U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2015–5134

Prepared in cooperation with the Oklahoma Department of Transportation

Methods for Estimating the Magnitude and Frequency 

of Peak Streamflows at Ungaged Sites In and 

Near the Oklahoma Panhandle
Front cover, Windmill and livestock supply well in the High Plains aquifer area, south of Hooker, Oklahoma 

(photograph by S. Jerrod Smith, July 28, 2015).

Back cover, Windmill and livestock pen in the Oklahoma Panhandle near Boise City, Oklahoma 

(photograph by William J. Andrews, February 2004).
Methods for Estimating the Magnitude 

and Frequency of Peak Streamflows at 

Ungaged Sites In and Near the Oklahoma 

Panhandle

By S. Jerrod Smith, Jason M. Lewis, and Grant M. Graves

Prepared in cooperation with the Oklahoma Department of Transportation

Scientific Investigations Report 2015–5134

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2015

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Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials 

as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.

Suggested citation:

Smith, S.J., Lewis, J.M., and Graves, G.M., 2015, Methods for estimating the magnitude and frequency 

of peak streamflows at ungaged sites in and near the Oklahoma Panhandle: U.S. Geological Survey Scientific 

Investigations Report 2015–5134, 35 p., http://dx.doi.org/10.3133/sir20155134.

ISSN 2328-0328 (online)
iii

Contents

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

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

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

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

Streamflow-Gaging Station Selection and Data Analysis ...................................................................14

Basin Characteristics ........................................................................................................................14

Trend Analysis ....................................................................................................................................16

Precipitation Trend Analysis ...................................................................................................16

Annual Peak Data Trend Analysis ..........................................................................................18

Peak-Streamflow Frequency Analysis ...........................................................................................18

Estimates of Magnitude and Frequency of Peak Streamflows at Ungaged Sites ...........................29

Regression Analysis ..........................................................................................................................29

Regression Equations ........................................................................................................................31

Accuracy and Limitations .................................................................................................................31

Summary .......................................................................................................................................................33

References Cited .........................................................................................................................................33

Figures

1. Map showing selected U.S. Geological Survey streamflow-gaging stations 

and changes in water level of the High Plains (or Ogallala) aquifer in and near 

the Oklahoma Panhandle ...........................................................................................................3

2. Graph showing changes in annual peak streamflow and annual percentage 

of no-flow days at the Beaver River near Guymon, Oklahoma (U.S. Geological 

Survey streamflow-gaging station 07232500), 1938–93 .........................................................4

3. Images showing A, an artistic rendering of Optima Lake as it was expected 

to appear after construction (U.S. Army Corps of Engineers, 1966); and 

B, a panoramic photograph of Optima Lake in September 2004 ..........................................5

4. Graphs showing period of record and count of selected operating streamflowgaging stations in and near the Oklahoma Panhandle, 1925–2014 ...................................15

5. Graphs showing annual precipitation trends for the entire period of record 

(1925–2014) and the irrigated period of record (1978–2014) for selected climate 

divisions in and near the Oklahoma Panhandle ...................................................................17

6. Graphs showing annual peak-streamflow trends for the entire period of record 

(1925–2014) and the irrigated period of record (1978–2014) for selected 

streamflow-gaging stations in and near the Oklahoma Panhandle ..................................19

7. Graph showing computed and regression-estimated peak-streamflow 

frequency statistics for the irrigated period of record (1978–2014) at selected 

streamflow-gaging stations in and near the Oklahoma Panhandle ..................................29

8. Graphs showing performance metrics from the Weighted-Multiple-Linear 

Regression (WREG) computer program for the 32 selected streamflow-gaging 

stations including A, residuals; B, leverage; and C, influence for a 10-percent 

annual exceedance probability peak-streamflow generalized-least-squares 

(GLS) regression model ............................................................................................................30
iv

Tables

1. Streamflow-gaging station information, basin characteristics, and peakstreamflow frequency statistics for unregulated drainage basins in and near 

the Oklahoma Panhandle ...........................................................................................................6

2. Results of trend tests on annual precipitation for the entire period of record 

(1925–2014) and the irrigated period of record (1978–2014) for selected climate 

divisions in and near the Oklahoma Panhandle ...................................................................18

3. Results of trend tests on annual peak streamflow for the entire period of 

record (1925–2014) and the irrigated period of record (1978–2014) at selected 

streamflow-gaging stations in and near the Oklahoma Panhandle ..................................27

4. Accuracy of regression-estimated peak-streamflow frequency statistics for 

sites on unregulated streams in and near the Oklahoma Panhandle ...............................32
v

Conversion Factors

Inch/Pound to International System of Units

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)

Area

square mile (mi2

) 259.0 hectare (ha)

square mile (mi2

) 2.590 square kilometer (km2) 

Flow rate

cubic foot per second (ft3

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

inch per hour (in/h) 0.0254 meter per hour (m/h)

inch per year (in/yr) 25.4 millimeter per year (mm/yr)

Hydraulic gradient

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

Datum

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).

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

Supplemental Information

A water year is a period of 12 consecutive months that includes January through September 

of the named calendar year and October through December of the previous calendar year. The 

2015 water year, for example, begins on October 1, 2014, and ends on September 30, 2015. 
vi

Abbreviations

BSLDEM10M Mean drainage-basin slope

CANOPY_PCT Percentage of forest-canopy cover 

CONTDA Contributing drainage area 

CSL10_85FM 10–85 stream channel slope 

GIS Geographic information system

GLS Generalized least squares

IACWD Interagency Advisory Committee on Water Data

IMPNLCD01 Percentage of impervious cover

LC01CROP Percentage of drainage area with crop cover

LPIII Log-Pearson Type III

LOWESS Locally weighted scatterplot smoothing

NWISWeb National Water Information System Website

ODOT Oklahoma Department of Transportation

OK_HIPERMA Percentage of drainage area on the High Plains aquifer

OLS Ordinary least squares

OUTLETELEV Outlet elevation 

PRCOUT61 Outlet mean annual precipitation from 1961 to 1990 

PRCOUT71 Outlet mean annual precipitation from 1971 to 2000

PRECIP Mean annual precipitation

Pseudo-R2 Pseudo coefficient of determination

Q50% Annual peak streamflow with a 50-percent annual exceedance probability 

Q20% Annual peak streamflow with a 20-percent annual exceedance probability

Q10% Annual peak streamflow with a 10-percent annual exceedance probability

Q4% Annual peak streamflow with a 4-percent annual exceedance probability

Q2% Annual peak streamflow with a 2-percent annual exceedance probability

Q1% Annual peak streamflow with a 1-percent annual exceedance probability

Q0.2% Annual peak streamflow with a 0.2-percent annual exceedance probability

R2 Coefficient of determination

RMSE Root mean square error

SOILPERM Mean soil permeability

Sp Standard error of prediction

USGS U.S. Geological Survey

WLS Weighted least squares

WREG Weighted-Multiple-Linear Regression
Methods for Estimating the Magnitude and Frequency 

of Peak Streamflows at Ungaged Sites In and Near the 

Oklahoma Panhandle

By S. Jerrod Smith, Jason M. Lewis, and Grant M. Graves

Abstract

This report presents the results of a cooperative study by 

the U.S. Geological Survey and the Oklahoma Department 

of Transportation to estimate the magnitude and frequency 

of peak streamflows from regional regression equations for 

ungaged stream sites in and near the Oklahoma Panhandle. 

These methods relate basin characteristics (physiographic and 

climatic attributes) to selected peak streamflow frequency 

statistics with the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent 

annual exceedance probabilities. These relations were 

developed based on data from 32 selected streamflow-gaging 

stations in the Oklahoma Panhandle and in neighboring parts 

of Colorado, Kansas, New Mexico, and Texas. The basin 

characteristics for the selected streamflow-gaging stations 

were determined by using a geographic information system 

and the Oklahoma StreamStats application. Peak-streamflow 

frequency statistics were computed from annual peakstreamflow records from the irrigated period of record from 

water year 1978 through water year 2014.

Generalized-least-squares multiple-linear regression 

analysis was used to formulate regression relations between 

peak-streamflow frequency statistics and basin characteristics. 

Contributing drainage area was the only basin characteristic 

determined to be statistically significant for all percentage 

of annual exceedance probabilities and was the only 

basin characteristic used in regional regression equations 

for estimating peak-streamflow frequency statistics on 

unregulated streams in and near the Oklahoma Panhandle. 

The regression model pseudo-coefficient of determination, 

converted to percent, for the Oklahoma Panhandle regional 

regression equations ranged from about 38 to 63 percent. 

The standard errors of prediction and the standard model 

errors for the Oklahoma Panhandle regional regression 

equations ranged from about 84 to 148 percent and from 

about 76 to 138 percent, respectively. These errors were 

comparable to those reported for regional peak-streamflow 

frequency regression equations for the High Plains areas of 

Texas and Colorado. The root mean square errors for the 

Oklahoma Panhandle regional regression equations (ranging 

from 3,170 to 92,000 cubic feet per second) were less than 

the root mean square errors for the Oklahoma statewide 

regression equations (ranging from 18,900 to 412,000 

cubic feet per second); therefore, the Oklahoma Panhandle 

regional regression equations produce more accurate peakstreamflow statistic estimates for the irrigated period of 

record in the Oklahoma Panhandle than do the Oklahoma 

statewide regression equations. The regression equations 

developed in this report are applicable to streams that are not 

substantially affected by regulation, impoundment, or surfacewater withdrawals. These regression equations are intended 

for use for stream sites with contributing drainage areas less 

than or equal to about 2,060 square miles, the maximum 

value for the independent variable used in the regression 

analysis.

Introduction

Knowledge of the magnitude and frequency of peak 

streamflows (floods) is required for the safe and economical 

design of roads, bridges, and culverts near streams (Jennings 

and others, 1994). The Bridge Division of the Oklahoma 

Department of Transportation is tasked with reviewing 

and approving the bridge and culvert design plans for all 

major highways in Oklahoma (Oklahoma Department of 

Transportation, 2009). To properly design these structures, 

estimates of peak-streamflow frequency statistics commonly 

are needed at ungaged stream sites where these statistics are 

unknown; therefore, relating peak-streamflow frequency 

statistics from gaged stream sites to ungaged stream sites 

is necessary. This relation usually is achieved by defining 

regression relations between selected peak-streamflow 

frequency statistics (dependent variables) and selected basin 

characteristics (independent variables) (Jennings and others, 

1994). To address this need, the U.S. Geological Survey 

(USGS) in cooperation with the Oklahoma Department of 

Transportation (ODOT) prepared regression equations to 

estimate peak-streamflow statistics at ungaged sites in the 

Oklahoma Panhandle.
2

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Previous Studies

In 2010, updated statewide peak-streamflow frequency 

regression equations were published for Oklahoma (Lewis, 

2010). These regression equations incorporated contributing 

drainage area, mean annual precipitation, and stream slope 

to compute estimates of peak-streamflow frequency statistics 

for ungaged streams. Those statewide regressions may have 

overestimated recent peak-streamflow frequency statistics 

in the Oklahoma Panhandle (fig. 1) because of changes to 

the hydrology of that area. If regression-computed peakstreamflow frequency statistics are overestimated in the 

Oklahoma Panhandle, engineers are designing structures to 

withstand greater peak streamflow than is necessary at a cost 

to the State that is greater than necessary.

In the late 20th century, the hydrology of the Oklahoma 

Panhandle changed as a result of development of the 

High Plains (or Ogallala) aquifer (fig. 1; Wahl and Wahl, 

1988; Wahl and Tortorelli, 1997). Prior to the early 1960s 

(predevelopment), groundwater levels in the aquifer were 

relatively constant over time (Wahl and Wahl, 1988). For 

example, at the Texhoma observation well (fig. 1), completed 

at a depth of 386 feet (ft), the average annual depth to water 

was about 189 ft from 1956 to 1965 (fig. 2; U.S. Geological 

Survey, 2015b). The introduction of center-pivot irrigation in 

the 1960s prompted a rapid increase in high-capacity irrigation 

well construction and groundwater withdrawals in the 1960s 

and 1970s (Oklahoma Water Resources Board, 1984). Since 

that time, groundwater levels have steadily declined over 

much of the aquifer, and groundwater-level declines greater 

than 150 ft (as compared to predevelopment groundwater 

levels) have been measured recently in some areas of the 

Oklahoma Panhandle statistical region (fig. 1; McGuire, 

2014). As early as the 1970s, area residents began to perceive 

a change in the streamflow characteristics of the Beaver River, 

the principal stream draining the Oklahoma Panhandle (fig. 1; 

Wahl and Wahl, 1988). During the 1970s, the Beaver River 

near Guymon, Okla. (U.S. Geological Survey streamflowgaging station 07232500, fig. 1), transitioned from a stream 

that ceased flowing occasionally in summer to a stream 

that ceased flowing for about half of the year (fig. 2). The 

decreasing trend in streamflow continued into the 1990s, 

when the Beaver River near Guymon, Okla., ceased flowing 

for more than 90 percent of the year (fig. 2). The changes 

in streamflow, especially base flow and peak streamflow, 

observed at this and other stations prompted Lewis and 

Esralew (2009) and Esralew and Lewis (2010) to break the 

streamflow record into an irrigation-affected period of record 

beginning around 1978 for streamflow-gaging stations in and 

near the Oklahoma Panhandle. 

Annual peak streamflows have decreased significantly 

at selected long-term streamflow-gaging stations on several 

large streams (including the Beaver River, North Canadian 

River, Cimarron River, Coldwater Creek, and Wolf Creek) 

that drain the High Plains aquifer (Wahl and Tortorelli, 1997; 

Esralew and Lewis, 2010) (fig. 1). Optima Lake on the Beaver 

River (fig. 1) is a good illustration of the degree to which 

the surface-water hydrology has changed in the Oklahoma 

Panhandle. Optima Dam is about 30 miles downstream from 

the Beaver River near Guymon, Okla. (U.S. Geological 

Survey streamflow-gaging station 07232500, fig. 1). Optima 

Dam was designed and authorized using streamflow data from 

the predevelopment period and was constructed from 1966 to 

1978. Because of decreased streamflows in the irrigated period 

from 1978 to present (2015), Optima Lake never filled to more 

than 6 percent of the conservation pool storage and never met 

expectations for municipal water supply and recreation in the 

Oklahoma Panhandle (U.S. Army Corps of Engineers, 1966; 

Wahl and Wahl, 1988; fig. 3).

Purpose and Scope

This report presents the results of a cooperative study 

by the USGS and the ODOT to estimate the magnitude and 

frequency of peak streamflows from regional regression 

equations for ungaged stream sites in and near the Oklahoma 

Panhandle. This report describes revised methods for 

estimating peak-streamflow frequency statistics with the 

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

probabilities. These methods apply to sites on unregulated 

streams with contributing drainage areas of less than or 

equal to about 2,060 square miles (mi2). This report also 

provides computed basin characteristics (physiographic 

and climatic attributes) and peak-streamflow frequency 

statistics for 32 selected streamflow-gaging stations in the 

Oklahoma Panhandle and in neighboring parts of Colorado, 

Kansas, New Mexico, and Texas (table 1). Peak-streamflow 

frequency statistics were computed from annual peakstreamflow records from water year 1978 through water 

year 2014 (U.S. Geological Survey, 2015b). A water year 

is a period of 12 consecutive months that includes January 

through September of the named calendar year and October 

through December of the previous calendar year. Peakstreamflow frequency statistics from the 32 streamflowgaging stations were related to basin characteristics by using 

generalized-least-squares multiple-linear-regression analysis. 

The regression equations derived from this analysis can 

be used to estimate peak-streamflow frequency statistics 

(flood magnitudes) over the irrigated period of record 

(1978 to present) for unregulated streams in the Oklahoma 

Panhandle. This report supersedes the report by Lewis (2010) 

for unregulated streams in the Oklahoma Panhandle. The 

revised regional regression equations in this report can be 

incorporated into the Oklahoma StreamStats application, a 

Web-based map tool that allows rapid delineation of drainage 

basins, computation of basin characteristics, and estimation of 

streamflow statistics at user-defined ungaged sites (Ries and 

others, 2004, 2008; Smith and Esralew, 2010).
Base political boundaries from U.S. Census Bureau (2014)Streams from Horizon Systems Corporation (2010)Arkansas River Basin from U.S. Geological Survey (2014b)Climate divisions from National Oceanic and Atmospheric Administration (2015b)Albers Equal-Area Conic projectionNorth American Datum of 1983

0 20 40 60 80 MILES

0 20 40 60 80 KILOMETERS

07

07134990

07140300

07140850

07141175

07142100

07

07154400

07156220

07156600

07156700

07157100

07157700

07157960

07227200

07227295

07227920

07233500

07139700

07139800

07154500

07157400

07157500

07232500

07234100

07140600

07141200

0714230

0707

07134990

07140300

07140850

07141175

07142100

07

07154400

07156220

07156600

07156700

07157100

07157700

07157960

07227200

07227295

07227920

07233500

07139700

07139800

07154500

07157400

07157500

07232500

07234100

07140600

07141200

0714230

Texhoma

observationwell Texhoma

COLORADO

KANSAS

OKLAHOMA

NEW MEXICO

TEXAS

COLORAD

NEW MEXICO

ArkansasRiverBasin

S

OPTIMA DAM

104° 103° 102° 101° 100° 99°

38°37°36°

 Optima

Lake

 Optima

Lake Coldwater Creek Coldwater Creek

River

North Cimar

River Arkansas

River

Wolf Creek

Canadian

Canadian

Beaver River Beaver River 

Cimarron River

07134990

EXPLANATION

High Plains (or Ogallala) aquifer water-level change, predevelopment to 2013, in feet (McGuire, 2014) 

Decline More than 150 101 to 150 51 to 100 26 to 50 11 to 25 1 to 10

No change 0Rise 1 to 10 11 to 25 More than 25

Irrigated land cover (Qi and others, 2002)Oklahoma Panhandle statistical region boundary  (Esralew and Smith, 2010)U.S. Geological Survey streamflow-gaging station and station numberObservation well

Figure 1. Selected U.S. Geological Survey streamflow-gaging stations and changes in water level of the High Plains (or Ogallala) aquifer in and near 
0 10,000 20,000 30,000 40,000 50,000 60,000 01020304050

Annual peak flow, in cubic feet per second

Annual precipitation, in inches

1938

1939

1940

1941

1942

1943

1944

1945

1946

1947

1948

1949

1950

1951

1952

1953

1954

1955

1956

1957

1958

1959

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

1972

1973

1974

1975

1976

1977

1978

1979

1980

1981

1982

1983

1984

1985

1986

1987

1988

1989

1990

1991

1992

Water year (October 1–September 30)

Predevelopment period Transition period Irrigated period

Optima Dam construction

Modifie

Annual peak streamflow at the Beaver River near Guymon, Oklahoma (USGS 07232500)Annual percentage of no-flow days at the Beaver River near Guymon, Oklahoma (USGS 07232500)Water level in the Texhoma observation well5-year weighted average of annual precipitation for the Oklahoma PanhandleAnnual precipitation for the Oklahoma Panhandle (National Oceanic and Atmospheric Administration, 2015a)USGS, U.S. Geological Survey

EXPLANATION

Figure 2. Changes in annual peak streamflow and annual percentage of no-flow days at the Beaver River near Guymon, Oklahoma (U.S. Geological S

station 07232500), 1938–93.
Introduction

A

B

Figure 3. Images showing A, an artistic rendering of Optima Lake as it was expected to appear after construction (U.S. Army Corps of 

Engineers, 1966); and B, a panoramic photograph of Optima Lake in September 2004. 
6

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Streamflow-gaging station information

Site 

number

Station 

number 

(fig. 1)

Station name Latitude

(degrees)

Longitude

(degrees)

WBD subbasin 

number

1 07134990 Wild Horse Creek above Holly, Colorado 38.057062 -102.138434 11020009

2 07139700 Arkansas River tributary near Dodge City, Kansas 37.714447 -100.015082 11030004

3 07139800 Mulberry Creek near Dodge City, Kansas 37.598078 -100.015187 11030004

4 07140300 Whitewoman Creek near Bellefont, Kansas 37.921854 -99.642931 11030004

5 07140600 Pawnee River tributary near Kalvesta, Kansas 38.059058 -100.3499 11030005

6 07140850 Pawnee River near Burdett, Kansas 38.207104 -99.643454 11030005

7 07141175 Buckner Creek near Burdett, Kansas 38.163015 -99.642884 11030006

8 07141200 Pawnee River at Rozel, Kansas 38.207397 -99.406266 11030005

9 07142100 Rattlesnake Creek tributary near Mullinville, Kansas 37.586383 -99.421775 11030009

10 07142300 Rattlesnake Creek near Macksville, Kansas 37.871248 -98.875751 11030009

11 07142575 Rattlesnake Creek near Zenith, Kansas 38.093477 -98.546204 11030009

12 07143100 Little Cheyenne Creek tributary near Claflin, Kansas 38.456756 -98.535914 11030011

13 07144900 South Fork Ninnescah River tributary near Pratt, 

Kansas

37.675063 -98.723389 11030015

14 07148350 Salt Fork Arkansas River near Winchester, 

Oklahoma

36.961691 -98.781906 11060002

15 07148400 Salt Fork Arkansas River near Alva, Oklahoma 36.814972 -98.647982 11060002

16 07149000 Medicine Lodge River near Kiowa, Kansas 37.039373 -98.469518 11060003

17 07154400 Carrizozo Creek near Kenton, Oklahoma 36.883418 -103.018143 11040001

18 07154500 Cimarron River near Kenton, Oklahoma 36.926584 -102.959022 11040001

19 07156220 Bear Creek near Johnson, Kansas 37.628442 -101.761683 11040005

20 07156600 Cimarron River tributary near Moscow, Kansas 37.336123 -101.050162 11040006

21 07156700 Cimarron River tributary near Satanta, Kansas 37.271424 -100.926528 11040006

22 07157100 Crooked Creek near Copeland, Kansas 37.565336 -100.554344 11040007

23 07157400 Crooked Creek tributary at Meade, Kansas 37.296355 -100.339968 11040007

24 07157500 Crooked Creek near Englewood, Kansas 37.031644 -100.209176 11040007

25 07157700 Keiger Creek near Ashland, Kansas 37.193987 -99.918292 11040008

26 07157960 Buffalo Creek near Lovedale, Oklahoma 36.77067 -99.36689 11050001

27 07227200 Tramperos Creek near Stead, New Mexico 36.070833 -103.203344 11090102

28 07227295 Sandy Arroyo tributary near Clayton, New Mexico 36.387354 -103.319956 11090103

29 07227920 Dixon Creek near Borger, Texas 35.664756 -101.350894 11090106

30 07232500 Beaver River near Guymon, Oklahoma 36.721457 -101.489782 11100101

31 07233500 Palo Duro Creek near Spearman, Texas 36.202169 -101.306342 11100104

32 07234100 Clear Creek near Elmwood, Oklahoma 36.645486 -100.503058 11100201
Introduction

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site number

Basin characteristics1

Contributing 

drainage area

(square miles) 

(CONTDA)

Mean annual 

precipitation

(inches) 

(PRECIP)

10–85 stream

channel slope

(feet per mile) 

(CSL10_85FM)

Mean soil 

permeability

(inches per 

hour) 

(SOILPERM)

Outlet 

elevation

(feet above 

NAVD 88) 

(OUTLETELEV)

Outlet 

mean annual 

precipitation 

(1961–90)

(inches) 

(PRCOUT61)

Outlet 

mean annual 

precipitation 

(1971–2000)

(inches) 

(PRCOUT71)

1 126.53 16.57 17.68 1.43 3,402.84 15.53 16.88

2 9.40 22.50 14.16 1.49 2,502.74 21.72 22.45

3 68.50 22.37 7.93 1.38 2,519.59 22.05 22.62

4 17.39 23.32 11.29 1.06 2,300.07 23.17 23.49

5 8.30 20.92 13.03 0.79 2,647.83 19.94 20.98

6 1,038.62 21.15 4.32 1.12 2,109.42 21.78 22.64

7 717.27 22.49 6.35 1.03 2,115.69 21.84 22.81

8 2,057.39 21.87 4.06 1.09 2,052.80 22.15 23.71

9 10.19 25.05 8.88 1.06 2,289.48 23.97 25.00

10 474.66 25.38 3.99 4.18 1,970.00 24.55 26.38

11 729.11 25.67 3.82 4.40 1,797.51 25.12 26.84

12 1.45 26.91 18.99 1.03 1,785.86 25.82 26.94

13 1.58 27.32 24.40 2.09 1,892.40 25.75 27.36

14 827.23 26.46 9.30 2.63 1,413.85 25.13 27.59

15 982.10 26.67 8.45 2.71 1,297.93 26.45 28.94

16 885.08 27.35 7.97 2.42 1,289.63 27.50 29.52

17 112.28 16.60 26.95 1.70 4,361.96 16.95 17.21

18 1,111.61 16.84 23.55 1.73 4,281.76 16.90 17.21

19 826.15 17.05 13.44 1.20 3,302.24 15.75 16.87

20 21.42 18.62 23.02 1.96 2,811.00 18.25 18.84

21 4.23 19.30 25.88 2.44 2,740.96 18.97 19.25

22 47.74 20.26 13.06 0.94 2,695.94 20.31 20.65

23 6.89 21.63 38.24 1.04 2,458.39 21.64 21.66

24 821.97 21.35 3.99 1.84 2,168.28 21.71 22.37

25 34.57 23.15 26.95 1.55 2,066.97 22.28 23.31

26 401.31 25.21 11.68 2.49 1,618.27 24.40 25.66

27 461.88 16.28 14.33 1.17 4,485.35 15.23 15.96

28 1.21 16.24 53.32 1.84 5,108.80 15.47 16.23

29 133.02 22.00 19.94 2.33 2,838.22 19.99 21.83

30 1,611.86 17.28 14.02 1.57 2,980.01 17.39 18.11

31 624.68 18.25 8.00 0.79 2,973.65 18.66 19.96

32 161.87 21.25 11.36 0.96 2,545.42 21.08 21.72

Average for 

all stations:

448.05 21.67 15.38 1.73 2,588.28 21.17 22.22
8

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site number

Basin characteristics1

Percentage of

forest-canopy cover

(CANOPY_PCT)

Percentage of

impervious cover 

(IMPNLCD01)

Percentage of 

drainage area on the 

High Plains aquifer 

(OK_HIPERMA)

Percentage of 

drainage area 

with crop cover 

(LC01CROP)

Mean drainagebasin slope 

(percent)

(BSLDEM10M)

1 0.10 0.28 69.89 42.73 1.79

2 0.04 0.09 100.00 81.32 1.77

3 0.04 0.13 100.00 77.44 2.14

4 0.16 0.34 100.00 79.57 1.15

5 0.00 0.07 84.32 67.00 1.20

6 0.19 0.10 27.93 56.29 2.61

7 0.18 0.29 71.07 55.74 2.85

8 0.19 0.18 43.42 56.17 2.42

9 0.05 0.22 100.00 75.61 2.15

10 0.40 0.37 100.00 63.35 1.81

11 0.77 0.40 100.00 63.48 1.07

12 1.32 0.28 100.00 82.21 1.27

13 0.00 0.79 100.00 88.56 2.01

14 0.64 0.10 19.03 13.10 5.97

15 0.71 0.21 16.03 14.26 6.07

16 1.68 0.25 41.67 22.64 5.95

17 6.43 0.06 0.00 0.00 11.77

18 11.22 0.09 0.24 0.32 13.25

19 0.04 0.24 91.90 42.98 1.53

20 0.00 0.37 100.00 67.63 1.71

21 0.01 0.14 100.00 79.08 1.90

22 0.06 0.33 100.00 88.63 1.22

23 0.24 0.22 100.00 40.61 4.68

24 0.23 0.18 99.50 60.94 2.54

25 0.06 0.05 67.73 11.48 6.69

26 0.38 0.22 10.93 20.52 5.94

27 1.57 0.06 8.09 0.27 6.26

28 0.00 0.11 100.00 0.00 2.01

29 0.12 0.73 87.94 3.75 5.86

30 0.47 0.24 78.12 10.83 3.53

31 0.01 0.47 100.00 49.90 1.61

32 0.07 0.23 100.00 38.14 2.67

Average for 

all stations:

0.86 0.24 72.43 45.45 3.61
Introduction

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site 

number

Streamflow-gaging station information Peak-streamflow frequency analysis information

Station 

number 

(fig. 1)

Station name

Entire 

period of 

record 

(water 

years)2

Irrigated 

period of 

record 

length 

(1978–2014; 

years)

Number 

of noflow 

years 

(1978–

2014)

Historical 

record 

length 

(years)

Number 

of high 

outliers

Highoutlier 

threshold 

(ft3

/s)

Lowoutlier 

threshold 

(ft3

/s)

1 07134990 Wild Horse Creek above Holly, Colorado 1996–2014 19 0 -- -- -- --

2 07139700 Arkansas River tributary near Dodge City, 

Kansas

1957–2012 33 0 -- -- -- --

3 07139800 Mulberry Creek near Dodge City, Kansas 1969–90 13 1 -- -- -- --

4 07140300 Whitewoman Creek near Bellefont, Kansas 1957–89 12 1 -- -- -- --

5 07140600 Pawnee River tributary near Kalvesta, Kansas 1957–89 12 0 -- -- -- --

6 07140850 Pawnee River near Burdett, Kansas 1982–2014 33 2 -- -- -- --

7 07141175 Buckner Creek near Burdett, Kansas 1996–2012 17 0 -- -- -- --

8 07141200 Pawnee River at Rozel, Kansas 1925–2014 37 1 -- -- -- --

9 07142100 Rattlesnake Creek tributary near Mullinville, 

Kansas

1957–89 12 2 -- -- -- --

10 07142300 Rattlesnake Creek near Macksville, Kansas 1960–2014 37 0 -- -- -- --

11 07142575 Rattlesnake Creek near Zenith, Kansas 1973–2014 37 0 -- -- -- --

12 07143100 Little Cheyenne Creek tributary near Claflin, 

Kansas

1957–2012 35 3 -- -- -- --

13 07144900 South Fork Ninnescah River tributary near 

Pratt, Kansas

1957–89 12 0 -- -- -- --

14 07148350 Salt Fork Arkansas River near Winchester, 

Oklahoma

1957–93 16 0 -- -- -- --

15 07148400 Salt Fork Arkansas River near Alva, Oklahoma 1938–2014 35 0 -- -- -- --

16 07149000 Medicine Lodge River near Kiowa, Kansas 1938–2014 37 0 -- -- -- --

17 07154400 Carrizozo Creek near Kenton, Oklahoma 1953–2014 37 2 -- -- -- --

18 07154500 Cimarron River near Kenton, Oklahoma 1951–2014 37 0 -- -- -- --

19 07156220 Bear Creek near Johnson, Kansas 1967–98 21 3 -- -- -- --

20 07156600 Cimarron River tributary near Moscow, Kansas 1957–89 12 3 -- -- -- --

21 07156700 Cimarron River tributary near Satanta, Kansas 1957–2010 28 4 -- -- -- --

22 07157100 Crooked Creek near Copeland, Kansas 1957–89 12 0 -- -- -- --

23 07157400 Crooked Creek tributary at Meade, Kansas 1957–89 12 2 -- -- -- --

24 07157500 Crooked Creek near Englewood, Kansas 1943–2014 37 0 -- -- -- --

25 07157700 Keiger Creek near Ashland, Kansas 1957–1989 12 1 -- -- -- --

26 07157960 Buffalo Creek near Lovedale, Oklahoma 1966–93 16 0 -- -- -- --

27 07227200 Tramperos Creek near Stead, New Mexico 1965–2014 35 4 -- -- -- --

28 07227295 Sandy Arroyo tributary near Clayton, New 

Mexico

1952–1996 17 3 -- -- -- --

29 07227920 Dixon Creek near Borger, Texas 1975–1989 12 0 -- -- -- --

30 07232500 Beaver River near Guymon, Oklahoma 1937–1993 16 0 -- -- -- --

31 07233500 Palo Duro Creek near Spearman, Texas 1936–2014 16 0 36 -- -- --

32 07234100 Clear Creek near Elmwood, Oklahoma 1966–1993 16 0 -- -- -- --
10

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site 

number

Skew coefficient for 

LP III distribution

Generalized 

skew 

source3

Computed peak-streamflow frequency statistics, in cubic feet per 

second, for indicated annual exceedance probability (percent), 

irrigated period of record (1978–2014)

Station Gener

alized Weighted 50 20 10 4 2 1 0.2

1 0.268 -0.408 -0.331 a 208 447 647 941 1,180 1,450 2,120

2 -1.221 -0.413 -0.420 a 103 315 543 940 1,320 1,770 3,090

3 -1.173 -0.365 -0.408 a 36.8 272 704 1,820 3,230 5,290 13,400

4 0.648 -0.361 -0.287 a 103 409 803 1,590 2,440 3,530 7,230

5 -0.878 -0.405 -0.406 a 300 1,110 2,070 3,860 5,630 7,780 14,300

6 -1.351 -0.213 -0.280 a 429 1,310 2,270 3,970 5,610 7,590 13,600

7 -1.145 -0.229 -0.198 a 489 1,380 2,320 3,960 5,540 7,450 13,400

8 -0.666 -0.182 -0.149 a 1,040 2,300 3,440 5,230 6,810 8,620 13,700

9 -0.126 -0.390 -0.368 a 410 772 1,050 1,420 1,710 2,010 2,730

10 -0.030 -0.236 -0.193 a 159 583 1,120 2,200 3,360 4,880 10,200

11 1.305 -0.188 -0.044 a 340 918 1,540 2,650 3,760 5,140 9,650

12 -0.229 -0.316 -0.157 a 78.4 159 227 328 415 510 769

13 -1.337 -0.399 -0.317 a 515 917 1,220 1,620 1,920 2,240 3,000

14 -1.144 -0.142 -0.271 b 5,630 10,400 14,100 19,300 23,400 27,600 38,300

15 -0.663 -0.128 -0.281 b 3,790 7,100 9,660 13,200 16,100 19,000 26,500

16 -0.765 -0.408 -0.303 a 2,910 4,810 6,150 7,890 9,200 10,500 13,600

17 0.383 0.320 0.340 b 1,470 2,750 3,920 5,820 7,600 9,740 16,400

18 -0.039 0.284 0.168 b 2,330 6,390 11,000 19,900 29,400 42,000 87,500

19 -0.987 -0.385 -0.407 a 708 2,880 5,610 10,900 16,300 23,100 44,400

20 -0.545 -0.505 -0.508 a 167 645 1,210 2,230 3,210 4,360 7,710

21 -0.054 -0.538 -0.440 a 50.7 266 582 1,260 2,020 3,010 6,350

22 -1.221 -0.410 -0.428 a 89.1 532 1,230 2,830 4,660 7,130 15,800

23 -0.052 -0.477 -0.442 a 255 1,130 2,280 4,550 6,920 9,890 19,300

24 0.139 -0.361 -0.264 a 139 499 938 1,790 2,680 3,810 7,550

25 -0.421 -0.419 -0.419 a 339 542 677 845 966 1,080 1,340

26 -0.672 -0.329 -0.390 b 915 3,830 7,600 15,100 22,800 32,700 64,300

27 -0.391 0.455 0.261 b 769 1,860 3,040 5,210 7,470 10,400 20,800

28 0.456 0.471 0.468 b 32.3 63 92.5 143 193 254 459

29 -0.491 0.000 -0.131 c 746 1,980 3,240 5,440 7,560 10,100 18,000

30 -1.119 -0.290 -0.227 b 167 993 2,410 6,000 10,600 17,500 46,600

31 -1.189 0.000 0.231 c 716 2,400 4,660 9,670 15,700 24,500 61,900

32 -0.998 -0.271 -0.339 b 950 3,950 7,880 15,800 24,200 35,100 71,300

Average for 

all stations:

824 2,000 3,260 5,580 7,940 10,900 21,100
Introduction

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site 

number

Streamflow-gaging station information Estimated peak-streamflow frequency statistics, in cubic feet per 

second, for indicated annual exceedance probability (percent)

Station 

number 

(fig. 1)

Station name

Oklahoma statewide regression estimates (Lewis, 2010)

50 20 10 4 2 1 0.2

1 07134990 Wild Horse Creek above Holly, Colorado 804 2,350 4,180 7,530 11,200 15,100 29,100

2 07139700 Arkansas River tributary near Dodge City, 

Kansas

262 667 1,110 1,880 2,650 3,530 6,420

3 07139800 Mulberry Creek near Dodge City, Kansas 875 2,190 3,610 6,060 8,660 11,300 20,400

4 07140300 Whitewoman Creek near Bellefont, Kansas 408 1,020 1,670 2,800 3,940 5,190 9,320

5 07140600 Pawnee River tributary near Kalvesta, 

Kansas

205 537 905 1,550 2,230 3,000 5,570

6 07140850 Pawnee River near Burdett, Kansas 4,260 10,700 17,700 29,600 43,200 55,400 100,000

7 07141175 Buckner Creek near Burdett, Kansas 4,020 10,000 16,400 27,300 39,200 49,900 88,300

8 07141200 Pawnee River at Rozel, Kansas 7,080 17,600 28,700 47,700 69,400 87,900 156,000

9 07142100 Rattlesnake Creek tributary near 

Mullinville, Kansas

320 767 1,230 2,030 2,840 3,730 6,620

10 07142300 Rattlesnake Creek near Macksville, Kansas 3,650 8,490 13,400 21,700 30,700 38,700 67,000

11 07142575 Rattlesnake Creek near Zenith, Kansas 4,920 11,400 17,900 28,900 40,900 51,200 88,100

12 07143100 Little Cheyenne Creek tributary near 

Claflin, Kansas

116 275 443 731 991 1,310 2,300

13 07144900 South Fork Ninnescah River tributary near 

Pratt, Kansas

131 313 505 835 1,120 1,490 2,580

14 07148350 Salt Fork Arkansas River near Winchester, 

Oklahoma

6,560 15,400 24,500 40,000 55,300 68,900 115,000

15 07148400 Salt Fork Arkansas River near Alva, 

Oklahoma

7,360 17,200 27,200 44,300 61,200 76,100 127,000

16 07149000 Medicine Lodge River near Kiowa, Kansas 7,170 16,500 26,000 42,100 57,900 71,900 119,000

17 07154400 Carrizozo Creek near Kenton, Oklahoma 797 2,360 4,230 7,680 11,300 15,300 29,200

18 07154500 Cimarron River near Kenton, Oklahoma 3,650 10,700 19,100 34,400 50,800 67,000 125,000

19 07156220 Bear Creek near Johnson, Kansas 2,810 8,060 14,200 25,300 37,600 49,700 93,300

20 07156600 Cimarron River tributary near Moscow, 

Kansas

330 925 1,620 2,860 4,150 5,610 10,600

21 07156700 Cimarron River tributary near Satanta, 

Kansas

124 344 597 1,050 1,510 2,070 3,910

22 07157100 Crooked Creek near Copeland, Kansas 609 1,620 2,740 4,730 6,830 9,070 16,700

23 07157400 Crooked Creek tributary at Meade, Kansas 231 615 1,050 1,830 2,550 3,430 6,190

24 07157500 Crooked Creek near Englewood, Kansas 3,670 9,200 15,100 25,200 36,800 47,200 85,300

25 07157700 Keiger Creek near Ashland, Kansas 727 1,860 3,120 5,330 7,390 9,680 17,000

26 07157960 Buffalo Creek near Lovedale, Oklahoma 3,820 9,220 14,900 24,700 34,200 43,200 73,500

27 07227200 Tramperos Creek near Stead, New Mexico 1,760 5,150 9,170 16,500 24,700 33,000 63,200

28 07227295 Sandy Arroyo tributary near Clayton, New 

Mexico

42.8 130 238 440 644 913 1,810

29 07227920 Dixon Creek near Borger, Texas 1,520 3,940 6,630 11,400 16,000 20,800 36,800

30 07232500 Beaver River near Guymon, Oklahoma 4,530 12,900 22,700 40,300 59,800 78,300 146,000

31 07233500 Palo Duro Creek near Spearman, Texas 2,480 6,790 11,700 20,300 30,100 39,500 73,900

32 07234100 Clear Creek near Elmwood, Oklahoma 1,470 3,810 6,380 10,900 15,600 20,300 36,700

Average for all stations: 2,400 6,030 9,970 16,800 24,100 30,900 55,100

RMSE, in ft3

/s 18,900 46,500 76,100 128,000 183,000 233,000 412,000
12

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site 

number

Estimated peak-streamflow frequency statistics, in cubic feet per second, 

for indicated annual exceedance probability (percent)

Oklahoma Panhandle regional regression estimates (Smith and others, 2015; this report)

50 20 10 4 2 1 0.2

1 402 1,140 1,940 3,210 4,550 6,290 10,700

2 166 458 760 1,260 1,740 2,340 3,880

3 327 918 1,550 2,570 3,630 4,980 8,420

4 205 568 948 1,570 2,180 2,960 4,930

5 159 438 726 1,200 1,660 2,240 3,700

6 823 2,380 4,130 6,850 9,920 14,000 24,300

7 726 2,090 3,620 6,000 8,650 12,200 21,000

8 1,040 3,020 5,280 8,760 12,800 18,200 31,700

9 171 471 782 1,300 1,790 2,420 4,010

10 631 1,810 3,120 5,170 7,420 10,400 17,900

11 730 2,100 3,640 6,030 8,700 12,200 21,200

12 88.0 238 387 642 871 1,150 1,870

13 90.7 245 400 663 899 1,190 1,940

14 762 2,190 3,810 6,310 9,120 12,800 22,300

15 808 2,330 4,050 6,710 9,710 13,700 23,800

16 780 2,250 3,900 6,470 9,350 13,200 22,800

17 386 1,090 1,860 3,080 4,350 6,010 10,200

18 842 2,430 4,230 7,020 10,200 14,400 25,000

19 761 2,190 3,810 6,310 9,110 12,800 22,200

20 220 611 1,020 1,690 2,360 3,200 5,350

21 127 346 570 944 1,290 1,730 2,840

22 289 809 1,360 2,260 3,170 4,350 7,320

23 150 411 679 1,130 1,550 2,080 3,440

24 760 2,190 3,800 6,300 9,090 12,800 22,200

25 259 722 1,210 2,010 2,820 3,840 6,450

26 596 1,700 2,930 4,860 6,980 9,760 16,800

27 625 1,790 3,090 5,120 7,350 10,300 17,700

28 82.8 224 363 602 815 1,080 1,750

29 409 1,160 1,970 3,270 4,640 6,410 10,900

30 956 2,770 4,840 8,020 11,700 16,500 28,900

31 692 1,990 3,440 5,700 8,220 11,500 19,900

32 437 1,240 2,120 3,510 4,990 6,910 11,800

Average for 

all stations:

484 1,390 2,390 3,950 5,680 7,940 13,700

RMSE, in ft3

/s 3,170 9,110 15,800 26,200 37,800 53,100 92,000
Introduction

Table 1. Streamflow-gaging station information, basin characteristics, and peak-streamflow frequency statistics for unregulated 

drainage basins in and near the Oklahoma Panhandle.—Continued

[WBD, Watershed Boundary Dataset; NAVD 88, North American Vertical Datum of 1988; ft3/s, cubic feet per second; --, not applicable; LP III, Log-Pearson 

Type III; RMSE, root mean square error] 

Site 

number

Oklahoma statewide regression estimates (Lewis, 2010) percent error from computed 

peak-streamflow frequency statistics for the irrigated period of record (1978–2014)

50 20 10 4 2 1 0.2

1 287 426 546 700 849 941 1,270

2 154 112 104 100 101 99 108

3 2,280 705 413 233 168 114 52

4 296 149 108 76 61 47 29

5 -32 -52 -56 -60 -60 -61 -61

6 893 717 680 646 670 630 635

7 722 625 607 589 608 570 559

8 581 665 734 812 919 920 1,040

9 -22 -1 17 43 66 86 142

10 2,200 1,360 1,100 886 814 693 557

11 1,350 1,140 1,060 991 988 896 813

12 48 73 95 123 139 157 199

13 -75 -66 -59 -48 -42 -33 -14

14 17 48 74 107 136 150 200

15 94 142 182 236 280 301 379

16 146 243 323 434 529 585 775

17 -46 -14 8 32 49 57 78

18 57 67 74 73 73 60 43

19 297 180 153 132 131 115 110

20 98 43 34 28 29 29 37

21 145 29 3 -17 -25 -31 -38

22 584 205 123 67 47 27 6

23 -9 -46 -54 -60 -63 -65 -68

24 2,540 1,740 1,510 1,310 1,270 1,140 1,030

25 114 243 361 531 665 796 1,170

26 317 141 96 64 50 32 14

27 129 177 202 217 231 217 204

28 32 106 157 208 234 259 294

29 104 99 105 110 112 106 104

30 2,610 1,200 842 572 464 347 213

31 246 183 151 110 92 61 19

32 55 -4 -19 -31 -36 -42 -49

Average for 

all stations:

507 332 302 288 298 288 308

1

Basin characteristic names used in the StreamStats Web application are in uppercase and parentheses. Values for basin characteristics may vary slightly from 

the StreamStats Web application because of differences in rounding and the exact locations clicked.

2

A water year is a period of 12 consecutive months that includes January through September of the named calendar year and October through December of the 

previous calendar year.

3

Generalized skew obtained from (a) Rasmussen and Perry (2000), (b) Lewis (2010), or (c) Judd and others (1996).
14

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

In this report, the Oklahoma Panhandle refers to the 

portion of Oklahoma that extends west of the 100th meridian 

(100 degrees west longitude; fig. 1). The larger Oklahoma 

Panhandle statistical region includes the Oklahoma Panhandle, 

a part of Oklahoma east of the 100th meridian, and parts 

of several neighboring States. The Oklahoma Panhandle 

statistical region was delineated by Esralew and Smith (2010) 

for use in the Oklahoma StreamStats application (Smith 

and Esralew, 2010) to group streamflow-gaging stations 

with similar relations (regional regressions) between basin 

characteristics and streamflow statistics. The eastern boundary 

of the Oklahoma Panhandle statistical region approximately 

follows the boundary for flood-region 12 delineated by 

Crippen and Bue (1977). Though regional regressions 

described in this report apply to the Oklahoma Panhandle 

statistical region, only locations in Oklahoma are accessible 

in the Oklahoma StreamStats application (Smith and Esralew, 

2010). 

Streamflow-Gaging Station Selection 

and Data Analysis

Few streamflow-gaging stations currently (2015) are in 

operation in the Oklahoma Panhandle or the larger Oklahoma 

Panhandle statistical region (fig. 1). Many streamflowgaging stations, like the Beaver River near Guymon, Okla., 

(07232500, fig. 2), were discontinued in the 1980s or 1990s 

when no-flow conditions became prevalent in the Oklahoma 

Panhandle (fig. 4, table 1). Therefore, streamflow-gaging 

stations with similar physical and hydrologic settings in 

neighboring States were included to compile a statistically 

representative dataset for the Oklahoma Panhandle statistical 

region (fig. 1). 

U.S. Geological Survey streamflow-gaging stations with 

annual peak-streamflow data were selected for computation 

of basin (physical and climatic) characteristics and peakstreamflow frequency statistics over the entire period of record 

and the irrigated period of record. The entire period of record 

was defined to begin in the first year of peak-streamflow 

record (1925) and continue to 2014; the irrigated period of 

record was defined to begin in 1978 (Wahl and Tortorelli, 

1997; Lewis and Esralew, 2009; Esralew and Lewis, 2010) 

and continue to 2014. Only peak-streamflow data from 

streamflow-gaging stations in the Arkansas River drainage 

basin (fig. 1) with at least 10 years of peak-streamflow data 

in the irrigated period of record were selected for analysis. 

Gaps in the irrigated period of record were accepted. Data 

from some streamflow-gaging stations were excluded because 

of substantial regulation by large dams or because of surfacewater diversions upstream as described in station descriptions 

(Lewis and Esralew, 2009; U.S. Geological Survey, 2015a). 

Substantial regulation was defined as a contributing drainage 

basin where 20 percent or more of the basin is upstream 

from large dams (including floodwater retarding structures) 

(Heimann and Tortorelli, 1988). Most of the streamflowgaging stations selected for data analysis have drainage-basin 

area on the High Plains aquifer as defined by Qi (2010) 

(table 1). 

Basin Characteristics

Peak-streamflow frequency statistics (such as the peakstreamflow magnitude with a 1-percent annual exceedance 

probability) are influenced by a number of drainage-basin 

characteristics, though the most influential drainage-basin 

characteristics vary regionally; for example, many statewide 

studies of peak-streamflow frequency have concluded that 

drainage area, mean annual precipitation, and stream channel 

slope are useful basin characteristics (independent variables) 

for estimating peak-streamflow frequency statistics by using 

regionalized regression methods (Jennings and others, 1994). 

Peak-streamflow frequency regression equations have been 

developed for all 50 U.S. States and Puerto Rico; all 51 sets of 

regression equations use drainage area, 27 use stream channel 

slope, and 19 use mean annual precipitation as independent 

variables in computations of peak-streamflow frequency 

statistics (Jennings and others, 1994).

For each selected streamflow-gaging station, selected 

basin characteristics were computed for use as independent 

variables in peak-streamflow frequency regression equations 

for the areas in and near the Oklahoma Panhandle (table 1). 

Percentage of drainage area on the High Plains aquifer 

(OK_HIPERMA) was computed in a geographic information 

system (GIS) as the percentage of the contributing drainage 

basin area that intersected the aquifer as defined by Qi (2010). 

Percentage of drainage area with crop cover (LC01CROP) 

was computed in a GIS as the percentage of the contributing 

drainage basin area that intersected cropland cover as defined 

by the 2006 National Land Cover Database (Fry and others, 

2011; Multi-Resolution Land Characteristics Consortium, 

2011). Contributing drainage area (CONTDA), mean 

annual precipitation (PRECIP), 10–85 stream channel slope 

(CSL10_85FM), mean soil permeability (SOILPERM), 

outlet elevation (OUTLETELEV), outlet mean annual 

precipitation from 1961 to 1990 (PRCOUT61), outlet mean 

annual precipitation from 1971 to 2000 (PRCOUT71), 

percentage of forest-canopy cover (CANOPY_PCT), 

percentage of impervious cover (IMPNLCD01), and mean 

drainage-basin slope (BSLDEM10M) were computed using 

methods described in Esralew and Smith (2010) and Smith 

and Esralew (2010); these methods are the foundation 

of the Web-based Oklahoma StreamStats application. 

The Oklahoma StreamStats application was designed to 

automatically compute selected drainage-basin characteristics 

for user-selected sites of interest in Oklahoma. For selected 

streamflow-gaging stations in Oklahoma, basin characteristics 
Streamflow-Gaging Station Selection and Data Analysis

Count of operating

streamflow-gaging stations

0

5

10

15

20

25

30

Streamflow-gaging station number

07134990

07139700

07139800

07140300

07140600

07140850

07141175

07141200

07142100

07142300

07142575

07143100

07144900

07148350

07148400

07149000

07154400

07154500

07156220

07156600

07156700

07157100

07157400

07157500

07157700

07157960

07227200

07227295

07227920

07232500

07233500

07234100

Water year (October 1–September 30)

1925 1931 1937 1943 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015

1925 1931 1937 1943 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015

Beginning of irrigated period of record

Colorado station

Kansas station

Texas station

Oklahoma station

New Mexico station

EXPLANATION

Figure 4. Period of record and count of selected operating streamflow-gaging stations in and near the Oklahoma Panhandle, 1925–

2014.
16

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

were computed by using the Oklahoma StreamStats 

application (Smith and Esralew, 2010). For the remaining 

selected stations, basin characteristics were computed by using 

a desktop version of the Oklahoma StreamStats application, 

which uses the same data and methods as the Web-based 

version but enables computations to be made for areas outside 

of Oklahoma. Values for basin characteristics computed from 

the desktop version of the Oklahoma StreamStats application 

(table 1) may vary slightly from those computed by the 

Web-based Oklahoma StreamStats application because of 

differences in rounding and the exact locations selected on 

that application. Contributing drainage area values computed 

by using the Oklahoma StreamStats application may not 

match the values published on the National Water Information 

System Website (NWISWeb; U.S. Geological Survey, 2015b) 

because the methods used to compute contributing drainage 

area differ between States. 

The study area in Colorado, Kansas, New Mexico, 

Oklahoma, and Texas (fig. 1) contains numerous playa lakes 

that accumulate runoff during precipitation (Smith and 

Esralew, 2010). Accumulated runoff is slowly released from 

these lakes by infiltration and evapotranspiration (Gurdak 

and Roe, 2009). The areas that drain to these lakes are 

noncontributing areas because they do not directly contribute 

runoff to a stream. Noncontributing areas in and near the 

Oklahoma Panhandle statistical region were modeled by using 

drains (sinks) at playa lakes and large depressions (greater 

than about 0.06 mi2

 in area) to subtract playa drainage areas 

from the main stem drainage areas. These methods match 

those used by the Oklahoma StreamStats application (Smith 

and Esralew, 2010). Noncontributing areas also were excluded 

during computation of basin characteristics. Areas upstream 

from manmade dams were not modeled as noncontributing 

areas because those dams provide outlet works and spillways 

that allow runoff to flow downstream.

Trend Analysis

Trend analysis of relevant hydrologic data is prudent 

prior to performing regression analysis on peak streamflow 

data. Kendall’s tau (Kendall, 1938; Kendall, 1975) is a 

robust rank based statistic that tests for the presence of trend 

in a data series. The value of the Kendall’s tau statistic is 

a number between -1 and 1; endpoints that indicate strong 

decreasing and increasing trends, respectively. In this report, 

a probability (p) value is reported with each Kendall tau 

statistic, and a 95-percent confidence level or greater (p ≤ 

0.05) was deemed to indicate a significant trend with time. 

The Sen slope (Sen, 1968) also was computed to estimate 

the general slope (rate) of the trend. Trends are graphically 

represented in figures in this report using locally weighted 

scatterplot smoothing (LOWESS; Cleveland and McGill, 

1984; Cleveland, 1985) trend lines. 

Precipitation Trend Analysis

Trends in annual peak streamflows could be caused by 

trends in annual precipitation. Because of this possibility, 

the annual precipitation records from four climate divisions 

(Vose and others, 2014; National Oceanic and Atmospheric 

Administration, 2015a; National Oceanic and Atmospheric 

Administration, 2015b) were examined for trends (fig. 1). 

One significant trend, an increase of 0.05 inch per year for 

the South Central Kansas climate division (KS08, fig. 1), 

was observed over the entire (streamflow) period of record 

(1925–2014) (fig. 5, table 2). No significant trends in annual 

precipitation were observed over the irrigated (streamflow) 

period of record (1978–2014) (fig. 5, table 2); therefore, any 

trends observed in streamflow over the irrigated period of 

record are not likely to have been related to trends in annual 

precipitation.
trend: +0.05 inch/year

Precipitation (National Oceanic and Atmospheric Administration, 2015a)LOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scatterp

Annual precipitation, in inches Annual precipitation, in inches

0

10203040

0

10203040

0

10203040

0

10203040

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 

Water year (October 1–September 30) Water year (October 1–September 30)

Oklahoma Panhandle (OK01)Southwest Kansas (KS07) South Central Kansas (KS08)

Texas Panhandle (TX01)

Figure 5. Annual precipitation trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected climate d

Oklahoma Panhandle.
18

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Table 2. Results of trend tests on annual precipitation for the entire period of record (1925–2014) and the irrigated period of record 

(1978–2014) for selected climate divisions in and near the Oklahoma Panhandle.

[Precipitation data from National Oceanic and Atmospheric Administration (2015a); in/yr, inches per year; shaded values are statistically significant at the 

95-percent confidence level or greater (p≤0.05); ≤, less than or equal to]

Climate division 

(fig. 1)

Entire period of record (1925–2014) Irrigated period of record (1978–2014)

Record 

length 

(water 

years)1

Median 

(in/yr)

Kendall 

tau p-value

Trend 

slope 

(in/yr)

Record 

length 

(water 

years)1

Median 

(in/yr)

Kendall 

tau p-value

Trend 

slope 

(in/yr)

Southwest Kansas (KS07) 90 19.15 0.0752 0.3364 0.02 37 19.62 -0.0977 0.3364 -0.04

South Central Kansas (KS08) 90 26.71 0.1443 0.0304 0.05 37 29.70 0.0917 0.3437 0.08

Oklahoma Panhandle (OK01) 90 19.28 0.0550 0.5108 0.01 37 20.40 -0.1441 0.1624 -0.06

Texas Panhandle (TX01) 90 17.74 0.0345 0.6661 0.01 37 17.97 -0.1141 0.2761 -0.07

1

A water year is a period of 12 consecutive months that includes January through September of the named calendar year and October through December of the 

previous calendar year.

Annual Peak Data Trend Analysis

Annual peak-streamflow data from selected streamflowgaging stations were obtained from NWISWeb (U.S. 

Geological Survey, 2015b) and examined for trends over 

the entire period of record and the irrigated period of 

record (fig. 6). Eighteen significant streamflow trends were 

identified in the entire period of record; 17 of those 18 

significant trends were decreasing (table 3). Because peakstreamflow data from more than half of the streamflow-gaging 

stations significantly decreased with no coincident decreasing 

trends in precipitation, this finding reinforces the conclusions 

of previous studies that the hydrology of the Oklahoma 

Panhandle statistical region has changed primarily as a result 

of groundwater withdrawals. Six significant streamflow trends 

were determined in the irrigated period of record at selected 

streamflow-gaging stations; 5 of those 6 significant trends 

were decreasing (table 3). The decreasing trends in peak 

streamflow during the irrigated period of record indicate that 

the hydrologic balance of the area in and near the Oklahoma 

Panhandle has continued to change since 1978 and has not 

reached a long-term equilibrium. Though the presence of 

some trends was statistically confirmed, the type or pattern of 

these trends was not clear. Hydrologic trends may be gradual 

or step-change or a complex combination or series of both. 

If the type of trend is well characterized for each station, a 

statistical model of the trend can be used to remove the effects 

of the trend from the time-series data (Ries and Dillow, 2006; 

Sherwood and others, 2007). No attempt was made to remove 

trends from the annual peak-streamflow record in this report; 

however, this technique could be used in future reports to 

adjust pre-1978 peak-streamflow data and add them to the 

irrigated period of record.

Peak-Streamflow Frequency Analysis

The USGS computer program PeakFQ version 7.1 

(U.S. Geological Survey, 2014a) was used to compute peakstreamflow frequency statistics from annual peak-streamflow 

data for the selected streamflow-gaging stations. PeakFQ 

automates many of the analytical procedures recommended 

in USGS Bulletin 17B (Interagency Advisory Committee on 

Water Data, 1982). Computed peak-streamflow frequency 

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

annual exceedance probabilities are listed in table 1. To reduce 

errors resulting from a poor log-Pearson Type III (LPIII) fit, 

peak-streamflow frequency statistics were adjusted based 

on historical flood information (where available), skew 

coefficients, and Interagency Advisory Committee on Water 

Data (1982) guidelines (table 1; Lewis, 2010).

The computed peak-streamflow frequency statistics can 

be compared to estimated peak-streamflow frequency statistics 

by using the statewide regression equations for Oklahoma 

(Lewis, 2010) to evaluate the suspected bias in the previous 

regression estimates for the Oklahoma Panhandle. The 

statewide regression equations for Oklahoma (Lewis, 2010) 

estimated greater peak-streamflow frequency statistics, on 

average, than those computed for the irrigated period of record 

(fig. 7, table 1). The Oklahoma statewide regression-estimated 

peak-streamflow frequency statistics (Lewis, 2010) for the 

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

probabilities were, on average, 507, 332, 302, 288, 298, 288, 

and 308 percent greater, respectively, than the computed 

peak-streamflow frequency statistics for the irrigated period of 

record (fig. 7, table 1). 
No data

No data No data No data 

No data

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scatt

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 11925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

Water year (October 1–September 30) Water year (October 1–September 30)

0

500

1,0001,500

0

1,5001,000

500

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second

0

2,0001,5001,000

500

0

4,0003,0002,0001,000

07134990 Wild Horse Creek above Holly, Colorado 07139700 Arkansas River tributary near Dodge City, Kansas07139800 Mulberry Creek near Dodge City, Kansas 07140300 Whitewoman Creek near Bellefont, Kansas

Figure 6.

Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected strea

and near the Oklahoma Panhandle.
No data No data No data No da

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scat

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

Water year (October 1–September 30) Water year (October 1–September 30)

0

5,0004,0003,0002,0001,000

0

6,0005,0004,0003,0002,0001,000

Annual peak streamflow, in cubic feet per second

0

5,0003,0002,0004,0001,000

20,00015,00010,000

5,000

0

Annual peak streamflow, in cubic feet per second

07140600 Pawnee River tributary near Kalvesta, Kansas 07140850 Pawnee River near Burdett, Kansas07141175 Buckner Creek near Burdett, Kansas 07141200 Pawnee River at Rozel, Kansas

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
No da

No data

No data

No data No data

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scatt

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second

0

7,0006,0005,0004,0003,0002,0001,000

0

35,00030,00025,00020,00015,00010,000

5,000

0

20,00010,00015,000

5,000

0

1,000

800600400200

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

Water year (October 1–September 30) Water year (October 1–September 30)

07142100 Rattlesnake Creek tributary near Mullinville, Kansas 07142300 Rattlesnake Creek near Macksville, Kansas07142575 Rattlesnake Creek near Zenith, Kansas 07143100 Little Cheyenne Creek tributary near Claflin, Kansas

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
No data No data No data No data No data No data 

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scat

0

3,0002,5002,0001,5001,000

500

0

35,00030,00025,00010,00015,000

5,000

20,000

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second 0

100,000

40,00060,00020,00080,000

0

20,00015,00010,000

5,000

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

Water year (October 1–September 30) Water year (October 1–September 30)

07144900 South Fork Ninnescah River tributary near Pratt, Kansas 07148350 Salt Fork Arkansas River near Winchester, Oklahoma07148400 Salt Fork Arkansas River near Alva, Oklahoma 07149000 Medicine Lodge River near Kiowa, Kansas

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
No data

No data No data No data 

No data

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scatt

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

Water year (October 1–September 30) Water year (October 1–September 30)

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

0

20,00010,00015,000

5,000

0

20,00015,00010,000

5,000

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second 0

50,00040,00030,00020,00010,000

0

5,0002,0004,0001,0003,000

07154400 Carrizozo Creek near Kenton, Oklahoma 07154500 Cimarron River near Kenton, Oklahoma07156220 Bear Creek near Johnson, Kansas 07156600 Cimarron River tributary near Moscow, Kansas

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
No data No data No data No data No data No data 

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted sca

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

Water year (October 1–September 30) Water year (October 1–September 30)

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second 0

6,0003,0005,0002,0004,0001,000

0

5,0004,0003,0002,0001,000

0

15,000

5,000

10,000

0

3,0002,5002,0001,5001,000

500

07157100 Crooked Creek near Copeland, Kansas

07157400 Crooked Creek tributary at Meade, Kansas 07157500 Crooked Creek near Englewood, Kansas07156700 Cimarron River tributary near Satanta, Kansas

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
No da

No data

No data

No data No data

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted sca

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1

0 0

Water year (October 1–September 30) Water year (October 1–September 30)

0

20,00015,00010,000

5,000

400300200100

0

1,5001,000

500

15,00010,000

5,000

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second

07157700 Keiger Creek near Ashland, Kansas 07157960 Buffalo Creek near Lovedale, Oklahoma07227200 Tramperos Creek near Stead, New Mexico 07227295 Sandy Arroyo tributary ne

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
No data 

No data No data No data No data 

No data No da

Peak streamflowLOWESS trendline, 1925–2014LOWESS trendline, 1978–2014

EXPLANATION

LOWESS, Locally weighted scat

Annual peak streamflow, in cubic feet per second Annual peak streamflow, in cubic feet per second 0

4,0003,0002,0001,000

0

40,00030,00020,00010,000

0

60,00050,00040,00030,00020,00010,000

0

25,00020,00015,00010,000

5,000

Water year (October 1–September 30) Water year (October 1–September 30)

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 

1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 1991 1997 2003 2009 2015 1925 1931 19431937 1949 1955 1961 1967 1973 1979 1985 

07227920 Dixon Creek near Borger, Texas 07232500 Beaver River near Guymon, Oklahoma07233500 Palo Duro Creek near Spearman, Texas 07234100 Clear Creek near Elmwood, Oklahoma

Figure 6. Annual peak-streamflow trends for the entire period of record (1925–2014) and the irrigated period of record (1978–2014) for selected streaand near the Oklahoma Panhandle.—Continued
Streamflow-Gaging Station Selection and Data Analysis

Table 3. Results of trend tests on annual peak streamflow for the entire period of record (1925–2014) and the irrigated period of record

(1978–2014) at selected streamflow-gaging stations in and near the Oklahoma Panhandle.

[ft3/s, cubic feet per second; ft3/s/yr, cubic feet per second per year; shaded values are statistically significant at the 95-percent confidence level or greater 

(p≤0.05); ≤, less than or equal to]

Site 

number

Station 

number 

(fig. 1)

Station name

Record 

span 

(water 

year)1

Entire period of record (1925–2014)

Record 

length 

(water 

years)1

Median 

annual 

peak flow 

(ft3

/s)

Kendall’s 

tau p-value

Trend 

slope 

(ft3

/s/yr)

1 07134990 Wild Horse Creek above Holly, Colo. 1996–2014 19 185 -0.4620 0.0368 -23.25

2 07139700 Arkansas River Trib. near Dodge City, 

Kans.

1957–2012 54 165 -0.2872 0.0023 -3.91

3 07139800 Mulberry Creek near Dodge City, Kans. 1969–90 22 106 -0.3818 0.0056 -19.67

4 07140300 Whitewoman Creek near Bellefont, Kans. 1957–89 33 170 -0.1856 0.2066 -6.16

5 07140600 Pawnee River Trib. near Kalvesta, Kans. 1957–89 33 250 -0.0858 0.4512 -3.43

6 07140850 Pawnee River near Burdett, Kans. 1982–2014 33 581 -0.0246 0.8395 -0.77

7 07141175 Buckner Creek near Burdett, Kans. 1996–2012 17 457 -0.2288 0.3047 -43.59

8 07141200 Pawnee River at Rozel, Kans. 1925–2014 90 1,710 -0.3084 0.0000 -23.61

9 07142100 Rattlesnake Creek Trib. near Mullinville, 

Kans.

1957–89 33 420 -0.0229 0.8458 -0.57

10 07142300 Rattlesnake Creek near Macksville, Kans. 1960–2014 55 218 -0.2883 0.0041 -6.42

11 07142575 Rattlesnake Creek near Zenith, Kans. 1973–2014 42 384.5 -0.3101 0.0028 -12.62

12 07143100 Little Cheyenne Creek Trib. near Claflin, 

Kans.

1957–2012 56 92 -0.2803 0.0018 -2.02

13 07144900 South Fork Ninnescah River Trib. near 

Pratt, Kans.

1957–89 33 340 0.1953 0.0248 8.00

14 07148350 Salt Fork Arkansas River near Winchester, 

Okla.

1957–93 35 7,770 -0.2826 0.0177 -290.00

15 07148400 Salt Fork Arkansas River near Alva, Okla. 1938–2014 49 5,040 -0.4983 0.0000 -150.91

16 07149000 Medicine Lodge River near Kiowa, Kans. 1938–2014 69 3,200 -0.3241 0.0001 -55.98

17 07154400 Carrizozo Creek near Kenton, Okla. 1953–2014 62 1,750 -0.1199 0.1921 -15.00

18 07154500 Cimarron River near Kenton, Okla. 1951–2014 64 4,020 -0.2695 0.0171 -84.10

19 07156220 Bear Creek near Johnson, Kans. 1967–98 32 1,105 -0.1638 0.1357 -17.46

20 07156600 Cimarron River Trib. near Moscow, Kans. 1957–89 33 650 -0.1884 0.0315 -18.43

21 07156700 Cimarron River Trib. near Satanta, Kans. 1957–2010 49 160 -0.3614 0.0003 -5.09

22 07157100 Crooked Creek near Copeland, Kans. 1957–89 33 500 -0.3597 0.0016 -30.00

23 07157400 Crooked Creek Trib. at Meade, Kans. 1957–89 33 300 -0.2019 0.1285 -12.50

24 07157500 Crooked Creek near Englewood, Kans. 1943–2014 72 637.5 -0.5753 0.0000 -36.84

25 07157700 Keiger Creek near Ashland, Kans. 1957–89 32 370 -0.0871 0.4955 -5.00

26 07157960 Buffalo Creek near Lovedale, Okla. 1966–93 28 1,020 -0.1217 0.4404 -24.10

27 07227200 Tramperos Creek near Stead, New Mex. 1965–2014 48 992.5 -0.0604 0.5514 -5.87

28 07227295 Sandy Arroyo Trib. near Clayton, New 

Mex.

1952–96 43 36 -0.2008 0.0608 -1.12

29 07227920 Dixon Creek near Borger, Tex. 1975–89 15 1,100 -0.1429 0.6773 -57.50

30 07232500 Beaver River near Guymon, Okla. 1937–93 57 3,410 -0.4790 0.0001 -220.44

31 07233500 Palo Duro Creek near Spearman, Tex. 1936–2014 50 1,755 -0.3861 0.0001 -47.73

32 07234100 Clear Creek near Elmwood, Okla. 1966–93 28 976.5 -0.0529 0.7545 -17.24
28

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

Table 3. Results of trend tests on annual peak streamflow for the entire period of record (1925–2014) and the irrigated period of record

(1978–2014) at selected streamflow-gaging stations in and near the Oklahoma Panhandle.—Continued

[ft3/s, cubic feet per second; ft3/s/yr, cubic feet per second per year; shaded values are statistically significant at the 95-percent confidence level or greater 

(p≤0.05); ≤, less than or equal to]

Site 

number

Irrigated period of record (1978–2014)

Record length 

(water years)1

Median annual 

peak flow 

(ft3

/s)

Kendall’s 

tau p-value Trend slope (ft3

/s/yr)

1 19 185 -0.4620 0.0368 -23.25

2 33 100 -0.2315 0.0608 -2.92

3 13 64 -0.3590 0.0926 -12.36

4 12 94 0.0303 0.9491 2.86

5 12 350 -0.1679 0.4070 -17.78

6 33 581 -0.0246 0.8395 -0.77

7 17 457 -0.2288 0.3047 -43.59

8 37 1,150 -0.1592 0.1169 -22.84

9 12 370 0.0923 0.7212 28.75

10 37 145 -0.3140 0.0041 -6.63

11 37 321 -0.1441 0.1913 -5.56

12 35 69 -0.1485 0.1830 -1.59

13 12 400 0.0606 0.7479 6.25

14 16 6,880 -0.3333 0.0414 -436.88

15 35 4,070 -0.2672 0.0712 -102.73

16 37 2,730 -0.2583 0.0752 -75.33

17 37 1,400 0.0030 0.9879 0.00

18 37 3,270 -0.1201 0.3717 -50.69

19 21 1,050 -0.1103 0.4524 -11.77

20 12 168 0.0155 1.0000 0.00

21 28 42.5 -0.3423 0.0119 -3.42

22 12 121.5 -0.1069 0.6254 -4.08

23 12 290 -0.3817 0.0551 -71.33

24 37 128 -0.3759 0.0034 -9.50

25 12 355 0.3206 0.0274 36.02

26 16 1,029.5 -0.0333 0.8695 -4.48

27 35 755 0.1166 0.3338 13.54

28 17 34 0.1053 0.5900 1.00

29 12 1,040 0.0909 0.8595 58.25

30 16 177.5 -0.3333 0.0549 -14.58

31 16 633.5 -0.1167 0.5584 -10.04

32 16 976.5 0.2167 0.1999 46.53

1

A water year is a period of 12 consecutive months that includes January through September of the named calendar year and October through December of the 

previous calendar year.
Estimates of Magnitude and Frequency of Peak Streamflows at Ungaged Sites

Estimates of Magnitude and Frequency 

of Peak Streamflows at Ungaged Sites

The regression analysis used in this report incorporated 

logarithmic (base 10) transformations of the peak-streamflow 

frequency statistics 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-streamflow frequency statistics) and independent 

variables (basin characteristics) acceptable for linear leastsquares regression procedures. The multiple-linear regression 

equations based on logarithmic transformation of the variables 

has the following form:

Log10Y = b0 + b1log10X1+b2log10X2+......+bn log10 Xn, (1)

and the following form after taking antilogs,

Y = 10b0 (X1

b1

) (X2

b2

)......(Xn

bn

) (2)

where

Y is the dependent variable (peak-streamflow 

frequency statistic for selected annual 

exceedance probability),

b0 to bn are the regression model coefficients, and

X1 to Xn are independent variables (basin 

characteristics).

Regression Analysis 

Previous regression analysis of peak-streamflow 

frequency for Oklahoma (Lewis, 2010) used a combination of 

ordinary-least-squares (OLS), weighted-least-squares (WLS), 

and generalized-least-squares (GLS) multiple-linear regression 

analysis methods to formulate statewide regression equations 

for Oklahoma; this report used the same methods as Lewis 

(2010) to formulate regional regression equations for the 

Oklahoma Panhandle statistical region. The USGS WeightedMultiple-Linear Regression (WREG) computer program 

50

20

10

4

2

1

0.2

1:1 line

10 100 1,000 10,000 100,000 1,000,000

Computed peak-streamflow frequency statistic for the irrigated 

period of record (1978–2014), in cubic feet per second

10

100

1,000

10,000

100,000

1,000,000

Regression-estimated peak-streamflow frequency statistic 

(Lewis, 2010), in cubic feet per second

Peak-streamflow frequency statistic for selected

 streamflow-gaging station

Average peak-streamflow frequency statistic for

 given annual exceedance probability, in percent

50

EXPLANATION

Figure 7. Computed and regression-estimated peak-streamflow frequency statistics for the irrigated period of record (1978–2014) at 

selected streamflow-gaging stations in and near the Oklahoma Panhandle.
30

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

(Eng and others, 2009) facilitated OLS, WLS, and GLS 

regression analysis by performing logarithmic transformations 

on the dependent and independent variables, estimating 

regression model coefficients, and graphing performance 

metrics. 

The OLS and WLS regression analysis methods were used 

to eliminate statistically insignificant (p > 0.05) independent 

variables from consideration (Ries and Dillow, 2006), and 

the GLS regression analysis method was used to formulate 

the final regression equations. The GLS regression analysis 

method entails weighting each basin in accordance with the 

variance (time-sampling error) and spatial-correlation structure 

of the peak-streamflow frequency statistic (among streamflowgaging stations) (Lumia and others, 2006). The residual error 

is portioned into regression model error (error in assuming an 

incomplete regression form) and sampling error (time- and 

spatial-sampling errors). When using the GLS regression 

analysis method, 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 regression model 

coefficients), but it is different from the time-sampling and 

spatial-sampling error. The GLS regression analysis 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 but also for cross-correlation of 

the annual time series on which the peak-streamflow frequency 

statistics for the streamflow-gaging station data are based and 

for spatial correlation among the streamflow-gaging station 

data (Stedinger and Tasker, 1985). Annual peak streamflows of 

basins were cross-correlated because a single storm can cause 

the annual peak in several basins. An advantage of using the 

GLS regression analysis method is that cross-correlation among 

basins is taken into account.

Several performance metrics from the WREG computer 

program were used to identify data points with unusual weight 

or control on the regression relation. The residuals metric 

shows differences between regression-estimated and computed 

peak-streamflow frequency statistics; homoscedastic residuals 

(residuals randomly distributed around zero) are preferred. 

The leverage metric is used to measure how distant the values 

of 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 data from a streamflow-gaging station had a large 

influence on the estimated regression model coefficients (Eng 

and others, 2009). Data from streamflow-gaging stations 

identified as having high influence and leverage (for example, 

fig. 8) were not necessarily removed from the dataset because 

a station may have been the only streamflow-gaging station 

in a particular geographic area. The high-leverage and highinfluence limits were computed by the WREG computer 

program by using equations from Eng and others (2009). The 

final performance metrics for the 10-percent annual exceedance 

probability regression model are shown in figure 8 as an 

example.

Figure 8. Performance metrics from the Weighted-MultipleLinear Regression (WREG) computer program for the 32 selected 

streamflow-gaging stations including A, residuals; B, leverage; and 

C, influence for a 10-percent annual exceedance probability peakstreamflow generalized-least-squares (GLS) regression model.

high-leverage limit*

high-influence limit*

*Eng and others, 2009

0

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.6

0.4

0.2

-0.6

-0.8

-0.4

-0.2

0

Residual (log base 10)

0

0.04

0.08

0.12

0.16

0.20

Leverage Influence

Estimated peak-streamflow frequency statistic (log base 10)

Site number (table 1)

Site number (table 1)

2.5 3.0 3.5 4.0

0 5 10 15 20 25 30 35

0 5 10 15 20 25 30 35

A

B

C
Estimates of Magnitude and Frequency of Peak Streamflows at Ungaged Sites

Regression Equations

Regression equations were developed for use in 

estimating peak-streamflow frequency statistics associated 

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

exceedance probabilities. Combinations of independent 

variables were tested to minimize leverage or influence 

of individual data points and to avoid multicollinearity 

(correlation between independent variables), but most 

independent variables that were tested did not have a 

statistically significant relation with the dependent variable. 

Mean annual precipitation (PRECIP), 10–85 stream channel 

slope (CSL10_85FM), mean soil permeability (SOILPERM), 

outlet elevation (OUTLETELEV), outlet mean annual 

precipitation from 1961 to 1990 (PRCOUT61), outlet mean 

annual precipitation from 1971 to 2000 (PRCOUT71), 

percentage of forest-canopy cover (CANOPY_PCT), 

percentage of impervious cover (IMPNLCD01), and 

percentage of drainage area with crop cover (LC01CROP) 

were rejected as insignificant independent variables. Mean 

drainage-basin slope (BSLDEM10M) and percentage of 

drainage area on the High Plains aquifer (OK_HIPERMA) 

were statistically significant independent variables but only 

for percentage exceedance probabilities greater than 2 and 10 

percent, respectively. Contributing drainage area (CONTDA) 

was the only basin characteristic determined to be statistically 

significant for all annual exceedance probabilities and was the 

only basin characteristic used for estimating peak-streamflow 

frequency statistics on unregulated streams in this report. The 

following regression equations were computed for unregulated 

streams from the results of the GLS regression analysis in the 

WREG computer program:

Q50% = 77.6 (CONTDA)0.34 (3)

Q20% = 209 (CONTDA)0.35 (4)

Q10% = 339 (CONTDA)0.36 (5)

Q4% = 562 (CONTDA)0.36 (6)

Q2% = 759 (CONTDA)0.37 (7)

Q1% = 1,000 (CONTDA)0.38 (8)

Q0.2% = 1,620 (CONTDA)0.39 (9)

where

Q50%, Q20%,..., and Q0.2% are the peak-streamflow frequency 

statistics with annual 

exceedance probabilities of 50 

percent, 20 percent, ..., and 

0.2 percent, in cubic feet per 

second; and

CONTDA is the contributing drainage area, in 

square miles.

For estimating peak-streamflow frequency statistics at 

urban sites or sites that are affected by floodwater retarding 

structures, refer to procedures described by Lewis (2010). For 

sites on large streams that have long-term streamflow-gaging 

stations upstream and downstream from the site of interest, the 

drainage-area ratio method is preferred for estimating peakstreamflow frequency statistics (Lewis, 2010).

Accuracy and Limitations

Regression equations that produce estimates of 

streamflow statistics are statistical models that minimize 

differences between regression-estimated and computed 

streamflow statistics (residual errors).The accuracy of a 

regression equation depends on the combined model error and 

sampling error. Model error is the variability in the dependent 

variable that is unexplained by the selected dependent 

variables. Sampling error, which is more difficult to quantify, 

results from the limitations on the number of years of available 

streamflow-gaging station period of record and the assumption 

that streamflow measured during the available streamflowgaging station period of record is representative of long-term 

streamflow characteristics. The use of GLS regression analysis 

methods allows separation of the sampling error variance from 

the model error variance.

Three performance metrics were used to evaluate the 

accuracy of a regression-estimated peak-streamflow frequency 

statistic: the pseudo coefficient of determination (pseudo-R2), 

the average standard error of prediction (Sp), and the standard 

model error (table 4); the WREG computer program reports 

these performance metrics in the model output. The coefficient 

of determination (R2) is the proportion of the variability in 

the dependent variable (station computed peak-streamflow 

frequency statistic, Qx[s]) that is explained by the independent 

variable (the basin characteristic, CONTDA). A greater value 

for R2 indicates a better fit of the model, with a maximum 

value of 1.00 indicating that 100 percent of the variability 

in the dependent variable is explained by the independent 

variable (Helsel and Hirsch, 2002). The pseudo-R2 (Griffis and 

Stedinger, 2007), however, is a more appropriate performance 

metric for GLS regressions; the pseudo-R2 is a measure of 

the variability in the dependent variable explained by the 

regression after removing the effect of the time-sampling 

error (Eng and others, 2009). The pseudo-R2 values converted 

to percent (table 4) for the Oklahoma Panhandle regional 

regression equations ranged from about 38 to 63 percent and 

were less than the corresponding pseudo-R2 (which ranged 

from about 92 to 96 percent) for the Oklahoma statewide 

regression equations of Lewis (2010). However, the pseudo-R2

for the Oklahoma Panhandle regional regression equations 

were comparable to those reported by Capesius and Stephens 

(2009) for regional peak-streamflow frequency regression 

equations for the High Plains area of Colorado. 

The standard error of prediction is derived from the 

sum of the model error variance and the sampling error of 

the regression model coefficients and is a measure of the 
32

Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sit

expected accuracy of the regression estimates for the selected 

annual exceedance probabilities. The standard error of 

prediction generally ranges from 30 to 60 percent for most 

regional and statewide peak-streamflow frequency regression 

equations in the United States but often exceeds 60 percent 

for regions in the western United States where the network 

of streamflow-gaging stations is less dense and the periods 

of record are generally shorter (Jennings and others, 1994). 

The standard errors of prediction for the Oklahoma Panhandle 

regional regression equations ranged from about 84 to 148 

percent (table 4) and were greater than the corresponding 

standard error of prediction (which ranged from about 32 to 

47 percent) for the Oklahoma statewide regression equations 

of Lewis (2010). However, standard errors of prediction for 

the Oklahoma Panhandle regional regression equations were 

comparable to those reported by Asquith and Slade (1997) and 

Capesius and Stephens (2009) for regional peak-streamflow 

frequency regression equations for the High Plains areas of 

Texas and Colorado, respectively. 

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 statistics from the station records that were used 

to develop the equation. The standard model error typically 

is slightly smaller than the standard error of prediction 

(Jennings and others, 1994) for the same peak-streamflow 

frequency regression equation. The standard model errors for 

the Oklahoma Panhandle regional regression equations ranged 

from about 76 to 138 percent (table 4) and were greater than 

the corresponding standard model errors (which ranged from 

about 31 to 46 percent) for the Oklahoma statewide regression 

equations of Lewis (2010). However, standard model errors 

for the Oklahoma Panhandle regional regression equations 

were comparable to those reported by Capesius and Stephens 

(2009) for regional peak-streamflow frequency regression 

equations for the High Plains area of Colorado.

These three performance metrics, as presented in table 4, 

quantify the fit of a regression model with respect to the set of 

observations used to formulate the regression model. Because 

the Oklahoma Panhandle regional regression equations and 

the Oklahoma statewide regression equations were formulated 

using different sets of observations, these three performance 

metrics are not ideal for direct comparisons of accuracy 

between table 4 of this report and the corresponding table 4 

of Lewis (2010); therefore, a fourth performance metric, 

the root mean square error (RMSE) (Helsel and Hirsch, 

2002) was calculated to directly compare the accuracy of the 

estimated peak streamflow statistics for the irrigated period 

of record in the Oklahoma Panhandle using the Oklahoma 

Panhandle regional regression equations and the Oklahoma 

statewide regression equations. The RMSEs for the Oklahoma 

Panhandle regional regression equations (ranging from 3,170 

to 92,000 cubic feet per second [ft3/s]; table 1) were less than 

the RMSEs for the Oklahoma statewide regression equations 

(ranging from 18,900 to 412,000 ft3/s; table 1); therefore, the 

Oklahoma Panhandle regional regression equations produce 

more accurate peak-streamflow statistic estimates for the 

irrigated period of record in the Oklahoma Panhandle than do 

the Oklahoma statewide regression equations.

The regression equations developed in this report are 

applicable to streams in the Oklahoma Panhandle statistical 

region that are not substantially affected by regulation, 

impoundment, or surface-water withdrawals. These 

regression equations are intended for use for stream sites 

with contributing drainage areas less than or equal to about 

2,060 mi2, the maximum value for the independent variable 

used in the regression analysis (table 1).

Table 4. Accuracy of regression-estimated peak-streamflow frequency statistics for sites on unregulated streams in and near the 

Oklahoma Panhandle.

Annual 

exceedance 

probability 

(percent)

Recurrence 

interval 

(years)

Pseudo-R2

, 

(coefficient of 

determination)

(percent)

Average Sp

(standard error 

of prediction)

(percent)

Standard 

model error

(percent)

50 2 38.48 147.82 138.48

20 5 51.30 103.99 97.52

10 10 56.42 92.64 86.40

4 25 60.61 85.76 79.24

2 50 62.14 84.01 77.09

1 100 63.10 83.72 76.33

0.2 500 61.38 91.87 83.62
References Cited

Summary

This report presents the results of a cooperative study by 

the U.S. Geological Survey and the Oklahoma Department 

of Transportation to estimate the magnitude and frequency 

of peak streamflows from regional regression equations for 

ungaged stream sites in and near the Oklahoma Panhandle. 

These methods relate basin characteristics (physiographic and 

climatic attributes) to selected peak-streamflow frequency 

statistics with the 50-, 20-, 10-, 4-, 2-, 1-, and 0.2-percent 

annual exceedance probabilities. These relations were 

developed based on data from 32 selected streamflow-gaging 

stations in the Oklahoma Panhandle and in neighboring parts 

of Colorado, Kansas, New Mexico, and Texas. The basin 

characteristics for the selected streamflow-gaging stations 

were determined by using a geographic information system 

and the Oklahoma StreamStats application. Peak-streamflow 

frequency statistics were computed from annual peakstreamflow records from the irrigated period of record from 

water year 1978 through water year 2014.

Generalized-least-squares multiple-linear regression 

analysis was used to formulate regression relations between 

peak-streamflow frequency statistics and basin characteristics. 

Contributing drainage area was the only basin characteristic 

determined to be statistically significant for all percentage 

of annual exceedance probabilities and was the only basin 

characteristic used in this report for regional regression 

equations for estimating peak-streamflow frequency statistics 

on unregulated streams in and near the Oklahoma Panhandle. 

The regression model pseudo-coefficient of determination, 

converted to percent, for the Oklahoma Panhandle regional 

regression equations ranged from about 38 to 63 percent. 

The standard errors of prediction and the standard model 

errors for the Oklahoma Panhandle regional regression 

equations ranged from about 84 to 148 percent and from 

about 76 to 138 percent, respectively. These errors were 

comparable to those reported for regional peak-streamflow 

frequency regression equations for the High Plains areas of 

Texas and Colorado. The root mean square errors for the 

Oklahoma Panhandle regional regression equations (ranging 

from 3,170 to 92,000 cubic feet per second) were less than 

the root mean square errors for the Oklahoma statewide 

regression equations (ranging from 18,900 to 412,000 

cubic feet per second); therefore, the Oklahoma Panhandle 

regional regression equations produce more accurate peakstreamflow statistic estimates for the irrigated period of 

record in the Oklahoma Panhandle than do the Oklahoma 

statewide regression equations. The regression equations 

developed in this report are applicable to streams that are 

not substantially affected by regulation, impoundment, or 

surface-water withdrawals. These regression equations are 

intended for use on stream sites with contributing drainage 

areas less than or equal to about 2,060 square miles, the 

maximum value for the independent variable used in the 

regression analysis. 

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Smith and others—Methods for Estimating the Magnitude and Frequency of Peak Streamflows at Ungaged Sites—SIR 2015–5134

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20155134