Missouri (fig. 1). Of the 35 

USGS streamgages, 30 were spatially located in Missouri, 

3 were located in Arkansas, 1 was located in Kansas, and 1 

streamgage was located in Oklahoma. Streamgages outside of 

Missouri were selected to extend the range of data used for the 

independent variables. This report supersedes previous USGS 

urban flood frequency reports for Missouri.

This report describes the site selection, flood-frequency 

analyses, basin characteristics, and development and verification of the regression equations. In addition to observed data, 

previous studies in Missouri relied on calibration and simulation of flood peaks at selected streamgages. This study focused 

on using observed peak flows determined by direct or indirect 

measurements at all streamgages. The most recent statistical 

techniques in streamgage flood frequency (expected moments 

algorithm) and weighted least-squares regression analyses 

were used to develop the best possible regression equations. 

Independent variables were selected for data availability and 

computation in geographic information systems (GIS), as well 

as being statistically significant at the 0.05 probability level. 

Ordinary least-squares (OLS) regression was used to determine the best set of independent variables for estimation of 

flood peaks, and weighted least-squares (WLS) regression was 

used to compute the final regression coefficients.

Data Development

A reliable source of hydrologic information available for 

flood frequency estimation is the annual time series data collected at USGS streamgages. Data may be collected continuously by mechanical or digital recorders. Data also may be 

collected intermittently with devices that collect only the peak 

stage of an event. The highest recorded flood event each year 

reflects an annual time series at that specific streamgage. 

Site Selection

The study area included urban areas in the State of 

Missouri. An emphasis of this study was to develop a set of 

regression equations based on observed peak flow values at 

selected urban streamgages. The initial review of urbanized 

basins resulted in a list of more than 70 streamgages with sufficient record length of 9 years or longer. Further evaluation of 

the initial list of streamgages and upstream basins resulted in a 
4 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

Joplin

Arnold Mattese

Houston

Wellston Pagedale

Columbia

Mehlville

Maplewood

Lake City

Black Jack

Marshfield

Elm Springs

Kansas City

Springfield

Battlefield

Fayetteville

Poplar Bluff

Independence Overland Park

Jefferson City

West Siloam Springs

Bridgeton

Shrewsbury Ellisville

Creve Coeur

Chesterfield

University City

Bellefontaine Neighbors

St. Louis

County

95° 94° 93° 92° 91° 90° 89°

41°

40°

39°

38°

37°

36°

Location of urban areas with 

 U.S. Geological Survey streamgages

Urban area 

0 25 50 75 100 MILES

0 25 50 75 100 KILOMETERS

EXPLANATION

Base from U.S. Department of Commerce; U.S. Census Bureau, 2008

U.S. Geological Survey digital data, 1995, 1:100,000

Universal Transverse Mercator projection 

Zone 15

North American Datum of 1983 (NAD83)

IOWA

MISSOURI

NEBRASKA

KANSAS

OKLAHOMA

ARKANSAS

TENNESSEEKENTUCKY

ILLINOIS

MISSOURI

Figure 1. Location of urban areas in and adjacent to Missouri and selected urban areas with U.S. Geological Survey 

streamgages used in this study.
Data Development 5

Table 1. Description of selected streamgages in urban areas in and adjacent to Missouri.

[USGS, U.S. Geological Survey; ddmmss, degree, minute, second]

Site

number

(fig. 2)

Streamgage name

USGS

streamgage

number

Latitude

(ddmmss)

Longitude

(ddmmss)

Period

of record

(water year)

1 Indian Creek at Overland Park, Kan. 06893300 395626 944016 1964–2008

2 Blue River at Kansas City, Mo. 06893500 395725 943332 1939–2008

3 Brush Creek at Kansas City, Mo. 06893560 390222 943506 1971–1982, 1999

4 Brush Creek at Rockhill Road in Kansas City, Mo. 06893562 390221 943443 1999–2008

5 Rock Creek at Independence, Mo. 06893600 390436 942702 1967–1975

6 Little Blue River near Lake City, Mo. 06894000 390602 941801 1948–2008

7 Cow Branch near Columbia, Mo. 06910200 390010 921925 1955–1979

8 Hinkson Creek at Columbia, Mo. 06910230 395539 922023 1967–1981, 

1987–1991

9 Dickerson Creek Tributary near Jefferson City, Mo. 06910430 393445 921643 1970–1979

10 Niangua Branch at Marshfield, Mo. 06923000 392049 925445 1951–1979

11 Coyle Branch at Houston, Mo. 06929000 391925 915711 1950–1979

12 Shotwell Creek at Highway 340 near Ellisville, Mo. 06935800 393705 903459 1960–1979

13 Creve Coeur Creek at Chesterfield, Mo. 06935850 393847 903137 1998–2008

14 Creve Coeur Creek near Creve Coeur, Mo. 06935890 394057 902920 1972–1979, 

1997–2008

15 Fee Fee Creek near Bridgeton, Mo. 06935955 394340 902650 1972–1979, 

1996–2008

16 Cowmire Creek at Bridgeton, Mo. 06935980 394551 902558 1972–1979, 

1998–2008

17 Coldwater Creek near Black Jack, Mo. 06936475 394904 901504 1997–2008

18 Maline Creek at Bellefontaine Neighbors, Mo. 07005000 394412 901334 1996–2008

19 River Des Peres near University City, Mo. 07010022 394005 901925 1997–2008

20 River Des Peres Trib. at Pagedale, Mo. 07010030 394036 901853 1997–2008

21 Engelholm Creek near Wellston, Mo. 07010035 394057 901810 1998–2008

22 Deer Creek at Maplewood, Mo. 07010086 393603 901934 1996–2008

23 MacKenzie Creek near Shrewsbury, Mo. 07010090 393436 901924 1997–2008

24 Gravois Creek near Mehlville, Mo. 07010180 393136 901758 1997–2008

25 Martigney Creek near Arnold, Mo. 07010208 392927 901734 1998–2008

26 Mattese Creek near Mattese, Mo. 07019317 392859 902027 1996–2008

27 Town Branch at B.R. 62 at Fayetteville, Ark. 07048480 390325 941031 1997–2008

28 Town Branch Tributary at Highway 16 at Fayetteville, Ark. 07048490 390253 940943 1997–2008

29 Wilson Creek at Springfield, Mo. 07052000 391113 931952 1999–2008

30 Wilson Creek near Springfield, Mo. 07052100 391006 932213 1972–1980, 

1999–2008

31 Wilson Creek near Battlefield, Mo. 07052160 390703 932413 1969–1970, 

1973–1980,

 2000–2004

32 Pike Creek Tributary near Poplar Bluff, Mo. 07063200 391730 931654 1955–1969

33 Turkey Creek near Joplin, Mo. 07186600 390716 943455 1964–1972

34 Osage Creek near Elm Springs, Ark. 07195000 391318 941717 1950–1979, 

1996–2008

35 Sager Creek near West Siloam Springs, Okla. 07195865 391206 943618 1997–2008
6 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

final list of 35 streamgages for streamgage frequency analyses (table 1). Criteria used for the selection of streamgages 

included: (1) streamgage record length of 9 years or greater; 

(2) urbanization with development resulting in an increase in 

impervious area within the upstream basin had to exist, relative to original basin condition, and be relatively stable during 

the data-collection period; (3) no major diversions into or out 

of the basin upstream from the streamgage; (4) minimal storage effects from retention, detention structures, or road crossings; and (5) computed annual peak flows from stable ratings 

with sufficient measurements to define the rating adequately. 

Streamgage data were retrieved from the USGS National 

Water Information System (NWIS) at http://nwis.waterdata.

usgs.gov/usa/nwis/peak. The annual peak flows for all potential streamgages were retrieved and evaluated for accuracy and 

length of record. Aerial imagery from local sources and/or the 

USGS digital orthophoto quarter-quadrangles were used to 

evaluate basins for urbanization and possible storage or retention of floodwaters. 

Spatial distribution of the 35 USGS streamgages is 

shown in figure 2. The largest concentration of streamgages is 

located in St. Louis County (fig. 2) in eastern Missouri with 15 

of the 35 streamgages in the study. Five streamgages located 

outside of Missouri were included because the basins upstream 

from the streamgages were similar to basins in Missouri, and 

to potentially improve the range of independent variables in 

the regression equations. Pertinent information such as the 

streamgage name, number, location, and period of record is 

provided in table 1. Most streamgages had 10 to 12 years of 

data. The longest period of record was Blue River at Kansas 

City, Missouri, with 70 years of record. 

Flood-Frequency Analyses

Flood-frequency estimates provided in this report were 

computed from an annual series of peak flow data for the 

streamgages according to methods recommended in Bulletin 

17B by the Hydrology Subcommittee of Interagency Advisory 

Committee on Water Data (IACWD) in 1982. Flood-frequency 

estimates often are expressed as T-year discharges, where T 

is the recurrence interval representing the average number of 

years between occurrences of a discharge greater than a given 

magnitude. Flood-frequency estimates also can be expressed 

in terms of exceedance probabilities, which are the reciprocals 

of the recurrence intervals. Exceedance probability can further 

be expressed as a percentage, and a particular flood-frequency 

estimate can then be termed “P-percent chance discharge”, 

where P is the probability, expressed as a percentage, that the 

discharge will be exceeded in any year. For example, a 100-

year flood discharge is the same as a discharge having a 0.01 

annual exceedance probability; this flood discharge also can be 

termed a 1-percent chance flood discharge. Because the T-year 

expression often is misinterpreted, this report will present 

the flood-frequency estimates as percent annual exceedance 

probabilities. 

The IACWD recommends determining the floodfrequency distributions by fitting a log-Pearson Type III 

frequency distribution to the logarithms of the annual peak 

flows (Interagency Advisory Committee on Water Data, 1982). 

Fitting the distribution requires calculating the mean, standard 

deviation, and skew coefficient of the logarithms of the annual 

peak-flow series. The mean, standard deviation, and skew 

coefficient describe the mid-point, slope, and curvature of 

the peak-flow frequency curve, respectively. Estimates of the 

P-percent chance flood peaks are computed by inserting the 

three statistics of the frequency distribution into the equation:

(1)

where:

X is the logarithm of the magnitude of a given 

annual exceedance probability peak flow, 

in cubic feet per second;

 is the mean of the logarithms of the annual 

peak flows;

K is an integration factor based on the skew 

of the logarithms and the given annual 

exceedance probability, and is tabulated 

in Bulletin 17B (Interagency Advisory 

Committee on Water Data, 1982); and, 

S is the standard deviation of the logarithms, 

and is a measure of the variation of the 

peaks about the mean.

The skew coefficient is a measure of the asymmetry of 

the frequency distribution and is strongly affected by the presence of high or low outliers (annual peaks that are substantially higher or lower than other peaks in the series). Large 

positive skews typically are the result of high outliers, and 

large negative skews typically are the result of low outliers. 

Following the Bulletin 17B method, a conditional 

probability adjustment is to be applied when low outliers 

are detected to improve the fit of the frequency curve to the 

log-Pearson Type III distribution (Interagency Advisory Committee on Water Data, 1982). When high outliers are detected 

and historical information on flood magnitudes outside the 

systematic record are available, appendix 6 of Bulletin 17B 

outlines a method for applying a historical adjustment. If 

additional historical information is not available, high outliers 

simply are treated as part of the systematic record, and no further adjustments are made. The expected moments algorithm 

(EMA) is an updated method for fitting the frequency curve 

that has been shown to be a more effective means of incorporating historical and paleoflood information into a flood-frequency analysis. EMA is consistent with Bulletin 17B in that 

it fits a log-Pearson Type III distribution using the method of 

moments. When historical information is absent, EMA results 

are indistinguishable from standard Bulletin 17B methods. 

The algorithm uses an iterated least-squares method for fitting 

regression models to censored data. From a user’s perspective, 

the key difference in using EMA is that data can be represented using intervals rather than a single value. For example, 

X

X X = + KS
Data Development 7

95° 94° 93° 92° 91° 90° 89°

41°

40°

39°

38°

37°

36°

U.S. Geological Survey streamgage and 

 site number (tables 1–5; table 11)

Urban area 

0 25 50 75 100 MILES

0 25 50 75 100 KILOMETERS

EXPLANATION

Base from U.S. Department of Commerce; U.S. Census Bureau, 2008

U.S. Geological Survey digital data, 1995, 1:100,000

Universal Transverse Mercator projection 

Zone 15

North American Datum of 1983 (NAD83)

IOWA

MISSOURI

NEBRASKA

KANSAS

OKLAHOMA

ARKANSAS

TENNESSEEKENTUCKY

ILLINOIS

MISSOURI

# #

##

# #

#

#

#

# #

##

# #

# #

##

#

##

#

#

#

#

#

#

##

##

#

##

#

130 142

1

5 6 3 4

8 2

9

7

35 34

27

28

17

15 16 18

21

20

19

14 13

12

22

2326

24

25

10

30 29

31 33

32

11

1

Figure 2. Location of streamgages in and adjacent to Missouri used in this study.
8 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

if information on a historical flood is limited to the knowledge 

that it was larger than any peak in the systematic record, this 

flood can be represented as having a magnitude between the 

largest peak in the systematic record and infinity. During a 

period outside of the systematic record, there may be evidence that flood levels never exceeded a level that would have 

overtopped a bridge or other road. In these years, the annual 

peaks can be represented as having a magnitude between zero 

and the value that would overtop the road. Low outliers also 

may be represented as an interval so that they do not distort 

the upper tail of the frequency curve. A complete description 

and application of the algorithm is given in Cohn and others, 

(1997). Computation of the confidence intervals for the EMA 

flood quantile estimates is given in Cohn and others, (2001).

The detection of high outliers may lead to an historical 

adjustment, whereby the annual peaks are assumed to apply to 

a period longer than the period of systematic data collection, 

and peaks are assigned weightings based on their magnitudes 

relative to a high threshold value. The assignment of a longer 

historic period is based on examination of longer flood records 

for nearby similar streamgages. For example, if a major flood 

is identified as a high outlier, the short historic period at the 

streamgage of interest might be extended to encompass the 

period during which a flood of similar rarity was experienced 

at a nearby streamgage having a longer period of record. The 

detection of low outliers may lead to deletion of the peaks 

lower than the low threshold and necessitate a probability 

adjustment. Detection of outliers and adjustment of the peak 

data are described in Bulletin 17B, appendix 6 (Interagency 

Advisory Committee on Water Data, 1982).

The USGS computer program PEAKFQ was used to 

compute the flood-frequency estimates for streamgages 

presented in this report (Flynn and others, 2006). PEAKFQ 

automates many of the analyses procedures recommended in 

Bulletin 17B, including identifying and adjusting for high and 

low outliers and historical periods, and fitting the log-Pearson, 

Type III distribution to the streamflow data. The PEAKFQ 

program also applies the EMA procedure. The PEAKFQ 

program and associated documentation are available at http://

water.usgs.gov/software/peakfq.html.

The EMA technique was applied to sites 3 and 4, which 

are located on the same stream in Kansas City, Missouri (fig. 

2). The period of record for site 3 is from water years 1971 

to 1982 and 1999, and the period of record for site 4 is from 

water years 1999 to 2008 (table 1). The large flood of 1977 

was part of the systematic record for site 3; however, site 4 

was not in operation in 1977. In 1999, another large flood 

occurred on the stream and at site 4 the annual peak is part of 

the systematic record. A historical peak flow was obtained at 

site 3 for the 1999 flood. Using EMA techniques and the 1977 

and 1999 peak discharges as threshold values, the historical 

record length (including the systematic period) was extended 

from 12 years to 47 years at site 3. The historical record length 

for site 4 also was extended to 31 years from 10 years of available systematic record. 

The process generally followed in this study when computing flood-frequency estimates for streamgages consists of 

the following steps:

1. Retrieve the annual time series of peak flows for 

the streamgage from the USGS NWIS-Web on-line 

database at http://nwis.waterdata.usgs.gov/usa/nwis/

peak;

2. Compare the time series of the streamgage to 

the time series for upstream and downstream 

streamgages, and for streamgages in adjacent basins 

to determine if the records for the other streamgages 

can be used as the basis for a historical adjustment;

3. Consult the USGS Water Science Center for the state 

in which the streamgage is located, do a literature 

search, or both, to obtain any information that can be 

used as a basis for historical adjustments;

4. Plot the annual time series to find unusual observations that will require further investigation and to 

visually detect monotonic or step trends;

5. Run the Kendall’s tau test on the time series of each 

streamgage to determine if monotonic trends are 

statistically significant (Helsel and Hirsch, 1992);

6. Evaluate the data for trends to make adjustments 

to the time series data for trends or eliminate the 

streamgage from further analyses;

7. Run PEAKFQ, applying any necessary historical adjustments, to obtain initial flood-frequency 

estimates for the streamgage. Use at-site streamgage 

skews for urban streamgages if a generalized 

regional skew is not available; 

8. Plot the initial flood-frequency curve to determine if 

it adequately fits the annual peak data, or if low- or 

high-outlier thresholds or other adjustments need to 

be made for the curve to better fit the data; 

9. Run the PEAKFQ analyses with Bulletin 17B 

procedures or run the EMA within PEAKFQ for 

streamgages with historical data to improve the fit of 

the frequency curve to the annual peak data; and

10. If necessary, re-run PEAKFQ to apply any adjustments to obtain a satisfactory flood-frequency curve. 

 Basin Characteristics

 Basin characteristics were selected for use as potential 

independent variables in the regression analyses on the basis 

of their theoretical relation to flood flows, results of previous 

studies in similar hydrologic regions, and the ability to measure the basin characteristics using digital datasets and GIS 

technology. The ability to measure the basin characteristics by 
Data Development 9

using GIS methods was important to facilitate eventual automation of the process for measuring the basin characteristics 

and solving the regression equations for ungaged sites. 

The most common basin characteristic present in existing urban flood frequency equations is drainage area. GIS 

algorithms and a Digital Elevation Model (DEM) were used 

to delineate the drainage area basin characteristic for a gaged 

site. The State of Missouri has a 10-meter resolution DEM 

available for hydrologic analyses. The DEM data and associated documentation area are available at http://msdis.missouri.

edu/data/10mDEM/10mDEM.htm. In general, the 10-meter 

DEM was based on 1:24000 scale hypsography, spot elevations, and the National Hydrography Data (NHD) dataset. If 

higher resolution or more accurate elevation data existed for 

an urban area, these data superseded the 10-meter data set. The 

boundary and the resulting drainage area were computed for 

all 35 streamgages in this study.

As a means of quality assurance, the drainage areas 

computed by using the GIS were compared to drainage area 

values in the USGS NWIS-WEB on-line database for the 

streamgages. Also, drainage area boundaries were compared 

to basin boundaries obtained from the communities. Flow patterns within a basin may change to improve stormwater runoff 

characteristics and direct flow away from buildings or towards 

drainage structures. The changes to flow patterns sometimes 

occur along basin boundaries and may not be represented on 

older datasets. The measured and published drainage areas 

agreed within 5 percent for most streamgages with few exceptions. For most of the exceptions, the published drainage areas 

were determined from older topographic maps with 10- or 

20-ft contour intervals dating back more than 30 years. Where 

exceptions did occur, the drainage areas determined using GIS 

techniques and more accurate elevation data were considered 

superior in accuracy to the previously published data. The 

drainage areas shown in table 2 are those determined for this 

study using GIS techniques.

A literature review of existing urban flood frequency 

studies indicated the second most commonly used variable 

in urban flood frequency equations after drainage area was 

impervious area, followed by a basin development factor, 

main channel slope, basin storage, and the 2-hour 2-year rainfall. Several other basin characteristics have been included in 

specific studies, but not repeated in other studies. The computation of the basin characteristics digitally using GIS technology precluded the basin development factor from consideration in this study because of the need to define the amount 

of channel improvements, channel linings, storm drains, and 

curbs and gutters on streets. Few, if any, GIS layers currently 

(2009) available include this type of information. Main channel slope along with mean basin slope were computed for each 

streamgage. Less than 10 percent of the drainage area was 

affected by storage structures for any given basin included in 

this study; thus, basin storage characteristic was not computed 

for each streamgage. The 2-hour 2-year rainfall variability for 

Missouri was less than 0.5 inch across the state, and also was 

not computed for the study basins.

The four basin characteristics calculated for this study for 

possible inclusion into the urban regression equations were: 

(1) drainage area, (2) main channel slope, (3) mean basin 

slope, and (4) percent impervious area. Other characteristics 

evaluated for potential inclusion into the regression equations were housing density (U.S. Census, 2001), mean annual 

rainfall (Missouri Climate Center, 2009), average channel 

conditions, and bank-full channel conveyance. Mean annual 

rainfall had minimal variability in Missouri. Average channel 

conditions, bank-full channel conveyance data were unavailable digitally for the basins used in this study and were not 

computed.

The resolution of the data sets did not bias the results of 

the drainage area computations. The statewide 10-meter DEM 

represented the basin boundary accurately compared to higher 

resolution data sets when urbanization did not exist along the 

boundaries; however, where basin boundaries were changed 

because of urbanization, the higher resolution elevation data 

sets reflected the changes more accurately. The higher resolution data sets were more accurate primarily because they were 

developed after the urbanization had occurred and their resulting digital elevation models consisted of smaller grid cells 

than the 10-meter DEM for the state. 

The main channel slope was measured in feet per mile 

and computed as the difference in elevation between the 10- 

and 85-percent points along the stream channel divided by 

the length between those two points. Mean basin slope was 

measured by computing the mean of the slope grid values 

of the DEM used in the drainage area computations. Percent 

impervious area was computed from the National Land Cover 

Dataset (NLCD) 2001 impervious area at the following link: 

http://www.mrlc.gov/mrlc2k_nlcd.asp. The USGS Land Cover 

Institute (LCI) has developed a tool to retrieve the impervious area data from the 2001 NLCD based on a predetermined 

basin boundary that can be uploaded to their Web site http://

lcat.usgs.gov/lcat2/. Percent impervious area was determined 

by computing the mean of the percent impervious area of all 

grid cells within the study basin from the NLCD 2001 data. 

The NLCD 2001 percent impervious area measurements were 

compared to impervious area calculated from high-resolution 

impervious area GIS data available for some urban areas. 

The correlation coefficient from the national data set and the 

local data sets was 0.99. Because the NLCD 2001 impervious 

area data are available for all urban areas in the state, these 

data were used to compute the impervious area for the urban 

basins used in this study. The percentage of impervious area 

from the NLCD 2001 dataset was adjusted based on historical imagery and 7.5-minute topographic maps for any basins 

that had undergone substantial development since the peak 

flow data were collected. Of the 35 streamgages in the study, 

8 streamgages had impervious area computations from the 

NLCD 2001 dataset adjusted. The NLCD data was lowered 

from 1 to 23 percent at the 8 streamgages. The percent impervious area shown in table 2 for each streamgage is the adjusted 

value for the period of streamgage data collection.
10 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

Table 2. Basin characteristics of streamgages in urban areas in and adjacent to Missouri used in the 

development of urban regression equations.

[USGS, U.S. Geological Survey; mi2, square miles]

Site

number

(fig. 2)

Streamgage name

USGS

streamgage

number

Drainage 

area

(mi2)

Impervious

area1

(percent)

1 Indian Creek at Overland Park, Kan. 06893300 26.5 36.3 

2 Blue River at Kansas City, Mo. 06893500 184 16.8 

3 Brush Creek at Kansas City, Mo. 06893560 15.6 32.7 

4 Brush Creek at Rockhill Road in Kansas City, Mo. 06893562 18.1 33.1 

5 Rock Creek at Independence, Mo. 06893600 4.97 31.2 

6 Little Blue River near Lake City, Mo. 06894000 189 14.1 

7 Cow Branch near Columbia, Mo. 06910200 1.17 8.48 

8 Hinkson Creek at Columbia, Mo. 06910230 70.3 5.15 

9 Dickerson Creek Tributary near Jefferson City, Mo. 06910430 .51 2.33 

10 Niangua Branch at Marshfield, Mo. 06923000 .77 14 

11 Coyle Branch at Houston, Mo. 06929000 1.1 11.5 

12 Shotwell Creek at Highway 340 near Ellisville, Mo. 06935800 .76 25.2 

13 Creve Coeur Creek at Chesterfield, Mo. 06935850 6.49 29.5 

14 Creve Coeur Creek near Creve Coeur, Mo. 06935890 22.2 26 

15 Fee Fee Creek near Bridgeton, Mo. 06935955 11.7 39.8 

16 Cowmire Creek at Bridgeton, Mo. 06935980 3.41 42.3 

17 Coldwater Creek near Black Jack, Mo. 06936475 41 40 

18 Maline Creek at Bellefontaine Neighbors, Mo. 07005000 23.8 32.8 

19 River Des Peres near University City, Mo. 07010022 8.74 43.5 

20 River Des Peres Trib. at Pagedale, Mo. 07010030 1.93 26.5 

21 Engelholm Creek near Wellston, Mo. 07010035 1.47 27.3 

22 Deer Creek at Maplewood, Mo. 07010086 36.3 31.6 

23 MacKenzie Creek near Shrewsbury, Mo. 07010090 3.51 35.5 

24 Gravois Creek near Mehlville, Mo. 07010180 18.2 37.2 

25 Martigney Creek near Arnold, Mo. 07010208 2.25 37.7 

26 Mattese Creek near Mattese, Mo. 07019317 7.89 39.4 

27 Town Branch at B.R. 62 at Fayetteville, Ark. 07048480 .84 33.6 

28 Town Branch Tributary at Highway 16 at Fayetteville, Ark. 07048490 1.29 35.7 

29 Wilson Creek at Springfield, Mo. 07052000 19.5 46 

30 Wilson Creek near Springfield, Mo. 07052100 35.3 35.6 

31 Wilson Creek near Battlefield, Mo. 07052160 58.4 17.8 

32 Pike Creek Tributary near Poplar Bluff, Mo. 07063200 .28 7.94 

33 Turkey Creek near Joplin, Mo. 07186600 42.3 13 

34 Osage Creek near Elm Springs, Ark. 07195000 129.7 8.67 

35 Sager Creek near West Siloam Springs, Okla. 07195865 19.5 8.35 

1

Impervious area used in the regression equations for period of streamgage data collection.
Estimation Of The Magnitude And Frequency Of Floods 11

Regionalization

Physical features within a state or region can have a 

pronounced effect on the flood frequency characteristics of 

a basin (Alexander and Wilson, 1995). (Urban areas located 

in distinctively different regions such as in wide meandering 

flood plains with low to moderate valley slopes or in narrow 

flood plains with sharp, well- defined ridges with moderate to 

high slopes may result in bias in the residuals from regression 

results when all streamgages are included in the analyses.) 

Evaluation of possible biases in the regression analyses was 

considered in this study to define distinct regions.

Estimation Of The Magnitude And 

Frequency Of Floods

The Interagency Advisory Committee on Water Data 

(1982) recommends that the log-Pearson Type III distribution be used as the standard flood-frequency technique for 

Federal planning involving water and related land resources. 

This technique uses the method of moments to relate the 

annual maximum discharge data to selected frequencies. For 

this study, the frequencies reported for hydrologically similar 

regions are the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent annual 

exceedance probabilities.

Definition of Regions

The number and spatial distribution of the streamgages in 

this study limited the definition of separate hydrologic regions 

for the state. Additional streamgages outside of Missouri were 

used to supplement the Missouri streamgages to increase the 

range of applicability of the regression equations for urban 

areas throughout the state. [The residuals from the ordinary 

least-squares (OLS) analyses were plotted on a state map.] 

The residuals are the differences between the streamgage 

flood-frequency data and the corresponding OLS regression 

equation results (see Model Development Section). The magnitude and numerical sign of the residuals were checked for 

possible regional biases. Overall, no geographic bias existed 

in the results. OLS analyses residuals also were plotted in 

relation to drainage area and impervious area for the 50-, 10-, 

and 1-percent annual exceedance probabilities (fig. 3). The 

residual plots of figure 3 were used as a diagnostic tool for the 

regression equations. The random scatter of the points above 

and below the zero reference line indicates that the model 

is satisfactorily meeting the assumptions of multiple-linearregression techniques. Additional plots were done with the 

50-, 10-, and 1-percent annual exceedance probabilities for 

the observed peak flows and the estimated peak flows (fig 4). 

These plots were used to evaluate the regression equations 

for potential climatic and temporal bias. Results of these plots 

indicated no climatic or temporal bias existed in the data.

 Model Development

Regression equations were developed for use in estimating peak flows with selected annual exceedance probabilities 

of 50 to 0.2 percent at gaged and ungaged locations for urban 

areas within the state of Missouri. OLS regression techniques 

were used to select the basin characteristics used as the 

independent variables. Linear relations between the independent variables and the dependent variable are required for 

OLS regression. To satisfy this criterion, variables often are 

transformed, and in hydrologic analyses typically the base10 logarithm transformation is used. The dependent variable, 

flood-peak discharge, was transformed to logarithms before 

the regression analyses. The independent variables of drainage area, main channel slope, and mean basin slope also were 

transformed to logarithms (base 10); however, the independent 

variable percent impervious area was not transformed. 

Homoscedasticity (a constant variance in the dependent 

variable over the range of the independent variables) about the 

regression line and normality of residuals also are criteria for 

OLS regression. Transformation of the flow data and certain 

other variables to logarithms often enhances the homoscedasticity of the data about the regression line. Linearity, homoscedasticity, and normality of residuals were examined in residual 

plots. 

The hydrologic model used in the regression analysis is 

of the form:

QT = aAbBc10dC, (2)

where

QT is the dependent variable, a flood discharge 

having a given annual exceedance 

probability of T, in cubic feet per second;

A, B are base-10 logarithm, transformed 

independent variables (basin 

characteristics);

C is an untransformed independent variable 

(basin characteristic);

and

a, b, c, d are regression coefficients.

If the dependent variable QT and the independent variables A and B are logarithmically transformed and the independent variable, C, untransformed then the hydrologic model 

has the following linear form:

Log QT = log a + b(logA) + c(logB) + d(C) + . . . ,

where the variables are as previously defined. A combination 

of the arithmetic and logarithmic relation was used in this 

investigation because the impervious area variable was used as 

a percentage and the resulting logarithmic transformation did 

not improve the linear relation with the dependent variable, 

QT.

The independent variables of drainage area, impervious 

area, main channel slope, and mean basin slope were included 
12 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

0 10 20 30 40 50

IMPERVIOUS AREA, IN PERCENT

-0.4

-0.3

-0.2

-0.1

 0

0.1

0.2

0.3

0.4

0.1 1.0 10 100 1,000

DRAINAGE AREA, IN SQUARE MILES

-0.4

-0.3

-0.2

-0.1

 0

0.1

0.2

0.3

0.4

RESIDUAL, IN LOGARTHMIC UNITS

-0.4

-0.3

-0.2

-0.1

 0

0.1

0.2

0.3

0.4

50-Percent Annual Exceedance Probablility Flood 

10-Percent Annual Exceedance Probability Flood

1-Percent Annual Exceedance Probability Flood

50-Percent Annual Exceedance Probablility Flood 

10-Percent Annual Exceedance Probability Flood

1-Percent Annual Exceedance Probability Flood

A

B

C

Figure 3. Residuals of the regression equations for estimating the magnitude of the (A) 50-, (B) 10-, and (C) 1-percent 

annual exceedance probability flood in relation to drainage area and percent impervious area.
Estimation Of The Magnitude And Frequency Of Floods 13

in the OLS regression analyses. The OLS results were evaluated on the basis of Mallow’s Cp statistic, the adjusted coefficient of determination (R2

), and the statistical significance of 

the independent variables at the 95-percent confidence level.

Statistically significant variables were tested for multicollinearity using the variance inflation factor. The basin 

characteristics selected were determined to not be affected 

by multicollinearity. The affect of individual streamgages on 

the regression coefficients was measured by the statistical 

test Cook’s D (Cook, 1977). The test indicated no individual 

streamgages had an undue affect on the regression results.

The statistical parameters used to fit the log-Pearson Type 

III distribution to the observed annual peak flows for each 

streamgage are the mean of the logarithms, standard deviation of the logs, and skew of the logarithms (table 3). These 

fitting parameters describe the mid-point, slope, and curvature 

of the peak-flow frequency curve, respectively. The skew of 

the logarithms is positive when the mean of the peak flows 

exceeds the median value and negative when the mean is less 

than the median. Peak flows that are substantially higher or 

lower than other peaks in the annual series are considered outliers, and these peak flows strongly affect the skew parameter. 

Streamgages with peak flow outliers were processed using the 

10

100

1,000

10,000

100,000

10 100 1,000 10,000 100,000

OBSERVED PEAK FLOW, IN CUBIC FEET PER SECOND

10

100

1,000

10,000

100,000

ESTIMATED PEAK FLOW, IN CUBIC FEET PER SECOND 

10

100

1,000

10,000

100,000

50-Percent Annual Exceedance Probablility Flood

10-Percent Annual Exceedance Probability Flood

1-Percent Annual Exceedance Probability Flood

LINE OF EQUALITY

LINE OF EQUALITY

LINE OF EQUALITY

A

B

C

Figure 4. Comparison of observed and estimated peak flows of the (A) 50-, (B) 10-, and (C) 1-percent annual 

exceedance probability flood.
14 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

Table 3. Flood-frequency statistics for annual peak flow data from 35 U.S. Geological Survey streamgages in urban areas in and 

adjacent to Missouri.

[USGS, U.S. Geological Survey]

Statistical data for water-year peak flows

Site

number

(fig. 2)

Streamgage name

USGS

streamgage

number

Mean

(logarithm)

Standard

deviation

(logarithm)

Skew of 

logarithms

1 Indian Creek at Overland Park, Kan. 06893300 3.634 0.196 0.212

2 Blue River at Kansas City, Mo. 06893500 4.019 .220 .367

3 Brush Creek at Kansas City, Mo. 06893560 3.528 .299 .605

4 Brush Creek at Rockhill Road in Kansas City, Mo. 06893562 3.683 .211 1.382

5 Rock Creek at Independence, Mo. 06893600 3.151 .227 -.579

6 Little Blue River near Lake City, Mo. 06894000 3.711 .277 .312

7 Cow Branch near Columbia, Mo. 06910200 2.505 .270 -.370

8 Hinkson Creek at Columbia, Mo. 06910230 3.634 .228 -.011

9 Dickerson Creek Tributary near Jefferson City, Mo. 06910430 1.993 .365 .436

10 Niangua Branch at Marshfield, Mo. 06923000 2.289 .240 .124

11 Coyle Branch at Houston, Mo. 06929000 2.292 .389 -.091

12 Shotwell Creek at Highway 340 near Ellisville, Mo. 06935800 2.584 .265 -.466

13 Creve Coeur Creek at Chesterfield, Mo. 06935850 3.150 .159 .262

14 Creve Coeur Creek near Creve Coeur, Mo. 06935890 3.408 .266 .198

15 Fee Fee Creek near Bridgeton, Mo. 06935955 3.338 .201 -.144

16 Cowmire Creek at Bridgeton, Mo. 06935980 3.227 .226 -.415

17 Coldwater Creek near Black Jack, Mo. 06936475 3.710 .177 -.417

18 Maline Creek at Bellefontaine Neighbors, Mo. 07005000 3.777 .177 .184

19 River Des Peres near University City, Mo. 07010022 3.509 .123 -.185

20 River Des Peres Trib. at Pagedale, Mo. 07010030 2.893 .227 .027

21 Engelholm Creek near Wellston, Mo. 07010035 2.770 .309 -.665

22 Deer Creek at Maplewood, Mo. 07010086 3.658 .150 .777

23 MacKenzie Creek near Shrewsbury, Mo. 07010090 3.078 .161 -.790

24 Gravois Creek near Mehlville, Mo. 07010180 3.533 .117 .459

25 Martigney Creek near Arnold, Mo. 07010208 3.024 .201 -.088

26 Mattese Creek near Mattese, Mo. 07019317 3.610 .188 .158

27 Town Branch at B.R. 62 at Fayetteville, Ark. 07048480 2.771 .225 .502

28 Town Branch Tributary at Highway 16 at Fayetteville, Ark. 07048490 2.816 .176 .333

29 Wilson Creek at Springfield, Mo. 07052000 3.459 .226 .538

30 Wilson Creek near Springfield, Mo. 07052100 3.420 .228 .834

31 Wilson Creek near Battlefield, Mo. 07052160 3.451 .218 .546

32 Pike Creek Tributary near Poplar Bluff, Mo. 07063200 2.068 .297 -.514

33 Turkey Creek near Joplin, Mo. 07186600 3.286 .208 -.288

34 Osage Creek near Elm Springs, Ark. 07195000 3.726 .345 -.280

35 Sager Creek near West Siloam Springs, Okla. 07195865 3.231 .270 .005
Estimation Of The Magnitude And Frequency Of Floods 15

Table 4. Flood discharges at given annual exceeedance probabilities for streamgages in urban areas in and adjacent to Missouri.

[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; G, estimated from the Bulletin 17B (IACWD, 1982) analyses of the streamgage; R, estimated 

from the regression equation; W, weighted Bulletin 17B analyses and regression equation results]

Flood discharges at percent annual exceedance probabilities (ft3/s)

50 20 10

Site

number

(fig. 2)

USGS

streamgage

number

G R W G R W G R W

1 06893300 4,240 4,320 4,310 6,260 6,160 6,170 7,750 7,840 7,840 

2 06893500 10,100 7,350 7,760 15,800 11,800 12,100 20,300 15,800 16,000 

3 06893560 3,150 2,800 2,820 5,850 4,100 4,140 8,430 5,260 5,290 

4 06893562 4,320 3,100 3,170 6,790 4,520 4,570 9,230 5,790 5,820 

5 06893600 1,490 1,340 1,340 2,210 2,000 2,000 2,650 2,570 2,570 

6 06894000 4,970 6,850 6,630 8,680 11,200 11,100 11,800 15,100 15,000 

7 06910200 332 271 273 544 479 481 690 646 647

8 06910230 4,310 2,840 2,900 6,690 4,970 5,010 8,420 6,820 6,840 

9 06910430 93 135 134 195 251 251 298 342 342 

10 06923000 192 252 248 308 430 425 397 572 568 

11 06929000 198 289 286 418 499 498 612 668 668 

12 06935800 403 360 362 648 567 569 810 735 736 

13 06935850 1,390 1,490 1,480 1,910 2,250 2,240 2,280 2,900 2,890 

14 06935890 2,510 2,780 2,770 4,250 4,260 4,260 5,670 5,550 5,550 

15 06935955 2,200 2,960 2,900 3,220 4,140 4,120 3,910 5,210 5,170 

16 06935980 1,750 1,530 1,540 2,630 2,120 2,140 3,200 2,660 2,670 

17 06936475 5,280 6,310 6,250 7,270 8,730 8,680 8,460 11,000 10,900 

18 07005000 5,900 3,610 3,710 8,390 5,270 5,340 10,200 6,770 6,810 

19 07010022 3,260 2,800 2,840 4,110 3,820 3,840 4,620 4,780 4,770 

20 07010030 780 655 659 1,210 1,020 1,020 1,530 1,320 1,320 

21 07010035 638 570 571 1,080 882 884 1,370 1,140 1,140 

22 07010086 4,350 4,480 4,470 5,960 6,580 6,560 7,210 8,470 8,450 

23 07010090 1,260 1,250 1,250 1,640 1,820 1,810 1,850 2,310 2,290 

24 07010180 3,340 3,540 3,520 4,240 5,020 4,980 4,870 6,380 6,340 

25 07010208 1,060 1,030 1,030 1,560 1,480 1,480 1,900 1,870 1,870 

26 07019317 4,030 2,310 2,380 5,840 3,240 3,290 7,130 4,090 4,120 

27 07048480 565 500 502 896 744 746 1,170 946 947 

28 07048490 639 691 688 912 1,010 1,010 1,110 1,280 1,280 

29 07052000 2,750 4,920 4,840 4,380 6,560 6,530 5,740 8,160 8,140 

30 07052100 2,450 5,010 4,860 3,950 7,150 7,080 5,300 9,130 9,090 

31 07052160 2,700 3,810 3,760 4,220 6,130 6,090 5,480 8,160 8,130 

32 07063200 124 113 113 210 203 203 268 273 273 

33 07186600 1,980 2,690 2,670 2,910 4,490 4,460 3,510 6,040 6,000 

34 07195000 5,520 4,580 4,620 10,500 7,810 7,880 14,400 10,600 10,700

35 07195865 1,700 1,460 1,460 2,870 2,530 2,530 3,780 3,430 3,430 
16 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

Table 4. Flood discharges at given annual exceeedance probabilities for streamgages in urban areas in and adjacent to 

Missouri.—Continued

[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; G, estimated from the Bulletin 17B (IACWD, 1982) analyses of the streamgage; R, estimated 

from the regression equation; W, weighted Bulletin 17B analyses and regression equation results]

Flood discharges at percent annual exceedance probabilities (ft3/s)

4 2 1

Site

number

(fig. 2)

USGS

streamgage

number

G R W G R W G R W

1 06893300 9,800 9,340 9,350 11,400 11,700 11,700 13,200 13,100 13,100 

2 06893500 26,900 20,800 20,900 32,500 26,300 26,400 38,700 31,000 31,100 

3 06893560 12,800 6,360 6,390 17,200 7,940 7,970 22,600 8,930 8,970 

4 06893562 13,500 6,990 7,010 17,900 8,730 8,750 23,500 9,820 9,840 

5 06893600 3,160 3,110 3,110 3,500 3,860 3,860 3,810 4,340 340 

6 06894000 16,800 20,100 20,000 21,100 25,400 25,300 26,200 30,100 30,000 

7 06910200 875 862 86 1,010 1,060 1,060 1,150 1,250 1,250

8 06910230 10,800 9,430 9,440 12,600 11,800 11,800 14,500 14,300 14,300 

9 06910430 482 468 468 669 574 574 906 683 683 

10 06923000 523 743 740 627 913 913 739 1,060 1,060 

11 06929000 913 879 879 1,180 1,080 1,080 1,480 1,260 1,260 

12 06935800 1,010 906 907 1,150 1,110 1,110 1,290 1,260 1,260 

13 06935850 2,770 3,540 3,530 3,150 4,400 4,390 3,550 4,970 4,960 

14 06935890 7,770 6,940 6,940 9,580 8,670 8,670 11,600 9,920 9,930 

15 06935955 4,780 6,090 6,070 5,430 7,590 7,560 6,080 8,390 8,360 

16 06935980 3,880 3,050 3,060 4,370 3,780 3,790 4,830 4,130 4,140 

17 06936475 9,840 13,000 12,900 10,800 16,200 16,100 11,700 18,000 17,900 

18 07005000 12,500 8,200 8,230 14,400 10,200 10,200 16,300 11,500 11,500 

19 07010022 5,210 5,480 5,470 5,620 6,820 6,790 6,010 7,470 7,440 

20 07010030 1,960 1,620 1,620 2,300 2,000 2,000 2,660 2,270 2,270 

21 07010035 1,720 1,400 1,400 1,950 1,720 1,720 2,170 1,940 1,940 

22 07010086 9,030 10,300 10,300 10,600 13,000 13,000 12,300 14,700 14,700 

23 07010090 2,050 2,740 2,720 2,180 3,390 3,370 2,280 3,770 3,740 

24 07010180 5,680 7,560 7,530 6,320 9,440 9,400 6,970 10,500 10,400 

25 07010208 2,340 2,190 2,190 2,680 2,700 2,700 3,010 2,980 2,980 

26 07019317 8,880 4,780 4,800 10,200 5,940 5,960 11,700 6,570 6,590 

27 07048480 1,590 1,120 1,120 1,950 1,380 1,380 2,370 1,530 1,530 

28 07048490 1,390 1,510 1,510 1,610 1,860 1,860 1,850 2,060 2,060 

29 07052000 7,820 9,290 9,290 9,680 11,600 11,600 11,800 12,700 12,700 

30 07052100 7,520 10,900 10,900 9,600 13,700 13,700 12,100 15,400 15,400 

31 07052160 7,400 10,600 10,600 9,080 13,400 13,400 11,000 15,600 15,600 

32 07063200 340 362 362 392 443 443 442 519 519 

33 07186600 4,260 8,030 7,990 4,800 10,100 10,000 5,320 11,900 11,800 

34 07195000 19,800 14,500 14,600 24,100 18,300 18,400 28,700 22,000 22,000

35 07195865 5,060 4,640 4,640 6,110 5,800 5,800 7,250 6,910 6,910 
Estimation Of The Magnitude And Frequency Of Floods 17

Table 4. Flood discharges at given annual exceeedance probabilities for streamgages in urban areas in and adjacent to 

Missouri.—Continued

[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; G, estimated from the Bulletin 17B (IACWD, 1982) analyses of the streamgage; R, estimated 

from the regression equation; W, weighted Bulletin 17B analyses and regression equation results]

Flood discharges at percent annual exceedance probabilities (ft3/s)

0.2 Maximum recorded flood

Site

number

(fig. 2)

USGS

streamgage

number

G R W Discharge

(ft3/s) Date

1 06893300 17,800 17,800 17,800 12,800 06/09/84

2 06893500 56,100 45,200 45,500 41,000 09/13/61

3 06893560 40,700 12,200 12,300 17,600 09/12/77

4 06893562 43,700 13,400 13,400 21,700 10/04/98

5 06893600 4,440 5,890 5,880 2,520 06/19/67

6 06894000 41,100 44,300 44,200 42,300 08/13/82

7 06910200 1,460 1,760 1,760 625 07/18/58

06/22/69

8 06910230 19,300 21,200 21,200 10,000 04/11/79

9 06910430 1,730 967 968 500 12/15/75

10 06923000 1,040 1,470 1,460 605 06/20/77

11 06929000 2,340 1,770 1,770 1,030 06/30/51

12 06935800 1,590 1,700 1,700 1,030 08/09/70

13 06935850 4,560 6,790 6,760 2,820 09/14/08

14 06935890 17,200 13,800 13,800 8,780 09/14/08

15 06935955 7,610 11,300 11,200 4,680 09/14/08

16 06935980 5,840 5,440 5,450 3,580 09/14/08

17 06936475 13,500 24,600 24,300 9,690 09/14/08

18 07005000 21,200 15,900 16,000 12,800 09/14/08

19 07010022 6,850 9,910 9,790 5,050 09/14/08

20 07010030 3,580 3,080 3,080 2,160 09/14/08

21 07010035 2,620 2,630 2,630 1,570 09/14/08

22 07010086 17,000 20,300 20,300 10,300 09/14/08

23 07010090 2,480 5,050 4,980 1,970 09/14/08

24 07010180 8,590 14,300 14,200 5,870 09/14/08

25 07010208 3,820 3,950 3,950 2,120 09/14/08

26 07019317 15,400 8,790 8,840 9,200 09/14/08

27 07048480 3,590 2,030 2,040 1,440 06/30/99

28 07048490 2,470 2,720 2,720 1,390 07/03/04

29 07052000 18,100 16,900 16,900 6,750 07/12/00

30 07052100 20,200 21,100 21,100 6,410 06/13/08

31 07052160 16,600 22,500 22,500 7,240 05/20/79

32 07063200 551 721 719 366 03/08/64

33 07186600 6,500 17,200 17,000 3,520 06/13/64

34 07195000 40,100 32,500 32,600 22,500 05/10/50

05/19/61

35 07195865 10,200 10,000 10,000 4,130 06/21/00
18 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

EMA algorithm described in the Flood-Frequency Analysis 

Section of this report. The final flood discharges for selected 

annual exceedance probabilities for each streamgage are 

shown in table 4, along with the maximum recorded flood. 

Weighted least-squares (WLS) regression was used to 

compute the final regression coefficients and the measures of 

accuracy for the regression equations using the computer program Weighted-Multiple-Linear-Regression Model Program, 

WREG (Eng and others, 2009). Stedinger and Tasker (1985) 

compared ordinary, weighted, and generalized least-squares 

regression techniques. The results of their study determined 

that weighted and generalized regression techniques provided better estimates of the accuracy of the equations than 

ordinary least-squares. Improvements in the weighted equations occurred when streamflow records at streamgages are 

of different and varying lengths. Also, improvements were 

noted when concurrent flows at different streamgages were 

correlated. WLS techniques give less weight to streamgages 

that have shorter periods of record than streamgages with 

longer periods of record (Tasker, 1980). The results of the 

WLS regression analyses for the selected annual exceedance 

probabilities of 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent for 

Missouri are given in table 5. Flood discharges for the at-site 

(Bulletin 17B), WLS regression, and weighted (Bulletin 17B 

and WLS) analyses for each selected probability are included 

in table 4. 

The Hydrology Subcommittee of Interagency Advisory 

Committee on Water Data (1982) recommended that better 

estimates of flood-frequency statistics for a gaged station can 

be obtained by combining (weighting) at-site flow estimates 

determined from the log-Pearson Type III analysis of the 

annual peaks with flow estimates obtained for the station from 

regression equations. Optimal weighted flow estimates can be 

obtained if the variance of estimation for each of the two estimates is known or can be estimated accurately. The variance 

of estimation can be thought of as a measure of the uncertainty 

in either the at-site estimate or the regional regression results. 

If the two estimates can be assumed to be independent and are 

weighted in inverse proportion to the associated variances, 

the variance of the weighted estimate will be less than the 

variance of either of the independent estimates (Gotvald and 

others, 2009).

The variance of estimates corresponding to the at-site 

flow estimate from the log-Pearson Type III analysis is computed using the asymptotic formula given in Cohn and others 

(2001) with the addition of the mean-squared error of generalized skew (Griffis and others, 2004). This variance varies 

as a function of the length of record, the fitted log-Pearson 

Type III distribution parameters (mean, standard deviation, 

and weighted skew), and the accuracy of the method used to 

determine the generalized-skew component of the weighted 

skew. The variance of estimates for the at-site value generally 

decreases with length of record and the quality of the log-Pearson Type III distribution fit. The variance of estimate from the 

regional regression equations is a function of the regression 

equations and the values of the independent variables used to 

Table 5. Weighted least-squares regression equations for streams in urban areas in Missouri.

[DRNAREA, drainage area, in square miles; IMPLNLCD01, impervious area from National Land Cover Dataset 2001, in percent]

Percent annual exceedance probability Flood recurrence interval

(years) Urban regression equations

50 2 Q2

=188(DRNAREA)0.599100.014(IMPNLCD01)

20 5 Q5

=352(DRNAREA)0.592100.011(IMPNLCD01)

10 10 Q10=484(DRNAREA)0.594100.010(IMPNLCD01)

4 25 Q25=671(DRNAREA)0.599100.008(IMPNLCD01)

2 50 Q50=826(DRNAREA)0.604100.008(IMPNLCD01)

1 100 Q100=991(DRNAREA)0.608100.007(IMPNLCD01)

.2 500 Q500=1,420(DRNAREA)0.619100.006(IMPNLCD01)
Estimation Of The Magnitude And Frequency Of Floods 19

develop the flow estimate from the regression equations. This 

variance generally increases as the values of the independent 

variables moves further from the mean values of the independent variables. 

Once the variances have been computed, the two independent flow estimates were weighted using the following: 

equation: 

log

log log

( )

, ( ) ( ) , ( ) ( )

, ( ) ,

Q

V Q V Q

V V P g w

p P g r P g s p P g s P g r

p P g s p P

= +

+ ( ) g r (3)

where 

QP(g)w is the weighted estimate of peak flow for any 

P-percent annual exceedance probability 

for a gaged station, in cubic feet per 

second;

Vp,P (g)r is the variance of estimate at the gaged station 

derived from the applicable regional 

regression equations for the selected 

P-percent annual exceedance probability, 

in log units;

QP(g)s is the estimate of peak flow at the gaged 

station from the log-Pearson Type III 

analysis for the selected P-percent annual 

exceedance probability, in cubic feet per 

second; 

Vp,P(g)s is the variance of estimate at the gaged station 

from the log-Pearson Type III analysis for 

the selected P-percent annual exceedance 

probability, in log units; and

Q P(g)r is the peak-flow estimate for the P-percent 

annual exceedance probability at the 

gaged station derived from the applicable 

regional regression equations, in cubic feet 

per second. 

When the variance of estimate corresponding to one 

of the estimates is high, the uncertainty also is high, and so 

the weight for that estimate is relatively small. Conversely, 

when the variance of estimate is low, the uncertainty also is 

low and so the weight is correspondingly large. The variance 

of estimate associated with the weighted estimate, Vp,P (g)w , is 

computed using the following equation:

V

V V

V V p P g w

p P g s p P g r

p P g s p P g r

, ( )

, ( ) , ( )

, ( ) , ( )

= +

(4)

The variance of estimated values associated with the 

weighted estimates is shown in table 6. Using variances provides an accurate characterization of the underlying uncertainty of the various flow estimates.

Model Verification and Diagnostics

The set of equations listed in table 4 are applicable for 

ungaged, unregulated streams in an urban drainage basin. 

These equations are statistical models that should be interpreted and applied within the limits of the independent 

variables. The results are best-fit estimates with an associated 

scatter or variance. 

One of the performance metrics used to measure the 

WLS regression analyses in WREG is the pseudo coefficient of determination R2

pseudo . For OLS regression analyses, 

the coefficient of determination, R2 , is used to measure the 

proportion of the variation in the dependent variable explained 

by the independent variables. In contrast, the statistic, R2

pseudo, 

for WLS analyses only considers the amount of variability 

in the dependent variable explained by the model, removing 

the effect of the time-sampling error. The highest R2

pseudo was 

96.7 percent for the 4 percent annual exceedance probability 

(table 7). The lowest R2

pseudo was 92.8 percent for the 0.2-percent annual exceedance probability. The accuracy of the 

regression analyses is lower with higher frequency floods. As 

station frequency curves are extrapolated out to the 0.2-percent annual exceedance probability, the uncertainty increases 

because of the short period of record at streamgages. Continuing to collect record at existing streamgages or documenting 

historical floods to extend record lengths at streamgages for 

EMA analyses may reduce the uncertainty in estimating rare 

floods.

The accuracy of peak-discharge regression equations 

are described by the standard model error and standard error 

of prediction (Ries and Dillow, 2006). The standard model 

error is a measure of how well the estimated peak discharges 

generated using an equation agree with the peak-flow statistics 

generated from streamgage records that were used to create the equation. The standard error of prediction is derived 

from the sum of the model error and the sampling error, and 

is a measure of how accurately the estimated peak discharges 

generated using an equation will be able to predict the true 

value of peak discharge for the selected recurrence interval. 

Approximately two thirds of the estimates obtained from the 

equations for ungaged sites will have errors less than than the 

noted standard errors of prediction. The standard model error 

ranged from 0.008 log units (-18.6 to 22.9 percent) for the 10-, 

4-, and 2-percent annual exceedance probabilities to 0.019 log 

units (-27.2 to 37.4 percent) for the 0.2-percent annual exceedance probabilities. The average standard model error of prediction was slightly higher with a range of 0.009 log units (-19.6 

to 24.4 percent) for the 10- and 4-percent annual exceedance 

probability to 0.022 log units (-28.9 to 40.7 percent) for the 

0.2-percent annual exceedance probability (table 7).

A prediction interval is a useful indicator of the uncertainty in the use of the regression equations and can be calculated for a specific streamgage (Ries and Dillow, 2006). A 

minimum and maximum value is computed with a stated probability that the true value of the estimated discharge is within 

the interval. A 90-percent prediction interval for the 1-percent 
20 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri Table 6. Variance of estimated values for U.S. Geological Survey streamgages in urban areas in and adjacent to Missouri. [USGS, U.S. Geological Survey; G, estimated from the Bulletin 17B (Hydrology Subcommittee of Interagency Advisory Committee on Water Data, 1982) analyses of the streamgage; W, weighted Bulletin 17B analyses and final weighted least-squares regression equation results] Site number (fig. 2) USGS streamgage number Variance of estimate, in log units Percent annual exceedance probabilities 50 20 10 4 2 1 0.2 G W G W G W G W G W G W G W 1 06893300 0.0010 0.0001 0.0013 0.0001 0.0019 0.0001 0.0035 0.0001 0.0054 0.0001 0.0079 0.0001 0.0160 0.0005 2 06893500 .0008 .0001 .0011 .0001 .0018 .0001 .0034 .0001 .0053 .0001 .0079 .0001 .0164 .0005 3 06893560 .0023 .0002 .0035 .0001 .0059 .0001 .0122 .0001 .0198 .0001 .0301 .0001 .0650 .0005 4 06893562 .0023 .0002 .0037 .0001 .0069 .0001 .0187 .0001 .0351 .0001 .0591 .0001 .1482 .0005 5 06893600 .0070 .0002 .0056 .0001 .0062 .0001 .0107 .0001 .0172 .0001 .0263 .0001 .0570 .0005 6 06894000 .0015 .0002 .0020 .0001 .0031 .0001 .0059 .0001 .0091 .0001 .0133 .0001 .0274 .0005 7 06910200 .0036 .0002 .0034 .0001 .0040 .0001 .0066 .0001 .0100 .0001 .0147 .0001 .0308 .0005 8 06910230 .0030 .0002 .0035 .0001 .0049 .0001 .0083 .0001 .0124 .0001 .0179 .0001 .0361 .0005 9 06910430 .0160 .0002 .0226 .0001 .0362 .0001 .0712 .0001 .1123 .0001 .1672 .0001 .3510 .0005 10 06923000 .0024 .0002 .0030 .0001 .0043 .0001 .0077 .0001 .0116 .0001 .0168 .0001 .0340 .0005 11 06929000 .0065 .0002 .0073 .0001 .0097 .0001 .0164 .0001 .0243 .0001 .0349 .0001 .0704 .0005 12 06935800 .0042 .0002 .0037 .0001 .0042 .0001 .0071 .0001 .0109 .0001 .0163 .0001 .0348 .0005 13 06935850 .0027 .0002 .0036 .0001 .0054 .0001 .0101 .0001 .0155 .0001 .0227 .0001 .0464 .0005 14 06935890 .0042 .0002 .0054 .0001 .0079 .0001 .0144 .0001 .0220 .0001 .0319 .0001 .0650 .0005 15 06935955 .0023 .0002 .0024 .0001 .0032 .0001 .0053 .0001 .0078 .0001 .0113 .0001 .0229 .0005 16 06935980 .0032 .0002 .0029 .0001 .0034 .0001 .0056 .0001 .0086 .0001 .0127 .0001 .0269 .0005 17 06936475 .0031 .0002 .0028 .0001 .0033 .0001 .0055 .0001 .0083 .0001 .0124 .0001 .0261 .0005 18 07005000 .0028 .0002 .0036 .0001 .0054 .0001 .0097 .0001 .0147 .0001 .0213 .0001 .0434 .0005 19 07010022 .0015 .0002 .0016 .0001 .0020 .0001 .0033 .0001 .0049 .0001 .0071 .0001 .0144 .0005 20 07010030 .0050 .0002 .0060 .0001 .0083 .0001 .0144 .0001 .0215 .0001 .0310 .0001 .0625 .0005 21 07010035 .0109 .0002 .0079 .0001 .0087 .0001 .0158 .0001 .0262 .0001 .0406 .0001 .0886 .0005 

22 07010086 .0022 .0002 .0034 .0001 .0060 .0001 .0132 .0001 .0222 .0001 .0344 .0001 .0768 .0005 23 07010090 .0028 .0002 .0018 .0001 .0020 .0001 .0039 .0001 .0068 .0001 .0108 .0001 .0234 .0005 24 07010180 .0014 .0002 .0020 .0001 .0032 .0001 .0063 .0001 .0099 .0001 .0148 .0001 .0311 .0005 25 07010208 .0047 .0002 .0053 .0001 .0070 .0001 .0118 .0001 .0176 .0001 .0252 .0001 .0509 .0005 26 07019317 .0032 .0002 .0040 .0001 .0059 .0001 .0106 .0001 .0160 .0001 .0232 .0001 .0471 .0005 27 07048480 .0051 .0002 .0074 .0001 .0121 .0001 .0242 .0001 .0387 .0001 .0579 .0001 .1231 .0005 28 07048490 .0031 .0002 .0042 .0001 .0065 .0001 .0123 .0001 .0191 .0001 .0281 .0001 .0581 .0005 29 07052000 .0062 .0002 .0091 .0001 .0150 .0001 .0305 .0001 .0489 .0001 .0737 .0001 .1575 .0005 30 07052100 .0038 .0002 .0058 .0001 .0104 .0001 .0233 .0001 .0395 .0001 .0618 .0001 .1394 .0005 31 07052160 .0039 .0002 .0056 .0001 .0094 .0001 .0191 .0001 .0307 .0001 .0462 .0001 .0989 .0005 32 07063200 .0071 .0002 .0060 .0001 .0068 .0001 .0114 .0001 .0180 .0001 .0271 .0001 .0582 .0005 33 07186600 .0057 .0002 .0056 .0001 .0069 .0001 .0113 .0001 .0169 .0001 .0247 .0001 .0508 .0005 34 07195000 .0033 .0002 .0032 .0001 .0040 .0001 .0066 .0001 .0098 .0001 .0143 .0001 .0294 .0005 35 07195865 .0071 .0002 .0083 .0001 .0115 .0001 .0199 .0001 .0297 .0001 .0427 .0001 .0860 .0005 
Estimation Of The Magnitude And Frequency Of Floods 21

Table 7. Accuracy statistics of weighted least-squares regression equations for urban basins in Missouri.

[R2, coefficient of determination]

Percent annual 

exceedance probability

Pseudo R2

(percent)

Standard model error Average standard error of prediction

Logarithm units Percent Logarithm units Percent

50 95.3 0.012 -22.3 to 28.7 0.013 -23.1 to 30.0

20 96.1 .009 -19.6 to 24.4 .010 -20.6 to 25.9

10 96.6 .008 -18.6 to 22.9 .009 -19.6 to 24.4

4 96.7 .008 -18.6 to 22.9 .009 -19.6 to 24.4

2 96.4 .008 -18.6 to 22.9 .010 -20.6 to 25.9

1 95.8 .010 -20.6 to 25.9 .012 -22.3 to 28.7

.2 92.8 .019 -27.2 to 37.4 .022 -28.9 to 40.7

Table 8. Model error variances, Student’s t distribution, and covariance matrices of regression equations for urban basins in 

Missouri.

[t, the critical value from the Student’s t distribution for the 90-percent prediction interval]

Percent annual 

exceedance 

probability

Model error 

variance, 

σ2

t

Covariance matrix

Intercept Drainage area 

(DRNAREA)

Impervious area

(IMPNLCD01)

50 0.0122 1.694 Intercept 0.002985 -0.000672 -0.000073

 Drainage Area -.000672 .000741 -.000001

 Impervious area -.000073 -.000001 .000003

20 .0094 1.694 Intercept .002701 -.000617 -.000066

 Drainage Area -.000617 .000654 .000000

 Impervious area -.000066 .000000 .000002

10 .0080 1.694 Intercept .002754 -.000639 -.000067

 Drainage Area -.000639 .000650 .000000

 Impervious area -.000067 .000000 .000003

4 .0076 1.694 Intercept .003139 -.000738 -.000076

 Drainage Area -.000738 .000722 .000001

 Impervious area -.000076 .000001 .000003

2 .0084 1.694 Intercept .003679 -.000869 -.000089

 Drainage Area -.000869 .000840 .000001

 Impervious area -.000089 .000001 .000004

1 .0103 1.694 Intercept .004443 -.001049 -.000108

 Drainage Area -.001049 .001015 .000001

 Impervious area -.000108 .000001 .000004

.2 .0186 1.694 Intercept .007091 -.001659 -.000172

 Drainage Area -.001659 .001648 .000001

 Impervious area -.000172 .000001 .000007
22 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

annual exceedance probability peak discharge should be interpreted to mean that there is 90-percent confidence that the true 

value of the estimated peak discharge is within the prediction 

interval. The parameters needed to compute the minimum and 

maximum values of the prediction interval are the model error 

variance, Student’s t distribution, and the covariance matrix. 

These parameters for each flood annual exceedance probability are presented in table 8. 

The urban equations presented in this report will be 

included in the USGS National Streamflow Statistics (NSS) 

program. The NSS program is a compilation of all current 

USGS regional regression equations for estimating streamflow 

statistics at ungaged sites in a user-friendly interface that operates on computers with Microsoft Windows operating systems. 

Output from NSS provides indicators of the accuracy of the 

estimated streamflow statistics, such as the 90-percent prediction interval. A frequency plot also can be generated with the 

program. The NSS software and accompanying database, 

and the documentation for the regression equations included 

in NSS, are available at http://water.usgs.gov/software/. The 

independent variables, drainage area and impervious area, 

are denoted as DRNAREA and IMPNLCD01 in the NSS 

software. 

The accuracy and prediction intervals for the equations in table 6 are valid for the range of basin characteristics 

used to develop the equations. For this study, the drainage 

area independent variable ranged from 0.28 to 189 square 

miles (table 9). In contrast, the range in drainage area was 

0.28 to 38.9 square miles for the previous statewide urban 

flood frequency study by Becker (1986). Impervious area is 

the other independent variable common to both studies. The 

range of impervious area for this study was 2.3 to 46.0 percent 

compared to 1 to 34 percent in Becker’s (1986) study. A plot 

indicating the spatial relation of drainage area and percent 

impervious area for the basins upstream from the 35 USGS 

streamgages used in this report is shown in figure 5.

The sensitivity of the equations to errors in the independent variables (drainage area and impervious area) was evaluated by changing each independent variable by 10 percent 

increments from +20 to -20 percent, while holding the other 

variable constant. The annual exceedance probabilities of 50-, 

20-, 10-, 4-, 2-, 1-, and 0.2-percent were used in the sensitivity 

analyses and the base computations were the mean values for 

each independent variable. For the +20 to -20 percent changes 

in drainage area, the percent change in peak flows ranged from 

+12.0 to -13.0 percent, respectively (table 10). For the +20 to 

-20 percent changes in impervious area, the percent change in 

peak flows ranged from +18.6 to -15.7 percent, respectively. 

The percent change in peak flows was fairly constant for 

each change in drainage area throughout the range in annual 

exceedance probabilities; however, for impervious area, the 

percent change in peak flows for each change in impervious area decreased when going from the 50-percent annual 

exceedance probability to the 0.2-percent annual exceedance 

probability. The sensitivity analyses indicates that as the magnitude of the flood event increases, the effect of the impervious area decreases as the soils become saturated and retain less 

precipitation, resulting in more runoff per unit area. 

A comparison of results from selected regression equations and the maximum recorded flood discharge at each 

streamgage was done to visualize the magnitude of floods 

experienced at the streamgages. A plot of the drainage area 

basin characteristic and maximum recorded flood discharge 

from table 4 is shown in figure 6. Two lines shown on the 

plot represent the results of the 1- and 0.2-percent annual 

exceedance probabilities derived from the regression equations using an impervious area of 46 percent, the maximum 

percent impervious area used to develop the equations. Two 

streamgages in the Brush Creek Basin in Kansas City, Missouri, (sites 3 and 4) recorded floods greater than a 0.2-percent 

annual exceedance probability estimate from the regression 

equations. The maximum flood at site 3 occurred on September 12, 1977, and the maximum flood at site 4 occurred 

on October 4, 1998 (site 4 was not in operation in 1977). At 

site 26, the flood of September 14, 2008, was greater than the 

Table 9. Ranges of basin characteristics used to develop the 

regression equations for urban basins in Missouri.

Basin

characteristic Basin characteristic statistics

Minimum Mean Maximum

Drainage area

(DRNAREA, 

in square miles)

0.28 28.8 189

Impervious area 

(IMPNLCD01, 

in percent)

2.3 6.5 46

1

10

100

0.1 1.0 10 100 1,000

IMPERVIOUS AREA, IN PERCENT

DRAINAGE AREA, IN SQUARE MILES 

Figure 5. Drainage area and impervious area basin 

characteristics at U.S. Geological Survey streamgages 

in urban areas in and adjacent to Missouri.
Estimation Of The Magnitude And Frequency Of Floods 23

Table 10. Results of sensitivity analyses presented as percent change in computed flood discharge as a result of a 10- 

and 20-percent change of the input basin characteristic.

Percent change 

in basin

characteristic

Percent change in computed flood discharge by the regression equation for estimating floods having a 

percent annual exceedance probability of

50 20 10 4 2 1 0.2

Drainage area (DRNAREA)

+20 11.6 11.5 11.5 11.6 11.7 11.8 12.0

+10 5.9 5.8 5.9 5.9 6.0 6.0 6.1

-10 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9 -1.9

-20 -12.6 -12.5 -12.5 -12.6 -12.7 -12.8 -13.0

Impervious area (IMPNLCD01)

+20 18.6 14.4 13.0 11.3 10.3 8.9 7.6

+10 9.1 7.1 6.4 5.1 5.1 4.4 3.8

-10 -8.3 -6.6 -6.0 -4.9 -4.9 -4.3 -3.7

-20 -15.7 -12.6 -11.5 -9.3 -9.3 -8.2 -7.1

100

1,000

10,000

100,000

0.1 1.0 10 100 1,000

DISCHARGE, IN CUBIC FEET PER SECOND

DRAINAGE AREA, IN SQUARE MILES

EXPLANATION

Estimated peak flows for the 1-percent 

 annual exceedance probability flood using

 46 percent impervious area

Estimated peak flows for the 0.2-percent 

 annual exceedance probability flood using

 46 percent impervious area

26

3

4

4 Maximum recorded flood discharge 

 greater than the 1-percent annual 

 exceedance probability flood at 

 U.S. Geological Survey streamgages

 (site number, table 4) 

Figure 6. Maximum recorded flood discharges at U.S. Geological Survey streamgages in urban areas in and adjacent to 

Missouri in relation to estimated peak flows from the regression equations for the 1- and 0.2-percent annual exceedance 

probability flood using 46 percent impervious area.
24 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

1-percent annual exceedance probability flood estimate from 

the regression equations.

The results of this study were compared to computed 

flows for the current rural (Alexander and Wilson, 1995) and 

existing urban (Becker, 1986) regression equations at seven 

selected streamgages for the 1-percent annual exceedance 

probability. The seven streamgages selected represent a variety 

of combinations of drainage area values and impervious area 

values used in this study. It should be noted that the rural 

equations are not intended to be used on urbanized basins and 

the range of basin characteristics for the urban equations in 

this study were outside of the range of basin characteristics 

that Becker (1986) used to develop his equations. The comparison was done to examine differences in the equations. The 

range in percent differences between the urban equation in this 

study and the rural equation presented in Alexander and Wilson was 3 to 52 percent (table 11). Comparing the percent differences from this study to the previous urban study (Becker, 

1986), with drainage area and percent impervious area as basin 

characteristics from Becker (1986), the range in percent differences was -255 to 10 percent. The largest differences shown in 

table 11 are at streamgages with drainage areas (70.3 and 189 

square miles) much larger than the maximum used to develop 

Becker’s 1986 equation (38.9 square miles), and direct comparisons may not be valid for these streamgages. Site 32 was 

the only streamgage with a positive difference, implying that 

for extremely small drainage areas Becker’s equation may 

result in slightly lower peak flow values. The overall comparison between the urban equations indicates a reduction in 

estimated peak flows for urban basins.

Summary

The report presents the results of regression analyses 

on streamgage frequencies using 35 U.S. Geological Survey 

streamgages located in urban basins in and adjacent to Missouri. It describes the need and purpose of the study, data 

development for the study, and regionalization of the regression equations. Model verification, diagnostics, and limits also 

are presented. This report supersedes previous urban flood 

frequency investigations in Missouri.

 The best available information is needed in the proper 

design of bridges and culverts, land-use planning, and flood 

risk assessments. Basin characteristics affect the hydraulic 

design of infrastructure along streams. Urbanized basins 

typically result in higher peak flows and decreased dependent times compared to rural basins. The last set of urban 

equations for the state of Missouri was developed in 1986 

using data through the 1984 water year. Since 1984, 24 years 

of additional streamflow data have been collected, and 15 

streamgages have been established or re-activated in urban 

basins enhancing the base data set used in regression analyses. 

Improvements in the characterization of basins exist today by 

implementation of high resolution digital datasets. Statistical 

analyses are more rigorous than in the mid-1980s with the use 

of expected moments algorithms and weighted least-squares 

regression techniques. Use of the additional data and improved 

statistical techniques will provide more accurate estimates 

of peak flow at gaged and ungaged sites in urban basins; 

therefore, the U.S. Geological Survey conducted a study, in 

cooperation with the Metropolitan St. Louis Sewer District, 

to develop and apply a new set of regression equations for 

Table 11. Flood discharges at the 1-percent annual exceedance probabilities for rural and urban regression equations at selected 

U.S. Geological Survey streamgages.

[ft3/s, cubic feet per second; USGS, U.S. Geological Survey; mi2, square miles; ft/mi; feet per mile]

Flood discharge (ft3/s)

Difference in rural

 and urban regression 

equations, in percent

Site

number

(fig. 2)

USGS 

station 

number

Drainage

area

(mi2)

Impervious

area

(percent)

Main-channel 

slope

(ft/mi)

Rural 

regression 

results

 (Alexander 

and Wilson, 

1995)

Urban 

regression 

results 

(Becker, 

1986)

Urban 

regression 

results

(this study)

Rural Urban

6 06894000 189 14.1 7.4 22,900 107,000 30,100 24 -255

8 06910230 70.3 5.15 11.2 13,900 41,000 14,300 3 -187

17 06936475 41.0 40 8.0 8,690 35,400 18,000 52 -97

19 07010022 8.74 43.5 29 4,950 10,100 7,470 34 -35

21 07010035 1.47 27.3 50.2 1,870 2,180 1,940 4 -12

29 07052000 19.5 46 22.6 7,810 19,600 12,700 39 -54

32 07063200 .28 7.94 85.4 503 467 519 3 10
Summary 25

estimating the magnitude and frequency of floods in urban 

basins in Missouri.

Streamgages in urban areas throughout and adjacent 

to Missouri were evaluated for use in this study. Criteria 

in the selection of streamgages included period of record, 

minimal changes in urbanization during the record period, 

minimal diversions and storage in the basin, and well-defined 

streamgage ratings. The initial list of streamgages contained 

more than 70 streamgages. After application of the criteria, 

the final number of streamgages for use in this study was 35. 

Of the 35 streamgages, 30 were within Missouri and 5 were 

outside of the state. 

Flood-frequency estimates for each streamgage were 

computed from the annual series of peak-flow data retrieved 

from the U.S. Geological Survey National Water Information System. The analyses were done according to methods 

recommended in Bulletin 17B by the Interagency Advisory 

Committee on Water Data. The flood-frequency estimates 

are expressed in terms of exceedance probabilities, which 

are the reciprocals of the recurrence intervals. A log-Pearson 

Type III frequency distribution was fitted to the logarithms 

of the annual peak flows. The program PEAKFQ was used to 

compute the flood-frequency statistics. Within the PEAKFQ 

program is the Expected Moments Algorithm that employs the 

method of moments technique, which is compatible with Bulletin 17B. The algorithm uses an iterated least-squares method 

for fitting regression models to censored data. 

Ordinary least-squares was used to determine the best set 

of independent variables for the regression equations. Three 

general criteria were used to select potential basin characteristics for use in the ordinary least-squares regression analyses. 

The first criterion was a basin characteristic’s theoretical relation to flood flows. The second criterion was the use of basin 

characteristics in previous studies. The third and final criterion 

was the ability to measure the basin characteristics using 

digital datasets and GIS technology. The results of the selection process resulted in four basin characteristics for evaluation using ordinary least-squares regression: (1) drainage area, 

(2) main channel slope, (3) mean basin slope, and (4) percent 

impervious area.

The selection and location of the streamgages for this 

study limited the definition of separate hydrologic regions in 

the state. To test for potential geographic bias, the residuals 

from the ordinary least-square regression analyses were plotted on a state map. Overall, no geographic bias was present 

in the results that would require creating multiple regions. An 

examination of the residuals compared to drainage area and 

percent impervious area indicates that the model is satisfactorily meeting the assumptions of multiple-linear-regression 

techniques. Examination of observed peak flows and the 

estimated peak flows indicated no climatic or temporal bias 

existed in the data. 

The ordinary least-squares results were evaluated on 

the basis of Mallow’s Cp statistic, the adjusted coefficient of 

determination, and the statistical significance of the independent variables. The dependent variable peak flow from 

streamgage frequency analyses and independent variable 

drainage area were base-10 logarithmically transformed for 

use in the regression equations to improve the linear relation 

in the analyses. The independent variable, percent impervious 

area, was not transformed as it was used as a percentage and 

the resulting logarithmic transformation did not improve the 

linear relation with the dependent variable peak flow. 

Drainage area and impervious area were retained in the 

final regression equations from ordinary least-squares analysis. Drainage area was computed using GIS techniques and a 

statewide 10-meter grid (higher resolution elevation data from 

urban areas, when available). Impervious area was computed 

from National Land Cover Dataset 2001 percentage impervious area data. The impervious area computed for each urban 

basin was checked against historical imagery and 7.5-minute 

topographic maps to verify that substantial changes in development did not occur during or outside of the period of record. 

Of the 35 streamgages, 8 streamgages had National Land 

Cover Dataset impervious area computations lowered from 1 

to 23 percent to reflect the amount of urbanization during the 

period of streamflow data collection.

The final regression coefficients were computed using 

weighted least-squares techniques as weighted regression techniques provided better estimates of the accuracy of the equations than ordinary least-squares techniques. Improvements 

in the weighted equations occurred when streamflow records 

at streamgages are of different and varying lengths. Weighted 

least-squares techniques give less weight to streamgages that 

have shorter periods of record than streamgages with longer 

periods of records. The results of the weighted least-squares 

were compiled for the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent annual exceedance probabilities floods for Missouri. The 

results of this study will be included in the National Streamflow Statistics program by the U.S. Geological Survey at 

http://water.usgs.gov/software/.

The set of equations presented in this report are applicable for urban areas within Missouri that have drainage areas 

in the range of 0.28 to 189 square miles and impervious areas 

in the range of 2.3 to 46.0 percent. The standard model error 

ranged from 0.008 to 0.019 log units. The standard model 

error of prediction was slightly higher with a range of 0.009 

to 0.022 log units. The sensitivity of the equations to errors in 

the computation of the independent variables was evaluated. 

A +20 to -20 percent change in drainage area resulted in a 

percent change in peak flow from +12.0 to -13.0. For a +20 to 

-20 percent change in impervious area, the percent change in 

peak flows ranged from +18.6 to -15.7 percent. 

A plot of the regression results and maximum recorded 

flood discharges for each streamgage was created to visualize 

the magnitude of floods experienced at each streamgage. An 

impervious area of 46 percent was used in the regression equations for the 1- and 0.2-percent annual exceedance probabilities. The two largest floods occurred in the Brush Creek Basin 

in 1977 and 1998 at site numbers 3 and 4, respectively. These 

floods exceeded the 0.2-percent annual exceedance probability 

based on the regression equations. Another flood in 2008, at 
26 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri

site number 26, exceeded the 1-percent annual exceedance 

probability flood based on the regression equation. 

Seven streamgages were selected to compare the results 

of the existing rural flood frequency equations, the existing 

urban equations, and this study. This comparison was done to 

qualitatively define the differences in the three sets of equations for the 1-percent annual exceedance probability. The 

results of this study indicated that the peak flows were 3 to 52 

percent higher than estimates from the rural equation. Comparison of this study to the existing urban equations developed 

in 1986, using the independent variables drainage area and 

impervious, indicated the peak flows were 255 percent lower 

to 10 percent higher than estimates from the 1986 study. The 

overall comparison of the two urban equations indicates a 

reduction in estimated peak flow values for the 1-percent 

annual exceedance probability flood using regression equations from this study. 

Selected References

Alexander, T.W., and Wilson, G.L., 1995, Techniques for estimating the 2- to 500-year flood discharges on unregulated 

streams in rural Missouri: U.S. Geological Survey WaterResources Investigations Report 95–4231, 33 p.

Becker, L.D., 1986, Techniques for estimating flood-peak 

discharges from urban basins in Missouri: U.S. Geological 

Survey Water-Resources Investigations Report 86–4322, 

38 p.

Becker, L.D., and Alexander, T.W., 1983, Floods in Kansas 

City, Missouri and vicinity, August 12–13, 1982: U.S. 

Geological Survey Water-Resources Investigations Report 

83–4141, 35 p.

Cohn, T., Lane, W.M., and Baier, W.G., 1997, An algorithm 

for computing moments-based flood quantile estimates 

when historical flood information is available: Water 

Resources Research., v. 33 no. 9, p. 2,089–2,096.

Cohn, T., Lane, W.L., and Stedinger, J.R., 2001, Confidence 

intervals for Expected Moments Algorithm flood quantile 

estimates: Water Resources Research, v. 37, no. 6, 

p. 1,695–1,706.

Cook, R.D., 1977, Detection of influential observation in linear regression: Technometrics, v. 19, p. 15–18.

Eng, Ken, Chen, Yin-Yu, and Kiang, J.E., 2009, User’s guide 

to the weighted-multiple-linear-regression program (WREG 

version 1.0): U.S. Geological Survey Techniques and Methods, book 4, chap. A8, 21 p. (Also available at http://pubs.

usgs.gov/tm/tm4a8.)

Feaster, T.D., Guimaraes, W.B., 2004, Estimating the magnitude and frequency of floods in small urban streams in 

South Carolina, 2001: U.S. Geological Survey Scientific 

Investigations Report 2004–5030, 68 p.

Flynn, K.M., Kirby, W.H., and Hummel, P.R., 2006, User’s 

manual for program PeakFQ, Annual Flood Frequency 

Analysis Using Bulletin 17B Guidelines: U.S. Geological 

Survey Techniques and Methods book 4, chap. B4, 42 p.

Gotvald, A.J., Feaster, T.D., and Weaver, J.C., 2009, Magnitude and frequency of rural floods in the southeastern 

United States, 2006—Volume 1, Georgia: U.S. Geological 

Survey Scientific Investigations Report 2009–5043, 120 p.

Griffis, V.W., Stedinger, J.R., and Cohn, T.A., 2004, Log 

Pearson type 3 quantile estimators with regional skew 

information and low outlier adjustments: Water Resources 

Research, v. 40, W07503.

Griffis, V.W., and Stedinger, J.R., 2007a, The LP3 distribution 

and its application in flood frequency analysis, II—Parameter estimation methods: Journal of Hydrologic Engineering, 

v. 12, no. 5, p. 492–500.

Griffis, V.W., and Stedinger, J.R., 2007b, The use of GLS 

regression in regional hydrologic analyses: Journal of 

Hydrology, v. 344, p. 82–95.

Helsel, D.R., and Hirsch, R.M., 1992, Statistical methods in 

water resources: New York, Elsevier, p. 326.

Hydrology Subcommittee of Interagency Advisory Committee on Water Data, 1982, Guidelines for determining flood 

flow frequency (revised): U.S. Geological Survey, Office of 

Water Data Coordination, Bulletin 17B, 28 p., 14 app., and 

1 pl.

Missouri Climate Center, 2009, Climate of Missouri, accessed 

June 2009 at http://climate.missouri.edu/climate.php.

Ries, K.G. III, and Dillow, J.J.A., 2006, Magnitude and 

frequency of floods on nontidal streams in Delaware: U.S. 

Geological Survey Scientific Investigations Report 2006–

5146, 57 p.

Sauer, V.B., Thomas, W.O., Jr., Stricker, V.A., and Wilson, 

K.V., 1983, Flood characteristics of urban watersheds in the 

United States: U.S. Geological Survey Water-Supply Paper 

2207, 63 p.

Spencer, D.W., and Alexander, T.W., 1978, Techniques for 

estimating the magnitude and frequency of floods in St. 

Louis County, Missouri: U.S. Geological Survey WaterResources Investigations Report 78–139, 23p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic 

analysis 1—ordinary, weighted, and generalized least 

squares compared: Water Resources Research, v. 21, no. 9, 

p. 1,421–1,432.
Selected References 27

Tasker, G.D., 1980, Hydrologic regression with weighted 

least-squares: Water Resources Research, v. 16, no. 6, 

p. 1,107–1,113.

U.S. Census Bureau, 2001, Census 2000 summary file 1 

technical documentation: U.S. Census Bureau, Washington, 

D.C., U.S.A.

U.S. Geological Survey, 2001, Multi-Resolution Land Characteristics Consortium, accessed June 2009 at http://www.

mrlc.gov/mrlc2k_nlcd.asp.

Publishing support provided by: 

Rolla Publishing Service Center

For more information concerning this publication, contact:

Director, USGS Missouri Water Science Center

1400 Independence Road

Rolla, MO 65401

(573) 308–3667

Or visit the Missouri Water Science Center Web site at: 

http://mo.water.usgs.gov/
28 Estimation of the Magnitude and Frequency of Floods in Urban Areas in Missouri
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