U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2010–5137

Prepared in cooperation with the Oklahoma Department of Transportation

Methods for Estimating the Magnitude and Frequency of 

Peak Streamflows for Unregulated Streams in Oklahoma
On Cover: Photograph of the Cimarron River near Guthrie (U.S. Geological Survey station number 07160000) taken by Martin Schneider, U.S. Geological staff.
Methods for Estimating the Magnitude 

and Frequency of Peak Streamflows for 

Unregulated Streams in Oklahoma

By Jason M. Lewis

Prepared in cooperation with the Oklahoma Department of Transportation

Scientific Investigations Report 2010–5137

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

This and other USGS information products are available at http://store.usgs.gov/

U.S. Geological Survey

Box 25286, Denver Federal Center

Denver, CO 80225

To learn about the USGS and its information products visit http://www.usgs.gov/

1-888-ASK-USGS

Any use of trade, product, or firm names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to 

reproduce any copyrighted materials contained within this report.

Suggested citation:

Lewis, J.M., 2010, Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated 

Streams in Oklahoma: U.S. Geological Survey Scientific Investigations Report SIR 2010-5137, 41 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................2

General Description and Effects of Floodwater Retarding Structures ........................................2

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

Annual Peak Data .................................................................................................................................3

Basin Characteristics ...........................................................................................................................3

Estimate of Magnitude and Frequency of Peak Streamflows at Streamflow-Gaging Stations 

on Unregulated Streams .................................................................................................................4

Peak Streamflow Frequency ...............................................................................................................4

Low-Outlier Thresholds........................................................................................................................4

Weighted Skew .....................................................................................................................................9

Generalized-Skew Analysis ................................................................................................................9

Estimate of Magnitude and Frequency of Peak Streamflows at Ungaged Sites on 

Unregulated Streams .......................................................................................................................9

Regression Analysis ...........................................................................................................................10

Regression Equations.........................................................................................................................14

Accuracy and Limitations ..................................................................................................................15

Application of Methods...............................................................................................................................16

Estimate for a Streamflow-Gaging Station .....................................................................................16

Example .......................................................................................................................................16

Estimate for an Ungaged Site near a Streamflow-Gaging Station .............................................18

Example .......................................................................................................................................18

Adjustment for Ungaged Sites on Urban Streams ........................................................................19

Example .......................................................................................................................................19

Adjustment for Ungaged Sites on Streams Regulated by Floodwater 

Retarding Structures ............................................................................................................19

Example .......................................................................................................................................21

Summary........................................................................................................................................................21

References Cited..........................................................................................................................................21

Table 1 ...........................................................................................................................................................25

Figures

 1–3. Maps showing:

 1. Location of streamflow-gaging stations with unregulated periods of record 

used in report. ......................................................................................................................5

 2. Generalized skew coefficients of logarithms of annual maximum streamflow 

for Oklahoma streams with drainage area less than or equal to 

2,510 square miles. ............................................................................................................11

 3. Residuals from the 10-percent chance exceedance ordinary least squares 

(OLS) regression model for each site. ............................................................................13
iv

4. Scatterplots showing performance metrics from computer program WREG (A) residuals, 

(B) leverage, and (C) influence for a 10-percent chance exceedance peak-streamflow 

regression model. .......................................................................................................................14

5. WREG output for the 10-percent chance exceedance peak-streamflow regression 

model by using the generalized least squares (GLS) method, showing average 

standard error of prediction (Sp %), the pseudo coefficient of determination 

(Pseudo R2), and standard model error, in percent (%)........................................................17

6. Graph showing relation of urban adjustment factor, RL, to the percentage of area 

impervious,and served by storm sewer. .................................................................................20

Tables

2. Basin characteristics investigated as possible independent variables for 

regressions used to estimate peak streamflows for unregulated streams. .......................7

3. T-year recurrence intervals with corresponding annual exceedance probabilities 

and P-percent chance exceedances for peak-streamflow frequency estimates.............9

4. Accuracy of peak streamflows estimated for unregulated streams in Oklahoma..........16

5. Weighted peak-streamflow frequency estimates for Kiamichi River near Big 

Cedar, Oklahoma (07335700) .....................................................................................................17
v

Conversion Factors and Datums

Multiply By To obtain

Length

inch (in.) 2.54 centimeter (cm)

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

yard (yd) 0.9144 meter (m)

Area

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

square mile (mi2) 2.590 square kilometer (km2) 

Volume

cubic mile (mi3) 4.168 cubic kilometer (km3) 

acre-foot (acre-ft) 1,233 cubic meter (m3)

acre-foot (acre-ft) 0.001233 cubic hectometer (hm3) 

Flow rate

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

cubic foot per second per square

mile [(ft3/s)/mi2]

 0.01093 cubic meter per second per square

kilometer [(m3/s)/km2]

Hydraulic gradient

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

Water year is the 12-month period October 1 through September 30, designated by the calendar year in 

which the water year ends.

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 (NAVD 88).

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

Altitude, as used in this report, refers to distance above the vertical datum.
Abstract 

Peak-streamflow regression equations were determined 

for estimating flows with exceedance probabilities from 50 

to 0.2 percent for the state of Oklahoma. These regression 

equations incorporate basin characteristics to estimate peakstreamflow magnitude and frequency throughout the state by 

use of a generalized least squares regression analysis. The 

most statistically significant independent variables required 

to estimate peak-streamflow magnitude and frequency for 

unregulated streams in Oklahoma are contributing drainage 

area, mean-annual precipitation, and main-channel slope. 

The regression equations are applicable for watershed basins 

with drainage areas less than 2,510 square miles that are not 

affected by regulation. The resulting regression equations had 

a standard model error ranging from 31 to 46 percent. 

Annual-maximum peak flows observed at 231 streamflow-gaging stations through water year 2008 were used for 

the regression analysis. Gage peak-streamflow estimates were 

used from previous work unless 2008 gaging-station data were 

available, in which new peak-streamflow estimates were calculated. The U.S. Geological Survey StreamStats web application was used to obtain the independent variables required for 

the peak-streamflow regression equations. Limitations on the 

use of the regression equations and the reliability of regression estimates for natural unregulated streams are described. 

Log-Person Type III analysis information, basin and climate 

characteristics, and the peak-streamflow frequency estimates 

for the 231 gaging stations in and near Oklahoma are listed.

Methodologies are presented to estimate peak streamflows at ungaged sites by using estimates from gaging stations 

on unregulated streams. For ungaged sites on urban streams 

and streams regulated by small floodwater retarding structures, 

an adjustment of the statewide regression equations for natural 

unregulated streams can be used to estimate peak-streamflow 

magnitude and frequency.

Introduction

Estimates of the magnitude and frequency of floods 

is required for the safe and economical design of highway 

bridges, culverts, dams, levees, and other structures on or near 

streams. Flood plain management programs and flood-insurance rates also are based on flood magnitude and frequency 

information. Estimates of the magnitude and frequency of 

flooding events, or peak streamflows, are commonly needed 

at ungaged sites with no streamflow data available. Regional 

regression equations can be used to estimate peak streamflows 

at ungaged sites.

The U.S. Department of Agriculture, Natural Resources 

Conservation Service (NRCS) has constructed several floodwater retarding structures throughout Oklahoma that regulate flood peaks. Currently (2010), about 2,105 floodwater 

retarding structures are in more than 120 watershed basins in 

Oklahoma. On completion of the NRCS watershed protection 

and flood prevention program (G.W. Utley, Natural Resources 

Conservation Service, written commun., 1997) about 2,500 

floodwater retarding structures will regulate flood peaks for 

about 8,500 square miles (mi2) (about 12 percent) of the 

state. By design, floodwater retarding structures decrease the 

magnitude of main-stem flood peaks and decrease the rate of 

runoff recession of single storms (Bergman and Huntzinger, 

1981). Consideration of the flood peak modification capability 

of floodwater retarding structures can result in more hydraulically efficient, cost-effective culvert or bridge designs along 

downstream segments of streams regulated by floodwater 

retarding structures (Tortorelli, 1997).

The U.S. Geological Survey (USGS), in cooperation 

with the Oklahoma Department of Transportation, updated the 

regression equations for estimating peak-streamflow frequencies for Oklahoma streams with a drainage area less than 

2,510 mi2, as suggested by Tortorelli (1997). The methods 

used in this report should provide more accurate estimates of 

peak flows for Oklahoma than previous reports (Tortorelli, 

Methods for Estimating the Magnitude and Frequency of 

Peak Streamflows for Unregulated Streams in Oklahoma

By Jason M. Lewis
2 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

1997; Tortorelli and Bergman, 1985) because of the use of 

additional data and more rigorous statistical procedures. The 

generalized least squares (GLS) regression method was used 

in this report, as opposed to the weighted least squares method 

used in Tortorelli (1997) to better handle cross-correlation of 

peak streamflow between gaging stations and differing historic 

record lengths.

Purpose and Scope

This report presents methods for estimating the magnitude and frequency of peak streamflows for the 50-, 20-, 

10-, 4-, 2-, 1-, and 0.2-percent chance exceedance floods for 

ungaged sites on unregulated streams with drainage areas of 

less than 2,510 mi2 in Oklahoma. This report provides methods that can be used to estimate peak-streamflow frequencies for gaging stations on unregulated streams and by using 

this result to, in turn, estimate nearby ungaged sites on the 

same stream. Methods used to adjust estimates for ungaged 

urban streams and streams regulated by floodwater retarding 

structures also are presented. This report also provides peak 

streamflow frequency analyses and basin characteristics for all 

streamflow-gaging stations used in the regression analysis.

Flood-discharge records through the 2008 water year at 

231 streamflow-gaging stations throughout Oklahoma and 

in bordering parts of Arkansas, Kansas, Missouri, and Texas 

were used to develop statewide peak-streamflow frequency 

estimate equations. Estimates of peak-streamflow frequency 

from the 231 gaging stations were related to climatic and 

physiographic attributes, referred to as basin characteristics, 

by using multiple-linear regression. The regression equations 

derived from these analyses provide methods to estimate flood 

frequencies of unregulated streams.

This report provides methods to estimate peak streamflows for streams with drainage areas less than 2,510 mi2

. 

Peak-streamflow frequency for streams with greater than or 

equal to 2,510 mi2 drainage areas can be estimated by using 

methods described in Sauer (1974a) and Lewis and Esralew 

(2009). The Oklahoma generalized skew map (Lewis and 

Esralew, 2009), a necessary element in the development of 

the peak-streamflow frequencies for the 231 gaging stations, 

was updated in 2008. In this report, methods are presented to 

estimate peak-streamflow frequencies at sites on urban streams 

(based on Sauer, 1974b) and streams regulated by floodwater 

retarding structures (based on Tortorelli and Bergman, 1985).

This report supercedes the report by Tortorelli (1997) 

to estimate peak-streamflow frequencies for unregulated 

Oklahoma streams with a drainage area less than 2,510 mi2. 

The current report incorporates (1) an additional 13 years of 

annual peak-streamflow data, with major peak-streamflows 

recorded during water years 1999, 2000, 2004, 2007, and 

2008; (2) additional streamflow-gaging stations that now have 

adequate numbers of years for frequency analysis; (3) removal 

of gaging stations included in Tortorelli (1997) that were later 

determined to be influenced by regulation or were outside of 

the modified study area; (4) basin characteristics determined 

at each gaging station location by using a geographic information system (GIS); (5) mean-annual precipitation based on an 

updated period 1971–2000 and an area-weighted average of 

precipitation for the contributing drainage area, from which a 

point estimate of mean-annual precipitation was determined; 

and (6) a GLS regression method shown to be a better method 

at handling cross-correlation and differing record lengths of 

peak-streamflow at gaging stations (Tasker and Stedinger, 

1989). 

General Description and Effects of Floodwater 

Retarding Structures

This report includes an adjustment for the effects of 

floodwater retarding structures on peak streamflow because 

many areas of Oklahoma are regulated by these structures. 

Floodwater retarding structures built by the NRCS are used in 

watershed basin protection and flood-prevention programs. 

Floodwater retarding structures generally consist of 

an earthen dam, a valved drain pipe, a drop inlet principal 

spillway, and an open-channel earthen emergency spillway 

(Moore, 1969). The principal spillway is ungated and automatically limits the rate at which water can flow from a reservoir. 

Most of the structures built in Oklahoma have release rates 

of 10 to 15 cubic feet per seconf per square mile ((ft3/s)/mi2). 

The space in a reservoir between the elevation of the principal 

spillway crest and the emergency spillway crest is used for 

floodwater detention.

Most floodwater retarding structures in Oklahoma are 

designed to draw down the floodwater-retarding pool in 10 

days or less (R. C. Riley, Natural Resources Conservation 

Service, written commun., 1984). The 10-day drawdown 

requirement serves two purposes. First, most vegetation in the 

floodwater retarding pool will survive as much as 10 days of 

inundation without destroying the viability of the stand. Second, a 10-day drawdown period will substantially reduce the 

effect from repetitive storms (Tortorelli, 1997).

Floodwater retarding structures have embankment 

heights ranging generally from 20 to 60 feet (ft) and drainage areas ranging generally from 1 to 20 mi2

 (Moore, 1969). 

Storage capacity is limited to 12,500 acre-ft for floodwater 

detention and 25,000 acre-ft total for combined uses, including 

recreation, municipal and industrial water, and others (Tortorelli, 1997).

The emergency spillway design, including storage above 

the emergency crest, and capacity of an emergency spillway is 

influenced by the size of the floodwater retarding structure and 

the location of the structure in the basin. Design details may be 

found in the NRCS National Engineering Handbook, Section 4 

(U.S. Soil Conservation Service, 1972).

The primary effect of a system of upstream floodwater 

retarding structures on a basin streamflow hydrograph at a 

point downstream from the floodwater retarding structures is 

that flood peak discharge is reduced. This reduction is related 
Data Development 3

to the percentage of the overall basin that is regulated by the 

floodwater retarding structures (Hartman and others, 1967; 

Moore, 1969; Moore and Coskun, 1970; DeCoursey, 1975; 

Schoof and others, 1980). The slope of the recession segment 

of the hydrograph will decrease as the number of floodwater 

retarding structures where the principal spillways are flowing 

increases.

Several factors substantially influence the effectiveness 

of the floodwater retarding structures in reducing peak flow 

on the main stem downstream from the floodwater retarding 

structures (Hartman and others, 1967; Moore, 1969; Moore 

and Coskun, 1970; Schoof and others, 1980). Those factors 

include rainfall distribution over the basin, contents of the 

reservoirs before the storm, and distribution of floodwater 

retarding structures in the basin. For example, rainfall that 

is only on the basin area controlled by floodwater retarding 

structures will generally result in greater peak reduction. The 

structures are more effective in reducing the flood peak if the 

structures are empty before the storm. Structures in the upper 

end of an elongated basin are less effective than structures in a 

fan-shaped basin (Tortorelli, 1997).

Data Development

Annual Peak Data

The first step in peak-streamflow frequency analysis is 

the compilation and review of all streamflow-gaging stations with peak-streamflow data. Streamflow-gaging stations 

selected for analysis (fig. 1) were in 8-digit hydrologic unit 

boundaries (based on the 8-digit hydrologic unit codes, or 

HUCs) that were in or were adjacent to the Oklahoma state 

boundary (http://www.ncgc.nrcs.usda.gov/products/datasets/

watershed/, accessed June 2009). Review was done to eliminate discrepancies in peak-streamflow data for gages across 

state lines. Peak-streamflow data from streamflow-gaging 

stations in the immediate bordering areas of Oklahoma with 

similar hydrologic characteristics also were selected for 

regression analysis.

The streamflow-gaging station flood-frequency analysis 

for natural unregulated streams of less than 2,510 mi2 drainage 

area provided in this report is based on annual peak-streamflow data systematically collected at 231 gaging stations (table 

1, back of report). 

The data were collected on the basis of a water year, from 

October 1 to September 30. Available data collected through 

September 30, 2008, were used from streamflow-gaging stations for this report. Only data from those streamflow-gaging 

stations with at least 8 years of flood peak data were used in 

the analysis. The Interagency Advisory Committee on Water 

Data (IACWD) recommends at least 10 years of data (Interagency Advisory Committee on Water Data, 1982). Asquith 

and Slade (1997) and Tortorelli (1997) used 8 years to utilize 

more streamflow-gaging stations to improve coverage in 

certain areas. Data from 8 streamflow-gaging stations with less 

than 10 years of peak-streamflow record were retained and 

carefully reviewed. All streamflow-gaging stations selected 

are on streams that are not substantially regulated by dams 

and floodwater retarding structures. Substantial regulation is 

defined as a contributing drainage basin where 20 percent or 

more of the basin is upstream of dams and floodwater retarding structures (Heimann and Tortorelli, 1988).

Basin Characteristics

Several basin characteristics were investigated for use as 

potential independent variables in the regression analyses. In 

this report, the basin characteristics (table 2) are the independent variables and the resulting peak-streamflow frequency 

values are the dependant variables. 

Basin characteristics were calculated for each streamflow-gaging station by using geographic information system 

(GIS) techniques and the USGS StreamStats application (Ries 

and others, 2004; Ries and others, 2008, Smith and Esralew, 

2010) to ensure consistency and reproducibility. Regression 

equations and flow statistics at gaging stations are integrated 

into the USGS StreamStats Web-based tool available at http://

water.usgs.gov/osw/streamstats/index.html. StreamStats allows 

users to obtain flow statistics, basin characteristics, and other 

information for user-selected stream locations. The user can 

‘point and click’ on a stream location or a GIS-based interactive map of Oklahoma and StreamStats will delineate the 

drainage-basin upstream from the selected location, compute basin characteristics, and compute flow statistics at the 

ungaged stream locations by using regression estimates (Smith 

and Esralew, 2010). 

Selection of the final characteristics were based on several factors including ease of measurement of the characteristic, coefficient of determination (R2

), Mallow’s Cp statistic, 

multicollinearity, and statistical significance (p-value <0.05) of 

the independent variables. Multicollinearity among the independent variables was assessed by the variance inflation factor 

(VIF) that describes correlation among independent variables. 

Of the possible basin characteristics used in the regression 

analysis, contributing drainage-basin area (CONTDA), mean 

annual precipitation (PRECIP), and main channel 10-85 slope 

(CSL10_85fm) were selected as the most appropriate independent variables for the regression analyses. CONTDA, PRECIP, 

and CSL10_85fm short names were selected to be consistent 

with StreamStats terminology.

The contributing drainage-basin area can be defined by 

a point on a stream to which all areas in the basin contribute 

runoff. The StreamStats application takes a user-defined outlet 

on a stream and delineates the drainage basin of the stream at 

that location. The basin outlet and delineated basin are used as 

the templates for estimating basin characteristics. The contributing drainage areas calculated by using StreamStats were 

compared to previously published drainage areas for those 
4 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

streams with gaging stations. The drainage areas were within 2 

percent of each other in 95 percent of cases. 

Mean-annual precipitation proved to be an influential 

independent variable in past analyses (Sauer, 1974a; Thomas 

and Corley, 1977; Tortorelli and Bergman, 1985; Tortorelli, 

1997). Mean-annual precipitation data over the drainage basin 

for the period 1971 to 2000 (PRISM Climate Group, 2008), 

computed by using an area-weighted method, were used to 

define a point estimate of mean-annual precipitation for a 

streamflow gage.

The Oklahoma StreamStats application was used to 

compute 10–85 channel slope, which is defined as the difference in elevation between points at 10 and 85 percent of the 

stream length starting from the outlet and along the longest 

flow path (also referred to as main-channel length). StreamStats computes the longest flow path from the USGS National 

Hydrography Dataset (NHD) and the corresponding elevations 

by using a Digital Elevation Model (DEM) from the USGS 

National Elevation Dataset (NED, U.S. Geological Survey, 

2006). The automated slope computation procedures used in 

StreamStats are similar to the manual computation procedures 

used by Tortorelli (1997), but generally are more precise 

because the automated slope computations are performed 

exclusively on 1:24,000-scale data (Smith and Esralew, U.S. 

Geological Survey, written commun., 2010) but previous 

methods used slope computations at different scales. The computed slope is reported in units of feet per mile (ft/mi).

Estimate of Magnitude and Frequency 

of Peak Streamflows at StreamflowGaging Stations on Unregulated 

Streams

This section describes the procedures applied to estimate 

peak streamflow at specific frequencies for gaging stations on 

unregulated streams.

Flood magnitude and frequency can be estimated for a 

specific gaging station by analysis of peak annual streamflow 

at that gaging station. These estimates, in the past, have been 

reported in terms of a T-year flood (for example, 100-year 

flood) based on the recurrence interval for that flood. The 

terminology associated with flood-frequency estimates has 

shifted away from the T-year recurrence interval flood to the 

P-percent chance exceedance flood. T-year recurrence intervals with corresponding annual exceedance probabilities and 

P-percent chance exceedances are shown in table 3. Throughout the remaining sections of this report the P-percent chance 

exceedance terminology will be used to describe peak-streamflow frequency estimates.

Peak Streamflow Frequency

The IACWD provides a standard procedure for peakstreamflow frequency estimate, U.S. Geological Survey Bulletin 17B, that involves a standard frequency distribution, the 

log-Pearson Type III (LPIII) (Interagency Advisory Committee on Water Data, 1982). Systematically collected and historic 

peak streamflows are fit to the LPIII distribution. The asymmetry in the shape of the distribution is defined by a skew 

coefficient that is used in the estimate procedure. Estimates of 

the P-percent chance exceedance flows can be computed by 

the following equation:

logQx = X + KS, (1)

where

Qx is the P-percent chance exceedance flow, in 

cubic feet per second;

X is the mean of the logarithms of the annual 

peak flows;

K is a factor based on the skew coefficient and 

the given percent chance exceedance, 

which can be obtained from appendix 3 in 

U.S. Geological Survey Bulletin 17B; and

S is the standard deviation of the logarithms 

(base 10) of the annual peak-streamflows 

that is a measure of the degree of variation 

of the annual log of peak-streamflow about 

the mean log peak-streamflow.

Because of variation in the climatic and physiographic 

characteristics in Oklahoma and the bordering areas, the LPIII 

distribution does not always adequately define a suitable 

distribution of peak-streamflow values (Tortorelli, 1997). To 

reduce errors in peak-streamflow frequency resulting from 

a poor LPIII fit, estimates of peak-streamflow frequency for 

the streamflow-gaging stations evaluated in this report were 

adjusted based on historic flood information (where available), 

low-outlier thresholds, and skew coefficients, and IACWD 

guidelines. 

The USGS computer program PEAKFQWin version 

5.2.0 was used to compute flood-frequency estimates for 

the 231 streamflow-gaging stations on unregulated streams 

evaluated in this report. PEAKFQWin automates many of 

the analytical procedures recommended in U.S. Geological 

Survey Bulletin 17B (Interagency Advisory Committee on 

Water Data, 1982). The PEAKFQWin program and associated 

documentation can be downloaded from the Web at http://

water.usgs.gov/software/PeakFQ/. Peak-streamflow frequency 

estimates of the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent 

chance exceedances are given in table 1 for each streamflowgaging station used in this report.
100°

98°

36°

100°

98°

96°

96°

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TEXAS

KANSAS

NE W ME X IC O

TEXAS

ARKANSAS

MISSOURI

COLORADO

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Beaver R iv er

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C aney

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R iv er

North C anadian

C anadian

River

Washita

Deep Fork

R ed

R iv er

0 25 50 75 100 MILES

0 25 50 75 100 KILOMETERS

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231 230

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105 104

102101

100

177

87

75

188

103

EXPLANATION

# Streamflow-gaging station

Number corresponds to table 1

State border

Study area boundary

147

Streams

Albers Equal-Area Conic Projection.

North American Datum 1983.

Figure 1. Location of streamflow-gaging stations with unregulated periods of record used in report.
6 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma
Estimate of Magnitude and Frequency of Peak Streamflows at Streamflow-Gaging Stations on Unregulated Streams 7

Table 2. Basin characteristics investigated as possible independent variables for regressions used to estimate peak-streamflows for unregulated streams.(NED, National Elevation Dataset; NHD, National Hydrography Dataset; WBD, Watershed Boundary Dataset; PRISM, Parameter-elevation Regressions on Independent Slopes Model; FWRS, Floodwater Retarding Structures)

Characteristic Name Units Method Source data

Contributing Drainage Area(CONTDA)

Square miles ArcHydro method NED 10-meter resolution elevation data (http://seamless.usgs.gov/index.php), 

high resolution NHD (http://nhdgeo.usgs.gov/viewer/htm, accessed July 2006) and WBD (source: http://www.ncgc.nrcs.usda.gov/products/datasets/watershed/, accessed July 2006)

Mean annual precipitation1971–2000 (PRECIP)

Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008

Main-channel slope(CSL10_85_fm)

Feet per mile ArcHydro method of computing stream 

slope from points 10 and 85 percent of the distance from the site to the basin divide, along the main channel

NED 10-meter resolution elevation data (http://seamless.usgs.gov/index.php), 

and high resolution NHD (http://nhdgeo.usgs.gov/viewer.htm, accessed July 2006)

Drainage area behind FWRS Square miles ArcHydro method NED 10-meter resolution elevation data (http://seamless.usgs.gov/index.php), 

high resolution NHD (http://nhdgeo.usgs.gov/viewer/htm, accessed July 2006) and WBD (source: http://www.ncgc.nrcs.usda.gov/products/datasets/watershed/, accessed July 2006)

Forest canopy Percent Area-weighted average National Land-Cover Dataset 2001, 30-meter resolution data layer from the 

Multi-Resolution Land Characterisitics Consortium, accessed August 2001

Impervious cover Percent Area-weighted average National Land-Cover Dataset 2001, 30-meter resolution data layer from the 

Multi-Resolution Land Characterisitics Consortium, accessed August 2001

Mean annual precipitation at 

basin outlet

Inches Point extract PRISM (http://www.prism.oregonstate.edu/, accessed July 2008)

Elevation at basin outlet Feet Point extract NED 10-meter resolution elevation data (http://seamless.usgs.gov/index.php), 

and high resolution NHD (http://nhdgeo.usgs.gov/viewer.htm, accessed July 2006)

Soil permeability Inches per hour Area-weighted average State Soil Geographic (STATSGO) Data (http://www.ncgc.nrcs.udsa.gov/products/datasets/statsgo/, accessed July 2008)
8 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma Table 2. Basin characteristics investigated as possible independent variables for regressions used to estimate peak-streamflows for unregulated streams. (NED, National Elevation Dataset; NHD, National Hydrography Dataset; WBD, Watershed Boundary Dataset; PRISM, Parameter-elevation Regressions on Independent Slopes Model; FWRS, Floodwater Retarding Structures) Characteristic Name Units Method Source data Mean precipitation June- October Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean precipitation November- May Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean annual precipitation 1961-1990 Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean June precipitation Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean May precipitation Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean February precipitation Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean March precipitation Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean April precipitation Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean December precipitation Inches Area-weighted average PRISM (http://www.prism.oregonstate.edu/, accessed July 2008) Mean basin elevation Feet Area-weighted average NED 10-meter resolution elevation data (http://seamless.usgs.gov/index.php) Mean basin slope Feet per mile Area-weighted average Local slope derived from NED 10-meter resolution elevation data (http:// seamless.usgs.gov/index.php)
Estimate of Magnitude and Frequency of Peak Streamflows at Ungaged Sites on Unregulated Streams 9

Low-Outlier Thresholds

Determining low-outlier thresholds are necessary in 

peak-streamflow frequency analyses because of the fact that 

these low outliers have a strong influence on the skew coefficient. Past flood frequency analyses for Oklahoma have shown 

that extremely small annual peak-streamflow discharges (low 

outliers) occasionally happen. The effects of low outliers can 

been seen visually by fitting the LPIII distribution, but the 

U.S. Geological Survey Bulletin 17B method specifies a mathematical low-outlier threshold based on skew and standard 

deviation of the peak-streamflow time series. The fit of the 

LPIII distribution to the data needs to adjusted to account for 

low outliers because these outliers can substantially affect the 

distribution curve. All peak-streamflow discharges (including 

zero) below the threshold are excluded from the fitting of the 

LPIII distribution. The computer program PEAKFQWin was 

used to identify these low outliers.

PEAKFQWin, which incorporates the IACWD guidelines, provides a procedure for low-outlier threshold selection 

based on a 90-percent confidence interval for a standard distribution. However, the IACWD procedure may not always produce appropriate low-outlier thresholds for streamflow-gaging 

stations. Therefore, the preliminary LPIII distribution for each 

streamflow-gaging station was then visually inspected and 

some streamflow-gaging stations were assigned a low-outlier 

threshold based on that inspection. The low-outlier thresholds 

for appropriate streamflow-gaging stations are listed in table 1.

Weighted Skew

Determining skew coefficients is the next step in peakstreamflow frequency analyses. The skew coefficient measures 

the asymmetry of the probability distribution of a set of annual 

peaks and is difficult to estimate reliably for streamflowgaging stations with short periods of record. Therefore, the 

IACWD recommends applying a weighted skew coefficient 

to the LPIII distribution. This skew coefficient is calculated 

by weighting the skew coefficient computed from the peakstreamflow data at the gaging station (station skew) and a 

generalized skew coefficient representative of the surrounding 

area (fig. 2). The weighted skew coefficient is based on the 

inverse of the respective mean square errors for each of the 

two skew coefficients (Interagency Advisory Committee on 

Water Data, 1982).

The weighted skew coefficient generally is preferred for 

peak-streamflow frequency estimates. The station skew and 

weighted skew are listed in table 1 (back of report) for each 

gaging station. Weighted skew coefficients (station skews 

weighted with generalized skews from Lewis and Esralew, 

(2009)) were used for all streamflow-gaging stations in this 

report.

Generalized-Skew Analysis

A nationwide generalized-skew map is provided in 

U.S. Geological Survey Bulletin 17B (Interagency Advisory 

Committee on Water Data, 1982). However, a more accurate 

generalized skew map was needed for Oklahoma instead of 

a map prepared at a national scale. Previously, a report of 

generalized skew coefficients was done for Oklahoma (Lewis 

and Esralew, 2009) that used adjusted station skew coefficients 

from streamflow-gaging stations with at least 20 years of 

peak-streamflow data and drainage basins greater than 10 mi2

and less than 2,510 mi2 with streamflow data through 2007. 

The generalized skew map for Oklahoma was created 

in GIS by using a point interpolation (pointintrp) method and 

contour smoothing functions (Lewis and Esralew, 2009). The 

streamflow-gaging stations used to develop the Oklahoma 

generalized skew map are noted in table 1 with footnote 7. The 

generalized skew values for all streamflow-gaging stations 

were obtained by using GIS.

Estimate of Magnitude and Frequency 

of Peak Streamflows at Ungaged Sites 

on Unregulated Streams

Estimates of magnitude and frequency of peak streamflows commonly are needed at ungaged sites. These estimates 

can be achieved by defining regression equations that relate 

peak discharges of selected frequencies at streamflow-gaging 

stations to basin characteristics. Multiple-linear regression analysis was used to establish the statistical relations 

between one dependent variable (peak streamflow) and one 

or more independent variables (basin characteristics). The 

50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent chance exceedance 

flows, respectively, were used as dependent variables, and the 

selected basin characteristics were used as independent variables. Logarithmic transformations of the dependent and independent variables were used to increase the linearity between 

Table 3. T-year recurrence intervals with corresponding 

annual exceedance probabilities and P-percent chance 

exceedances for peak-streamflow frequency estimates.

T-year recurrence 

interval

Annual exceedance probabilityP-percent chance 

exceedance

2 0.5 50

5 0.2 20

10 0.1 10

25 0.04 4

50 0.02 2

100 0.01 1

500 0.002 0.2
10 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

the dependent and independent variables. The general steps 

followed in this report to develop regression equations are:

1. Basin characteristics were screened to identify possible explanatory variables used in the regression 

equations.

2. Peak-streamflow percent chance exceedance flows 

and basin characteristics were log transformed to 

obtain better linear relations between the dependent 

variables and the independent variables.

3. Stepwise regression analysis was used to assess the 

most appropriate basin characteristics.

4. Preliminary multiple linear regression models were 

formed by using ordinary least squares (OLS). 

5. Residual plots were examined, and leverage and 

influence statistics were computed and plotted to 

identify data observations that may substantially 

influence regression results. Outliers were removed 

based on this procedure.

6. Iterations of steps 2–5 were completed, for OLS 

regression models, in an attempt to reduce the number of independent variables.

7. Weighting procedures were developed.

8. Significance of coefficients in the weighted least 

squares (WLS) regression model was checked along 

with residuals, and streamflow-gaging stations with 

large leverage and influence were identified.

9. From the same dataset, a generalized least squares 

(GLS) regression model was formed by using the 

USGS computer program weighted-multiple-linear 

regression WREG v.1 (Eng and others, 2009).

OLS regression analysis was performed on streamflow 

data from the 231 streamflow-gaging stations to determine 

if regression equations for separate hydrologic regions in the 

state was warranted. A similar check was performed on the 

GLS models. No geographic patterns were evident after the 

residuals (differences between estimated peak streamflow and 

measured peak streamflow) were examined (fig. 3).

Regression Analysis

Previous regression analysis of peak-streamflow frequency for Oklahoma (Tortorelli, 1997) used WLS procedures. 

In this report OLS, WLS, and GLS regression procedures were 

used. WLS regression was used to test the statistical significance (p<0.05) of possible independent variables (Ries and 

Dillow, 2006). The GLS method was then used to determine 

the final regression equations. Stedinger and Tasker (1985) 

showed that the GLS method can be used to assign weights 

to the streamflow-gaging station data used in the regression 

analysis to adjust not only for differences in record length, as 

in WLS, but also for cross-correlation of the annual time series 

on which the peak-flow statistics for the gaging station data 

are based, and for spatial correlation among the gaging station 

data. Annual peak flows of basins are cross-correlated because 

a single storm can cause the annual peak in several basins. 

One advantage of using GLS is that cross-correlation among 

basins is taken into account.

GLS regression entails weighting each basin in accordance with the variance (time-sampling error) and spatialcorrelation structure of the streamflow characteristic (annual 

peak-discharge among streamflow-gaging stations) (Lumia 

and others, 2006). The residual mean square error for ungaged 

sites is portioned into regression model error (error in assuming an incomplete regression form) and sampling error (timeand spatial-sampling errors). When using GLS, the variance of 

prediction (and the square root, the standard error of prediction) is the sum of the model error variance and an additional 

term. This additional term has been called a sampling error 

variance (of the coefficients), but is different from the timesampling and spatial-sampling error. 

The GLS regression analysis used in this report incorporated logarithmic (base 10) transformations of the streamflow 

(annual peak discharges) and basin characteristics to obtain 

a constant variance of the residuals about the regression line, 

and to make the relation between the dependent variable 

(peak-discharge) and independent variables (basin characteristics) acceptable for linear least-squares regression procedures. 

The multiple-regression equations based on logarithmic transformation of the variables has the following form:

Log10Y = b0 + b1log10X1+b2log10X2+......+bn log10 Xn, (2)

and the following form after taking antilogs,

Y = 10b0 (X1

b1) (X2b2)......(Xnbn) (3)

where

Y = dependent variable (peak-discharge for

selected exceedance),

 bo to bn = regression model coefficient estimate

by using GLS procedures, and

 X1 to Xn = independent variables (basin

 characteristics).

The USGS computer program WREG applying OLS, 

WLS, and GLS approaches was used to estimate the regression parameters (Eng and others, 2009). WREG allows for 

selection between the three approaches and also for transformations on the dependent and independent variables. The 

multiple performance metrics from the WREG program were 

used to identify possible problem sites used in the regression. 

The residuals metric is used to show differences between 

estimated and measured flow at various flow magnitudes. 

Residuals randomly distributed around zero are preferred. The 

leverage metric is used to measure how distant the values of 
0.0

+0.1

+0

+

.2

0.3

-0.1

+0.4

-0.2

-0.3

+0.5

+0.6

-0.4

+0.7

-0.1

-0.4

0.0

-0.3

+0.2

+0.3

0.0

-0.1

-0.3

+0.5

+

0.1

-0.2

-0.2

-0.2

-0.2

+0.1

-0.3

+0.2

0.0 -0.2

-0.1

+0.4

0.0

+0.1

-0.3

+

0.5

100°

98°

102°

36°

100°

98°

96°

96°

36°

34°

NE W ME X IC O

TEXAS

TEXAS

ARKANSAS

MISSOURI

KANSAS COLORADO

Beaver R iv er

C imarron

R iver

Fork

Salt

R iver

A rkansas

C aney

R iver

R iver Verdigris

Neosho

R iver

R iv er

North

C anadian

C anadian

River

R iv er

R ed

Washita

R iv er

Deep Fork

R ed

R iv er

0 25 50 75 100 MILES

0 25 50 75 100 KILOMETERS

EXPLANATION

Line of equal generalized skew

coefficient of logarithms of annual

maximum streamflow , based on

streamflow-gaging station records 

through 2007 greater than or equal 

to 20 years in length. Basin drainage

area between 10 and 2,510 square

miles. Interval is 0.1.

State border

Oklahoma county border

Streams

Albers Equal-Area Conic Projection.

North American Datum 1983.

0.0

Figure 2. Generalized skew coefficients of logarithms of annual maximum streamflow for Oklahoma streams with drainage area less than than or equal to 2,510 square miles.
12 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma
Estimate of Magnitude and Frequency of Peak Streamflows at Ungaged Sites on Unregulated Streams 13

0

0

0

0.3

0.2 0.1

0.08

0.15

0.19 0.11 0.19 0.07

-0.2 0.22

0.01

0.12

0.11

-0.2

0.06

0.24

0.18

0.11

0.16

0.06

0.05

0.19

0.22 0.24

0.04

0.36

0.32

0.13

0.32

0.05

0.22

0.02

0.52

0.17

0.07

0.11

0.12

0.37

0.04

0.07 0.24

0.51 -0.7

0.14

0.12 0.01

0.07

0.08

0.03

0.28

0.22

0.04

-0.1

0.05

-0.2

0.28

0.03

0.19

0.36

0.17

0.08 0.01

0.12

0.24

0.07

0.050.04

0.23

0.08 0.24

0.11

0.02

0.05

0.12

0.05

0.11

0.05

0.06

-0.2

0.52

0.15

0.38

0.220.01

0.09

0.04 0.06

0.25

0.37

0.15

0.15

0.02

-0.1 0.05

0.13

0.01

0.14

0.14

0.37

-0.1

0.37 0.16

0.15

0.14 0.09

0.23

0.23 0.05

0.15

0.07

0.06 0.14

0.03

0.29

-0.31

-0.04

-0.31 -0.21

-0.09

-0.18

-0.06

-0.16

-0.07

-0.28

-0.43

-0.12

-0.09

-0.12

-0.07

-0.08

-0.16

-0.03

-0.11 -0.02

-0.05

-0.22

-0.14

-0.16

-0.32 -0.01

-0.16

-0.28

-0.09

-0.01

-0.78

-0.19

-0.22

-0.44

-0.19

-0.25

-0.16

-0.12

-0.23

-0.26

-0.24

-0.19

-0.04 -0.04

-0.03

-0.14

-0.05 -0.35

-0.05 -0.11 -0.02

-0.03

-0.03 -0.06

-0.05

-0.11

-0.28

-0.22 -0.09

-0.12

-0.01

-0.16

-0.41

-0.35

-0.13

-0.16

-0.12

-0.12

-0.19 -0.02

-0.24

-0.05

-0.13

-0.05

-0.08

-0.24

-0.04

-0.38

-0.05

-0.08

-0.27

-0.23

-0.34

-0.17

-0.05

-0.11

-0.04

-0.26 -0.05

-0.08

-0.02

-0.12

-0.15

TEXAS

A R K A NSA S

MISSOURI

OKLAHOMA

KANSAS

COLORADO

NE W ME X IC O

EXPLANATION

State border

OLS model regression residual

Albers Equal-Area Conic Projection.

North American Datum 1983.

0.12

Residuals from the 10-percent chance exceedance ordinary least squares (OLS) regression model for each site. Figure 3.
14 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

independent variables at one streamflow-gaging station are 

from the centroid of values of the same variables at all other 

streamflow-gaging stations. The influence metric indicates 

whether a streamflow-gaging station had a large influence on 

the estimated regression parameter values (Eng and others, 

2009). Streamflow-gaging stations, identified as having large 

influence and leverage, were not necessarily removed because 

the gaging station may have been the only gaging station in 

a particular area or because removal did not alter the regression. After examining the leverage and influence plots, the 

following sites were removed: Dry Cimarron River near Guy, 

New Mexico, (07153500), Fly Creek near Faulkner, Kansas, 

(07184600), Lelia Lake Creek below Bell Creek near Hedley, Texas, (07299890), Salt Fork Red River near Wellington, Texas, (07300000), and Sweetwater Creek near Kelton, 

Texas, (07301410). Caution is needed when estimating peak 

streamflows in areas near the streamflow-gaging stations listed 

because of irrigation practices. The final performance metrics 

for the 10-percent chance exceedance regression model are 

shown in figure 4.

Regression Equations

Regression equations were developed for use in estimating peak streamflows associated with 50-, 20-, 10-, 4-, 2-, 1-, 

and 0.2-percent chance exceedances. Combinations of independent variables that did not have substantially large leverage 

or influence, and multicollinearity that also provided the lowest estimated error for each percent exceedance, were selected 

for inclusion in the final regression equations. Contributing 

drainage area, mean-annual precipitation, and main-channel 

slope were the most appropriate basin characteristics used to 

estimate peak-streamflow frequency on unregulated streams. 

The three characteristics used in the regression equations are 

listed in table 1 for each streamflow-gaging station used in the 

analysis.

The following equations were computed for unregulated 

streams from the results of the GLS regression analysis in 

WREG and are listed according to percent chance exceedance.

Q50% = 0.064 (CONTDA)0.66 (PRECIP)2.06 (CSL10_85fm)0.16 (4)

Q 0.66 1.63 0.19 

20% = 0.574 (CONTDA) (PRECIP) (CSL10_85fm) (5)

Q10% = 1.74 (CONTDA)0.66 (PRECIP)1.42 (CSL10_85fm)0.21 (6)

Q4% = 4.90 (CONTDA)0.66 (PRECIP)1.24 (CSL10_85fm)0.23 (7)

Q2% = 13.18 (CONTDA)0.66 (PRECIP)1.05 (CSL10_85fm)0.21 (8)

Figure 4. Performance metrics from computer program WREG 

(A) residuals, (B) leverage, and (C) influence for a 10-percent 

chance exceedance peak-streamflow regression model.

2 2.5 3 3.5 4 4.5 5 -0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Estimated Flow Characteristic (log base 10)

Residual (log base 10)

Residuals versus Estimated Flow Characteristics

A.

0 50 100 150 200 250

Observation

-0.

0.

0.

0.

0.

0.

0.

0.

Leverage Value

01

0

01

02

03

04

05

06

07

Leverage Values versus Observations

0 50 100 150 200 250 0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

Observation

Influence Value

Influence Values versus Observations

C.

B.
Estimate of Magnitude and Frequency of Peak Streamflows at Ungaged Sites on Unregulated Streams 15

Q1% = 26.9 (CONTDA)0.65 (PRECIP)0.92 (CSL10_85fm)0.21 (9)

Q0.2% = 126 (CONTDA)0.64 (PRECIP)0.64 (CSL10-85fm)0.19 (10)

where

Q50%, Q20%,......, and Q0.2% = the peakstreamflows with percent chance 

exceedances of 50 percent, 20 percent,

......, and 0.2 percent, in cubic feet per 

second;

CONTDA = the contributing drainage area, in square 

miles;

PRECIP mean-annual precipitation, the point 

mean-annual precipitation from the period 

1971-2000;

CSL10_85fm = the main-channel slope, measured at the 

points that are 10 percent and 85 percent 

upstream from the station or ungaged site, 

on the main-channel length between the 

study site and the drainage divide, in feet 

per mile.

Accuracy and Limitations

Regression equations are statistical models in which the 

results are inexact. Regression equations needs to be applied 

within the limits of the data with the understanding that the 

results are best-fit estimates with associated variances. Three 

measures that can be used to assess the accuracy of a regression peak-discharge estimate are: the adjusted coefficient of 

determination (R2), the average standard error of prediction, 

and the standard model error.

Residual errors in the model (differences between 

estimated and measured values) are examined to determine 

variables that optimize the accuracy of a regression equation, 

which depends on the model and sampling error. Model errors 

represent errors that result from an incomplete model. These 

errors are described by the standard model error. Sampling 

errors result from the limitations on the number of years of 

streamflow-gaging station record, the assumption of gaging 

station record being representative of long-term streamflow, 

and from hydrologic conditions during the particular period 

represented by samples. Although the use of GLS methodology allows separation of the sampling error variance from the 

total mean square error of the residuals, the GLS methodology 

does not prevent this type of error. 

R2 is the proportion of the variability in the dependent 

variable (site peak discharge, Qx(s)) that is accounted for by 

the independent variables (the basin characteristics, CONTDA, PRECIP, and CSL10_85fm) — the larger the R2

 the 

better the fit of the model — with a value of 1.00 indicating 

that 100 percent of the variability in the dependent variable is 

accounted for by the independent variables (Helsel and Hirsch, 

2002). Griffis and Stedinger (2007) state that R2

pseudo is a more 

appropriate performance metric for WLS and GLS regressions. R2

pseudo is based on the variability in the dependent variable explained by the regression, after removing the effect of 

the time-sampling error (Eng and others, 2009). Table 4 lists 

all R2

pseudo values for each of the percent exceedance chance 

peak streamflows. 

The standard error of prediction is derived from the sum 

of the model error variance and the sampling error of the 

coefficients, and is a measure of the expected accuracy of the 

regression estimates for the selected percent chance exceedances. The standard model error, which depends on the number and predictive power of the independent variables, measures the ability of these variables to estimate peak-streamflow 

frequency from the site records that were used to develop the 

equation. The WREG program reports average standard error 

of prediction (Sp), standard model error, and R2

pseudo in the 

model output (fig. 5). The average standard error of prediction 

ranges from 32 to 47 percent and the standard model error 

ranges from 31 to 46 percent for the percent chance exceedances computed (table 4).

Equivalent years of record, proposed by Hardison (1971), 

is another way of measuring the reliability of peak-streamflow 

regression equations. Equivalent years of record, which is an 

approximation, is the number of actual years of record needed 

to provide estimates equal in accuracy to those estimates 

computed by the regression equations. The accuracy of the 

regression equations for unregulated streams, expressed as 

equivalent years, is summarized in table 4.

The regression equations developed in this report are 

applicable to streams in Oklahoma with drainage areas less 

than 2,510 mi2 that are not substantially affected by regulation. 

The equations are intended for use on unregulated streams 

in Oklahoma and should not be used outside the range of the 

independent variables used in the analysis:

CONTDA

equal to or greater 

than 0.100 square 

mile

and less than or 

equal to 2,510 

square miles

PRECIP equal to or greater 

than 16.6 inches

and less than or 

equal to 62.1 

inches

CSL10_85fm

equal to or greater 

than 1.98 foot per 

mile

and less than or 

equal to 342 feet 

per mile

The same cautions are applicable for estimating flows 

on streams regulated with floodwater retarding structures as 

with unregulated drainage basin peak-streamflow estimates. 

The adjusted equations described in “Adjustment for Ungaged 

Sites on Urban Streams” can be used when the percent of 

regulated drainage area is not greater than 86 percent of the 

basin, which is the upper limit of the range of regulated data 

used to check the validity of the adjustment (Tortorelli, 1997; 
16 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Tortorelli and Bergman, 1985). The adjusted equations are 

intended for use on parts of a basin with NRCS floodwater 

retarding structures and not with any other floodwater retarding structures. When the regulated drainage area is greater 

than 86 percent of the basin, the flow routing techniques in 

Chow and others (1988) may be used.

Application of Methods

This section presents methods for use of the regression 

equations to make a weighted peak-streamflow estimate for 

streamflow-gaging station data on unregulated streams with a 

drainage area less than 2,510 mi2 in Oklahoma, and to use this 

result to make an estimate for a nearby ungaged site on the 

same stream. For ungaged sites on urban streams and ungaged 

sites on streams regulated by floodwater retarding structures, an adjustment of the statewide regression equations for 

unregulated stream can be used to estimate peak-streamflow 

frequency.

Estimate for a Streamflow-Gaging Station

Interagency Advisory Committee on Water Data (1982) 

recommends that peak-streamflow frequency estimates for 

streamflow-gaging station sites on unregulated streams are 

combinations of streamflow-gaging station data and regression 

estimates. The estimates weighted by years of record are considered to be more reliable than either the regression estimate 

or gaging-station data when making estimates of peak-streamflow frequency relations at gaging-station sites (Sauer, 1974a; 

Thomas and Corley, 1977). The equivalent years of record 

concept is used to combine gaging-station estimates with 

regression estimates to obtain weighted estimates of peakstreamflow at a gaging station site. 

The locations of the streamflow-gaging stations with 

unregulated periods of record used in the report are shown in 

figure 1. Figure 1 is used to obtain the gaging-station number 

of the gaging station of interest. This number is used to obtain 

the appropriate station peak-streamflow (Qx(s)), for percent 

chance exceedance x, from table 1. The streamflow-gaging 

stations that have unregulated periods of record, but are now 

regulated, are noted with footnote 8 in table 1. If the gaging 

station of interest is still unregulated, then this peak-streamflow is used with the regression estimate Qx(r) in a weighting 

procedure described by Sauer (1974a) and Thomas and Corley 

(1977):

Qx(w) = [Qx(s) (N) + Qx(r) (E)] / (N + E) (11)

where

Qx(w)= the weighted estimate of peak

streamflow, for percent chance

exceedance x, in cubic feet per

second,

Qx(s) = the gaging station estimate of peak

streamflow, for percent chance

exceedance x (table 1), in cubic feet

per second,

Qx(r) = the regression estimate of peak

streamflow, for percent chance

exceedance x (equations 4-10), in

cubic feet per second,

N = number of actual years of record at

the gaging station site (table 1),

E = equivalent years of record for percent

chance exceedance x (table 4).

Example

The following example illustrates how the method 

described is used to determine weighted peak-streamflow 

estimates for a streamflow-gaging station on an unregulated 

stream. The example computation is for Kiamichi River near 

Big Cedar, Okla., (07335700) and the results are presented in 

table 5.

The column Qx(s) in table 5 indicates the computed peakstreamflow frequency relations derived from the 43 years of 

record (column N) at gaging station 07335700 (site 206, table 

1). The values in the column labeled Qx(r) were estimated by 

using equations 4–10 and the following basin characteristics 

(table 1):

CONTDA = 39.6 square miles

 PRECIP = 62.1 inches

CSL10_85fm = 54.9 feet per mile

The Qx(r) estimates computed from equations 4–10 are 

presented in table 5. The weighted estimates, Qx(w) were computed from equation 11 by using appropriate years of E from 

table 4.

Table 4. Accuracy of peak-streamflows estimated for 

unregulated streams in Oklahoma.

[R2; coefficient of determination; %, percent]

Percent

chance

exceedance

R2

pseudo

Sp (average

standard error

of prediction,

in %)

Standard

model

error (%)

50 92.36 46.74 45.89

20 94.98 35.11 34.26

10 95.70 31.80 30.88

4 94.88 34.66 32.98

2 94.98 33.98 32.86

1 94.51 35.72 34.52

0.2 92.36 43.26 41.87
Application of Methods 17

Table 5. Weighted peak-streamflow frequency estimates for Kiamichi River near Big Cedar, Oklahoma (07335700)

[ft3/s, cubic feet per second; %, percent]

Percent chance Q 1 2

x(s) N Q 3x(r) E4 Q 5x(w)

exceedance (%) (ft3

/s) (years) (ft3/s) (years) (ft3/s)

50 9,200 43 6,800 2 9,090

20 15,100 43 11,700 5 14,700

10 19,300 43 16,100 8 18,800

4 24,800 43 23,300 9 24,500

2 29,000 43 26,400 11 28,500

1 33,300 43 30,400 12 32,700

0.2 43,400 43 39,900 12 42,600

1

Station estimate of peak discharge, for percent chance exceedance x, table 1.

2

 Number of actual years of streamflow record at streamflow-gaging station, table 1.

3

 Regression estimate of peak discharge, for percent chance exceedance x, equations 4-10.

4

 Equivalent years of unregulated streamflow record for percent chance exceedance x, table 4.

5

 Weighted estimate of peak discharge, for percent chance exceedance x, equation 11.

Figure 5. WREG output for the 

10-percent chance exceedance peakstreamflow regression model by using 

the generalized least squares (GLS) 

method, showing average standard 

error of prediction (Sp %), the pseudo 

coefficient of determination (Pseudo R2

), 

and standard model error, in percent (%). 

SPL1085FM is CSL10_85fm (main-channel 

slope), CONTDA is contributing drainage 

area, and PRECIP is mean-annual 

precipitation used in regression equations 

(4–10).
Application of Methods 18

Estimate for an Ungaged Site near a 

Streamflow-Gaging Station

The combined use of the regression equations and 

the gaging-station data can yield an estimate of the peakstreamflow magnitude and frequency for ungaged sites near 

streamflow-gaging stations on the same stream. The following 

method is indicated for use if the ungaged site has a drainage area within 50 percent of the drainage area of the gaging 

station (Sauer, 1974a). The ratio, Rw, represents the correction 

needed to adjust the regression estimate, Qx(r), to the weighted 

estimate, Qx(w), at the streamflow-gaging station:

Qx(w) R w

  (12) Qx(r)

where

 Qx(w) is the weighted estimate of peak

 streamflow at the gaging-station

 site, for percent chance exceedance

 x (equation 11), in cubic feet per

 second, and

 Qx(r) is the regression estimate of peak

 streamflow at the gaging-station

 site, for percent chance exceedance

 x (equations 4–10), in cubic feet 

 per second. 

 Rw is then used to determine the correction

 factor Rc for the ungaged site.

 The following equation derived

 by Sauer (1974a) gives the

 correction factor Rc

, for an ungaged

 site that is near a gaging-station site

 on the same stream, 

∆CONTDA R c

 = R w − ( R w1 .0 0 ) (13) 

0.5CONTDAg

where 

 ΔCONTDA is the difference between the

 drainage areas of the

 gaging-station site and 

 ungaged site, and

 CONTDAg

 is the drainage area of the gaging- 

 station site. 

The regression estimate, Qx(r), for the ungaged site is 

multiplied by the correction factor Rc to improve the estimate 

by using nearby gaging-station data. If the drainage area of the 

ungaged site is within 50 percent of two gaging-station sites, 

the peak-streamflow frequency estimate for the ungaged site 

can be made by interpolation of the weighted station peakstreamflow (Qx(w)) for each gaging-station site. Interpolation is 

on the basis of drainage area. If the peak streamflows for the 

ungaged site are affected by urbanization, the peak streamflows need to be modified by methods given in the following 

section “Adjustment for Ungaged Sites on Urban Streams”. If 

the drainage area of the ungaged site is 50 percent more than 

or less than that of the gaging-station site (that is, ΔCONTDA/

CONTDAg

 is greater than 0.5), equation 11 is not used and 

the regression equations 4–10 are used without adjustment. 

Example

The following example illustrates how to adjust a 

weighted estimate calculated for a streamflow-gaging-station 

site on an unregulated stream for an ungaged site on the same 

stream. Assume an estimate of the 1 percent chance exceedance flood is needed at an ungaged site upstream from gaging 

station 07335700 on the Kiamichi River (table 5). Assume the 

following hypothetical basin characteristics:

 CONTDA = 20.5 square miles

 PRECIP = 54.0 inches

 CSL10_85fm = 42.0 feet per mile

The following data and calculations are needed to estimate Q1% at the ungaged site.

 Gaging station site, 07335700, Kiamichi River near Big 

Cedar

 CONTDAg

 = 39.6 square miles

 Q1%(r) = 30,400 cubic feet per second, 

 from equation 9, table 5

 Q1%(w) = 32,700 cubic feet per second, 

 from equation 11, table 5

 Rw = Q1%(w)/ Q1%(r) = 1.08

Ungaged site on Kiamichi River

 CONTDA = 20.5 square miles

 Q1%(r) = 16,500 cubic feet per second, from 

 equation 9

 ΔCONTDA = 19.1 square miles

 ΔCONTDA/CONTDAg = 0.48 (Because 0.48 is less than

 0.5, Rc

 is computed from

 equation 12 and used to adjust 

 Q1%(r))

19.1 Rc =1.08− (1.08 −1.00 = 1.00

0.5(39.6)

Q1% = Q1%(r) (Rc) = 16,500 (1.00) = 16,500 cubic feet per

 second

The estimate of the 1 percent chance exceedance flood 

at the ungaged site on the Kiamichi River is a discharge of 

18 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma
Application of Methods 19

16,500 ft3/s, after the regression estimate is adjusted for the 

data for gaging station 07335700.

Adjustment for Ungaged Sites on Urban Streams

The percentage of the basin that is impervious and the 

percentage of the basin served by storm sewers is required in 

addition to the variables needed for ungaged sites on unregulated streams to estimate flood magnitude and frequency for 

ungaged sites on urban streams. The percentage of the basin 

that is impervious can be determined from the StreamStats 

web application, aerial photographs, recent USGS topographic 

maps, or field surveys. The percentage of the basin served by 

storm sewers needs to be determined from the best available 

storm sewer and drainage map. 

After the percentages of the area impervious and area 

served by storm sewers are obtained, RL, the urban adjustment 

factor, is obtained from figure 6 (Leopold, 1968). 

The urban adjustment factor, RL, is the ratio of the mean 

annual flood in urban areas to that in rural areas. The following equations computed by Sauer (1974b) can be used to 

adjust estimates from equations 4–10 to urban areas:

Q50%(u) = RL Q50%(r) (14)

Q20%(u) = 1.60 (RL-1) Q50%(r) + 0.167 (7-RL) Q20%(r) (15)

Q10%(u) = 1.87 (RL-1) Q50%(r) + 0.167 (7-RL) Q10%(r) (16)

Q4%(u) = 2.21 (RL-1) Q50%(r) + 0.167 (7-RL) Q4%(r) (17)

Q2%(u) = 2.46 (RL-1) Q50%(r) + 0.167 (7-RL) Q2%(r) (18)

Q1%(u) = 2.72 (RL-1) Q50%(r) + 0.167 (7-RL) Q1%(r) (19)

Q0.2%(u) = 3.30 (RL-1) Q50%(r) + 0.167 (7-RL) Q0.2%(r) (20)

where 

Qx(u) = the adjusted regression estimate of

peak discharge for ungaged sites

on urban streams, for percent

chance exceedance x, in cubic feet

per second,

RL= urban adjustment factor (fig. 6), and

Qx(r) = the regression estimate of peak

discharge for ungaged sites on

unregulated streams, for percent

chance exceedance x (equations

4–10), in cubic feet per second.

A nationwide seven-parameter urban adjustment equation 

set is presented in Jennings and others (1994). These equations may be compared to or used instead of the Oklahoma 

equations.

Example

This example shows how the 1 percent chance exceedance flood can be calculated for a hypothetical stream in an 

urban environment. The calculation is based on the basin 

being 50 percent impervious and that 65 percent of the basin 

is served by storm sewers. The 1 percent chance exceedance 

flood (Q1%(u)) can be estimated for this hypothetical urban site 

with the following additional basin characteristic values:

 CONTDA = 25.0 square miles

 PRECIP = 33.0 inches

 CSL10_85fm = 11.5 feet per mile

Q1%(r) = 9,080 cubic feet per second, from

equation 9 (rural areas)

Q50%(r) = 1,060 cubic feet per second, from

equation 4 (rural areas)

RL = 3.0, from figure 6

Q1%(u) = 11,800 cubic feet per second, from

equation 19 (urban areas)

The estimate of the 1 percent chance exceedance flood 

in urban areas for this ungaged watershed is a discharge of 

11,800 ft3/s. This estimate is an increase of 33 percent more 

than the 1 percent chance exceedance flood for rural areas.

Adjustment for Ungaged Sites on Streams 

Regulated by Floodwater Retarding Structures

An adjustment needs to be made when estimating peakstreamflow magnitude and frequency in basins regulated 

by floodwater retarding structures. The regression estimate 

of peak-streamflow for ungaged sites on regulated streams, 

or Fx(r), for percent chance exceedance x, can be computed 

from equations 4–10 by substituting the drainage area of the 

unregulated part of the basin or drainage area downstream 

from the floodwater retarding structures, DUANREG, for 

CONTDA. A complete discussion of the analysis can be found 

in Tortorelli and Bergman (1985). These authors indicated that 

the main-channel slope for the entire basin be used to estimate 

a conservative result (this method will result in a larger peak 

streamflow than by using main-channel slope downstream 

from floodwater retarding structures only). 

If floodwater retarding structures regulate less than 86 

percent of the basin, the following equations are used to adjust 

the regression estimate of peak-streamflow of ungaged sites on 

unregulated streams:

F50%(r) = 0.064 (DUANREG)0.66 (PRECIP)2.06(CSL10_85fm)0.16 (21)

F20%(r) = 0.574 (DUANREG)0.66 (PRECIP)1.63(CSL10_8 fm)0.19 (22)
20 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

PERCENT IMPERVIOUS AREA

PERCENT OF AREA SERVED BY STORM SEWERAGE

0

100

20

40

60

80

0 20 40 60 80 100

RL

6

5

4

3

2.5

1.5

2

R = 1 L

R =L

discharge after urbanization

discharge before urbanization

EXPLANATION

 = 7

Figure 6. Relation of urban adjustment factor, RL, to the percentage of area impervious,and served by storm sewer (adapted from 

Leopold, 1968).
Summary 21

F10%(r) = 1.74 (DUANREG)0.66 (PRECIP)1.42(CSL10_85fm)0.21 (23)

F4%(r) = 4.90 (DUANREG)0.66 (PRECIP)1.24(CSL10_85fm)0.23 (24)

F2%(r) = 13.18 (DUANREG)0.66 (PRECIP)1.05(CSL10_85fm)0.21 (25)

F1%(r) = 26.9 (DUANREG)0.65 (PRECIP)0.92(CSL10_85fm)0.21(26)

F0.2%(r) = 126 (DUANREG)0.64 (PRECIP)0.64(CSL10_85

fm)0.19(27)

where 

 Fx(r) = the regression peak-streamflow estimate

 adjusted for floodwater retarding

 structures, for percent chance

 exceedance x, in cubic feet per second,

 DUANREG = the contributing drainage area of the

 unregulated part of the basin or

 drainage area downstream from the

 floodwater retarding structures, in

 square miles, 

 PRECIP = the point mean-annual precipitation at the

 station or ungaged site, for the period

 1971-2000, in inches, and

 CSL10_85fm = the main-channel slope, measured at the

 points that are 10 percent and 85

 percent of the main-channel length

 between the station or ungaged site and

 the drainage divide, in feet per mile.

The adjusted equations can be used when the percent of 

regulated drainage area is not greater than 86 percent of the 

basin, the upper limit of the range of regulated data used to 

check the validity of the adjustment (Tortorelli and Bergman, 

1985). When the percent of regulated drainage area is greater 

than 86 percent of the basin, flow routing techniques, such as 

outlined in Chow and others (1988), may be used.

Example

This example illustrates how a peak-streamflow estimate is calculated for an ungaged site on a stream regulated 

by floodwater retarding structures. An estimate of the Q1% is 

needed for this example on an ungaged site on Uncle Johns 

Creek in Kingfisher County that is regulated by floodwater 

retarding structures.

To obtain the regression flood-frequency estimate for 

an ungaged site on a stream regulated by floodwater retarding structures, F1%(r), equation 26 is used. Equation 26 uses 

DUANREG, the area of the drainage basin unregulated by 

floodwater retarding structures, instead of CONTDA. The 

following data and calculations are needed to estimate Q1% for 

the ungaged site on a stream regulated by floodwater retarding 

structures:

CONTDA = 155 square miles

DUANREG = 65.1 square miles

PRECIP = 31.0 inches

CSL10_85fm = 12.0 feet per mile

The following step is required to obtain the needed peakstreamflow estimate:

F1%(r) = 16,100 cubic feet per second from equation 26

The estimate of the 1 percent chance exceedance flood 

with 58 percent of the basin regulated by floodwater retarding 

structures is a discharge of 16,100 ft3/s.

Summary

This report presents the results of a cooperative study 

by the U.S. Geological Survey (USGS) and the Oklahoma 

Department of Transportation to estimate the magnitude and 

frequency of peak streamflows from regional regression equations for Oklahoma by using generalized least squares regression methods. Annual-maximum peak flows observed at 231 

streamflow-gaging stations through water year 2008 were used 

for the regression analysis. Gage peak-streamflow estimates 

were used from previous work unless 2008 gaging-station 

data were available, in which new peak-streamflow estimates 

were calculated. The basin characteristics for each site were 

determined by using a geographical information system and 

the USGS web application StreamStats. The most statistically 

significant basin characteristics required to estimate peakstreamflow frequency for unregulated streams in Oklahoma 

are contributing drainage area, mean-annual precipitation, and 

main-channel slope. Multiple-regression analyses were used 

to define the relations between peak-streamflow frequency and 

basin characteristics. The resulting regression equations can 

be used to estimate peak discharge and frequency of floods 

for selected percent chance exceedance floods ranging from 

50–0.2 percent. 

 The regression equations are applicable for basins with 

a drainage area less than 2,510 square miles that are not 

substantially affected by regulation. The estimated standard 

error of prediction for the regression equations ranged from 

32 to 47 percent, and standard model error ranged from 31 to 

46 percent. This report also presents methods on estimating 

peak-streamflow magnitude and frequency for ungaged sites 

on streams with streamflow-gaging stations and for sites on 

urban streams and streams regulated by floodwater retarding 

structures. Log-Pearson Type III analysis information, basin 

characteristics, and the peak-streamflow frequency estimates 
22 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

for 231 streamflow-gaging stations in and near Oklahoma are 

listed in this report.

References Cited

Asquith, W.H., and Slade, R.M., Jr., 1997, Regional equations 

for estimation of peak-streamflow frequency for natural 

basins in Texas: U.S. Geological Survey Water-Resources 

Investigations Report 96–4307, 68 p.

Bergman, D.L., and Huntzinger, T.L., 1981, Rainfall-runoff 

hydrograph and basin characteristics data for small streams 

in Oklahoma: U.S. Geological Survey Open-File Report 

81–824, 320 p.

Chow, V.T., Maidment, D.R., and Mays, L.W., 1988, Applied 

hydrology: New York, McGraw-Hill, 572 p.

DeCoursey, D.G., 1975, Implications of floodwater-retarding 

structures: Transactions of the American Society of Agricultural Engineers, v. 18, no. 5, Sept.–Oct. 1975, p. 897–904.

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.

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

regression in regional hydrologic analyses: Journal of 

Hydrology, v. 344, p. 82–95.

Hardison, C.H., 1971, Prediction error of regression estimates 

of streamflow characteristics at ungaged sites, in Geological Survey research 1971, chap. C: U.S. Geological Survey 

Professional Paper 750–C, p. C228–C236.

Hartman, M.A., Ree, W.O., Schoof, R.R., and Blanchard, B.J., 

1967, Hydrologic influences of a flood control program: 

American Society of Civil Engineers, Journal Hydraulics 

Division, v. 93, no. 3, May 1967, p. 17–25.

Heimann, D.C., and Tortorelli, R.L., 1988, Statistical summaries of streamflow records in Oklahoma and parts of 

Arkansas, Missouri, and Texas through 1984: U.S. Geological Survey Water-Resources Investigations Report 87–4205, 

387 p.

Helsel, D.R., and Hirsch, R.M., 2002. Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water Resources Investigations, book 4, chap. A3, 522 p.

Interagency Advisory Committee on Water Data, 1982, Guidelines for determining flood flow frequency: Reston, Va., 

U.S. Geological Survey, Office of Water Data Coordination, 

Hydrology Subcommittee Bulletin 17B [variously paged].

Jennings, M.E., Thomas, W.O., Jr., and Riggs, H.C., comps., 

1994, Nationwide summary of the U.S. Geological Survey 

regional regression equations for estimating magnitude and 

frequency of floods for ungaged sites, 1993: U.S. Geological Survey Water-Resources Investigations 94–4002, 196 p.

Leopold, L.B., 1968, Hydrology for urban land planning—A 

guidebook on the hydrologic effects of urban land use: U.S. 

Geological Survey Circular 554, 18 p.

Lewis, J.M., and Esralew, R.A., 2009, Statistical summaries of 

streamflow in and near Oklahoma through 2007: U.S. Geological Survey Scientific Investigations Report 2009–5135, 

633 p.

Lumia, Richard, Freehafer, D.A., and Smith, M.J., 2006, Magnitude and frequency of floods in New York: U.S. Geological Survey Scientific Investigations Report 2006–5112, 152 

p.

Moore, C.M., 1969, Effects of small structures on peak flow, 

in Moore, W.L., and Morgan, C.W., eds., Water Resources 

Symposium No. 2: Center for Research in Water Resources, 

University of Texas, Austin, Tex., p. 101–117.

Moore, W.L., and Coskun, Erdal, 1970, Numerical simulation 

of a watershed as a means to evaluate some effects of floodwater-retarding structures on runoff: Center for Research in 

Water Resources Technical Report CRWR-45, University of 

Texas, Austin, Tex., 79 p.

PRISM Climate Group, 2008, Normal annual precipitation 

grid for the conterminous United States, available online 

at http://www.prism.oregonstate.edu/state_products/maps.

phtml?id=US. (Accessed March 24, 2008).

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, 59 p.

Ries, K.G., III, Guthrie, J.G., Rea, A.H., Steeves, P.A., and 

Stewart, D.W., 2008, StreamStats—A water resources web 

application: U.S. Geological Survey Fact Sheet 2008–3067, 

6 p.

Ries, K.G., III, Steeves, P.A., Coles, J.D., Rea, A.H., and 

Stewart, D.W., 2004, StreamStats—A U.S. Geological Survey web application for stream information: U.S. Geological Survey Fact Sheet 2004–3115, 4 p.

Sauer, V.B., 1974a, Flood characteristics of Oklahoma 

streams: U.S. Geological Survey Water-Resources Investigations Report 52–73, 301 p.

Sauer, V.B., 1974b, An approach to estimating flood frequency 

for urban areas in Oklahoma: U.S. Geological Survey 

Water-Resources Investigations Report 23–74, 10 p.
References Cited 23

Schoof, R.R., Thomas, W.O., Jr., and Boxley, W.M., 1980, 

Hydrologic effects of the flood abatement program in southwestern Oklahoma: Water Resources Bulletin, v. 16, no. 2, 

p. 348–352.

Smith, S.J., Esralew, R.A., 2010, StreamStats in Oklahoma—

Drainage-basin characteristics and peak-flow frequency 

statistics for ungaged streams: U.S. Geological Survey 

Scientific Investigations Report 2009–5255 58 p.

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.

Tasker, G.D., and Stedinger, J.R.., 1989, An operational GLS 

model for hydrologic regression: Journal of Hydrology, v. 3, 

p. 361-–375.

Thomas, W.O., Jr. and Corley, R.K., 1977, Techniques for 

estimating flood discharges for Oklahoma streams: U.S. 

Geological Survey Water-Resources Investigations Report 

77–54, 170 p.

Tortorelli, R.L., 1997, Techniques for estimating peak streamflow frequency for unregulated streams and streams regulated by small floodwater retarding structures in Oklahoma: 

U.S. Geological Survey Water-Resources Investigations 

Report 97–4202, 39 p.

Tortorelli, R.L., and Bergman, D.L., 1985, Techniques for estimating flood peak discharges for unregulated streams and 

streams regulated by small floodwater retarding structures 

in Oklahoma: U.S. Geological Survey Water-Resources 

Investigations Report 84–4358, 85 p.

U.S. Geological Survey, 2006, National Elevation Dataset: 

U.S. Geological Survey, available only online at http://ned.

usgs.gov/.

U.S. Soil Conservation Service (now Natural Resources Conservation Service), 1972, Hydrology: National Engineering 

Handbook, Section 4, Washington, D.C., [variously paged].
24 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma
Table 1 25

Table 1
26 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic 

record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

1 07148100 Grouse Creek near Dexter, Kans.7 30

2 07148350 Salt Fork Arkansas R. nr Winchester, Okla.7 34 37

3 07148400 Salt Fork Arkansas R. near Alva, Okla. 43 71

4 07148700 Dog Creek near Deerhead, Kans. 21

5 07148800 Medicine Lodge River Trib. nr Medicine Lodge, Kans.7 21 5

6 07150580 Sand Creek Trib. near Kremlin, Okla. 12 1 11,500 10

7 07150870 Salt Fork Arkansas River Trib. near Eddy, Okla. 22

8 07151500 Chikaskia River near Corbin, Kans.7 59 86 1,000

9 07151600 Rush Creek near Harper, Kans.7 33 77

10 07152000 Chikaskia River near Blackwell, Okla.7 72 86 2,000

11 07152360 Elm Creek near Foraker, Okla. 12 200

12 07152410 Rock Creek near Shidler, Okla. 8

13 07152520 Black Bear Creek Trib. near Garber, Okla. 12 10

14 07152842 Subwatershed W–4 near Morrison, Okla. 22 10

15 07152846 Subwatershed W–3 near Morrison, Okla. 25 1

16 07153000 Black Bear Creek at Pawnee, Okla.7, 8 20 55 1 30,000

17 07154400 Carrizozo Creek near Kenton, Okla. 56

18 07154500 Cimarron River near Kenton, Okla.7 20 577

19 07155000 Cimarron River above Ute Creek nr Boise City, Okla. 13 49 1 76,600

20 07155100 Cold Springs Creek near Wheeless, Okla. 17 21

21 07156600 Cimarron River Trib. near Moscow, Kans. 33 12

22 07156700 Cimarron River Trib. near Satanta, Kans. 52

23 07157100 Crooked Creek near Copeland, Kans.7 33 15

24 07157400 Crooked Creek Trib. at Meade, Kans. 33 10

25 07157500 Crooked Creek near Englewood, Kans. 21 200

26 07157550 West Fork Creek near Knowles, Okla. 22 25

27 07157900 Cavalry Creek at Coldwater, Kans.7 28

28 07157960 Buffalo Creek near Lovedale, Okla. 28

29 07158020 Cimarron River Trib. near Lone Wolf, Okla. 12

30 07158080 Sand Creek Trib. near Waynoka, Okla. 12 24 1 990
Table 1 27

peak-streamflow data from unregulated basins in and near Oklahoma.

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 

1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area (mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance 

(%)

Station Weighted 50 20 10 4 2 1 0.02

1 0.185 -0.062 171.34 36.3 8.63 8,730 18,000 26,200 38,900 50,100 62,800 98,900

2 -0.390 -0.118 827.23 26.4 9.40 6,640 16,100 25,200 40,400 54,600 71,200 121,000

3 -0.513 -0.306 982.09 26.7 8.43 6,520 13,300 18,800 26,700 33,100 40,000 57,600

4 -0.145 -0.066 5.05 27.1 64.44 251 924 1,810 3,670 5,780 8,660 19,500

5 -0.730 -0.146 2.15 28.5 38.81 143 477 876 1,650 2,470 3,530 7,150

6 -0.591 0.105 7.13 34.0 14.76 479 1,260 2,110 3,700 5,330 7,440 14,700

7 0.225 0.000 2.51 34.9 19.55 259 525 761 1,130 1,460 1,830 2,910

8 -0.688 -0.160 812.58 30.5 7.67 9,610 18,800 26,400 37,600 46,900 57,200 84,400

9 -1.311 -0.203 11.78 31.0 20.10 1,170 2,280 3,180 4,480 5,560 6,730 9,770

10 -0.500 -0.083 1873.05 31.8 6.58 19,200 38,000 54,100 78,300 99,200 122,000 187,000

11 -0.648 -0.127 18.34 38.7 14.65 2,230 4,590 6,630 9,750 12,400 15,500 23,800

12 -0.014 -0.140 9.06 39.2 33.19 1,640 2,100 2,380 2,700 2,940 3,160 3,650

13 -0.083 0.087 1.02 34.7 24.01 92.5 286 522 1,000 1,530 2,250 4,940

14 -1.240 0.006 0.33 37.1 52.70 134 239 324 447 551 666 975

15 -1.184 0.089 0.08 37.2 182.11 68.9 181 304 530 763 1,060 2,090

16 0.730 0.372 538.32 36.6 3.39 6,030 10,000 13,400 18,500 23,000 28,100 43,100

17 0.313 0.337 112.28 16.6 26.94 1,690 3,920 6,270 10,600 15,100 20,900 41,700

18 -0.617 0.371 1111.58 16.8 23.56 6,860 14,300 21,600 34,400 47,000 62,800 116,000

19 0.251 0.152 1966.87 16.8 19.48 9,660 21,700 33,500 53,900 73,700 98,000 177,000

20 -0.005 0.253 10.70 17.1 27.54 58.2 306 762 2,090 4,100 7,600 27,600

21 -1.028 -0.499 21.42 18.6 23.11 459 1,400 2,360 3,920 5,310 6,870 11,000

22 -0.357 -0.370 4.23 19.3 25.88 152 515 924 1,660 2,380 3,240 5,820

23 -1.203 -0.257 47.74 20.3 13.09 512 1,500 2,560 4,400 6,180 8,310 14,800

24 -0.424 -0.253 6.89 21.6 38.27 294 1,250 2,550 5,300 8,350 12,400 27,000

25 -1.288 -0.266 821.97 21.3 3.98 3,750 7,400 10,400 14,600 18,000 21,700 31,100

26 -0.261 -0.219 4.44 22.7 55.00 108 267 420 667 892 1,150 1,900

27 -0.107 -0.085 41.54 26.1 11.08 470 1,270 2,120 3,640 5,130 6,970 12,900

28 -0.515 -0.428 401.31 25.2 11.77 1,090 4,120 7,750 14,500 21,100 29,200 53,600

29 -0.478 -0.135 4.20 28.4 28.55 534 771 923 1,130 1,280 1,420 1,770

30 -0.281 -0.148 1.77 28.0 57.50 151 358 554 874 1,160 1,500 2,490
28 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

31 07158180 Salt Creek Trib. near Okeene, Okla. 12

32 07158400 Salt Creek near Okeene, Okla. 12

33 07158500 Preacher Creek near Dover, Okla. 27 1 6,000

34 07158550 Turkey Creek Trib. near Goltry, Okla. 19

35 07159000 Turkey Creek near Drummond, Okla.7 27 43 1 30,000

36 07159200 Kingfisher Creek near Kingfisher, Okla. 15 40

37 07159810 Watershed W–VI near Guthrie, Okla. 14

38 07160350 Skeleton Creek at Enid, Okla. 12

39 07160500 Skeleton Creek near Lovell, Okla.7 51 77

40 07160550 West Beaver Creek near Orlando, Okla. 22

41 07163000 Council Creek near Stillwater, Okla.7 60 82

42 07163020 Corral Creek near Yale, Okla. 12

43 07165550 Snake Creek near Bixby, Okla. 15 500

44 07170600 Cherry Creek near Cherryvale, Kans. 21 1 15,500

45 07170700 Big Hill Creek near Cherryvale, Kans.7 23 30 1 35,000

46 07170800 Mud Creek near Mound Valley, Kans. 34 175

47 07171700 Spring Branch near Cedar Vale, Kans. 38 15

48 07171800 Cedar Creek Trib. near Hooser, Kans. 34

49 07172000 Caney River near Elgin, Kans.7, 8 26

50 07173000 Caney River near Hulah, Okla.8 12

51 07174200 L. Caney River blw Cotton Creek near Copan, Okla.7, 8 21

52 07174570 Dry Hollow near Pawhuska, Okla. 8

53 07174600 Sand Creek at Okesa, Okla.7 34

54 07174720 Hogshooter Creek Trib. near Bartlesville, Okla. 21 83

55 07176500 Bird Creek at Avant, Okla.7, 8 31 1,904

56 07176800 Candy Creek near Wolco, Okla. 12

57 07177000 Hominy Creek near Skiatook, Okla.7, 8 38 1 31,100 1,498

58 07177500 Bird Creek near Sperry, Okla.7, 8 46 2,186

59 07178640 Bull Creek near Inola, Okla. 11

60 07183800 Limestone Creek near Beulah, Kans.7 33
Table 1 29

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 

1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area 

(mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance (%)

Station Weighted 50 20 10 4 2 1 0.02

31 -0.038 0.168 8.37 30.9 12.71 687 2,160 4,010 7,890 12,300 18,500 43,100

32 0.433 0.214 181.49 30.9 8.45 4,770 7,690 9,980 13,300 16,100 19,100 27,400

33 0.829 0.348 14.33 32.8 14.47 219 617 1,100 2,120 3,280 4,910 11,500

34 0.149 0.031 4.82 31.8 15.13 342 999 1,760 3,210 4,750 6,760 13,900

35 0.008 0.035 254.76 32.4 4.31 2,630 7,190 12,200 21,600 31,200 43,400 85,400

36 0.035 0.261 165.14 31.8 6.44 2,490 7,740 14,500 29,000 45,900 70,200 170,000

37 -0.097 0.202 0.15 35.9 132.65 30.2 80.3 137 246 362 516 1,080

38 0.406 0.095 69.95 34.0 12.63 3,460 5,720 7,480 10,000 12,100 14,400 20,400

39 0.110 0.146 412.05 33.6 5.67 5,890 15,600 26,500 47,000 68,600 96,700 197,000

40 -0.354 0.035 13.58 35.0 19.55 992 2,170 3,280 5,110 6,800 8,810 14,900

41 0.312 0.368 30.03 38.4 13.88 2,200 4,610 7,000 11,200 15,300 20,600 38,200

42 -0.327 0.183 3.01 38.5 45.65 590 912 1,160 1,500 1,780 2,080 2,880

43 -1.370 0.263 47.69 42.7 9.45 3,280 5,770 7,890 11,100 14,000 17,300 27,000

44 0.578 0.231 15.23 43.2 16.34 2,350 4,590 6,620 9,900 13,000 16,600 27,600

45 1.307 0.020 36.84 43.1 8.80 3,590 6,600 9,090 12,800 16,000 19,500 29,200

46 -0.366 0.228 4.40 44.2 27.39 1,230 2,150 2,930 4,100 5,130 6,310 9,680

47 -1.777 -0.553 3.08 37.9 42.41 832 2,160 3,340 5,100 6,550 8,080 11,800

48 -0.661 -0.410 0.51 37.6 153.63 157 324 457 645 794 950 1,330

49 -0.933 -0.581 428.50 37.7 7.02 14,300 30,500 43,200 60,200 73,200 86,100 116,000

50 -0.336 -0.413 710.78 38.2 5.45 15,400 28,400 37,900 50,500 60,200 69,900 92,600

51 -0.608 -0.428 503.37 40.0 4.92 10,800 21,900 30,500 42,400 51,800 61,400 84,600

52 -0.381 -0.339 1.72 40.1 84.08 316 606 832 1,140 1,390 1,650 2,280

53 -0.821 -0.433 137.83 40.3 9.67 8,140 13,300 16,800 21,100 24,300 27,400 34,200

54 -0.895 -0.244 0.78 40.6 65.71 346 515 627 766 869 970 1,200

55 -1.216 -0.146 368.55 41.4 6.05 12,100 19,800 25,300 32,800 38,600 44,700 59,500

56 -0.482 -0.092 31.35 41.1 15.15 5,080 7,870 9,860 12,500 14,500 16,600 21,700

57 -0.835 0.350 340.11 40.9 4.50 8,400 12,900 16,300 21,400 25,600 30,200 43,000

58 0.216 0.488 906.98 41.1 4.09 14,500 25,600 35,700 51,900 67,100 85,200 142,000

59 -1.052 -0.063 10.83 43.6 13.30 827 1,400 1,840 2,450 2,940 3,470 4,830

60 -0.513 -0.162 13.27 45.1 15.78 3,100 6,520 9,490 14,000 17,900 22,300 34,300
30 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic 

record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

61 07184000 Lightning Creek near McCune, Kans.7 58

62 07184500 Labette Creek near Oswego, Kans.7 37 56 1,342

63 07185500 Stahl Creek near Miller, Mo.7 34

64 07185600 South Fork Stahl Creek near Miller, Mo. 28

65 07185700 Spring River at LaRussell, Mo.7 26

66 07185765 Spring River at Carthage, Mo. 19

67 07185900 O’Possum Creek at Jasper, Mo. 23

68 07186000 Spring River near Waco, Mo.7 86

69 07186400 Center Creek near Carterville, Mo.7 30

70 07187000 Shoal Creek above Joplin, Mo.7 85

71 07188000 Spring River near Quapaw, Okla.7 69

72 07188140 Flint Branch near Peoria, Okla. 22

73 07188500 Lost Creek at Seneca, Mo.7 11

74 07188900 Butler Creek Trib. near Gravette, Ark. 21 2

75 07189000 Elk River near Tiff City, Mo.7 68

76 07189540 Cave Springs Branch near South West City, Mo. 11

77 07189542 Honey Creek near South West City, Mo. 10

78 07190600 Big Cabin Creek near Pyramid Corners, Okla. 15 457

79 07191000 Big Cabin Creek near Big Cabin, Okla.7 68 74 4 41,000

80 07191220 Spavinaw Creek near Sycamore, Okla.7 49

81 07191260 Brushy Creek near Jay, Okla. 8 10 1 4,640

82 07192000 Pryor Creek near Pryor, Okla.7 21

83 07194515 Mill Creek near Park Hill, Okla. 20 17

84 07194800 Illinois River at Savoy, Ark. 13

85 07195000 Osage Creek near Elm Springs, Ark.7 59 508

86 07195200 Brush Creek Trib. near Tontitown, Ark. 21

87 07195430 Illinois River South of Siloam Springs, Ark. 13 5,811

88 07195450 Ballard Creek at Summers, Ark. 24

89 07195500 Illinois River near Watts, Okla.7 53

90 07195800 Flint Creek at Springtown, Ark.7 48
Table 1 31

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 

1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area (mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance (%)

Station Weighted 50 20 10 4 2 1 0.02

61 0.462 0.216 195.94 44.8 3.43 6,760 15,300 24,000 39,200 54,400 73,300 136,000

62 -1.189 -0.055 213.21 43.0 3.71 8,160 12,900 16,300 20,800 24,400 28,200 37,500

63 -0.554 -0.197 4.02 44.9 27.03 612 1,020 1,310 1,700 2,000 2,320 3,090

64 0.254 0.033 0.96 45.0 45.18 201 392 558 813 1,040 1,300 2,030

65 0.232 0.048 305.59 45.1 6.04 5,850 11,200 15,800 22,800 28,900 35,900 55,700

66 -0.446 -0.122 447.81 45.1 5.18 7,910 17,200 25,600 38,700 50,400 63,600 101,000

67 -0.332 -0.113 9.82 45.1 11.37 1,170 1,860 2,360 3,020 3,540 4,080 5,400

68 -0.159 -0.120 1158.12 45.1 2.51 18,800 36,000 50,000 70,600 87,900 107,000 157,000

69 0.526 0.115 228.93 45.1 7.75 5,430 11,000 16,100 24,200 31,700 40,500 66,900

70 0.028 -0.011 427.45 45.6 5.83 7,260 14,610 21,040 31,020 39,850 49,910 78,660

71 -0.084 -0.080 2515.63 45.2 2.07 35,800 66,400 91,100 127,000 158,000 190,000 279,000

72 0.483 0.038 4.88 44.4 34.84 782 1,480 2,070 2,970 3,750 4,640 7,130

73 0.264 -0.007 40.75 45.1 22.59 892 3,220 6,290 12,800 20,400 30,800 71,200

74 -0.956 -0.359 0.99 46.9 128.02 101 295 494 828 1,140 1,500 2,520

75 -0.411 -0.302 850.68 45.9 6.81 20,100 39,400 54,800 76,500 94,000 112,000 159,000

76 -0.105 -0.215 8.00 45.7 28.52 690 1,240 1,650 2,220 2,680 3,160 4,370

77 0.122 -0.177 48.64 46.1 23.24 1,070 2,490 3,810 5,920 7,820 10,000 16,200

78 -1.380 -0.071 71.06 43.9 9.61 4,710 8,430 11,400 15,600 19,100 22,900 32,800

79 -0.123 -0.137 450.31 44.1 4.45 16,100 28,100 37,300 50,000 60,300 71,200 98,800

80 -0.383 -0.315 131.55 47.2 14.18 3,410 9,510 15,700 26,000 35,500 46,500 78,200

81 1.093 -0.120 16.51 46.6 26.63 854 2,170 3,490 5,740 7,880 10,400 18,200

82 0.193 0.017 227.41 43.5 3.71 5,300 11,700 17,800 27,800 37,200 48,200 81,700

83 -1.584 -0.228 2.10 47.0 99.43 414 896 1,310 1,950 2,490 3,090 4,720

84 0.425 -0.193 167.44 48.1 13.37 11,900 20,700 27,200 36,100 43,200 50,600 69,000

85 -0.547 -0.297 129.96 47.0 15.77 5,540 10,500 14,300 19,700 23,900 28,400 39,500

86 -0.332 -0.317 0.38 46.8 127.96 68.0 177 281 450 601 773 1,250

87 -1.102 -0.371 567.80 47.4 7.08 24,100 35,800 43,300 52,400 58,900 65,100 78,800

88 -1.052 -0.455 14.31 49.0 43.10 1,710 4,010 5,990 8,890 11,300 13,800 20,200

89 -0.549 -0.394 629.77 47.5 6.59 18,800 33,200 43,600 57,100 67,300 77,600 101,000

90 0.115 -0.120 14.72 47.6 38.21 758 1,940 3,130 5,170 7,110 9,430 16,600
32 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic 

record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

91 07195865 Sager Creek near West Siloam Springs, Okla. 12 264

92 07196000 Flint Creek near Kansas, Okla.7 53

93 07196380 Steely Hollow near Tahlequah, Okla. 11

94 07196500 Illinois River near Tahlequah, Okla.7 74 93

95 07196900 Baron Fork at Dutch Mills, Ark.7 51 436

96 07196973 Peacheater Creek at Christie, Okla. 10 109

97 07197000 Baron Fork at Eldon, Okla.7 61 1,500

98 07197360 Caney Creek near Barber, Okla. 11 475

99 07228290 Rough Creek near Thomas, Okla. 22 100

100 07228450 Deer Creek Trib. near Hydro, Okla. 12

101 07228930 Worley Creek near Tuttle, Okla. 15 87

102 07228960 Canadian River Trib. near Newcastle, Okla. 11

103 07229220 Walnut Creek near Blanchard, Okla. 9

104 07229300 Walnut Creek at Purcell, Okla. 28 1 67,100

105 07229420 Julian Creek Trib. near Asher, Okla. 21 55

106 07229430 Arbeca Creek near Allen, Okla. 11 150

107 07230000 Little River blw Lk Thunderbird near Norman, Okla.8 12 1 26,400

108 07230500 Little River near Tecumseh, Okla.7, 8 21 33 1 38,190

109 07231000 Little River near Sasakwa, Okla.8 19 23 1 33,000 3,000

110 07231320 Leader Creek Trib. near Atwood, Okla. 22

111 07231560 Middle Creek near Carson, Okla. 11 300

112 07231950 Pine Creek near Higgins, Okla. 22 650

113 07232000 Gaines Creek near Krebs, Okla.7 21 26 1 60,900

114 07232500 Beaver River near Guymon, Okla.7 35 272

115 07232650 Aqua Frio Creek near Felt, Okla. 12

116 07233000 Coldwater Creek near Hardesty, Okla.7 26 100

117 07233500 Palo Duro Creek near Spearman, Tex.7 26 36 2 26,100

118 07234050 North Fork Clear Creek Trib. near Balko, Okla. 22 10

119 07234100 Clear Creek near Elmwood, Okla. 28

120 07234150 White Woman Creek Trib. near Darrouzett, Tex. 9
Table 1 33

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area 

(mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance 

(%)

Station Weighted 50 20 10 4 2 1 0.02

91 -1.016 -0.239 19.11 47.9 22.45 1,750 2,890 3,710 4,800 5,630 6,480 8,520

92 -0.256 -0.271 115.59 47.8 15.33 3,950 10,300 16,600 26,900 36,200 47,100 78,300

93 -0.292 -0.244 3.84 47.8 78.25 540 1,770 3,180 5,800 8,440 11,700 22,300

94 -0.177 -0.208 950.25 47.6 4.54 19,600 38,100 53,000 74,500 92,300 111,000 161,000

95 -1.436 -0.494 41.09 50.1 39.02 7,140 13,700 18,600 25,100 30,000 34,800 46,000

96 -1.860 -0.383 24.85 48.7 32.83 1,360 2,370 3,100 4,050 4,770 5,480 7,160

97 -1.427 -0.242 311.58 49.4 10.28 15,600 27,500 36,400 48,600 58,100 68,000 92,500

98 -2.588 -0.165 90.21 49.0 21.91 4,990 6,910 8,140 9,650 10,700 11,800 14,200

99 -0.493 0.205 10.19 29.8 39.26 772 2,120 3,690 6,760 10,100 14,600 31,300

100 0.518 0.480 2.32 31.1 62.25 298 534 748 1,100 1,420 1,810 3,050

101 -2.470 0.234 11.22 35.2 17.11 1,240 2,110 2,820 3,880 4,790 5,820 8,730

102 -0.244 0.317 3.27 36.1 44.15 702 1,170 1,560 2,140 2,650 3,220 4,870

103 -0.501 0.317 1.27 34.8 67.78 374 662 911 1,300 1,650 2,060 3,260

104 0.014 0.229 202.13 36.7 6.61 8,670 17,300 25,200 38,200 50,400 64,900 110,000

105 -0.434 0.573 2.30 39.4 27.35 398 740 1,060 1,620 2,160 2,830 5,060

106 -0.584 0.551 2.12 42.4 30.67 653 1,180 1,670 2,490 3,270 4,220 7,310

107 1.396 0.595 257.09 38.0 6.15 5,780 10,600 15,200 23,100 30,700 40,200 71,600

108 1.271 0.855 462.50 38.3 5.54 8,950 16,300 23,600 36,600 49,800 66,900 128,000

109 -0.610 0.327 888.35 39.2 3.30 15,000 26,600 36,800 53,000 67,700 85,000 138,000

110 0.275 0.514 0.73 42.1 75.47 293 583 869 1,370 1,870 2,510 4,680

111 -0.978 0.500 7.34 43.8 27.16 1,630 2,980 4,220 6,280 8,240 10,600 18,300

112 -0.374 0.150 10.83 51.2 48.66 4,120 7,890 11,200 16,400 21,100 26,500 42,500

113 0.609 0.541 585.08 47.9 3.07 12,200 23,200 33,800 52,000 69,800 92,100 167,000

114 -0.825 -0.451 1,611.74 17.3 14.03 8,630 21,500 33,000 50,400 65,000 80,800 121,000

115 -0.356 0.161 31.52 16.6 17.89 124 677 1,690 4,610 8,910 16,300 56,400

116 -0.642 -0.265 1028.81 17.9 9.71 2,730 7,470 12,300 20,300 27,900 36,700 62,600

117 0.257 0.262 624.68 18.2 8.27 2,890 7,410 12,500 22,200 32,700 46,500 97,500

118 -0.483 -0.252 4.30 21.1 25.53 59.4 297 658 1,480 2,460 3,840 9,120

119 -0.779 -0.397 161.87 21.2 11.38 957 5,420 12,400 28,300 46,800 72,000 163,000

120 0.072 -0.191 4.10 23.4 16.30 78.2 210 344 574 793 1,050 1,840
34 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic 

record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

121 07234290 Clear Creek Trib. near Catesby, Okla. 20 25

122 07235700 Little Wolf Creek Trib. near Gage, Okla. 11

123 07236000 Wolf Creek near Fargo, Okla. 16 1 62,300

124 07237750 Cottonwood Creek near Vici, Okla. 21 22

125 07237800 Bent Creek near Seiling, Okla. 20

126 07239050 North Canadian River Trib. near Eagle City, Okla. 12

127 07241880 Sand Creek near Cromwell, Okla. 22 220

128 07242160 Alabama Creek near Weleetka, Okla. 19 1,000

129 07243000 Dry Creek near Kendrick, Okla.7 39

130 07243500 Deep Fork near Beggs, Okla.7, 8 29

131 07243550 Adams Creek near Beggs, Okla. 20 64

132 07244000 Deep Fork near Dewar, Okla. 18 47 2 29,000

133 07244790 Brooken Creek near Enterprise, Okla. 11

134 07245500 Sallisaw Creek near Sallisaw, Okla.7, 8 22

135 07246610 Pecan Creek near Spiro, Okla. 12

136 07246630 Big Black Fox Creek near Long, Okla. 21 250

137 07247000 Poteau River at Cauthron, Ark.7, 8 34

138 07247250 Black Fork below Big Creek near Page, Okla. 16

139 07247500 Fourche Maline near Red Oak, Okla.7, 8 25

140 07249000 Poteau River at Poteau, Okla. 12 23 3 21,000

141 07249300 James Fork near Midland, Ark. 20

142 07249400 James Fork near Hackett, Ark.7 51

143 07249500 Cove Creek near Lee Creek, Ark.7 55

144 07249650 Mountain Fork near Evansville, Ark. 20

145 07250000 Lee Creek near Van Buren, Ark.7 50 62 1 112,000

146 07299300 Little Red R nr Turkey, Tex. 14

147 07299670 Groesbeck Creek at S.H. 6 near Quanah, Tex.7 46 56

148 07299705 Bitter Creek near Hollis, Okla. 9

149 07300150 Bear Creek near Vinson, Okla. 22 100

150 07300500 Salt Fork Red River at Mangum, Okla.7 71
Table 1 35

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area (mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance 

(%)

Station Weighted 50 20 10 4 2 1 0.02

121 -0.431 -0.327 8.56 23.6 34.18 119 456 875 1,690 2,540 3,600 7,080

122 0.276 -0.135 17.53 24.4 17.90 504 1,390 2,320 3,960 5,560 7,520 13,700

123 0.756 -0.097 1,473.01 23.0 6.54 7,220 15,900 23,800 36,500 47,800 60,900 98,500

124 -0.977 -0.152 11.65 27.6 40.31 434 1,010 1,540 2,400 3,180 4,070 6,660

125 -0.342 -0.075 129.00 27.4 9.77 2,360 4,480 6,230 8,820 11,000 13,400 20,000

126 -0.080 0.216 0.55 30.0 90.87 88.8 223 370 645 931 1,300 2,630

127 -2.167 0.450 9.52 41.3 24.37 1,400 2,150 2,750 3,640 4,400 5,250 7,660

128 -1.255 0.366 16.21 42.7 19.12 2,080 3,090 3,870 4,980 5,900 6,900 9,620

129 0.141 0.205 68.37 38.4 13.76 3,930 6,990 9,570 13,500 17,000 20,900 32,300

130 0.322 0.364 2,004.26 39.3 2.41 9,400 22,600 37,000 64,300 93,300 132,000 273,000

131 -2.030 0.171 5.69 41.9 37.72 1,080 2,090 2,970 4,380 5,660 7,140 11,600

132 -0.050 0.287 2,295.99 39.8 1.98 11,000 23,500 35,900 57,300 78,400 105,000 192,000

133 -0.418 0.135 5.95 46.9 34.94 1,830 3,380 4,710 6,750 8,540 10,600 16,500

134 0.111 -0.102 181.11 49.3 13.25 13,100 28,800 43,000 65,500 85,600 109,000 175,000

135 -0.095 -0.131 0.92 47.5 44.53 269 409 506 632 728 825 1,060

136 -0.961 -0.300 5.51 48.4 55.79 887 1,410 1,770 2,230 2,570 2,910 3,700

137 -0.319 -0.265 203.56 52.2 8.89 11,400 19,900 26,200 34,700 41,400 48,200 64,900

138 -0.673 -0.303 94.32 59.9 41.18 11,100 20,500 27,500 37,200 44,800 52,700 72,000

139 0.089 -0.039 120.35 49.9 14.67 6,700 14,200 20,900 31,500 41,100 52,100 84,000

140 -0.749 -0.083 1,250.72 51.8 2.82 23,000 46,400 66,500 97,100 124,000 153,000 236,000

141 0.038 -0.148 43.81 52.4 52.27 5,310 11,100 16,100 23,800 30,400 37,800 58,200

142 -0.109 -0.155 146.67 49.4 16.23 6,840 11,700 15,300 20,200 24,100 28,200 38,500

143 -0.147 -0.230 34.84 51.9 34.01 5,000 10,600 15,400 22,600 28,800 35,500 53,600

144 -0.408 -0.315 8.40 52.1 128.70 1,290 2,460 3,380 4,650 5,660 6,720 9,340

145 -0.350 -0.243 437.97 50.2 15.12 24,400 42,900 56,700 75,600 90,400 106,000 144,000

146 -1.063 -0.140 147.54 22.0 23.59 2,470 3,410 4,020 4,780 5,320 5,860 7,100

147 -0.852 0.175 320.00 25.7 7.10 1,860 4,700 7,770 13,500 19,400 27,000 53,700

148 -0.553 -0.072 11.48 25.8 34.08 126 383 679 1,240 1,830 2,580 5,160

149 -0.715 -0.085 7.18 25.9 38.79 668 1,600 2,500 4,010 5,420 7,080 12,100

150 -0.241 -0.154 1,319.45 24.0 11.66 9,560 22,000 33,500 51,900 68,400 87,500 142,000
36 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site 

number 

(fig. 1)

Station 

number Station name

Analysis Information

Available 

systematic 

record1

(years)

His- Hightorical Number outlier 

record of high threshlength2 outliers old3

(years) (ft3/s)

Lowoutlier 

threshold4

(ft3/s)

151

152

153

154

155

156

157

158

159

160

161

162

163

164

165

166

167

168

169

170

171

172

173

174

175

176

177

178

179

180

07301110

07301300

07301455

07301480

07301500

07303400

07303450

07303500

07304500

07309480

07311000

07311200

07311420

07311500

07312850

07312950

07313000

07313500

07313600

07315680

07315700

07315880

07316130

07316140

07316500

07317500

07318500

07319000

07320000

07321500

Salt Fork Red River near Elmer, Okla.

N Fk Red R nr Shamrock, Tex.

Turkey Creek near Erick, Okla.

Short Creek near Sayre, Okla.

North Fork Red River near Carter, Okla.7

Elm Fork of North Fork Red River near Carl, Okla.7

Deer Creek near Plainview, Okla.

Elm Fork of North Fk Red River near Mangum, Okla.7

Elk Creek near Hobart, Okla.

Canyon Creek near Medicine Park, Okla.

East Cache Creek near Walters, Okla.8

Blue Beaver Creek near Cache, Okla.

Deadman Creek Trib. at Manitou, Okla.

Deep Red Creek near Randlett, Okla.7

Nine Mile Beaver Creek near Elgin, Okla.

Little Beaver Creek near Marlow, Okla.

Little Beaver Creek near Duncan, Okla.

Beaver Creek near Waurika, Okla.7, 8

Cow Creek at Waurika, Okla.

Cottonwood Creek Trib. near Loco, Okla.

Mud Creek near Courtney, Okla.7

Demijohn Creek near Wilson, Okla.

Wilson Creek Trib. near McMillan, Okla.

Brier Creek near Powell, Okla.

Washita River near Cheyenne, Okla.7, 8

Sandstone Creek SWS 16A near Cheyenne, Okla.9

Sandstone Creek SWS 14 near Cheyenne, Okla.9

Sandstone Creek SWS 17 near Cheyenne, Okla.9

Sandstone Creek SWS 10A near Elk City, Okla.9

Sandstone Creek SWS 3 near Elk City, Okla.9

29

15

17

20

32

34

12

72

20

11

22

39

8

59

22

12

15

24

20

21

48

10

11

21

23

21

12

20

19

14

22

59

11

26

31

52

27

20

21

19

2

1

1

1

1

2

14,300

18,300

900

18,100

30,000

1,160

218

1,375

250

30

974

118

100

211

49
Table 1 37

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area (mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance 

(%)

Station Weighted 50 20 10 4 2 1 0.02

151 0.508 0.256 1847.90 25.1 9.77 5,970 13,900 22,200 37,200 52,500 72,000 139,000

152 0.780 -0.024 816.73 22.9 10.36 6,460 10,100 12,700 16,200 19,000 21,900 29,200

153 -1.204 -0.382 21.87 26.1 17.30 1,070 1,910 2,520 3,320 3,930 4,550 6,000

154 0.298 0.044 9.28 26.3 31.62 456 926 1,340 2,010 2,600 3,300 5,320

155 -0.285 -0.151 2072.51 24.1 9.57 8,410 14,800 19,600 26,400 31,900 37,600 52,300

156 -0.202 -0.106 437.96 24.8 15.76 3,810 10,400 17,300 29,600 41,600 56,400 103,000

157 -0.669 -0.086 26.78 26.8 25.58 940 1,660 2,220 3,020 3,670 4,370 6,200

158 -0.548 -0.203 846.33 26.2 10.87 7,300 15,900 23,600 35,200 45,400 56,700 87,800

159 0.818 0.244 549.28 28.7 6.33 3,990 6,880 9,280 12,900 16,100 19,700 30,000

160 -1.697 0.159 3.39 32.8 56.74 762 1,880 3,070 5,230 7,430 10,200 19,800

161 -0.985 0.159 693.50 32.9 5.07 7,590 13,400 18,200 25,500 31,800 38,800 58,900

162 -0.302 0.211 24.67 32.6 35.58 1,650 3,600 5,500 8,780 12,000 15,900 28,700

163 -0.238 0.080 2.58 30.1 31.93 357 771 1,160 1,810 2,410 3,130 5,340

164 -0.044 0.019 604.08 30.8 5.92 7,220 16,800 26,100 41,900 56,900 75,000 131,000

165 -0.589 0.259 6.36 33.9 39.94 703 1,740 2,880 5,000 7,240 10,200 20,600

166 0.238 0.384 34.86 35.6 22.37 799 2,000 3,350 5,990 8,870 12,800 27,600

167 -0.422 -0.365 156.58 35.4 9.11 15,600 29,700 40,500 55,300 66,900 78,800 108,000

168 0.433 0.335 564.36 34.6 3.98 4,350 11,900 20,800 39,000 59,400 87,800 199,000

169 0.054 0.308 192.66 35.3 6.32 3,080 6,410 9,640 15,200 20,600 27,200 49,100

170 -0.419 0.115 1.81 36.3 56.06 486 1,080 1,670 2,650 3,600 4,750 8,400

171 -0.353 0.190 574.41 35.1 3.89 5,920 15,200 25,400 44,530 64,560 90,690 183,400

172 -0.949 0.065 6.44 36.9 30.34 1,880 2,160 2,330 2,530 2,660 2,790 3,070

173 -0.327 0.068 2.95 40.3 43.67 768 1,110 1,350 1,660 1,900 2,150 2,770

174 0.281 0.152 11.99 42.2 25.65 2,930 5,450 7,630 11,000 14,000 17,400 27,400

175 0.108 0.043 762.59 24.2 8.96 5,610 15,500 26,600 47,200 68,700 96,300 192,000

176 0.337 0.066 9.68 25.8 45.39 451 1,070 1,700 2,780 3,830 5,130 9,290

177 -0.220 -0.014 1.01 26.7 116.64 274 632 979 1,560 2,100 2,750 4,740

178 -0.858 -0.095 11.11 26.0 51.32 979 2,370 3,740 6,020 8,150 10,700 18,400

179 -1.300 -0.078 2.79 27.0 75.30 750 1,250 1,620 2,130 2,540 2,970 4,060

180 -1.041 0.116 0.65 27.4 107.51 311 616 890 1,320 1,720 2,180 3,540
38 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic 

record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

181 07322000 Sandstone Creek SWS 9 near Elk City, Okla.9 18 22

182 07324000 Sandstone Creek SWS 1 near Cheyenne, Okla.9 18 22

183 07325000 Washita River near Clinton, Okla.7, 8 27

184 07325850 Lake Creek near Eakly, Okla. 13

185 07326000 Cobb Creek near Fort Cobb, Okla.8 19 22 1 32,500

186 07327150 Salt Creek near Chickasha, Okla. 11

187 07327420 West Bitter Creek near Tabler, Okla. 15 206

188 07327440 East Bitter Creek near Tabler, Okla.8 10

189 073274406 Little Washita River ab SCS Pond No 26 nr Cyril, Okla. 14

190 07327490 Little Washita River near Ninnekah, Okla.7, 8 22 27 1 24,900

191 07329000 Rush Creek at Purdy, Okla.8 15

192 07329500 Rush Creek near Maysville, Okla.8 11

193 07329810 Honey Creek near Davis, Okla. 21 37

194 07329900 Rock Creek at Dougherty, Okla.8 15 273

195 07330500 Caddo Creek near Ardmore, Okla. 14 926

196 07332070 Rock Creek near Achille, Okla. 10

197 07332400 Blue River at Milburn, Okla. 22 1 35,000

198 07332500 Blue River near Blue, Okla.7 72 984

199 07332600 Bois D’Arc Ck nr Randolph, Tex.7 23 1,800

200 07333500 Chickasaw Creek near Stringtown, Okla. 20 1,800

201 07333800 McGee Creek near Stringtown, Okla. 20 2,900

202 07334000 Muddy Boggy Creek near Farris, Okla.7, 8 49

203 07335000 Clear Boggy Creek near Caney, Okla.7, 8 20 24 1 54,600

204 07335310 Rock Creek near Boswell, Okla. 21

205 07335320 Bokchito Creek near Soper, Okla. 11 670

206 07335700 Kiamichi River near Big Cedar, Okla. 43 1,428

207 07335760 Kiamichi River Trib. near Albion, Okla. 8

208 07336000 Tenmile Creek near Miller, Okla. 29 1 9,810

209 07336500 Kiamichi River near Belzoni, Okla.7 47 57

210 07336520 Frazier Creek near Oleta, Okla. 22
Table 1 39

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 

1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area (mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance (%)

Station Weighted 50 20 10 4 2 1 0.02

181 -0.197 0.010 3.36 27.4 60.09 868 1,580 2,160 3,010 3,740 4,550 6,740

182 -0.340 0.082 5.39 27.5 46.93 812 1,930 3,070 5,050 7,000 9,400 17,200

183 0.678 0.507 1,948.58 26.4 6.79 7,650 18,200 30,000 53,100 78,500 113,000 247,000

184 0.413 0.459 52.46 31.6 15.90 935 2,840 5,380 11,100 18,200 28,800 76,500

185 0.851 0.556 310.72 31.4 7.23 4,220 10,200 17,200 31,200 47,000 68,900 157,000

186 0.089 0.436 23.79 34.1 13.17 694 1,620 2,620 4,530 6,560 9,260 19,300

187 -1.523 0.270 59.70 34.0 10.89 1,630 3,080 4,380 6,470 8,380 10,600 17,600

188 -0.582 0.338 35.38 34.6 12.23 1,710 2,990 4,100 5,820 7,360 9,150 14,500

189 -0.717 0.263 3.65 33.4 37.74 391 1,350 2,660 5,670 9,380 14,900 39,200

190 0.413 0.544 207.96 34.4 8.52 3,250 7,430 12,000 20,900 30,500 43,500 93,300

191 0.244 0.344 139.68 36.6 9.97 10,000 16,100 21,000 28,300 34,500 41,500 61,200

192 0.003 0.280 201.75 36.9 8.78 9,390 17,800 25,300 37,400 48,600 61,900 102,000

193 -2.175 0.132 18.75 39.6 41.48 1,940 4,610 7,340 12,200 16,900 22,900 42,600

194 -1.027 0.226 136.76 41.2 13.71 4,650 10,500 16,500 27,000 37,400 50,500 94,200

195 -1.260 0.054 296.30 38.0 5.81 8,300 15,500 21,600 30,800 38,800 47,800 73,200

196 0.587 0.199 0.71 43.5 27.10 397 684 919 1,270 1,580 1,920 2,890

197 -0.426 -0.120 203.19 42.3 10.26 8,700 17,300 24,500 35,300 44,600 54,800 82,700

198 -0.216 0.367 477.45 43.5 6.98 9,300 17,100 24,000 35,300 45,650 58,000 96,200

199 -2.187 -0.322 72.09 43.3 8.38 8,880 12,500 14,700 17,400 19,300 21,000 25,000

200 -1.184 0.177 32.62 45.5 25.39 7,570 10,800 13,200 16,300 18,700 21,300 27,700

201 -1.761 0.113 88.76 47.4 6.10 6,840 8,630 9,770 11,200 12,200 13,200 15,600

202 -0.164 0.056 1088.92 45.0 3.18 19,200 29,800 37,600 48,300 56,900 65,900 88,900

203 0.050 0.167 713.37 43.4 3.37 14,000 28,600 42,200 64,400 85,200 110,000 186,000

204 -0.685 -0.067 1.01 46.0 33.38 249 427 564 756 912 1,080 1,510

205 -1.270 -0.071 17.48 47.1 15.74 3,230 5,090 6,430 8,230 9,640 11,100 14,700

206 -0.647 -0.258 39.63 62.1 54.89 9,200 15,100 19,300 24,800 29,000 33,300 43,400

207 0.530 -0.511 1.51 55.9 342.93 246 549 797 1,150 1,420 1,710 2,400

208 0.617 0.281 68.31 48.1 12.21 3,620 5,080 6,120 7,530 8,650 9,830 12,800

209 -0.147 -0.059 1415.94 51.3 3.35 34,300 49,400 59,600 72,700 82,500 92,500 116,000

210 -0.184 -0.061 18.54 50.8 25.32 2,480 4,560 6,250 8,710 10,800 13,000 19,100
40 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

Table 1. Peak-streamflow frequency estimates and basin characteristics for selected stations with at least 8 years of annual

[ft3/s, cubic feet per second; LPIII, Log-Pearson Type III; mi2, square miles; ft/mi, feet per mile; wt, weighted; Trib., Tributary; Ck, creek; Res., Reservoir;

Site

number

(fig. 1)

Station

number Station name

Analysis Information

Available 

systematic 

record1

(years)

Historical

record

length2

(years)

Number

of high

outliers

Highoutlier

threshold3

(ft3/s)

Lowoutlier

threshold4

(ft3/s)

211 07336710 Rock Creek near Sawyer, Okla. 11

212 07336750 Little Pine Creek near Kanawha, Tex. 12

213 07336780 Perry Creek near Idabel, Okla. 10 714

214 07336785 Bokchito Creek near Garvin, Okla. 12 240

215 07336800 Pecan Bayou near Clarksville, Tex. 16

216 07337220 Big Branch near Ringold, Okla. 11

217 07337500 Little River near Wright City, Okla.7, 8 26

218 07337900 Glover River near Glover, Okla.7 48

219 07338500 Little River blw Lukfata Creek near Idabel, Okla.7, 8 39

220 07338520 Yanubbee Creek near Broken Bow, Okla. 22

221 07338700 Twomile Creek near Hatfield, Ark. 21

222 07338780 Mountain Fork Trib. near Smithville, Okla. 20 1 1,017

223 07339000 Mountain Fork near Eagletown, Okla.7, 8 39 54 67,500

224 07339500 Rolling Fork near DeQueen, Ark.7, 8 25 27 1 87,700

225 07339800 Pepper Creek near DeQueen, Ark. 26

226 07340200 West Flat Creek near Foreman, Ark. 20 22

227 07340300 Cossatot River near Vandervoort, Ark.7 41 48 1 48,000

228 07340500 Cossatot River near DeQueen, Ark.7, 8 37

229 07340530 Mill Slough Trib. near Locksburg, Ark. 24

230 07341000 Saline River near Dierks, Ark.7, 8 34 53 2 42,000

231 07341100 Rock Creek near Dierks, Ark. 23 350

1

Available systematic record reflects number of annual peak discharges from natural basins. Many stations became regulated during the period of operation. 

Regulated annual peak discharges not included in peak-streamflow frequency analysis.

2

Historical record length reflects that known as of 2008 water year.

3

High-outlier threshold based on available historical streamflow data.

4

Low-outlier threshold used in frequency analysis; provided by PeakFQ by using Interagency Advisory Committee on Water Data (1982) techniques or 

visual by author.

5

Reflects weighting adjusted station skew with skew value from Oklahoma generalized skew map (fig. 2; Lewis and Esralew, 2009).

6

Values at station location derived from geographical information system using gridded mean-annual precipitation based on 1971-2000 data.

7

Station used in construction of Oklahoma generalized skew map (fig. 2; Lewis and Esralew, 2009).

8

Station has an unregulated period of record used in the analysis, but now is regulated.

9

Streamflow data computed from inflow to floodwater retarding structure.
Table 1 41

peak-streamflow data from unregulated basins in and near Oklahoma.—Continued

L., Little; Lk, Lake; blw, below; SWS, subwatershed; Fk, Fork; R, river; nr, near; %, percent; SH, State highway; N, north; ab, above]

Basin characteristics Peak-streamflow frequency estimates

Site 

number 

(fig. 1)

Skew coefficient for

LP III distribution5 Contributing 

drainage 

area (mi2)

Area-wt 

mean 

annual 

precipitation6

(inches)

Steam

slope

(ft/mi)

Peak discharge; in ft3/s, for indicated percent chance exceedance (%)

Station Weighted 50 20 10 4 2 1 0.02

211 0.156 -0.022 3.33 49.4 33.06 794 1,170 1,430 1,770 2,040 2,310 2,960

212 -0.142 -0.118 75.27 48.8 5.24 6,180 12,600 18,200 26,600 33,900 42,000 64,500

213 -0.955 0.054 7.60 51.1 22.72 2,240 3,020 3,540 4,190 4,680 5,180 6,350

214 -1.071 -0.172 2.89 51.1 22.67 731 1,020 1,200 1,430 1,600 1,760 2,130

215 -0.422 -0.201 98.91 49.2 4.30 4,060 8,050 11,300 16,100 20,200 24,500 36,000

216 0.385 0.023 1.99 52.2 72.35 448 856 1,200 1,730 2,190 2,710 4,160

217 -0.042 -0.047 648.22 53.9 9.74 30,500 49,700 64,100 83,800 99,500 116,000 158,000

218 0.150 0.033 320.28 55.3 13.52 27,700 45,100 58,300 76,800 91,700 108,000 149,000

219 -0.055 -0.058 1,228.14 53.9 5.67 27,600 46,100 60,000 79,400 95,100 112,000 154,000

220 -0.394 -0.145 9.03 53.8 42.27 1,770 3,100 4,130 5,550 6,700 7,920 11,000

221 0.394 -0.070 16.22 60.0 44.03 2,040 3,570 4,760 6,460 7,850 9,340 13,200

222 0.505 -0.020 0.65 56.1 69.96 203 359 482 660 808 968 1,400

223 -0.469 -0.223 799.80 57.4 6.82 37,400 62,900 81,600 106,000 126,000 146,000 194,000

224 0.139 -0.098 183.37 56.4 17.52 16,300 31,600 44,300 63,100 79,200 96,800 145,000

225 -0.503 -0.138 6.27 55.9 41.72 976 2,410 3,800 6,130 8,300 10,800 18,500

226 -0.633 -0.151 10.65 50.8 10.62 1,540 2,640 3,470 4,610 5,520 6,480 8,880

227 -0.525 -0.253 89.10 62.0 28.55 14,300 24,000 31,000 40,300 47,500 54,800 72,400

228 0.225 0.076 361.22 58.7 15.46 28,100 46,800 61,300 82,100 99,200 118,000 168,000

229 -0.351 -0.079 0.69 54.7 55.83 183 344 476 669 838 1,010 1,490

230 0.113 0.009 120.21 59.1 20.90 9,740 18,500 26,000 37,200 46,900 57,900 88,500

231 -0.552 -0.027 9.39 56.9 41.95 2,220 4,280 6,020 8,640 10,900 13,400 20,500
42 Methods for Estimating the Magnitude and Frequency of Peak Streamflows for Unregulated Streams in Oklahoma

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