U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2009–5009

Prepared in cooperation with the U.S. Fish and Wildlife Service

Estimation of Streamflow Characteristics for 

Charles M. Russell National Wildlife Refuge, 

Northeastern Montana
Cover photograph: Hell Creek upstream from Hart Creek near Charles M. Russell National Wildlife Refuge. Photograph by 

Martha Kaufmann, World Wildlife Fund, taken June 2007. Published with permission by Martha Kaufmann.
Estimation of Streamflow Characteristics 

for Charles M. Russell National Wildlife 

Refuge, Northeastern Montana

By Steven K. Sando, Timothy J. Morgan, DeAnn M. Dutton, and 

Peter M. McCarthy

Prepared in cooperation with the U.S. Fish and Wildlife Service

Scientific Investigations Report 2009–5009

U.S. Department of the Interior

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

DIRK KEMPTHORNE, Secretary

U.S. Geological Survey

Mark D. Myers, Director

U.S. Geological Survey, Reston, Virginia: 2009

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Sando, S.K., Morgan, T.J., Dutton, D.M., and McCarthy, P.M., 2009, Estimation of streamflow characteristics for 

Charles M. Russell National Wildlife Refuge, northeastern Montana: U.S. Geological Survey Scientific Investigations 

Report 2009–5009, 60 p.
iii

Contents

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

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

Purpose and Scope ..............................................................................................................................1

Acknowledgments................................................................................................................................2

Description of Study Area ............................................................................................................................2

Previous Studies ............................................................................................................................................4

Estimation of Streamflow Characteristics.................................................................................................5

Estimates of Monthly and Annual Streamflow Characteristics for 

Short-Term Gaging Stations ..................................................................................................5

Estimates of T-Year Peak Flows for Short-Term Gaging Stations...............................................22

Estimation of Streamflow Characteristics at Ungaged Sites ......................................................22

Estimation of Monthly and Annual Streamflow Characteristics 

at Ungaged Sites ..........................................................................................................22

Estimation of Peak-Flow Characteristics at Ungaged Sites...............................................25

Limitations on Use of the Regression Equations ..................................................................26

Estimated Streamflow Characteristics for Selected Ungaged 

Sites in Charles M. Russell National Wildlife Refuge ............................................26

Summary........................................................................................................................................................34

References Cited..........................................................................................................................................35

Supplemental Data ......................................................................................................................................37

Figures

1. Map showing locations of study area, gaging stations used in various 

analyses, and Charles M. Russell National Wildlife Refuge, 

northeastern Montana.................................................................................................................3

2–7. Graphs showing:

2. Monthly precipitation and temperature characteristics (1971–2000) 

for Jordan, Mont. .................................................................................................................4

3. Annual mean streamflow for selected gaging stations ................................................9

4. Regional Adjustment Relationship regression relations used to 

estimate the long-term 50-percent exceedance (median) and 

mean annual streamflows for the short-term gaging stations...................................13

5. Comparison of actual study period (water years 2000–2004) 

and estimated long-term selected monthly streamflow 

characteristics for the short-term gaging stations......................................................17

6. Comparison of actual study period (water years 2000–2004) and 

actual long-term selected monthly streamflow characteristics 

for selected long-term index gaging stations used in the Regional 

Adjustment Relationship...................................................................................................20

7. Regional Adjustment Relationship regression relations used to 

estimate the 2-year recurrence interval peak flow for the short-term 

gaging stations...................................................................................................................23
iv

8. Map showing locations of selected ungaged sites on tributaries that 

cross Charles M. Russell National Wildlife Refuge, northeastern Montana....................28

9–11. Graphs showing:

9. Estimated long-term monthly streamflow characteristics for 

selected ungaged sites.....................................................................................................29

10. Estimated annual streamflow for various exceedance probabilities 

for selected ungaged sites...............................................................................................31

11. Estimated 1.5-, 2-, and 2.33-year recurrence interval peak flows for 

selected ungaged sites.....................................................................................................33

Tables

1. Site information for selected gaging stations, northeastern Montana ...............................6

2. Regression equations used to estimate long-term monthly and 

annual streamflow characteristics for the short-term gaging stations ............................11

3. Estimation coefficients used to estimate long-term streamflow characteristics ...........14

4. Actual study period (water years 2000–2004) mean monthly and annual 

streamflows and estimated long-term monthly and annual streamflow 

characteristics for the short-term gaging stations...............................................................15

5. Regression equations for estimating peak-flow characteristics for the 

short-term gaging stations........................................................................................................23

6. Estimates of peak-flow characteristics for the short-term gaging stations.....................24

7. Selected basin and climatic characteristics considered as potential 

explanatory variables in regression analyses for estimating streamflow 

characteristics at ungaged sites .............................................................................................24

8. Regression equations for estimating annual streamflow characteristics 

at ungaged sites..........................................................................................................................26

9. Regression equations for estimating peak-flow characteristics at 

ungaged sites ..............................................................................................................................27

10. Ranges for basin characteristics used to develop regression equations 

for estimating streamflow characteristics at ungaged sites ..............................................27

Supplements 1–8.

1. Monthly and annual streamflow characteristics for long-term index 

gaging stations used in the Regional Adjustment Relationship (RAR) ..............................38

2. Selected peak-flow information for long-term index gaging stations 

used in the Regional Adjustment Relationship......................................................................41

3. Long-term monthly and annual streamflow characteristics for 

selected gaging stations used to develop regression equations.......................................42

4. Selected basin and climatic characteristics for gaging stations 

used in various analyses to estimate streamflow characteristics.....................................46

5. Selected peak-flow characteristics for selected gaging 

stations used to develop regression equations.....................................................................48

6. Selected basin and climatic characteristics for selected ungaged 

sites on tributaries that cross Charles M. Russell National Wildlife Refuge....................49

7. Estimates of long-term monthly and annual streamflow characteristics 

for selected ungaged sites on tributaries that cross Charles M. Russell 

National Wildlife Refuge............................................................................................................51

8. Estimates of selected peak-flow characteristics for selected ungaged 

sites on tributaries that cross Charles M. Russell National Wildlife Refuge....................59
v

Conversion Factors, Datum, Acronyms, and Definitions for 

Streamflow Terminology

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

acre 4,047 square meter (m2)

acre 0.4047 hectare (ha)

acre 0.004047 square kilometer (km2)

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)

Slope

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

Temperature in degrees Fahrenheit (°F) may be converted to degrees Celsius (°C) as follows:

°C=(°F-32)/1.8

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.

Water year is the 12-month period from October 1 through September 30 of the following 

calendar year. The water year is designated by the calendar year in which it ends. For 

example, water year 2008 is the period from October 1, 2007, through September 30, 2008.

Acronyms

BLM Bureau of Land Management

CMR Charles M. Russell National Wildlife Refuge

EYR equivalent years of record—the number of years of record at a gaged site that 

would be needed to provide the same reliability as the regression estimate

FWS U.S. Fish and Wildlife Service

GIS geographic information system

GLS generalized least squares

NHDPlus National Hydrography Dataset Plus

OLS ordinary least squares
vi

PK1.5 1.5-year recurrence interval peak flow

PK2 2-year recurrence interval peak flow

PK2.33 2.33-year recurrence interval peak flow

PKM mean of annual peak flows for specified period of years

p-value significance level or probability of obtaining a value of a test statistic at least as 

extreme as the one observed given that the null hypothesis is true

Q.90 90-percent exceedance streamflow

Q.80 80-percent exceedance streamflow

Q.50 50-percent exceedance streamflow

Q.20 20-percent exceedance streamflow

QM mean streamflow

PRISM Parameter-elevation Regressions on Independent Slopes Model

RAR Regional Adjustment Relationship

SEE average standard error of estimate (also sometimes referred to as the root mean 

square error or the standard deviation of the residuals)

SEP average standard error of prediction

USGS U.S. Geological Survey

WLS weighted least squares

Definitions for Streamflow Terminology

annual mean streamflow arithmetic mean of all daily mean streamflows for a single specified 

year

annual peak flow maximum instantaneous streamflow that occurred during a single 

specified year

daily mean streamflow mean streamflow for a single specified day

mean annual streamflow arithmetic mean of all annual mean streamflows for the period of 

record or for a specific period of multiple years

mean daily streamflow arithmetic mean of all daily mean streamflows for a specified day 

for the period of record or for a specific period of multiple years

mean monthly streamflow arithmetic mean of all monthly mean streamflows for a specified 

month for the period of record or for a specific period of multiple 

years

mean peak flow arithmetic mean of all annual peak flows for the period of record or 

for a specific period of multiple years

monthly mean streamflow arithmetic mean of all daily mean streamflows for a single specified 

month in a single specified year

T-year peak flow peak flow determined by statistical analysis of annual peak flows 

for the period of record or for a specific period of multiple years to 

occur on average once every T years
Estimation of Streamflow Characteristics for Charles M. 

Russell National Wildlife Refuge, Northeastern Montana

By Steven K. Sando, Timothy J. Morgan, DeAnn M. Dutton, and Peter M. McCarthy 

Abstract

Charles M. Russell National Wildlife Refuge (CMR) 

encompasses about 1.1 million acres (including Fort Peck 

Reservoir on the Missouri River) in northeastern Montana. 

To ensure that sufficient streamflow remains in the tributary 

streams to maintain the riparian corridors, the U.S. Fish and 

Wildlife Service is negotiating water-rights issues with the 

Reserved Water Rights Compact Commission of Montana. 

The U.S. Geological Survey, in cooperation with the U.S. Fish 

and Wildlife Service, conducted a study to gage, for a short 

period, selected streams that cross CMR, and analyze data 

to estimate long-term streamflow characteristics for CMR. 

The long-term streamflow characteristics of primary interest 

include the monthly and annual 90-, 80-, 50-, and 20-percent 

exceedance streamflows and mean streamflows (Q.90, Q.80, 

Q.50, Q.20, and QM, respectively), and the 1.5-, 2-, and 2.33-

year peak flows (PK1.5, PK2, and PK2.33, respectively). 

The Regional Adjustment Relationship (RAR) was investigated for estimating the monthly and annual Q.90, Q.80, 

Q.50, Q.20, and QM, and the PK1.5, PK2, and PK2.33 for 

the short-term CMR gaging stations (hereinafter referred to as 

CMR stations). The RAR was determined to provide acceptable results for estimating the long-term Q.90, Q.80, Q.50, 

Q.20, and QM on a monthly basis for the months of March 

through June, and also on an annual basis. For the months of 

September through January, the RAR regression equations did 

not provide acceptable results for any long-term streamflow 

characteristic. For the month of February, the RAR regression 

equations provided acceptable results for the long-term Q.50 

and QM, but poor results for the long-term Q.90, Q.80, and 

Q.20. For the months of July and August, the RAR provided 

acceptable results for the long-term Q.50, Q.20, and QM, 

but poor results for the long-term Q.90 and Q.80. Estimation coefficients were developed for estimating the long-term 

streamflow characteristics for which the RAR did not provide 

acceptable results. The RAR also was determined to provide 

acceptable results for estimating the PK1.5., PK2, and PK2.33 

for the three CMR stations that lacked suitable peak-flow 

records. 

Methods for estimating streamflow characteristics at 

ungaged sites also were derived. Regression analyses that 

relate individual streamflow characteristics to various basin 

and climatic characteristics for gaging stations were performed 

to develop regression equations to estimate streamflow characteristics at ungaged sites. Final equations for the annual 

Q.50, Q.20, and QM are reported. Acceptable equations also 

were developed for estimating QM for the months of February, 

March, April, June, and July, and Q.50, Q.20, and QM on an 

annual basis. However, equations for QM for the months of 

February, March, April, June, and July were determined to be 

less consistent and reliable than the use of estimation coefficients applied to the regression equation results for the annual 

QM. Acceptable regression equations also were developed for 

the PK1.5, PK2, and PK2.33.

Introduction

Charles M. Russell National Wildlife Refuge (CMR) 

encompasses about 1.1 million acres (including Fort Peck 

Reservoir on the Missouri River) in northeastern Montana. 

CMR consists of rugged land bordering the Missouri River, 

generally termed the Missouri River Breaks. The Missouri 

River Breaks provides important habitat, including riparian 

corridors along Missouri River tributary streams, for numerous animals and plants in CMR. To ensure that sufficient 

streamflow remains in the tributary streams to maintain the 

riparian corridors, the U.S. Fish and Wildlife Service (FWS) is 

negotiating water-rights issues with the Reserved Water Rights 

Compact Commission of Montana. These negotiations require 

accurate information about current and long-term streamflow 

characteristics for Missouri River tributary streams that cross 

CMR. However, there is very little long-term streamflow data 

for these streams. Thus, the U.S. Geological Survey (USGS), 

in cooperation with the FWS, conducted a study to gage, for 

a short period, selected streams that cross CMR, and analyze 

data to estimate long-term streamflow characteristics for 

CMR. 

Purpose and Scope

The purpose of this report is to describe methods to estimate streamflow characteristics for CMR. The report presents 

(1) methods and results of analyses to estimate long-term 
2 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

streamflow characteristics for short-term gaging stations and 

(2) methods and results of analyses to develop regional regression equations that estimate long-term streamflow characteristics at ungaged sites in or near CMR.

Acknowledgments

Special thanks are given to Patricia J. Fiedler, Danielle 

L. Kepford, and Megan A. Estep of the U.S. Fish and Wildlife 

Service for their support of this study. Technical reviews by 

Daniel G. Driscoll and Charles Parrett of the U.S. Geological 

survey are greatly appreciated.

Description of Study Area

The study area (fig. 1) is defined by the drainage boundary of the Missouri River between the points where the river 

enters and exits CMR; the study area does not include the 

drainage area of the Musselshell River upstream from where 

this river enters CMR. The study area encompasses about 

8,260 mi2 and includes parts of Fergus, Phillips, Petroleum, 

Garfield, Valley, McCone, Prairie, Custer, and Rosebud Counties in northeastern Montana.

CMR (originally designated as the Fort Peck Game 

Range) was established by an executive order in 1936 that 

withdrew about 1.1 million acres (including the 245,000-acre 

Fort Peck Reservoir) from the public domain (U.S. Fish and 

Wildlife Service, 2006). Tributary streams that cross CMR 

that are of primary interest in this study are those identified 

by solid lines in the 1:100,000-scale National Hydrography 

Dataset (U.S. Geological Survey, 2007), but excluding the 

Musselshell River. The watersheds of these streams are within 

the Northwestern Great Plains and/or Northwestern Glaciated Plains ecoregions described by Woods and others (2002) 

and range in area from 58 to 2,830 mi2. CMR itself is almost 

entirely within “river breaks” topography adjacent to major 

stream channels and characterized by very highly dissected 

terrain, steep slopes, erodible clayey soils, and high runoff 

potential.

Predominant vegetation in CMR includes native grasses 

(including grama, needle grass, western wheatgrass, and 

buffalo grass), several shrub species (including sagebrush, 

greasewood, buffaloberry, and chokecherry), and coniferous 

trees (including juniper, ponderosa pine, and Douglas fir) that 

occur in scattered patches of woodland. Wildlife is abundant 

and includes mule and white-tailed deer, elk, bighorn sheep, 

antelope, coyote, bobcat, beaver, sharp-tailed and sage grouse, 

and numerous other species (U.S. Fish and Wildlife Service, 

2006).

About 1,720 mi2 of the 8,260 mi2 study area lies within 

CMR where land use predominantly is shrub and mixed rangeland managed for wildlife habitat. Cattle grazing is allowed 

but is strictly regulated to prevent degradation of wildlife 

habitat. Land use for most of the study area outside of CMR is 

grazed grass, shrub, or mixed rangeland; relatively small areas 

are cropland, pasture, or mixed forest.

The geology of the study area is dominated by shale, 

siltstone, and sandstone. Most of the study area is underlain by 

the Tertiary Fort Union Formation and the Upper Cretaceous 

Hell Creek Formation, Fox Hills Sandstone, and Bearpaw 

Shale. The Fort Union Formation crops out over about 39 

percent of the study area and consists of sandstone, siltstone, and shale interbedded with thick continuous coal beds 

(Frahme, 1979). The Hell Creek Formation crops out over 

about 20 percent of the study area and predominantly is soft 

claystone but varies in composition from shale to mediumgrained sandstone and also has intermittent concretions 

(Jensen and Varnes, 1964). The Fox Hills Sandstone crops 

out over about 4 percent of the study area and ranges from 

soft claystone to fine sandstone. Cementation is variable but 

more pronounced in the upper part of this formation resulting in relatively erosion-resistant rimrock features (Jensen 

and Varnes, 1964) in some areas of exposure. The Bearpaw 

Shale crops out over about 33 percent of the study area and 

is dark grey marine shale with discontinuous interbedded silt 

and sand layers, and concretions (Jensen and Varnes, 1964). 

Where exposed at the surface, the Bearpaw Shale generally is 

highly erodible. The geologic characteristics of the study area 

contribute to the river breaks topography in areas where highly 

erodible shales occur at the surface and badlands topography 

in areas where materials with more variable erosive characteristics occur. Soil characteristics in the study area also are 

profoundly influenced by the bedrock from which the soils 

are derived. In general, soils within the study area are very 

fine grained (ranging from clays to silty clay loam) and poorly 

drained (Frahme, 1979). 

The general climate of the study area is semiarid continental and characterized by relatively low precipitation, cold 

winters, hot summers, and extreme variations in both precipitation and temperatures. Monthly (1971–2000) precipitation 

and temperature characteristics for Jordan, Mont., located 

within the study area south of CMR (fig. 1) are presented in 

figure 2 (Western Regional Climate Center, 2006). Average 

annual temperature at Jordan is 44.0oF. On average, coldest 

temperatures occur in January (mean monthly temperature 

of 14.1oF) and warmest temperatures occur in July (mean 

monthly temperature of 71.4oF). Average annual precipitation is 12.9 in.; about 70 percent occurs as rainfall during 

the months of May through September, and about 50 percent 

occurs during May through July. Cooper and Jean (2001) 

noted that although precipitation decreases in late summer in 

the CMR area, July through September precipitation in the 

area averages about 0.5 to 1.0 in. more than sites in western 

Montana that have about the same average annual precipitation. They also indicated that convective thunderstorms generally account for more of the late summer precipitation than 

frontal systems.
VALLEY

CO

PHILLIPS

CO

ROSEBUD

CO

FERGUS

CO

BLAINE CO

HILL CO

CHOTEAU

CO

CUSTER

CO

RICHLAND

CO

YELLOWSTONE

CO

PRAIRIE

CO

MC CONE

CO

ROOSEVELT

CO

JUDITH

BASIN

CO

DAWSON

CO

FALLON

CO

PETROLEUM

CO

SHERIDAN

CO

MUSSELSHELL

CO

DANIELS

CO

WHEATLAND

CO GOLDEN

VALLEY

CO TREASURE CO

WIBAUX

CO

GARFIELD

CO

110° 109° 108° 107° 106° 105° 104°

49°48°47°

Landusky

Yel ol

ws ot en

Poplar

River

River

River

Milk

River

Missouri River

River

Judith

Mussellshell River

Redwa et r

Fort PeckReservoir

A mr ells Creek

BigDry

Cr

Hell 

Creek

Creek

Nelson

Rock Creek

MONTANA

Study area

2(S+5)

45(−5)

44

43

42

41

41

40

39

38(−5)

37

36

35

34

33

32(−5) 31

30(N+5)

29

28 27

26

25(N+5)

24

23(N+5)

22

21(−5)

19

18

20(−5)

17

16

15(−5)

14(−5)

13

12

11

10

 9

 7

 6 5

 4(N+5) 3(−5)

 1

Charles M. Russell National Wildlife Refuge (CMR) Study area boundary

Site number (see table 1)Long-term gaging station used in regression analysis for estimation of peak-flow characteristics at ungaged sites (South Region)Long-term gaging station used in regression analysis for estimation of peak-flow characteristics at ungaged sites (North Region)Long-term continuous-record gaging station used in regression analysis for estimation of monthly and annual streamflow characteristics at ungaged sitesLong-term gaging station used in Regional Adjustment Relationship analysis for estimation of peak-flow characteristics for short-term gaging stationsLong-term continuous-record gaging station used in Regional Adjustment Relationship analysis for estimation of both monthly and annual streamflowcharacteristics for short-term gaging stations

Short-term continuous-record gaging station on Charles M. Russell National Wildlife Refuge gaged during study period (2000−2004)

EXPLANATION

CANADA

UNITED STATES

0 30 15 60 MILES

0 30 15 60 KILOMETERS

SASKATCHEWAN

MONTANA

Base map from U.S. Census Bureau TIGER digital data, 1993−2001, 1:100,000; Montana State Library, 2003, 1:100,000; and Montana Natural Heritage Program, 2002, 1:100,000 Albers Equal-Area Conic projection Standard parallels 29°30’N and 45°30’N, central meridian 107°00’WNorth American Datum of 1983 (NAD 83)Note: Gaging stations not centered on stream lines are on small drainages with stream channels too short to be appropriately displayed at the map scale.

VanNorman

Hays

Malta

Terry

Jordan

Glasgow

Big 

Sandy

Lewistown

Wolf 

Point

Circle

NORTH DAKOTA

Gaging station used to developestimation ratios for monthly streamflow characteristics for watersheds. N+5 in parentheses indicates station on the north side of the Missouri River with maximum elevation greater than about 5,000 feet above North American Vertical Datum of 1988 (NAVD 88); S+5 in parentheses indicates station on the south side of the Missouri River with maximum elevation greater than about 5,000 feet (above NAVD 88); −5 in parentheses indicates station with maximum elevation less than about 5,000 feet (above NAVD 88)

 8(S+5)

North Region of study area (includes parts of CMR)South Region of study area(includes parts of CMR)

Figure 1. Locations of study area, gaging stations used in various analyses, and Charles M. Russell National Wildlife Refuge, northeastern Montana.

Description of Study Area 3
0

1

2

3

4

5

6

7

8

9

10

PRECIPITATION, IN INCHES

0

10

20

30

40

50

60

70

80

90

TEMPERATURE, IN DEGREES FAHRENHEIT

Jan Feb Mar Apr May June July Aug Sep Oct Nov Dec

EXPLANATION

Maximum temperature

Mean temperature

Minimum temperature

Maximum precipitation

Mean precipitation

Minimum precipitation

Figure 2. Monthly precipitation and temperature characteristics (1971–2000) for Jordan, Mont. Data from Western Regional 

Climate Center (2006).

4 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

Previous Studies

Omang and Parrett (1984) developed ordinary least 

squares (OLS) regression equations that relate mean annual 

streamflow to various basin and climatic characteristics for 

estimating mean annual streamflow at ungaged sites in central 

and eastern Montana. These regression equations covered a 

larger area than the study area of this report, used streamflow 

data through water year 1982, and were developed by using 

manually determined basin characteristics. Omang and Parrett 

(1984) described the reliability of the regression equations that 

they developed by using the average standard error of estimate 

(SEE, also referred to as the root mean square error or the 

standard deviation of the residuals). The SEE is a measure 

of the overall reliability of regression equations, and smaller 

values of SEE generally indicate better reliability of regression equations than do larger values. The study area described 

in this report falls within two regions defined in Omang and 

Parrett (1984): Region 1 (north of the Missouri River) and 

Region 2 (south of the Missouri River). For Region 1, Omang 

and Parrett (1984) considered 17 gaging stations and developed a regression equation for mean annual streamflow with 

an SEE of 31 percent. For Region 2, Omang and Parrett (1984) 

considered 27 gaging stations and developed a three-variable 

regression equation for mean annual streamflow with an SEE 

of 51 percent, a two-variable regression equation with an 

SEE of 62 percent, and a 1-variable equation with an SEE of 

64 percent. The regression equations developed by Omang and 

Parrett (1984) require manual determination of basin characteristics (which is labor intensive), were developed from data 
Estimation of Streamflow Characteristics 5

only through water year 1982, and did not specifically address 

streams in CMR. Thus, the methods described in the following 

sections of this report are more conveniently applied and are 

considered to provide more consistent and reliable results than 

the methods described by Omang and Parrett (1984).

Parrett and Johnson (2003) developed generalized least 

squares (GLS) regression equations that relate peak-flow 

characteristics to various basin and climatic characteristics 

for estimating peak flows having recurrence intervals of 2, 

5, 10, 25, 50, 100, 200, and 500 years (T-year peak flows) at 

ungaged sites for all of Montana. Methods for estimating only 

the 2-year peak flow are most relevant to the specific objectives of this study of streamflow characteristics for CMR. The 

Parrett and Johnson (2003) regression equations covered a 

larger area than the study area of this report, used streamflow 

data through water year 1998, and were developed by using 

manually determined basin characteristics. Parrett and Johnson 

(2003) described the reliability of the regression equations that 

they developed by using the average standard error of prediction (SEP), which generally is similar to the SEE. However, 

the SEP incorporates time-sampling error (accounted for in the 

more rigorous GLS regression), which is not incorporated in 

the SEE. Smaller values of SEP generally indicate better reliability of regression equations than do larger values. The study 

area described in this report falls within two regions defined 

in Parrett and Johnson (2003): Northeast Plains Region and 

East-Central Plains Region. For the Northeast Plains Region, 

Parrett and Johnson (2003) considered 57 gaging stations and 

developed a regression equation for the 2-year peak flow with 

an average SEP of 91.0 percent. For the East-Central Plains 

Region, Parrett and Johnson (2003) considered 85 gaging 

stations and developed a regression equation for the 2-year 

peak flow with an average SEP of 99.9 percent. The regression 

equations developed by Parrett and Johnson (2003) require 

manual determination of basin characteristics (which is labor 

intensive), were developed from data only through water 

year 1998, and did not specifically address streams in CMR. 

Thus, the methods described in the following sections of this 

report are more conveniently applied and are considered to 

provide more consistent and reliable results than the methods 

described by Parrett and Johnson (2003).

Estimation of Streamflow 

Characteristics

To address the need for streamflow information in CMR, 

a three-phased approach was used that involved (1) collecting continuous records of daily mean streamflow for a 5-year 

period (water years 2000–2004, hereinafter referred to as the 

study period) for five streams that cross CMR, (2) estimating long-term streamflow characteristics for the five gaging 

stations by using relations between study-period streamflow 

characteristics and long-term streamflow characteristics for 

nearby long-term gaging stations to adjust recorded studyperiod streamflow characteristics, and (3) developing regional 

regression equations to relate streamflow characteristics to 

basin characteristics. The long-term streamflow characteristics of primary interest include the monthly and annual 90-, 

80-, 50-, and 20-percent exceedance streamflows and mean 

streamflows (Q.90, Q.80, Q.50, Q.20, and QM, respectively), 

and the 1.5-, 2-, and 2.33-year peak flows (PK1.5, PK2, and 

PK2.33, respectively). Q.50 is equivalent to the long-term 

median streamflow.

Estimates of Monthly and Annual Streamflow 

Characteristics for Short-Term Gaging Stations

Five continuous-record gaging stations were installed on 

five tributaries to the Missouri River that cross CMR (sites 2, 

3, 4, 14, and 21; table 1 and fig. 1). The gaging stations were 

installed between November 1999 and February 2000 and 

were operated through September 2004. Procedures used for 

measuring streamflow and operating the gaging stations are 

described by Rantz and others (1982).

The 5-year period during which the CMR streams 

were gaged was characterized by unusually dry conditions. 

Streamflow records for long-term gaging stations in or near 

CMR show that, on a regional basis, annual mean streamflows during the study period were among the lowest for any 

consecutive 5-year period since the start of streamflow-record 

collection (fig. 3). The very low streamflows that occurred 

during the study period complicated the use of typical procedures for estimating long-term streamflow characteristics by 

using short-term streamflow records. During the study period, 

variability in streamflow was much less than average and for 

months that typically have low streamflows (that is, September 

through January), streamflows for the gaged CMR streams 

generally were extremely low or equal to zero. Some methods 

for extending streamflow characteristics for short-term gaging 

stations (for example, the mixed-station procedure described 

by Alley and Burns, 1983) use correlation between concurrent streamflows of the short-term gaging stations and nearby 

long-term gaging stations that are hydrologically similar. Use 

of concurrent-correlation methods were investigated but were 

found to perform poorly because the small streamflow variability during the study period resulted in poor correlations 

between streamflows of the short-term gaging stations and 

those of the long-term gaging stations. Concurrent-correlation 

methods might have performed acceptably if more typical 

streamflow conditions had occurred during the study period.

The Regional Adjustment Relationship (RAR; Bakke and 

others, 1999) provides an alternative to concurrent-correlation 

methods. The conceptual basis of the RAR is that at individual 

stream sites the correlation between a streamflow characteristic for a short period of record and long-term streamflow 

characteristics is consistent over a somewhat broad and 

climatically homogeneous region. OLS regressions are used 

to relate a streamflow characteristic for the short-term period 

to long-term streamflow characteristics for many long-term 
Table 1. Site information for selected gaging stations, northeastern Montana.—Continued

[Abbreviations: CMRG, short-term gaging station in or near Charles M. Russell National Wildlife Refuge operated during study period (water years 2000–2004); ERAT1, gaging station used for developing monthly estimation coefficients for watersheds with maximum elevations less than about 5,000 feet (above the North American Vertical Datum of 1988); ERAT2, gaging station used for developing monthly estimation coefficients for watersheds south of the Missouri River with maximum elevations greater than about 5,000 feet; ERAT3, gaging station used for developing monthly estimation coefficients for watersheds north of the Missouri River with maximum elevations greater than about 5,000 feet; RAR1, long-term index gaging station used in Regional Adjustment Relationship for estimating long-term monthly and annual streamflow characteristics for short-term gaging stations; RAR2, long-term index gaging station used in Regional Adjustment Relationship for estimating peak-flow characteristics for short-term gaging stations; REGR1, gaging station used for developing regression equations for estimating long-term monthly and annual streamflow characteristics for ungaged sites on the basis of basin characteristics; REGR2N, gaging station used for developing regression equations for estimating peak-flow characteristics for ungaged sites on the basis of basin characteristics in North Region; REGR2S, gaging station used for developing regression equations for estimating peak-flow characteristics for ungaged sites on the basis of basin characteristics in South Region. Symbol: --, no data]

Site number 

(fig. 1)

Station 

number Station name Type of gaging station or use of gaging- station records Drainage area, in square miles

Period of daily mean 

streamflow records 

through 2005, 

water years

Period of annual 

peak-flow records 

through 2005, 

water years

1 06114900 Taffy Creek tributary near Winifred REGR2S 3.0 -- 1974–20022 06115270 Armells Creek near Landusky CMRG, ERAT2, REGR1, REGR2S 397 2000–2004 2000–20043 06115300 Duval Creek near Landusky CMRG, RAR2, ERAT1, REGR2N 3.3 2000–2004 1963–20054 06115350 Rock Creek near Landusky CMRG, ERAT3, REGR1, REGR2N 75 2000–2004 2000–20045 06127520 Home Creek near Sumatra REGR2S 2.0 -- 1973–20056 06127570 Butts Coulee near Melstone REGR2S 6.7 -- 1963–20057 06128900 Box Elder Creek tributary near 

Winnett

REGR2S 16 -- 1955–73

8 06129000 Box Elder Creek near Winnett ERAT2, REGR1, REGR2S 684 1930–33, 1934–36, 

1958–72

1931–32, 1934–38, 

1959–65, 1967–71, 1978

9 06129500 McDonald Creek at Winnett REGR2S 421 1930–32, 1934–45, 

1953–56

1931–32, 1934–45, 

1953–73, 1975

10 06129700 Gorman Coulee near Cat Creek REGR2S 2.3 -- 1955–59, 1962–73, 

1977, 1980, 1991–2005

11 06130600 Cat Creek near Cat Creek REGR2S 37 -- 1958–73, 1977, 

1980

12 06130610 Bair Coulee near Mosby REGR2S 1.8 -- 1974–200513 06130620 Blood Creek tributary near Valentine REGR2S 2.0 -- 1974–200514 06130650 Hell Creek near Jordan CMRG, ERAT1, REGR1, REGR2S 71 2000–2004 2000–200415 06130700 Sand Creek near Jordan ERAT1, REGR1, REGR2S 317 1957–67 1958–67, 198616 06130850 Second Creek tributary No. 2 near 

Jordan

REGR2S 2.1 -- 1958–90

17 06130915 Russian Coulee near Jordan REGR2S 3.5 -- 1974–2005

6 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Table 1. Site information for selected gaging stations, northeastern Montana.—Continued

[Abbreviations: CMRG, short-term gaging station in or near Charles M. Russell National Wildlife Refuge operated during study period (water years 2000–2004); ERAT1, gaging station used for developing monthly estimation coefficients for watersheds with maximum elevations less than about 5,000 feet (above the North American Vertical Datum of 1988); ERAT2, gaging station used for developing monthly estimation coefficients for watersheds south of the Missouri River with maximum elevations greater than about 5,000 feet; ERAT3, gaging station used for developing monthly estimation coefficients for watersheds north of the Missouri River with maximum elevations greater than about 5,000 feet; RAR1, long-term index gaging station used in Regional Adjustment Relationship for estimating long-term monthly and annual streamflow characteristics for short-term gaging stations; RAR2, long-term index gaging station used in Regional Adjustment Relationship for estimating peak-flow characteristics for short-term gaging stations; REGR1, gaging station used for developing regression equations for estimating long-term monthly and annual streamflow characteristics for ungaged sites on the basis of basin characteristics; REGR2N, gaging station used for developing regression equations for estimating peak-flow characteristics for ungaged sites on the basis of basin characteristics in North Region; REGR2S, gaging station used for developing regression equations for estimating peak-flow characteristics for ungaged sites on the basis of basin characteristics in South Region. Symbol: --, no data]

Site number 

(fig. 1)

Station 

number Station name Type of gaging station or use of gaging- station records Drainage area, in square miles

Period of daily mean 

streamflow records 

through 2005, 

water years

Period of annual 

peak-flow records 

through 2005, 

water years

18 06130940 Spring Creek tributary near Van 

Norman

REGR2S 1.4 -- 1974–2005

19 06130950 Little Dry Creek near Van Norman REGR2S 1,224 1980 1958–75, 1986, 

1995

20 06131000 Big Dry Creek near Van Norman RAR1, RAR2, , ERAT1, REGR1, REGR2S 2,554 1939–2005 1940–200521 06131200 Nelson Creek near Van Norman CMRG, RAR2, ERAT1, REGR1, REGR2S 100 1976–85, 2000–2004 1976–85, 1991, 

2000–2005

22 06137400 Big Sandy Creek at reservation 

boundary, near Rocky Boy

RAR1, RAR2 25 1982–2005 1982–2005

23 06154400 Peoples Creek near Hays RAR1, RAR2, , ERAT3, REGR1, REGR2N 220 1966–2005 1967–200524 06154410 Little Peoples Creek near Hays REGR2N 13 1973–2005 1973–200525 06154550 Peoples Creek below Kuhr Coulee, 

near Dodson

RAR1, RAR2, ERAT3, REGR1, REGR2N 675 1951–73, 1982–2005 1952–66, 1968–73, 

1982–2005

26 06155100 Black Coulee near Malta REGR2N 6.6 -- 1956–67, 198627 06155200 Alkali Creek near Malta REGR2N 162 -- 1956–59, 1961–73, 

1986

28 06155300 Disjardin Coulee near Malta REGR2N 4.8 -- 1956–200229 06164600 Beaver Creek tributary near Zortman REGR2N 3.9 -- 1974–200530 06164800 Beaver Creek above Dix Creek, near 

Malta

ERAT3, REGR1, REGR2N 929 1967–69, 1976–82 1967–69, 1974, 

1976–82, 1986

31 06173300 Willow Creek tributary near Fort Peck REGR2N .9 -- 1972, 1974–9132 06175540 Prairie Elk Creek near Oswego ERAT1, REGR1, REGR2S 352 1975–85 1976–8533 06175550 East Fork Sand Creek near Vida REGR2S 8.5 -- 1963–7734 06177050 East Fork Duck Creek near Brockway REGR2S 12 -- 1955–200235 06177100 Duck Creek near Brockway REGR2S 54 -- 1957–73

Estimation of Streamflow Characteristics 7
Table 1. Site information for selected gaging stations, northeastern Montana.—Continued

[Abbreviations: CMRG, short-term gaging station in or near Charles M. Russell National Wildlife Refuge operated during study period (water years 2000–2004); ERAT1, gaging station used for developing monthly estimation coefficients for watersheds with maximum elevations less than about 5,000 feet (above the North American Vertical Datum of 1988); ERAT2, gaging station used for developing monthly estimation coefficients for watersheds south of the Missouri River with maximum elevations greater than about 5,000 feet; ERAT3, gaging station used for developing monthly estimation coefficients for watersheds north of the Missouri River with maximum elevations greater than about 5,000 feet; RAR1, long-term index gaging station used in Regional Adjustment Relationship for estimating long-term monthly and annual streamflow characteristics for short-term gaging stations; RAR2, long-term index gaging station used in Regional Adjustment Relationship for estimating peak-flow characteristics for short-term gaging stations; REGR1, gaging station used for developing regression equations for estimating long-term monthly and annual streamflow characteristics for ungaged sites on the basis of basin characteristics; REGR2N, gaging station used for developing regression equations for estimating peak-flow characteristics for ungaged sites on the basis of basin characteristics in North Region; REGR2S, gaging station used for developing regression equations for estimating peak-flow characteristics for ungaged sites on the basis of basin characteristics in South Region. Symbol: --, no data]

Site number 

(fig. 1)

Station 

number Station name Type of gaging station or use of gaging- station records Drainage area, in square miles

Period of daily mean 

streamflow records 

through 2005, 

water years

Period of annual 

peak-flow records 

through 2005, 

water years

36 06177150 Redwater River at Brockway REGR2S 216 -- 1957–73, 198637 06177200 Tusler Creek near Brockway REGR2S 90 -- 1957–7238 06177500 Redwater River at Circle RAR1, RAR2, ERAT1, REGR1, REGR2S 547 1937–72, 1974–2004 1929–30, 1932–72, 

1975–2004

39 06177700 Cow Creek tributary near Vida REGR2S 1.7 1982–85 1963–200540 06181000 Poplar River near Poplar RAR1, RAR2 3,174 1908–24, 1947–69, 

1975–79, 1982–2005

1909, 1915, 1921, 

1923, 1946, 1948–63, 1965–69, 1975–79, 1982–2005

41 06183450 Big Muddy Creek near Antelope RAR1, RAR2 967 1979–2005 1979–200542 06294900 Middle Fork Froze to Death Creek 

tributary near Ingomar

REGR2S 1.4 -- 1962–76

43 06309020 Rock Springs Creek tributary at Rock 

Springs

REGR2S 1.0 -- 1963–78, 1987

44 06309040 Dry House Creek near Angela REGR2S 39 -- 1963–77, 198745 06329200 Burns Creek near Savage ERAT1, REGR1, REGR2S 233 1958–67, 1975–84, 

1986

1958–67, 1975–84, 

1986

8 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Figure 3. Annual mean streamflow for selected gaging stations. A, Big Dry Creek near Van Norman, Mont.; B, Redwater 

River at Circle, Mont.

0

50

100

150

200

250

1930 1940 1950 1960 1970 1980 1990 2000

0

10

20

30

40

50

60

70

STREAMFLOW, IN CUBIC FEET PER SECOND

Annual mean streamflow

Annual mean streamflow during study period (water years 2000–2004)

Long-term mean annual streamflow

Long-term median annual streamflow

A Big Dry Creek near Van Norman, Mont. (site 20)

 water years 1940–2005 

B Redwater River at Circle, Mont. (site 38)

 water years 1937–2005 

EXPLANATION

No data 

No data 

No data 

Estimation of Streamflow Characteristics 9
10 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

index gaging stations (hereinafter referred to as index stations) 

within the defined region.

Selection of appropriate index stations for estimating 

regional streamflow relations is critical to application of the 

RAR. Bakke and others (1999) specify that index stations 

need to (1) be active during an appropriate long-term period 

and also active during the short-term period of interest, (2) not 

be substantially affected by regulation or diversions, (3) not 

have a substantial number of missing-value or zero-streamflow 

days, and (4) have a range in drainage areas that span the 

range of drainage areas for which estimation is needed.

Seven index stations (sites 20, 22, 23, 25, 38, 40, and 

41; table 1 and fig. 1) were selected for use in estimating 

streamflow characteristics for the short-term CMR gaging 

stations (hereinafter referred to as CMR stations). The selected 

index stations generally are close to CMR and have more 

than 20 years of continuous streamflow records. The criteria 

specified by Bakke and others (1999) for selection of index 

stations generally were followed with the exception of the 

requirements that the index stations should not have a substantial number of zero-streamflow days and that the drainage 

areas span the range of drainage areas for which estimation are 

needed.

Zero streamflow is not unusual during the low-streamflow months of September through January for all but the 

largest Missouri River tributaries draining the northeastern 

plains of Montana. Thus, application of the RAR for lowstreamflow months is not possible if index stations that have 

a substantial number of zero-streamflow days are excluded. 

The RAR originally was developed for application in southern 

Oregon where zero streamflows are uncommon and excluding candidate index stations on the basis of occurrence of zero 

streamflows would not substantially affect the accuracy of 

the results. However, excluding index stations on the basis of 

occurrence of zero streamflows would be inappropriate when 

applying the RAR to CMR. Inclusion of zero streamflows in 

the RAR poses problems because streamflow data are transformed to base-10 logarithms prior to performing regression 

analyses. For this study, any streamflow characteristic that was 

less than 0.01 ft3/s was assigned a value of 0.01 ft3/s.

The requirement that the drainage areas of the index 

stations span the range of drainage areas for which estimation 

are needed also was not strictly adhered to. Drainage areas for 

four of the five CMR stations are within the range of drainage 

areas for the index stations. However, one of the CMR stations 

(site 3; Duval Creek near Landusky; drainage area of 3.3 mi2) 

has a drainage area that is smaller than the range for the index 

stations (25 to 3,174 mi2). Thus, it was necessary to extrapolate below the range of drainage areas of the index stations 

to provide estimates of streamflow characteristics for site 3 

(table 1 and fig. 1). Therefore, estimates of streamflow characteristics for this gaging station need to be used with caution.

For the CMR stations, the RAR was investigated for estimating the long-term Q.90, Q.80, Q.50, Q.20, and QM on a 

monthly basis and also on an annual basis. On a monthly basis, 

the RAR was applied by performing OLS regressions relating the long-term monthly characteristics of the index stations 

(dependent variables) to the study period mean monthly 

streamflows of the index stations (explanatory variables) for 

each streamflow characteristic and each month. All data were 

transformed to base-10 logarithms prior to analysis. For some 

months, improved regression results for a given month were 

obtained by averaging the study period mean monthly streamflows for the given month with those for the previous and/or 

following month(s). On an annual basis, the RAR was applied 

by performing OLS regressions relating each of the longterm annual characteristics of the index stations (dependent 

variables) to the study period mean annual streamflows of the 

index stations (explanatory variables). Study-period and longterm monthly and annual streamflow characteristics for the 

index stations used in the RAR are presented in Supplement 1 

(at the back of this report). 

The RAR regression results were reviewed for outliers, 

leverage, influence, distribution of residuals (that is, the differences between streamflow characteristics estimated by using 

regression-equations and streamflow characteristics estimated 

by using recorded streamflow data), and overall statistical significance (by using methods described by Helsel and 

Hirsch, 2002, pp. 228–251), and also evaluated for suitability 

for producing reliable estimates on the basis of the SEE. For 

some datasets, a regression equation can have a relatively 

high level of overall significance (that is, a low probability 

that the linear relation occurred by chance) but may not yield 

reliable results because of a large SEE. Strict guidelines for 

determining suitability of regression equations for producing reliable streamflow estimates are not well documented. 

Previous studies using regression methods for estimating 

various streamflow characteristics in northeastern Montana 

have reported values of SEE or SEP ranging from about 31 

to 130 percent (Omang and Parrett, 1984; Parrett and others, 

1989; Parrett and Johnson, 2003). For this study, the regression equations developed by using the RAR were determined 

to provide acceptable results when (1) the regression relations 

were not substantially affected by outliers, high-leverage 

values, high-influence values or non-normally distributed 

residuals; (2) the overall statistical significance exceeded about 

95 percent (that is, the p-value was less than about 0.05); and 

(3) the SEE was less than about 125 percent. The median SEE 

for the RAR regression equations was 51.6 percent. Values of 

SEE ranged from 29.6 to 122.6 percent (table 2).

For the CMR stations, the RAR regression equations 

were determined to provide acceptable results for estimating 

the long-term Q.90, Q.80, Q.50, Q.20, and QM on a monthly 

basis for the months of March through June, and also on an 

annual basis. For the months of September through January, 

the RAR regression equations did not provide acceptable 

results for any long-term streamflow characteristic. For the 

month of February, the RAR regression equations provided 

acceptable results for the long-term Q.50 and QM but poor 

results for the long-term Q.90, Q.80, and Q.20. For the months 

of July and August, the RAR provided acceptable results for 

the long-term Q.50, Q.20, and QM but poor results for the 
Table 2. Regression equations used to estimate long-term monthly and annual streamflow characteristics for the short-term gaging 

stations.

[Equations were developed by using the Regional Adjustment Relationship. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent 

exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow; RBCF, retransformation 

bias-correction factor; p-value, significance level; R2, coefficient of determination; SEE, average standard error of estimate (in percent). Symbol: <, less than]

Long-term 

streamflow 

characteristic

Equation RBCF R2 SEE p-value

February Q.50 = 3.0 QM(study period, February)0.40 1.04 0.48 81.5 0.083

February QM = 4.2 QM(study period, February/March)0.51 1.03 .58 72.9 .047

March Q.90 = 0.27 QM(study period, March)0.73 1.04 .71 85.9 .018

March Q.80 = 0.75 QM(study period, March)0.63 1.02 .75 62.8 .012

March Q.50 = 2.4 QM(study period, March)0.69 1.01 .92 33.4 <.001

March Q.20 = 3.8 QM(study period, March)0.93 1.03 .85 68.3 .003

March QM = 3.6 QM(study period, March)0.86 1.03 .83 66.5 .004

April Q.90 = 0.47 QM(study period, April/May)1.0 1.01 .95 41.0 <.001

April Q.80 = 0.80 QM(study period, April/May)0.95 1.01 .97 29.6 <.001

April Q.50 = 2.9 QM(study period, April/May)0.85 1.01 .94 40.8 <.001

April Q.20 = 2.8 QM(study period, March/April/May)0.97 1.03 .83 74.7 .004

April QM = 2.8 QM(study period, March/April/May)1.0 1.01 .94 39.0 <.001

May Q.90 = 0.28 QM(study period, May)1.0 1.03 .85 88.9 .003

May Q.80 = 0.78 QM(study period, May)0.86 1.01 .95 37.3 <.001

May Q.50 = 2.5 QM(study period, May)0.73 1.01 .95 31.7 <.001

May Q.20 = 8.0 QM(study period, May)0.64 1.01 .89 41.1 .001

May QM = 7.8 QM(study period, May)0.58 1.02 .77 63.7 .010

June Q.90 = 0.24 QM(study period, May/June)0.77 1.03 .83 74.3 .004

June Q.80 = 0.52 QM(study period, May/June)0.69 1.03 .79 78.1 .008

June Q.50 = 3.1 QM(study period, May/June)0.56 1.02 .80 57.3 .007

June Q.20 = 21 QM(study period, May/June)0.33 1.01 .69 44.6 .021

June QM = 14 QM(study period, May/June)0.31 1.02 .60 51.6 .040

July Q.50 = 0.75 QM(study period, June/July)0.86 1.04 .81 95.3 .006

July Q.20 = 9.5 QM(study period, June/July)0.47 1.01 .83 41.4 .004

July QM = 7.7 QM(study period, June/July)0.43 1.01 .88 31.0 .002

August Q.50 = 0.93 QM(study period, August/September)1.0 1.06 .84 122.6 .004

August Q.20 = 5.5 QM(study period, August/September)0.51 1.02 .82 54.6 .005

August QM = 5.4 QM(study period, August/September)0.46 1.01 .83 48.0 .005

Annual Q.90 = 0.55 QM(study period, annual)0.90 1.01 .90 49.0 .001

Annual Q.80 = 1.0 QM(study period, annual)0.82 1.01 .93 34.5 <.001

Annual Q.50 = 3.2 QM(study period, annual)0.71 1.01 .93 31.0 <.001

Annual Q.20 = 11 QM(study period, annual)0.61 1.02 .74 60.3 .013

Annual QM = 6.1 QM(study period, annual)0.64 1.01 .85 43.3 .003

Estimation of Streamflow Characteristics 11
12 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

long-term Q.90 and Q.80. RAR regression equations for longterm streamflow characteristics that had acceptable results are 

presented in table 2. Use of regression analysis on log-transformed data has been shown to result in systematic bias when 

the results are retransformed from log units to the original 

arithmetic units (Koch and Smillie, 1986). To compensate 

for this bias, retransformed results were multiplied by a 

nonparametric retransformation bias-correction factor (Duan, 

1983) that is shown in table 2. Example plots that illustrate 

the regression relations used for estimating long-term annual 

50-percent exceedance (median) and mean annual streamflows 

are presented in figure 4.

Estimation coefficients were developed for estimating 

the long-term streamflow characteristics for the CMR stations 

for the months that the RAR did not provide acceptable 

results. These coefficients were developed by using continuous streamflow records from streams in the study area or in 

nearby watersheds that generally are hydrologically similar 

to the streams that cross CMR. The estimation coefficients 

were determined by calculating the ratio of a given streamflow characteristic to the mean annual streamflow. Estimation 

coefficients were developed for three types of watersheds: 

(1) watersheds with maximum elevations less than about 

5,000 ft (above NAVD 88); (2) watersheds on the south side 

of the Missouri River with maximum elevations greater than 

about 5,000 ft; and (3) watersheds on the north side of the 

Missouri River with maximum elevations greater than about 

5,000 ft. Streamflow data for selected gaging stations (indicated in table 1 and fig. 1) in watersheds that met the criteria 

for each watershed type were analyzed to determine the ratio 

of each streamflow characteristic to the mean annual streamflow for each selected gaging station. Estimation coefficients 

for each watershed type and each streamflow characteristic 

(table 3) were calculated by determining the weighted average 

(weighting based on number of years of record) of the ratios 

of all the selected gaging stations for a given watershed 

type. Although the estimation coefficients were used only to 

estimate long-term streamflow characteristics for months that 

the RAR did not provide acceptable results, estimation coefficients for all streamflow characteristics and all months are 

presented in table 3 for informational purposes.

Actual study-period monthly and annual streamflow characteristics (calculated by using recorded data) and estimated 

long-term monthly and annual streamflow characteristics 

(determined by using the RAR and estimation coefficients) 

for the CMR stations are presented in table 4. Example plots 

showing the actual study period and the estimated long-term 

median and mean monthly streamflows for the CMR stations 

are presented in figure 5. Example plots showing the actual 

study period and the actual long-term median and mean 

monthly streamflows for selected index stations are presented 

in figure 6. The relations between the actual study period and 

estimated long-term streamflow characteristics for the CMR 

stations (fig. 5) generally are similar to the relations between 

the actual study period and actual long-term streamflow 

characteristics for the index stations (fig. 6). Streams in the 

northeastern plains of Montana generally are characterized by 

higher streamflows during February through August and lower 

streamflows during September through January. For most of 

the index stations, March and April, when most snowmelt 

runoff typically occurs in northeastern Montana, have the 

highest mean monthly streamflow. Spring rainstorms also 

contribute to higher streamflows in March and April. Mean 

monthly streamflow for February typically is larger than late 

fall and early winter streamflows, indicating that during some 

years snowmelt begins in February. Some of the index stations 

show a mid-spring (about April or May) decrease in streamflow following completion of snowmelt at lower elevations. 

Late spring and summer rainstorms can increase streamflow 

during the months of June and July. Streamflows then generally decrease from August through the fall. The estimated 

long-term streamflow characteristics for the CMR stations 

generally indicate similar annual streamflow patterns to those 

of the index stations.
Figure 4. Regional Adjustment Relationship regression relations used to estimate the long-term 50-percent 

exceedance (median) and mean annual streamflows for the short-term gaging stations.

EXPLANATION

0.0

0.5

1.0

1.5

2.0

2.5

0.0 0.5 1.0 1.5 2.0

0.0

0.5

1.0

1.5

2.0

2.5

R2 = 0.93

R2

 = 0.85

Long-term 50-percent exceedance (median) annual streamflow relative to 

 study period (water years 2000–2004) mean annual streamflow for a given 

 long-term index gaging station

Long-term mean annual streamflow relative to study period (water 

 years 2000–2004) mean annual streamflow for a given long-term index 

 gaging station

Ordinary least squares regression line for long-term 50-percent 

 exceedance (median) annual streamflow

Ordinary least squares regression line for long-term mean annual streamflow

LOG (BASE 10) OF STUDY-PERIOD (WATER YEARS 2000–2004) MEAN ANNUAL STREAMFLOW, 

IN CUBIC FEET PER SECOND

LOG (BASE 10) OF LONG-TERM 50-PERCENT EXCEEDANCE 

(MEDIAN) ANNUAL STREAMFLOW, 

IN CUBIC FEET PER SECOND

LOG (BASE 10) OF LONG-TERM MEAN ANNUAL STREAMFLOW, 

IN CUBIC FEET PER SECOND

Estimation of Streamflow Characteristics 13
Table 3. Estimation coefficients used to estimate long-term streamflow characteristics.

[Coefficients were developed to estimate streamflow characteristics when regression-based methods were determined to be inappropriate. Elevation information is referenced to the North American Vertical Datum of 1988. Multiply estimation coefficient by long-term mean annual streamflow to obtain indicated streamflow characteristic. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Long-term 

streamflow 

characteristic

Estimation coefficient for indicated characteristic

October November December January February March April May June July August September Annual

Watersheds with maximum elevations less than about 5,000 feet

Q.90 0.004 0.010 0.004 0.001 0.002 0.097 0.074 0.035 0.059 0.018 0.003 0.000 0.135Q.80 .008 .015 .009 .003 .010 .186 .110 .063 .082 .038 .005 .002 .191Q.50 .035 .031 .024 .013 .083 1.361 .278 .210 .309 .167 .043 .017 .589Q.20 .094 .068 .048 .070 1.801 8.216 1.079 .677 1.335 1.145 .320 .083 1.705

QM .089 .052 .047 .089 1.378 5.470 1.632 .562 1.171 .937 .295 .289 1.000

Watersheds south of the Missouri River with maximum elevations greater than about 5,000 feet

Q.90 0.000 0.000 0.000 0.000 0.000 0.054 0.006 0.002 0.065 0.001 0.000 0.000 0.206Q.80 .000 .000 .000 .000 .000 .099 .048 .029 .107 .004 .000 .000 .386Q.50 .000 .002 .002 .000 .009 1.171 .256 .554 .923 .102 .019 .000 .712Q.20 .002 .008 .010 .013 .875 5.982 .565 5.168 5.331 1.033 .288 .012 1.628

QM .016 .006 .009 .013 1.129 2.770 .570 2.654 4.019 .707 .135 .005 1.000

Watersheds north of the Missouri River with maximum elevations greater than about 5,000 feet

Q.90 0.000 0.001 0.001 0.003 0.018 0.193 0.113 0.065 0.052 0.000 0.000 0.000 0.127Q.80 .000 .002 .003 .007 .026 .370 .181 .193 .098 .047 .000 .000 .223Q.50 .031 .060 .050 .036 .199 1.415 .801 .665 .681 .209 .026 .006 .529Q.20 .349 .414 .329 .291 1.140 4.522 2.290 1.992 2.206 1.322 .176 .162 1.734

QM .277 .232 .193 .232 .918 3.285 1.821 2.135 1.574 .738 .152 .430 1.000

14 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Table 4. Actual study period (water years 2000–2004) mean monthly and annual streamflows and estimated long-term monthly and annual streamflow characteristics for the 

short-term gaging stations.—Continued[Long-term streamflow characteristics estimated by using the Regional Adjustment Relationship (shaded values) and estimation coefficients (unshaded values). All streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 2 (Armells Creek near Landusky)

Study period (water years 2000–2004) mean monthly or annual streamflow

Years of record 4 4 4 4 5 5 5 5 5 5 5 5 4QM 0.00 0.00 0.00 0.00 14 36 2.0 9.1 14 7.2 0.62 0.00 8.5

Estimated long-term streamflow characteristics

Q.90 <0.01 <0.01 <0.01 <0.01 <0.01 3.9 2.7 2.8 1.6 0.02 <0.01 <0.01 3.8Q.80 <.01 <.01 <.01 <.01 <.01 7.4 4.1 5.3 2.9 .10 <.01 <.01 6.1Q.50 <.01 .04 .04 <.01 8.9 29 13 13 12 6.0 0.31 <.01 14Q.20 .04 .20 .24 .31 21 110 43 33 47 29 3.1 .28 40QM .38 .13 .22 .31 22 81 45 29 31 21 3.2 .12 24

Site 3 (Duval Creek near Landusky)

Study period (water years 2000–2004) mean monthly or annual streamflow

Years of record 4 4 4 4 5 5 5 5 5 5 5 5 4QM 0.00 0.00 0.00 0.00 0.16 0.43 0.00 0.01 0.06 0.13 0.11 0.00 0.09

Estimated long-term streamflow characteristics

Q.90 <0.01 0.01 <0.01 <0.01 <0.01 0.15 <0.01 <0.01 0.02 0.02 <0.01 <0.01 0.07Q.80 .01 .02 .01 <.01 .01 .46 .01 .02 .06 .05 <.01 <.01 .15Q.50 .05 .04 .03 .02 1.5 1.3 .07 .12 .52 .11 .06 .02 .60Q.20 .13 .09 .06 .10 2.5 1.8 .47 .54 7.1 3.2 1.4 .11 2.6QM .12 .07 .06 .12 2.3 1.8 .42 .66 5.2 2.8 1.6 .39 1.4

Site 4 (Rock Creek near Landusky)

Study period (water years 2000–2004) mean monthly or annual streamflow

Years of record 4 5 5 5 5 5 5 5 5 5 5 5 4QM 0.39 1.2 1.1 1.0 2.0 13 2.7 1.6 1.3 4.2 .20 .00 2.4

Estimation of Streamflow Characteristics 15
Table 4. Actual study period (water years 2000–2004) mean monthly and annual streamflows and estimated long-term monthly and annual streamflow characteristics for the 

short-term gaging stations.—Continued[Long-term streamflow characteristics estimated by using the Regional Adjustment Relationship (shaded values) and estimation coefficients (unshaded values). All streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 4 (Rock Creek near Landusky)—Continued

Estimated long-term streamflow characteristics

Q.90 <0.01 <0.01 0.01 0.03 0.19 1.9 1.0 0.47 0.32 <0.01 <0.01 <0.01 1.2Q.80 <.01 .02 .03 .08 .27 4.0 1.6 1.2 .68 .50 <.01 <.01 2.1Q.50 .33 .64 .54 .39 4.1 14 5.5 3.5 3.9 1.9 .10 .06 5.9Q.20 3.7 4.4 3.5 3.1 12 44 16 11 23 15 1.8 1.7 18QM 3.0 2.5 2.1 2.5 12 34 17 10 16 12 2.0 4.6 11

Site 14 (Hell Creek near Jordan)

Study period (water years 2000–2004) mean monthly or annual streamflow

Years of record 4 4 4 4 5 5 5 5 5 5 5 5 4QM .33 .09 .03 .19 1.4 5.8 .47 2.4 7.8 6.9 1.6 .49 2.2

Estimated long-term streamflow characteristics

Q.90 0.05 0.11 0.04 0.01 0.02 1.0 0.68 0.73 0.87 0.18 0.03 <0.01 1.1Q.80 .08 .16 .09 .03 .10 2.3 1.1 1.7 1.7 .39 .05 .02 2.0Q.50 .36 .32 .24 .14 3.6 8.1 4.0 4.8 7.9 4.3 1.0 .17 5.6Q.20 .96 .70 .49 .72 19 20 8.2 14 36 24 5.7 .86 18QM .91 .53 .48 .91 8.3 17 8.2 13 24 18 5.6 3.0 10

Site 21 (Nelson Creek near Van Norman)

Study period (water years 2000–2004) mean monthly or annual streamflow

Years of record 4 4 4 4 5 5 5 5 5 5 5 5 4QM .00 .00 .00 .04 .45 5.2 .28 .18 .56 3.2 1.1 .00 .97

Estimated long-term streamflow characteristics

Q.90 0.03 0.06 0.03 <0.01 0.01 0.93 0.11 0.05 0.12 0.11 0.02 <0.01 0.54Q.80 .05 .09 .05 .02 .06 2.2 .20 .19 .27 .23 .03 .01 1.0Q.50 .21 .19 .14 .08 2.2 7.5 .86 .75 1.8 1.3 .54 .10 3.1Q.20 .57 .41 .29 .43 11 18 5.4 2.8 15 13 4.1 .50 11QM .54 .31 .29 .54 7.3 15 5.3 3.0 11 10 4.2 1.8 6.1

16 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
A Armells Creek near Landusky, Mont. (site 2)

 Drainage area 397 square miles

B Duval Creek near Landusky, Mont. (site 3)

 Drainage area 3.31 square miles

Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

0.01

0.1

10

100

1,000

0.01

0.1

10

100

1,000

1

1

STREAMFLOW, IN CUBIC FEET PER SECOND

Actual study period (water years 2000–2004) streamflow characteristics 

 (calculated by using recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

Estimated long-term streamflow characteristics (derived by using Regional 

 Adjustment Relationship and estimation coefficients)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

Figure 5. Comparison of actual study period (water years 2000–2004) and estimated long-term selected monthly 

streamflow characteristics for the short-term gaging stations. A, Armells Creek near Landusky, Mont.; B, Duval 

Creek near Landusky, Mont.; C, Rock Creek near Landusky, Mont.; D, Hell Creek near Jordan, Mont.; E, Nelson Creek 

near Van Norman, Mont.

Estimation of Streamflow Characteristics 17
C Rock Creek near Landusky, Mont. (site 4)

 Drainage area 75 square miles

D Hell Creek near Jordan, Mont. (site 14)

 Drainage area 71 square miles

Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

0.01

0.1

10

100

1,000

0.01

0.1

10

100

1,000

1

1

STREAMFLOW, IN CUBIC FEET PER SECOND

Actual study period (water years 2000–2004) streamflow characteristics 

 (calculated by using recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

Estimated long-term streamflow characteristics (derived by using 

 Regional Adjustment Relationship and estimation coefficients)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

Figure 5. Comparison of actual study period (water years 2000–2004) and estimated long-term selected monthly 

streamflow characteristics for the short-term gaging stations. A, Armells Creek near Landusky, Mont.; B, Duval 

Creek near Landusky, Mont.; C, Rock Creek near Landusky, Mont.; D, Hell Creek near Jordan, Mont.; E, Nelson Creek 

near Van Norman, Mont.—Continued

18 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

E Nelson Creek near Van Norman, Mont. (site 21)

 Drainage area 100 square miles

0.01

0.1

1

10

100

1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

Actual study period (water years 2000–2004) streamflow characteristics 

 (calculated by using recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

Estimated long-term streamflow characteristics (derived by using 

 Regional Adjustment Relationship and estimation coefficients)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

Figure 5. Comparison of actual study period (water years 2000–2004) and estimated long-term selected monthly 

streamflow characteristics for the short-term gaging stations. A, Armells Creek near Landusky, Mont.; B, Duval 

Creek near Landusky, Mont.; C, Rock Creek near Landusky, Mont.; D, Hell Creek near Jordan, Mont.; E, Nelson Creek 

near Van Norman, Mont.—Continued

Estimation of Streamflow Characteristics 19
Figure 6. Comparison of actual study period (water years 2000–2004) and actual long-term selected monthly 

streamflow characteristics for selected long-term index gaging stations used in the Regional Adjustment 

Relationship. A, Big Dry Creek near Van Norman, Mont.; B, Peoples Creek near Hays, Mont.; C, Peoples Creek below 

Kuhr Coulee, near Dodson, Mont.; D, Redwater River at Circle, Mont.

Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

A Big Dry Creek near Van Norman, Mont. (site 20)

 Drainage area 2,554 square miles

 63 years of streamflow records

B Peoples Creek near Hays, Mont. (site 23)

 Drainage area 220 square miles

 38 years of streamflow records

0.01

0.1

10

100

1,000

0.01

0.1

10

100

1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

Actual study period (water years 2000–2004) streamflow characteristics 

 (calculated by using recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

Actual long-term streamflow characteristics (calculated by using 

 recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

1

1

20 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Figure 6. Comparison of actual study period (water years 2000–2004) and actual long-term selected monthly 

streamflow characteristics for selected long-term index gaging stations used in the Regional Adjustment 

Relationship. A, Big Dry Creek near Van Norman, Mont.; B, Peoples Creek near Hays, Mont.; C, Peoples Creek below 

Kuhr Coulee, near Dodson, Mont.; D, Redwater River at Circle, Mont.—Continued

C Peoples Creek below Kuhr Coulee, near Dodson, Mont. (site 25)

 Drainage area 675 square miles

 47 years of streamflow records

D Redwater River at Circle, Mont. (site 38)

 Drainage area 547 square miles

 72 years of streamflow records

0.01

0.1

10

100

1,000

0.01

0.1

10

100

1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

Actual study period (water years 2000–2004) streamflow characteristics 

 (calculated by using recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

Actual long-term streamflow characteristics (calculated by using 

 recorded data)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

1

1

Estimation of Streamflow Characteristics 21
22 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

Estimates of T-Year Peak Flows for Short-Term 

Gaging Stations

The RAR also was investigated for estimating the longterm 1.5-, 2-, and 2.33-year peak flows (PK1.5, PK2, and 

PK2.33, respectively) for three of the CMR stations (sites 2, 

4, and 14; table 1 and fig. 1). Two of the CMR stations (sites 3 

and 21; table 1 and fig. 1) had suitable peak-flow records (43 

and 17 years, respectively) for determining T-year peak-flow 

characteristics directly and could serve as index stations. Thus, 

nine index stations (table 1) were used to represent regional 

study period and long-term peak-flow relations. Study-period 

mean peak flow (PKM) and long-term PK1.5, PK2, and 

PK2.33 for the index stations used in the RAR are presented 

in Supplement 2 (at the back of this report). The PK1.5, PK2, 

and PK2.33 were determined by using procedures described 

in Bulletin 17B, “Guidelines for Determining Flood Flow 

Frequency” (Interagency Advisory Committee on Water Data, 

1982; hereinafter referred to as Bulletin 17B). PeakFQ, a 

computer program developed by the USGS (Flynn and others, 

2006) was used to perform the Bulletin 17B flood-frequency 

analyses.

The nine index stations used in the RAR to estimate 

long-term PK1.5, PK2, and PK2.33 satisfied the criteria for 

selection of long-term index stations specified by Bakke and 

others (1999). For estimating long-term T-year peak flows 

at the three CMR stations, OLS regression equations relating the PK1.5, PK2, and PK2.33 (dependent variables) to the 

study period PKM (explanatory variable) were developed. 

Procedures to determine suitability of the regression to provide 

acceptable results were identical to those used for estimating 

monthly and annual streamflow characteristics.

The RAR regression equations (table 5) were determined 

to provide acceptable results for estimating the PK1.5, PK2, 

and PK2.33 for the three CMR stations (sites 2, 4, and 14; 

table 1 and fig. 1). As with the estimates for monthly and 

annual streamflow characteristics, retransformation bias for 

the PK1.5, PK2, and PK2.33 was compensated for by multiplying by a nonparametric bias-correction factor (Duan, 1983), 

which is presented in table 5. The relations used for estimating the PK2 are illustrated in figure 7. Estimates of the PK1.5, 

PK2, and PK2.33 for the short-term CMR gaging stations are 

presented in table 6. 

Estimation of Streamflow Characteristics at 

Ungaged Sites

Methods for estimating streamflow characteristics at 

ungaged sites also were needed by the U.S. Fish and Wildlife 

Service. Regression analyses that relate individual streamflow characteristics to various basin and climatic characteristics for gaging stations were performed to develop regional 

regression equations to estimate streamflow characteristics at 

ungaged sites. Of particular interest to the FWS in the process 

of negotiating water rights is the bankfull discharge, which 

is an index of streamflow that is considered to be closely 

related to channel shape, size, and slope (Lawlor, 2004). The 

PK2 commonly is used to approximate the bankfull discharge 

(Lawlor, 2004; Wilkerson, 2008). However, various studies 

have found that the peak-flow recurrence interval associated with the bankfull discharge is variable (Williams, 1978), 

generally is less than 5 years, and might be more closely 

approximated by the PK1.5 or the PK2.33 at many stream 

locations (U.S. Environmental Protection Agency, 2006). 

Accordingly, separate regression equations for the PK1.5, 

PK2, and PK2.33 were developed for this study. Determination of the T-year peak flow most closely associated with the 

bankfull discharge for tributaries that cross CMR was beyond 

the scope of the current (2008) study. However, the bankfull 

discharge for most streams probably will be within the range 

of the PK1.5 and PK2.33.

Selected basin and climatic characteristics that were 

considered as potential explanatory variables in regression 

analyses for estimating streamflow characteristics at ungaged 

sites are presented in table 7. All basin characteristics considered were determined by using a geographic information 

system (GIS) and NHDPlus (Horizon Systems Corporation, 

2006), which is an integrated suite of geospatial datasets that 

determine stream networks, drainage boundaries, selected 

topographic characteristics, selected climatic characteristics, 

and selected basin land-cover characteristics. Primary datasets incorporated into NHDPlus include the 1:100,000 scale 

National Hydrography Dataset (U.S. Geological Survey, 

2007), the 30-meter resolution National Elevation Dataset 

(U.S. Geological Survey, 2006), the 1:24,000 scale Watershed 

Boundary Dataset (Natural Resources Conservation Service, 

2008b), the 30-meter resolution 2006 National Land Cover 

Dataset (U.S. Environmental Protection Agency, 2007), 

and the 2-kilometer resolution Parameter-elevation Regressions on Independent Slopes Model (PRISM) for estimating 

climatic variables using 1971–2000 data (Daly, 1996; Natural 

Resources Conservation Service, 2008a).

Estimation of Monthly and Annual Streamflow 

Characteristics at Ungaged Sites

Thirteen gaging stations (table 1 and fig. 1) were used 

in developing regression equations for monthly and annual 

streamflow characteristics. These gaging stations were 

selected because they generally are close to the study area. 

The watersheds of the gaging stations located outside of 

the study area generally are topographically and hydrologically similar to watersheds within the study area. Ten of the 

13 stations (sites 8, 15, 20, 21, 23, 25, 30, 32, 38, and 45) had 

10 or more years of continuous streamflow records (through 

water year 2005); monthly and annual streamflow characteristics for these gaging stations were determined from recorded 

data (Supplement 3 at the back of this report). Three of the 

13 gaging stations (sites 2, 4, and 14) were CMR stations 

with record only during the study period. Estimated monthly 
Figure 7. Regional Adjustment Relationship regression relations used to estimate the 2-year recurrence interval 

peak flow for the short-term gaging stations.

1

2

3

4

1 2 3 4

LOG (BASE 10) OF STUDY-PERIOD (WATER YEARS 2000–2004) MEAN PEAK FLOW, IN CUBIC FEET PER SECOND

LOG (BASE 10) OF 2-YEAR RECURRENCE INTERVAL PEAK FLOW, 

IN CUBIC FEET PER SECOND

R2 = 0.80

2-year recurrence interval peak flow versus study period (water years 2000–2004) 

 mean peak flow for a given long-term index gaging station

Ordinary least-squares regression line for 2-year recurrence interval peak flow

EXPLANATION

Table 5. Regression equations for estimating peak-flow characteristics for the short-term gaging stations.

[Equations were developed by using the Regional Adjustment Relationship. Abbreviations: PK1.5, 1.5-year recurrence interval peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year recurrence interval peak flow; PKM, mean peak flow; RBCF, retransformation bias-correction factor; p-value, 

significance level; R2, coefficient of determination; SEE, average standard error of estimate (in percent)]

Long-term 

streamflow 

characteristic

Equation RBCF R2 SEE p-value

 PK1.5 = 2.1 PKM(study period)0.81 1.03 0.81 76.6 0.002

PK2 = 3.8 PKM(study period)0.80 1.03 .80 78.5 .003

PK2.33 = 5.0 PKM(study period)0.80 1.04 .80 79.9 .003

Estimation of Streamflow Characteristics 23

and annual streamflow characteristics (table 4) determined 

by using the RAR and estimation coefficients were used in 

the regression analyses for these stations. One of the CMR 

stations (site 3) had a much smaller drainage area than the 

other gaging stations and consistently had significantly highleverage and high-influence values (as discussed in Helsel 

and Hirsch, 2002, p. 245–248) that substantially affected 

regression results; this gaging station was excluded from the 

regression analyses for monthly and annual streamflow characteristics. All data were transformed to base-10 logarithms 

prior to analysis. Any streamflow characteristic that was less 

than 0.01 ft3/s was assigned a value of 0.01 ft3/s. 

For each monthly and annual streamflow characteristic 

(Q.90, Q.80, Q.50, Q.20, and QM), preliminary OLS regressions were performed to identify the most influential explanatory variables and select a regression model for subsequent 

weighted least squares (WLS) regression. Regression models 

were selected on the basis of (1) determining that explanatory 
Table 6. Estimates of peak-flow characteristics for the short-term gaging stations.

[Peak-flow characteristics (in cubic feet per second) estimated by using the Regional Adjustment Relationship. Abbreviations: PK1.5, 1.5-year recurrence 

interval peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year recurrence interval peak flow; PKM, mean peak flow]

Site number 

(fig. 1)

Station 

number Station name PKM for study period (water years 2000–2004) PK1.5 PK2 PK2.33

2 06115270 Armells Creek near Landusky 1,260 668 1,230 1,570

4 06115350 Rock Creek near Landusky 587 362 665 852

14 06130650 Hell Creek near Jordan 927 523 960 1,230

Table 7. Selected basin and climatic characteristics considered as potential explanatory variables in regression analyses for 

estimating streamflow characteristics at ungaged sites.

Basin or climatic 

characteristic Description References

Drainage area Area that drains to a stream point, in square miles, determined from 30-meter resolution National Elevation 

Dataset, 1:24,000 scale Watershed Boundary Dataset, 

and 1:100,000 scale National Hydrography Dataset

Horizon Systems Corporation (2006), Natural Resources 

Conservation Service (2008b), U.S. Geological Survey 

(2006).

Mean elevation Basinwide mean elevation, in feet, determined from 

30-meter resolution National Elevation Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2006).

Maximum elevation Maximum elevation of basin, in feet, determined from 

30-meter resolution National Elevation Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2006).

Minimum elevation Minimum elevation of basin, in feet, determined from 

30-meter resolution National Elevation Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2006).

Relief Difference between maximum and minimum elevation 

of basin, in feet, determined from 30-meter resolution 

National Elevation Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2006).

Mean slope Basinwide mean slope, in percent, determined from 

30-meter resolution National Elevation Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2006).

Mean annual 

precipitation

Basinwide mean annual precipitation, in inches, determined from 2-kilometer resolution Parameter-elevation 

Regressions on Independent Slopes Model (PRISM)

Daly (1996), Horizon Systems Corporation (2006), 

Natural Resources Conservation Service (2008a).

Percent forest Basinwide forest cover, in percent, determined from the 

30-meter resolution National Land Cover Dataset

Horizon Systems Corporation (2006), U.S. Environmental Protection Agency (2007).

Percent lakes Basinwide lake cover, in percent, determined from the 

1:100,000 scale National Hydrography Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2007).

Compactness ratio A measure of basin shape related to basin perimeter and 

drainage area, determined from 30-meter resolution 

National Elevation Dataset, 1:24,000 scale Watershed 

Boundary Dataset, and 1:100,000 scale National 

Hydrography Dataset

Horizon Systems Corporation (2006), Natural Resources 

Conservation Service (2008b), U.S. Geological Survey 

(2006).

Total stream length Basinwide length of mapped streams, in miles, determined from the 1:100,000 scale National Hydrography 

Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2007).

Stream density ratio Basinwide length of mapped streams, in miles, divided 

by the drainage area, in square miles, determined from 

30-meter resolution National Elevation Dataset and 

1:100,000 scale National Hydrography Dataset

Horizon Systems Corporation (2006), U.S. Geological 

Survey (2006), U.S. Geological Survey (2007).

24 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Estimation of Streamflow Characteristics 25

variables were statistically significant (p-value less than 0.05); 

(2) minimizing Mallow’s Cp and the Press statistic (Helsel 

and Hirsch, 2002, p. 313) among different candidate models; 

(3) reviewing regression diagnostics to ensure that final 

regression models were not substantially affected by outliers, 

high-leverage values, high-influence values, or non-normally 

distributed residuals (by using methods described by Helsel 

and Hirsch, 2002, p. 228–251); (4) determining that the overall 

statistical significance exceeded 95 percent (p-value was less 

than 0.05); and (5) determining that the SEE was less than 

about 100 percent. As a result of the preliminary OLS regression analyses, the explanatory variables used in the final WLS 

regression models for any of the monthly and annual streamflow characteristics were drainage area (A) and relief (REL). 

Data for these variables for all gaging stations are presented in 

Supplement 4 (at the back of this report). Supplement 4 also 

includes data for other basin and climatic characteristics (that 

were not used in final regression models), as well as manually 

determined basin and climatic characteristics for informational 

purposes.

Final regressions were performed by using WLS regression. Because individual gaging stations have varying periods 

of record that might be associated with climatically different 

conditions, the reliability of calculations of streamflow characteristics determined by using recorded data might vary among 

gaging stations. Generally, calculations of streamflow characteristics for gaging stations with shorter periods of record 

are expected to be less reliable than calculations for gaging 

stations with longer periods of record. Weighting the streamflow characteristics for a gaging station proportionally to 

record length of the station helps to compensate for differences 

in the reliability of the characteristics. However, appropriate 

weighting factors also incorporate information on the variance 

of the streamflow records for a given gaging station, which 

helps to reduce effects of nonconstant variance on regression 

results. For this study, a weighting factor developed by Ries 

and Friesz (2000) that considers both record length and variance of the streamflow characteristic was used. The weighting factor for each gaging station was calculated by using the 

following equation:

WTi = (Yi/Y1,N)/(Vi/V1,N), (1)

where

WTi is the weighting factor for gaging station i, 

dimensionless;

Yi is the number of years of record for gaging 

station i;

Y1,N is the mean number of years of record for all 

gaging stations;

N is the number of gaging stations used in the 

regression analysis;

Vi is the variance of the streamflow characteristic 

for gaging station i; and

V1,N is the mean variance of the streamflow 

characteristic for all gaging stations.

Regression equations for the annual Q.50, Q.20, and QM 

and retransformation bias-correction factors (Duan, 1983) 

are presented in table 8. Individual regression analyses were 

performed to investigate if acceptable equations for estimating 

Q.90, Q.80, Q.50, Q.20, and QM on a monthly basis and also 

on an annual basis could be developed. Acceptable equations 

were developed for estimating QM for the months of February, 

March, April, June, and July, and Q.50, Q.20, and QM on an 

annual basis. However, equations for QM for the months of 

February, March, April, June, and July were determined to be 

less consistent and reliable than the use of estimation coefficients (table 3) applied to the regression equation results for 

the annual QM (table 8). Thus, the regression equations for 

the long-term mean streamflows for the months of February, 

March, April, June, and July are not reported. The monthly 

and annual streamflow characteristics for which acceptable 

regression equations were not developed or reported can be 

estimated by using the estimation coefficients (table 3).

Estimation of Peak-Flow Characteristics at 

Ungaged Sites

Forty-two gaging stations (indicated in table 1) were used 

in developing regression equations for peak-flow characteristics. These gaging stations were selected because they are 

in or generally close to the study area. The watersheds of the 

gaging stations located outside of the study area generally 

are topographically and hydrologically similar to watersheds 

within the study area. Thirty-nine of the gaging stations had 

10 or more years of annual peak-flow records (on the basis of 

data through water year 2005). The PK1.5, PK2, and PK2.33 

for these 39 gaging stations (Supplement 5 at the back of 

this report) were determined from recorded data by using 

procedures described in Bulletin 17B (Interagency Advisory 

Committee on Water Data, 1982) and incorporated in the 

PEAKFQ computer program (Flynn and others, 2006). Three 

of the 42 gaging stations were CMR stations (sites 2, 4, and 

14) with annual peak-flow records only during the study 

period. Estimated PK1.5, PK2, and PK2.33 for these three 

gaging stations (table 6) were determined by using the RAR.

In developing regression equations for peak-flow characteristics, the study area was divided into two regions: (1) the 

North Region, which includes that part of the study area 

north of the Missouri River, and (2) the South Region, which 

includes that part of the study area south of the Missouri River 

(fig. 1). Eleven gaging stations north of the Missouri River 

(table 1 and fig. 1) were used to develop regression equations 

for the North Region. Thirty-one gaging stations south of 

the Missouri River (table 1 and fig. 1) were used to develop 

regression equations for the South Region.

For each region and each peak-flow characteristic, 

preliminary OLS regressions were performed to identify the 

most influential explanatory variables and select a regression model for subsequent GLS regression (Tasker and 

Stedinger, 1989). Regression models were selected on the 
Table 8. Regression equations for estimating annual streamflow characteristics at 

ungaged sites.

[Abbreviations: A, drainage area (in square miles); p-value, significance level; Q.50, 50-percent 

exceedance (median) streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow; 

RBCF, retransformation bias-correction factor; REL, relief (in feet); SEE, average standard error of 

estimate (in percent). Symbol: <, less than]

Long-term 

streamflow 

characteristic

Equation RBCF SEE p-value

Annual Q.50 = 0.30 A0.49 (REL/1,000)0.55 1.05 49.0 <0.001

Annual Q.20 = 0.69 A0.52 (REL/1,000)0.70 1.03 65.1 .001

Annual QM = 0.56 A0.48 (REL/1,000)0.59 1.04 52.0 <.001

26 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

basis of (1) determination of significant (p-value less than 

0.05) explanatory variables; (2) minimizing Mallow’s Cp 

and the Press statistic (Helsel and Hirsch, 2002, p. 313) 

among different candidate models; (3) reviewing regression diagnostics to ensure the final regression models were 

not substantially affected by outliers, high-leverage values, 

high-influence, values or non-normally distributed residuals (by using methods described by Helsel and Hirsch, 2002, 

p. 228–251); (4) determining that the overall statistical significance exceeded 95 percent (that is, the p-value was less than 

0.05); and (5) determining that the SEP was less than about 

100 percent. Explanatory variables used in final regression 

models for any of the peak-flow characteristics were area (A) 

and basinwide mean elevation (E). Data for these variables 

for all gaging stations are presented in Supplement 4. Supplement 4 also includes data for other basin and climatic characteristics (that were not used in final regression models), as well 

as manually determined basin and climatic characteristics for 

informational purposes.

For each region, final regressions were performed by 

using GLS regression (Tasker and Stedinger, 1989). GLS 

regression accounts for time-sampling error that is inherent when individual gaging stations have been operated for 

different lengths of time and under different climatic conditions. GLS regression also accounts for cross correlation of 

annual peak flows among different gaging stations. For this 

study, GLS regression was applied by using a program based 

on methods described by Stedinger and Tasker (1985) and 

Tasker and Stedinger (1989) and discussed in Kenney and 

others (2007). Numerical methods used in the program to 

estimate time-sampling error are based on statistics for the 

log-Pearson Type III probability distribution, which routinely 

is used for determining peak-flow magnitude and frequency 

relations (Interagency Advisory Committee on Water Data, 

1982). Thus, GLS regression is appropriate for developing 

regression equations for peak-flow characteristics but was 

not used for developing regression equations for monthly and 

annual streamflow characteristics, which are not necessarily well represented by the log-Pearson Type III probability 

distribution. Acceptable equations were developed for the 

PK1.5, PK2, and PK2.33. Regression equations for estimating 

peak-flow characteristics and retransformation bias-correction 

factors (Duan, 1983) are presented in table 9. SEPs for regression equations for the PK1.5, PK2, and PK2.33 for the North 

Region were 56.6, 62.1, and 63.8 percent, respectively. SEPs 

for regression equations for the PK1.5, PK2, and PK2.33 for 

the South Region were 62.1, 57.3, and 55.6 percent, respectively.

Limitations on Use of the Regression Equations

The following limitations need to be considered when 

using the regression equations presented in this report to 

estimate monthly and annual streamflow characteristics and 

peak-flow characteristics for ungaged sites in the study area: 

(1) the regression equations should not be used for sites near 

dams, flood-detention structures, and other manmade structures that might substantially affect the specific streamflow 

characteristics being estimated; (2) the regression equations 

generally should be used only for sites within the study area; 

(3) basin characteristics used in the regression equations 

should be determined by using methods identical to those used 

in this study; and (4) the regression equations generally should 

be used only for sites that have basin characteristics that are 

within the range of characteristics used to develop the regression equations (table 10).

Estimated Streamflow Characteristics for 

Selected Ungaged Sites in Charles M. Russell 

National Wildlife Refuge

Of particular interest to the FWS are estimates of 

monthly and annual streamflow characteristics and peak-flow 

characteristics at ungaged sites (fig. 8) on tributary streams 

where they enter CMR, and also where they enter Fort Peck 

Reservoir. Basin characteristics for these ungaged sites are 

presented in Supplement 6 (at the back of this report). Esti-
Table 9. Regression equations for estimating peak-flow characteristics at ungaged sites.

[Abbreviations: A, drainage area (in square miles); E, basinwide mean elevation (in feet above North American Vertical Datum of 1988); EYR, equivalent years 

of record; ME, average model error (in percent); PK1.5, 1.5-year recurrence interval peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year 

recurrence interval peak flow; RBCF, retransformation bias-correction factor; SEP, average standard error of prediction (in percent); TE, time-sampling error (in 

percent)]

Peak-flow characteristic Equation RBCF SEP TE ME EYR

North Region

PK1.5 = 16 A0.39 1.08 56.6 8.5 48.1 8.8

PK2 = 28 A0.42 1.06 62.1 8.8 53.3 7.1

PK2.33 = 35 A0.43 1.05 63.8 8.9 54.9 6.9

South Region

PK1.5 = 71 A0.62 (E/1,000)

-1.80 1.06 62.1 5.1 57.0 7.0

PK2 = 155 A0.60 (E/1,000)

-1.92 1.05 57.3 4.3 53.0 5.6

PK2.33 = 214 A0.59 (E/1,000)

-1.97 1.04 55.6 4.1 51.5 5.3

Table 10. Ranges for basin characteristics used to develop regression equations for estimating streamflow characteristics at ungaged 

sites.

[Elevation information is referenced to the North American Vertical Datum of 1988. Symbol: --, not applicable]

Type of regression equation Drainage area (A), 

in square miles

Relief (REL), 

in feet

Basinwide mean elevation (E), 

in feet

Annual streamflow characteristics (table 8) 70–2,551 606–4,149 --

Peak-flow characteristics (table 9) for North Region 0.9–920 -- --

Peak-flow characteristics (table 9) for South Region 1.1–2,551 -- 2,398–4,003

Estimation of Streamflow Characteristics 27

mated monthly and annual streamflow characteristics for 

these ungaged sites (derived by using regression equations, 

table 8, and estimation coefficients, table 3) are presented in 

Supplement 7 (at the back of this report) and example plots 

of monthly streamflow characteristics for selected ungaged 

sites are shown in figure 9. Example plots of selected annual 

streamflow characteristics for various exceedance probabilities 

for the selected ungaged sites are shown in figure 10.

The estimated mean and median monthly streamflows for 

the selected ungaged sites (fig. 9) are similar to those of longterm gaging stations close to the study area (fig. 6). Streams 

in the northeastern plains of Montana generally are characterized by higher streamflows during February through August 

and lower streamflows during September through January. For 

most streams, March and April, when most snowmelt runoff 

typically occurs in northeastern Montana, have the highest 

mean monthly streamflow. Spring rainstorms also contribute 

to higher streamflows in March and April. Mean monthly 

streamflow for February typically is larger than late fall and 

early winter streamflows, indicating that during some years 

snowmelt begins in February. Some streams show a midspring (about April or May) decrease in streamflow following 

completion of snowmelt at lower elevations. Late spring and 

summer rainstorms can increase streamflow during the months 

of June and July. Streamflows then generally decrease from 

August through the fall. 

The estimated median monthly and annual streamflows 

generally are substantially less than the estimated mean 

monthly and annual streamflows for the ungaged sites. This 

pattern also was noted by Parrett (2006) for several tributaries to the Milk River that are near the study area. Large 

differences between median and mean monthly and annual 

streamflows are typical of streams with highly variable 

streamflow from year to year. Differences between median 

and mean monthly streamflows are especially large for some 

months (including January, February, August, September, and 

October) when streamflows typically transition between baseflow and runoff dominance.

The estimated long-term streamflow characteristics 

for the selected ungaged sites generally indicate similar 

annual streamflow patterns to those of the long-term gaging 

stations. However, the methods used to estimate the monthly 

and annual streamflow characteristics (that is, the regression 

equations, table 8, and estimation coefficients, table 3) for 
VALLEY

CO

PHILLIPS

CO

ROSEBUD

CO

GARFIELD

CO

FERGUS CO

CUSTER

CO

PRAIRIE

CO

MC CONE

CO

PETROLEUM

CO

MUSSELSHELL

CO

ROOSEVELT

CO

WHEATLAND

CO

GOLDEN

VALLEY

CO

HILL

CO

CHOTEAU CO

BLAINE CO

Fort PeckReservoir

Creek

Beauchamp Fourchette Creek

Timber Creek

Nelson

Creek

Timber

Creek

Creek ll e H Seven Blackfoot Creek Creek

Big

Dry

Creek

Squaw

Sacajawea

Creek

Armells

Two Calf

Creek

Siparyann

Creek

Telegraph Cr

Ungaged site on tributary and site number

0 20 10 40 MILES

0 20 10 40 KILOMETERS

109° 108° 107° 106°

48°47°

Base map from U.S. Census Bureau TIGER digital data, 1993−2001, 1:100,000; Montana State Library, 2003, 1:100,000; and Montana Natural Heritage Program, 2002, 1:100,000 Albers Equal-Area Conic projection Standard parallels 29°30’N and 45°30’N, central meridian 107°00’WNorth American Datum of 1983 (NAD 83)

Charles M. Russell National Wildlife Refuge

EXPLANATION

Study area boundary

Circle

Wolf Point

Lewistown

Glasgow

Jordan

Hays

Landusky

Van

Norman

T2 T18

T20 T7 T9 T5

T3

T1

T8 T6

T4

T13

T15

T21 T25

T29

T23

T31

T19

T17 T11

T32

T30

T28

T27

T26

T24

T22

T16 T14

T12 T10

T27

Milk

River

River

Redwater

River

Musselshell

River

Missouri

River

Creek Rock

Creek

CK

Figure 8. Locations of selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife Refuge, northeastern Montana. 

28 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
A Armells Creek at confluence with Fort Peck Reservoir, Mont. (site T4)

 Drainage area 399 square miles

B Rock Creek at confluence with Fort Peck Reservoir, Mont. (site T8)

 Drainage area 98 square miles

0.01

0.1

10

1

100

1,000

0.01

0.1

10

100

1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

Estimated long-term streamflow characteristics (determined by 

 using regression equations and estimation coefficients)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

1

Figure 9. Estimated long-term monthly streamflow characteristics (derived by using regression equations, table 8, 

and estimation coefficients, table 3) for selected ungaged sites. A, Armells Creek at confluence with Fort Peck 

Reservoir, Mont.; B, Rock Creek at confluence with Fort Peck Reservoir, Mont.; C, Big Dry Creek at confluence with 

Fort Peck Reservoir, Mont.; D, Nelson Creek at confluence with Fort Peck Reservoir, Mont.

Estimation of Streamflow Characteristics 29
Figure 9. Estimated long-term monthly streamflow characteristics (derived by using regression equations, table 8, 

and estimation coefficients, table 3) for selected ungaged sites. A, Armells Creek at confluence with Fort Peck 

Reservoir, Mont.; B, Rock Creek at confluence with Fort Peck Reservoir, Mont.; C, Big Dry Creek at confluence with 

Fort Peck Reservoir, Mont.; D, Nelson Creek at confluence with Fort Peck Reservoir, Mont.—Continued

C Big Dry Creek at confluence with Fort Peck Reservoir, Mont. (site T28)

 Drainage area 2,830 square miles

Note: Big Dry Creek at confluence with Fort Peck Reservoir has values of one of more basin 

characteristics that are outside the range of values used to develop regression equations. 

Estimates of streamflow characteristics for this site should be used with caution.

D Nelson Creek at confluence with Fort Peck Reservoir (site T32)

 Drainage area 122 square miles

0.01

0.1

10

1

100

1,000

0.01

0.1

10

100

1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

Estimated long-term streamflow characteristics (determined by 

 using regression equations and estimation coefficients)

50-percent exceedance (median) monthly streamflow

Mean monthly streamflow

EXPLANATION

Oct Nov Dec Jan Feb Mar Apr May June July Aug Sep

1

30 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Figure 10. Estimated annual streamflow (derived by using regression equations, table 8, and estimation 

coefficients, table 3) for various exceedance probabilities for selected ungaged sites. A, Armells Creek at 

confluence with Fort Peck Reservoir, Mont.; B, Rock Creek at confluence with Fort Peck Reservoir, Mont.; C, Big 

Dry Creek at confluence with Fort Peck Reservoir, Mont.; D, Nelson Creek at confluence with Fort Peck Reservoir, 

Mont.

Estimated median annual streamflow

Estimated annual streamflow for indicated exceedance probability

Estimated mean annual streamflow

EXCEEDANCE PROBABILITY

Line connecting exceedance probabilities is presented to show general patterns; 

 variability between indicated exceedance probabilities might not be linear

0

10

20

30

40

50

0.9 0.8

0

5

10

15

20

1.0 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

STREAMFLOW, IN CUBIC FEET PER SECOND

A Armells Creek at confluence with Fort Peck Reservoir, Mont. (site T4)

 Drainage area 399 square miles

B Rock Creek at confluence with Fort Peck Reservoir, Mont. (site T8)

 Drainage area 98 square miles

EXPLANATION

Estimation of Streamflow Characteristics 31
Figure 10. Estimated annual streamflow (derived by using regression equations, table 8, and estimation 

coefficients, table 3) for various exceedance probabilities for selected ungaged sites. A, Armells Creek at 

confluence with Fort Peck Reservoir, Mont.; B, Rock Creek at confluence with Fort Peck Reservoir, Mont.; C, Big 

Dry Creek at confluence with Fort Peck Reservoir, Mont.; D, Nelson Creek at confluence with Fort Peck Reservoir, 

Mont.—Continued

0

20

40

60

80

100

0

2

4

6

8

STREAMFLOW, IN CUBIC FEET PER SECOND

Estimated median annual streamflow

Estimated annual streamflow for indicated exceedance probability

Estimated mean annual streamflow

EXCEEDANCE PROBABILITY

Line connecting exceedance probabilities is presented to show general patterns; 

 variability between indicated exceedance probabilities might not be linear

C Big Dry Creek at confluence with Fort Peck Reservoir, Mont. (site T28)

 Drainage area 2,830 square miles

Note: Big Dry Creek at confluence with Fort Peck Reservoir has values of one of more basin 

characteristics that are outside the range of values used to develop regression equations. 

Estimates of streamflow characteristics for this site should be used with caution.

D Nelson Creek at confluence with Fort Peck Reservoir, Mont. (site T32)

 Drainage area 122 square miles

EXPLANATION

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

32 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Figure 11. Estimated 1.5-, 2-, and 2.33-year recurrence interval peak flows (determined by using regression equations, 

table 9) for selected ungaged sites: T4 (Armells Creek at confluence with Fort Peck Reservoir, Mont.), T8 (Rock Creek at 

confluence with Fort Peck Reservoir, Mont.), T28 (Big Dry Creek at confluence with Fort Peck Reservoir, Mont.), and T32 

(Nelson Creek at confluence with Fort Peck Reservoir, Mont.).

EXPLANATION

T4 T8 T28 T32

 500

0

1,000

1,500

2,000

2,500

3,000

3,500

SITE

ESTIMATED PEAK FLOW, IN CUBIC FEET PER SECOND

2-year recurrence interval peak flow

1.5-year recurrence interval peak flow

2.33-year recurrence interval peak flow

Estimation of Streamflow Characteristics 33

the ungaged sites homogenize general regional streamflow 

patterns. Thus, actual site-to-site variability is very likely to 

be larger than that indicated by the estimates presented in 

Supplement 7 and figure 9.

Estimated peak-flow characteristics for the selected 

ungaged sites (estimated by using regression equations, 

table 9) are presented in Supplement 8 (at the back of this 

report), and example plots of peak-flow characteristics for 

ungaged sites are shown in figure 11. Parrett and Johnson 

(2003) noted that peak-flow characteristics for streams in 

eastern Montana tend to be more variable, both spatially and 

temporally, than those for streams in other parts of Montana 

and that most annual peak flows in the study area occur during 

the months of March through July.
34 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

Summary

Charles M. Russell National Wildlife Refuge (CMR) 

encompasses about 1.1 million acres (including Fort Peck 

Reservoir on the Missouri River) in northeastern Montana. 

To ensure that sufficient streamflow remains in the tributary 

streams to maintain the riparian corridors, the U.S. Fish and 

Wildlife Service (FWS) is negotiating water-rights issues with 

the Reserved Water Rights Compact Commission of Montana. 

These negotiations require accurate information about current 

and long-term streamflow characteristics for Missouri River 

tributary streams that cross CMR. However, there are very few 

long-term streamflow data for these streams. Thus, the U.S. 

Geological Survey (USGS), in cooperation with the FWS, 

conducted a study to gage, for a short period, selected streams 

that cross CMR, and analyze data to estimate long-term 

streamflow characteristics for CMR. 

To address the need for streamflow information in CMR, 

a three-phased approach was used that involved (1) collecting continuous records of daily mean streamflow for a 5-year 

period (water years 2000–2004, hereinafter referred to as the 

study period) for five streams that cross CMR, (2) estimating long-term streamflow characteristics for the five gaging 

stations by using relations between study-period streamflow 

characteristics and long-term streamflow characteristics for 

nearby long-term gaging stations to adjust recorded studyperiod streamflow characteristics, and (3) developing regional 

regression equations to relate streamflow characteristics to 

basin characteristics. The long-term streamflow characteristics 

of primary interest include the monthly and annual 90-, 80-, 

50-, and 20-percent exceedance streamflows and mean streamflows (Q.90, Q.80, Q.50, Q.20, and QM, respectively), and the 

1.5-, 2-, and 2.33-year peak flows (PK1.5, PK2, and PK2.33, 

respectively). 

The Regional Adjustment Relationship (RAR) was 

investigated for estimating the monthly and annual Q.90, 

Q.80, Q.50, Q.20, and QM, and the PK1.5, PK2, and PK2.33 

for the short-term CMR gaging stations (hereinafter referred 

to as CMR stations). The conceptual basis of the RAR is that 

at any given stream site the correlation between a streamflow characteristic for a short period of record and long-term 

streamflow characteristics is consistent over a somewhat broad 

and climatically homogeneous region. 

For the CMR stations, the RAR regression equations 

were determined to provide acceptable results for estimating 

the long-term Q.90, Q.80, Q.50, Q.20, and QM on a monthly 

basis for the months of March through June, and also on an 

annual basis. For the months of September through January, 

the RAR regression equations did not provide acceptable 

results for any long-term streamflow characteristic. For the 

month of February, the RAR regression equations provided 

acceptable results for the long-term Q.50 and QM but poor 

results for the long-term Q.90, Q.80, and Q.20. For the months 

of July and August, the RAR provided acceptable results for 

the long-term Q.50, Q.20, and QM but poor results for the 

long-term Q.90 and Q.80. 

Estimation coefficients were developed for estimating the 

long-term streamflow characteristics for which the RAR did 

not provide acceptable results. These coefficients were developed by using continuous streamflow records from streams 

in the study area or in nearby watersheds that generally are 

hydrologically similar to the streams that cross CMR. The estimation coefficients were determined by calculating the ratio of 

a given streamflow characteristic to the mean annual streamflow. Estimation coefficients were developed for three types of 

watersheds: (1) watersheds with maximum elevations less than 

about 5,000 ft (above NAVD 88), (2) watersheds on the south 

side of the Missouri River with maximum elevations greater 

than about 5,000 ft, and (3) watersheds on the north side of the 

Missouri River with maximum elevations greater than about 

5,000 ft. Estimation coefficients for each watershed type and 

each streamflow characteristic were calculated by determining 

the weighted average (weighting based on number of years of 

record) of the ratios of all the selected gaging stations for a 

given watershed type. 

The RAR also was investigated for estimating the longterm PK1.5, PK2, and PK2.33 for three of the CMR stations. 

The RAR regression equations were determined to provide 

acceptable results for estimating PK1.5, PK2, and PK2.33 for 

the three CMR stations. 

Methods for estimating streamflow characteristics at 

ungaged sites also were needed by the FWS. Regression 

analyses that relate individual streamflow characteristics to 

various basin and climatic characteristics for gaging stations 

were performed to develop regression equations to estimate 

streamflow characteristics at ungaged sites. Selected basin 

and climatic characteristics that were considered as potential 

explanatory variables in regression analyses were determined 

by using a geographic information system. 

Individual regression analyses were performed to determine if acceptable equations for estimating Q.90, Q.80, Q.50, 

Q.20, and QM on a monthly basis and an annual basis could 

be developed. Final equations for the annual Q.50, Q.20, and 

QM were developed by using weighted least squares regression. Acceptable equations also were developed for estimating 

QM for the months of February, March, April, June, and July, 

and Q.50, Q.20, and QM on an annual basis. However, equations for QM for the months of February, March, April, June, 

and July were determined to be less consistent and reliable 

than the use of estimation coefficients applied to the regression 

equation results for the annual QM. The monthly and annual 

streamflow characteristics for which acceptable regression 

equations were not developed or reported can be estimated by 

using the estimation coefficients.

Individual regression analyses also were performed to 

investigate if acceptable equations for the PK1.5, PK2, and 

PK2.33 could be developed. Final equations were developed 

using generalized least squares regression. In developing 

regression equations for peak-flow characteristics, the study 

area was divided into two regions: (1) the North Region, which 
References Cited 35

Interagency Advisory Committee on Water Data, 1982, Guidelines for determining flood flow frequency—Bulletin 17B 

of the Hydrology Subcommittee: U.S. Geological Survey, 

Office of Water Data Coordination, 183 p., accessed June 5, 

2008, at http://water.usgs.gov/osw/bulletin17b/bulletin_17B.

html

Jensen, F.S., and Varnes, H.D., 1964, Geology of the Fort Peck 

area, Garfield, McCone, and Valley Counties, Montana: 

U.S. Geological Survey Professional Paper 414–F, 48 p.

Kenney, T.A., Wilkowske, C.D., and Wright, S.J., 2007, 

Methods for estimating magnitude and frequency of peak 

flows for natural streams in Utah: U.S. Geological Survey 

Scientific Investigations Report 2007–5158, 28 p.

Koch, R.W., and Smillie, G.M., 1986, Bias in hydrologic 

prediction using log-transformed regression models: Water 

Resources Bulletin, v. 22, p. 717–723.

Lawlor, S.M., 2004, Determination of channel morphology 

characteristics, bankfull discharge, and various design-peak 

discharges in western Montana: U.S. Geological Survey 

Scientific Investigations Report 2004–5263, 19 p.

Natural Resources Conservation Service, 2008a, PRISM, 

accessed April 14, 2008, http://www.wcc.nrcs.usda.gov/

climate/prism.html

Natural Resources Conservation Service, 2008b, Watershed Boundary Dataset (WBD), accessed April 14, 2008, 

at http://www.ncgc.nrcs.usda.gov/products/datasets/

watershed/.

Omang, R.J., and Parrett, Charles, 1984, A method for estimating mean annual runoff of ungaged streams based on 

basin characteristics in central and eastern Montana: U.S. 

Geological Survey Water-Resources Investigations Report 

84–4143, 15 p.

Parrett, Charles, 2006, Synthesis of monthly and annual 

streamflow records (water years 1950-2003) for Big Sandy, 

Clear, Peoples, and Beaver Creeks in the Milk River basin, 

Montana: U.S. Geological Survey Scientific Investigations 

Report 2005-5216, 23 p. Available online only at http://

pubs.usgs.gov/sir/2005/5216/.

Parrett, Charles, and Johnson, D.R., 2003, Methods for estimating flood frequency in Montana based on data through 

water year 1998: U.S. Geological Survey Water-Resources 

Investigations Report 03–4308, 101 p.

Parrett, Charles, Johnson, D.R., and Hull, J.A., 1989, Estimates of monthly streamflow characteristics at selected sites 

in the upper Missouri River basin, base period water years 

1937–86: U.S. Geological Survey Water-Resources Investigations Report 89–4082, 103 p.

includes that part of the study area north of the Missouri River, 

and (2) the South Region, which includes that part of the study 

area south of the Missouri River. Acceptable regression equations were developed for the PK1.5, PK2, and PK2.33.

References Cited

Alley, W.M., and Burns, A.W., 1983, Mixed station extension of monthly streamflow records: Journal of Hydraulic 

Engineering, American Society of Civil Engineers, v. 109, 

no. 10, p. 1,272–1,284.

Bakke, P.D., Thomas, Robert, and Parrett, Charles, 1999, Estimation of long-term discharge characteristics by regional 

adjustment: Journal of the American Water Resources Association, v. 35, p. 911–921.

Cooper S.V., and Jean, C., 2001, Wildfire succession in plant 

communities natural to the Alkali Creek vicinity, Charles 

M. Russell National Wildlife Refuge, Montana: Technical 

Report of the Montana Natural Heritage Program, Helena, 

Montana, 32 p.

Daly, Christopher, 1996, Overview of the PRISM model, 

accessed December 30, 2008, at http://www.prism.oregonstate.edu/docs/overview.html

Duan, Naihua, 1983, A nonparametric retransformation 

method: Journal of the American Statistical Association, 

v. 78, no. 383, p. 2,353–2,363.

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

manual for program PeakFQ, annual flood frequency analysis using Bulletin 17B guidelines: U.S. Geological Survey 

Techniques and Methods, book 4, chapter B4, 42 p. Available online at http://pubs.usgs.gov/tm/2006/tm4b4/#title

Frahme, C.W., 1979, Mineral resources of the Charles M. Russell Wildlife Refuge, Fergus, Garfield, McCone, Petroleum, 

Phillips, and Valley Counties, Montana—Chapter B, Geology and evaluation of the mineral resources of the Charles 

M. Russell Wildlife Refuge: U.S. Geological Survey OpenFile Report 79–1204, p. 5–42.

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

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 524 p. 

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Horizon Systems Corporation, 2006, National Hydrography Dataset Plus, accessed April 14, 2008, at http://www.

horizon-systems.com/nhdplus/.
36 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

Rantz, S.E. and others, 1982, Measurement and computation 

of streamflow: U.S. Geological Survey Water-Supply Paper 

2175, 631 p. 

Ries, K.G., and Friesz, P.J., 2000, Methods for estimating lowflow statistics for Massachusetts streams: U.S. Geological 

Survey Water-Resources Investigations Report 00–4135, 

81 p.

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

analysis I—Ordinary, weighted, and generalized leastsquares compared: American Geophysical Union, Water 

Resources Research, v. 21, no. 9, p. 1,421–1,432.

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

model for hydrologic regression: Journal of Hydrology, 

v. 111, p. 361–375.

U.S. Environmental Protection Agency, 2006, Watershed 

Assessment of River Stability & Sediment Supply (WARSSS), Hydrologic Processes—Bankfull Discharge, accessed 

June 7, 2008, at http://www.epa.gov/warsss/sedsource/

bankfull.htm

U.S. Environmental Protection Agency, 2007, National Land 

Cover Data (NLCD 2006), accessed April 14, 2008, at 

http://www.epa.gov/mrlc/nlcd-2006.html

U.S. Fish and Wildlife Service, 2006, Charles M. Russell National Wildlife Refuge, Lewistown, Montana, 

accessed May 23, 2006, at http://cmr.fws.gov/Annual%20

Narratives/2002%20Annual%20Narrative/Introduction.htm

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

accessed April 14, 2008, at http://ned.usgs.gov/.

U.S. Geological Survey, 2007, National Hydrography Dataset, 

accessed April 14, 2008, at http://nhd.usgs.gov/.

Western Regional Climate Center, 2006, Montana climate 

summaries, Jordan, Montana, accessed June 13, 2006, at 

http://www.wrcc.dri.edu/cgi-bin/cliMAIN.pl?mtjord

Wilkerson, G.V., 2008, Improved bankfull discharge prediction using 2-year recurrence-period discharge: Journal of the 

American Water Resources Association, v. 44, p. 243–258.

Williams, G.P., 1978, Bankfull discharges of rivers: Water 

Resources Research, v. 14, no. 6, p. 1,141–1,154. 

Woods, A.J., Omernik, J.M., Nesser, J.A., Shelden, J., Comstock, J.A., Azevedo, S.H., 2002, Ecoregions of Montana, 

(2d ed.): U.S. Environmental Protection Agency, Western 

Ecology Division, accessed October 8, 2008 at http://www.

epa.gov/naaujydh/pages/ecoregions/mt_eco.htm
Supplemental Data
Supplement 1. Monthly and annual streamflow characteristics for long-term index gaging stations used in the Regional Adjustment Relationship (RAR).—Continued

[The gaging stations presented in this table are long-term index gaging stations used in the RAR to estimate long-term monthly and annual streamflow characteristics for short-term gaging stations in or near Charles M. Russell National Wildlife Refuge. All stations have 5 years of monthly mean streamflow (for all months) and annual mean streamflow record for the study period (water years 2000–2004). Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 20 (Big Dry Creek near Van Norman)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 1.9 2.2 2.1 1.4 1.6 78 5.7 4.3 65 81 7.0 1.2 21

Long-term monthly and annual streamflow characteristics (water years 1939–2005)

Years of record 63 63 63 63 63 63 64 64 64 65 64 64 62Q.90 .25 .36 .05 .00 .00 4.0 2.7 1.6 1.9 .78 .17 .05 5.7Q.80 .53 .72 .30 .00 .23 5.8 4.4 3.3 2.7 1.6 .46 .24 9.6Q.50 2.2 2.0 1.4 .27 3.5 50 9.4 8.2 16 11 3.8 1.7 27Q.20 5.7 4.0 2.6 2.9 83 281 44 19 76 58 13 6.8 88QM 6.1 3.0 2.6 6.4 71 250 81 28 59 43 16 16 49

Site 22 (Big Sandy Creek at reservation boundary, near Rocky Boy)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 2.7 2.6 2.1 2.0 1.8 4.3 5.1 5.6 9.6 5.0 2.9 2.4 3.8

Long-term monthly and annual streamflow characteristics (water years 1982–2005)

Years of record 23 23 23 23 23 23 23 24 24 24 24 24 23Q.90 2.1 1.7 1.7 1.5 1.2 2.1 4.5 3.3 2.3 2.3 1.1 1.5 3.4Q.80 2.4 2.4 1.8 1.7 1.7 3.6 4.8 5.3 5.6 3.2 1.7 2.3 3.9Q.50 4.3 3.8 3.4 2.9 3.3 4.9 8.0 9.5 14 9.8 5.8 4.4 6.4Q.20 6.7 5.5 4.5 4.0 4.9 7.8 12 18 30 17 8.3 6.7 11QM 5.2 4.5 4.0 3.4 4.1 6.3 10 13 18 13 6.5 5.3 7.7

Site 23 (Peoples Creek near Hays)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 0.04 0.08 0.23 0.11 0.18 12 1.5 3.7 2.6 0.79 0.08 0.01 1.8

Long-term monthly and annual streamflow characteristics (water years 1966–2005)

Years of record 38 38 39 39 39 39 39 39 39 39 39 39 38Q.90 .00 .01 .01 .00 .01 .92 .80 .25 .38 .00 .00 .00 .93Q.80 .01 .02 .02 .02 .05 2.5 1.5 2.4 .95 .12 .01 .01 2.6

38 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 1. Monthly and annual streamflow characteristics for long-term index gaging stations used in the Regional Adjustment Relationship (RAR).—Continued

[The gaging stations presented in this table are long-term index gaging stations used in the RAR to estimate long-term monthly and annual streamflow characteristics for short-term gaging stations in or near Charles M. Russell National Wildlife Refuge. All stations have 5 years of monthly mean streamflow (for all months) and annual mean streamflow record for the study period (water years 2000–2004). Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 23 (Peoples Creek near Hays)—Continued

Long-term monthly and annual streamflow characteristics (water years 1966–2005)—Continued

Q.50 0.12 0.35 0.78 0.34 2.2 14 9.0 7.3 9.2 1.7 0.11 0.06 4.7Q.20 5.1 6.8 5.3 5.1 7.8 27 27 26 31 18 2.0 1.7 18QM 3.2 3.2 2.6 3.3 8.5 28 17 29 20 7.9 2.2 3.4 11

Site 25 (Peoples Creek below Kuhr Coulee, near Dodson)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 0.00 0.03 0.17 0.15 0.23 37 3.5 10 10 6.2 1.5 0.00 5.8

Long-term monthly and annual streamflow characteristics (water years 1951–73, 1982–2005)

Years of record 47 47 46 46 46 46 49 50 51 51 50 51 46Q.90 .00 .00 .00 .00 .00 6.3 2.4 4.2 1.6 .00 .00 .00 3.9Q.80 .00 .02 .00 .00 .23 11 4.2 6.1 2.5 2.4 .00 .00 5.7Q.50 1.4 2.3 1.1 .52 4.9 32 21 18 16 7.40 .43 .16 16Q.20 8.0 7.7 5.5 4.2 40 120 61 46 65 34 5.3 3.7 47QM 8.1 5.5 4.3 5.0 29 78 52 52 41 22 3.2 12 26

Site 38 (Redwater River at Circle)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 0.23 0.11 0.09 0.1 0.14 11 1.3 0.54 0.58 1.4 0.43 0.2 1.4

Long-term monthly and annual streamflow characteristics (water years 1937–72, 1974–2004)

Years of record 72 72 69 67 68 70 72 73 73 72 72 72 66Q.90 .00 .00 .00 .00 .00 .63 .50 .21 .18 .02 .00 .00 .63Q.80 .02 .03 .01 .00 .02 2.0 .9 .37 .34 .05 .00 .00 1.0Q.50 .11 .11 .10 .06 .53 17 2.9 1.4 1.6 .28 .06 .07 5.7Q.20 .35 .34 .26 .37 17 109 10 5.5 19 8.2 1.5 .31 21QM .51 .36 .43 .35 15 71 17 3.6 14 11 2.0 2.3 11

Supplemental Data 39
Supplement 1. Monthly and annual streamflow characteristics for long-term index gaging stations used in the Regional Adjustment Relationship (RAR).—Continued

[The gaging stations presented in this table are long-term index gaging stations used in the RAR to estimate long-term monthly and annual streamflow characteristics for short-term gaging stations in or near Charles M. Russell National Wildlife Refuge. All stations have 5 years of monthly mean streamflow (for all months) and annual mean streamflow record for the study period (water years 2000–2004). Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 40 (Poplar River near Poplar)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 22 29 20 9.1 10 209 132 100 125 65 19 15 63

Long-term monthly and annual streamflow characteristics (water years 1908–24, 1947–69, 1975–79, 1982–2005)

Years of record 67 66 66 66 66 66 66 66 67 67 69 69 66Q.90 8.3 9.8 5.1 .67 .47 18 71 37 19 11 2.0 4.4 35Q.80 11 15 9.4 1.9 1.1 32 96 47 26 13 5.5 7.4 43Q.50 24 25 15 7.1 10 128 236 83 59 52 19 14 82Q.20 44 34 24 14 19 484 823 208 137 125 36 28 199QM 28 27 17 8.5 26 326 649 123 89 77 27 24 118

Site 41 (Big Muddy Creek near Antelope)

Study period (water years 2000–2004) mean monthly or annual streamflow

QM 5.0 6.3 3.4 1.9 1.6 126 47 27 32 10 4.2 2.4 23

Long-term streamflow characteristics (water years 1979–2005)

Years of record 27 27 27 27 27 27 27 27 27 27 27 27 27Q.90 .42 2.3 1.6 .31 .3 12 13 6.7 1.7 1.3 .44 .07 6.2Q.80 1.1 4.1 1.9 .65 .94 19 18 7.4 3.1 2.7 .72 .22 11Q.50 4.4 5.4 3.3 1.6 2.0 40 40 16 9.4 10 3.4 2.8 20Q.20 7.9 7.8 5.7 3.3 13 238 70 35 30 26 6.2 5.2 38QM 5.3 5.8 3.6 1.9 22 133 109 26 19 24 8.5 4.2 30

40 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 2. Selected peak-flow information for long-term index gaging stations used in the Regional Adjustment Relationship (RAR).

[The gaging stations presented in this table are long-term index gaging stations used in the RAR to estimate peak-flow characteristics for short-term gaging stations. All stations have 5 years of annual peakflow records for the study period. Streamflow values are in cubic feet per second. Abbreviations: PK1.5, 1.5-year recurrence interval peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year recurrence interval peak flow; PKM, mean peak flow]

Site number 

(fig. 1)

Station 

number Station name

PKM for study 

period 

(water years 

2000–2004)

PKM for 

period of record 

(through water 

year 2005)

Years of 

annual peak 

flow records 

(through water 

year 2005)

PK1.5 PK2 PK2.33

3 06115300 Duval Creek near Landusky 80 126 43 31 62 82

20 06131000 Big Dry Creek near Van Norman 4,210 4,160 66 1,180 2,240 2,90021 06131200 Nelson Creek near Van Norman 386 579 17 259 432 52922 06137400 Big Sandy Creek at reservation boundary, near 

Rocky Boy

37 108 24 37 60 74

23 06154400 Peoples Creek near Hays 163 547 39 72 148 19925 06154550 Peoples Creek below Kuhr Coulee, near Dodson 414 1,080 45 320 558 70038 06177500 Redwater River at Circle 113 1,390 73 304 628 84240 06181000 Poplar River near Poplar 1,490 5,790 55 1,170 2,260 2,97041 06183450 Big Muddy Creek near Antelope 807 1,030 27 405 657 800

Supplemental Data 41
Supplement 3. Long-term monthly and annual streamflow characteristics (calculated by using period-of-record data through water year 2005) for selected gaging stations 

used to develop regression equations.—Continued[The gaging stations presented in this table are stations that have 10 or more years of streamflow records and were used to develop regression equations that estimate monthly and annual streamflow characteristics for ungaged sites in or near Charles M. Russell National Wildlife Refuge. Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 8 (Box Elder Creek near Winnett)

Long-term monthly and annual streamflow characteristics (water years 1930–33, 1934–36, 1958–72)

Years of record 19 19 19 18 18 19 20 21 22 21 20 20 17Q.90 .00 .00 .00 .00 .00 .72 .09 .00 .00 .00 .00 .00 4.7Q.80 .00 .00 .00 .00 .00 1.7 1.2 .11 .16 .05 .00 .00 9.3Q.50 .00 .05 .05 .00 .25 8.0 6.9 9.3 20 4.0 .21 .00 16Q.20 .12 .26 .27 .35 7.9 112 17 49 175 21 6.6 .45 38QM .42 .16 .24 .34 20 51 14 57 100 23 3.1 .83 23

Site 15 (Sand Creek near Jordan)

Long-term monthly and annual streamflow characteristics (water years 1957–67)

Years of record 10 10 10 10 10 10 10 10 10 10 11 11 10Q.90 .00 .00 .00 .00 .00 .28 .48 .14 .01 .00 .00 .00 1.3Q.80 .00 .00 .00 .00 .06 .34 .54 .31 .06 .03 .00 .00 1.8Q.50 .05 .06 .02 .04 .53 6.0 .75 .99 1.1 1.7 .00 .00 4.1Q.20 .26 .41 .30 .19 11 29 7.0 3.5 5.7 20 .08 .10 6.6QM .11 .18 .11 .14 6.1 36 6.8 2.6 5.7 8.0 .15 .06 5.5

Site 20 (Big Dry Creek near Van Norman)

Long-term monthly and annual streamflow characteristics (water years 1939–2005)

Years of record 63 63 63 63 63 63 64 64 64 65 64 64 62Q.90 .25 .36 .05 .00 .00 4.0 2.7 1.6 1.9 .78 .17 .05 5.7Q.80 .53 .72 .30 .00 .23 5.8 4.4 3.3 2.7 1.6 .46 .24 9.6Q.50 2.2 2.0 1.4 .27 3.5 50 9.4 8.2 16 11 3.8 1.7 27Q.20 5.7 4.0 2.6 2.9 83 281 44 19 76 58 13 6.8 88QM 6.1 3.0 2.6 6.4 71 250 81 28 59 43 16 16 49

42 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 3. Long-term monthly and annual streamflow characteristics (calculated by using period-of-record data through water year 2005) for selected gaging stations 

used to develop regression equations.—Continued[The gaging stations presented in this table are stations that have 10 or more years of streamflow records and were used to develop regression equations that estimate monthly and annual streamflow characteristics for ungaged sites in or near Charles M. Russell National Wildlife Refuge. Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 21 (Nelson Creek near Van Norman)

Long-term monthly and annual streamflow characteristics (water years 1976–85, 2000–2004)

Years of record 14 14 14 14 15 15 15 15 15 15 15 15 14Q.90 .00 .00 .00 .00 .00 .18 .10 .00 .01 .00 .00 .00 .58Q.80 .00 .00 .00 .00 .00 .51 .11 .00 .02 .00 .00 .00 .60Q.50 .00 .00 .00 .00 .07 1.3 .30 .14 .42 .20 .01 .00 .97Q.20 .11 .02 .00 .34 3.1 9.8 .75 .69 3.6 4.0 1.4 .00 1.6QM .16 .02 .02 .35 2.2 5.5 3.1 1.4 1.6 2.4 1.2 1.1 1.6

Site 23 (Peoples Creek near Hays)

Long-term monthly and annual streamflow characteristics (water years 1966–2005)

Years of record 38 38 39 39 39 39 39 39 39 39 39 39 38Q.90 .00 .01 .01 .00 .01 .92 .80 .25 .38 .00 .00 .00 .93Q.80 .01 .02 .02 .02 .05 2.5 1.5 2.4 .95 .12 .01 .01 2.6Q.50 .12 .35 .78 .34 2.2 14 9.0 7.3 9.2 1.7 .11 .06 4.7Q.20 5.1 6.8 5.3 5.1 7.8 27 27 26 31 18 2.0 1.7 18QM 3.2 3.2 2.6 3.3 8.5 28 17 29 20 7.9 2.2 3.4 11

Site 25 (Peoples Creek below Kuhr Coulee, near Dodson)

Long-term monthly and annual streamflow characteristics (water years 1951–73, 1982–2005)

Years of record 47 47 46 46 46 46 49 50 51 51 50 51 46Q.90 .00 .00 .00 .00 .00 6.3 2.4 4.2 1.6 .00 .00 .00 3.9Q.80 .00 .02 .00 .00 .23 11 4.2 6.1 2.5 2.4 .00 .00 5.7Q.50 1.4 2.3 1.1 .52 4.9 32 21 18 16 7.4 .43 .16 16Q.20 8.0 7.7 5.5 4.2 40 120 61 46 65 34 5.3 3.7 47QM 8.1 5.5 4.3 5.0 29 78 52 52 41 22 3.2 12 26

Supplemental Data 43
Supplement 3. Long-term monthly and annual streamflow characteristics (calculated by using period-of-record data through water year 2005) for selected gaging stations 

used to develop regression equations.—Continued[The gaging stations presented in this table are stations that have 10 or more years of streamflow records and were used to develop regression equations that estimate monthly and annual streamflow characteristics for ungaged sites in or near Charles M. Russell National Wildlife Refuge. Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 30 (Beaver Creek above Dix Creek near Malta)

Long-term monthly and annual streamflow characteristics (water years 1967–69, 1976–82)

Years of record 10 10 10 10 10 10 10 10 10 10 10 10 10

Q.90 .00 .00 .00 .00 2.1 5.7 2.3 .53 .04 .00 .00 .00 2.2Q.80 .00 .00 .00 .60 2.4 11 6.9 1.5 1.4 .00 .00 .00 4.5Q.50 0.16 0.51 1.1 1.9 4.4 126 31 38 7.7 2.6 0.00 0.00 26Q.20 3.6 2.7 4.4 3.4 38 524 194 156 38 46 .63 8.8 94QM 2.6 1.7 2.8 3.9 28 318 117 68 34 26 1.5 33 53

Site 32 (Prairie Elk Creek near Oswego)

Long-term monthly and annual streamflow characteristics (water years 1975–85)

Years of record 10 10 10 10 10 10 10 10 10 10 10 10 10Q.90 1.6 1.3 .47 .05 .04 3.4 1.7 1.6 2.6 .87 .68 .96 3.3Q.80 1.8 1.3 .61 .10 .10 4.3 1.9 2.0 3.0 1.1 .80 1.0 4.0Q.50 3.6 1.6 .78 .43 5.9 12 5.2 4.9 6.9 4.3 1.7 1.7 8.9Q.20 9.3 2.1 1.0 11 33 77 14 15 73 21 4.5 5.3 24QM 5.6 1.8 .9 3.8 30 70 24 10 27 12 3.3 8.5 16

Site 38 (Redwater River at Circle)

Long-term monthly and annual streamflow characteristics (water years 1937–72, 1974–2004)

Years of record 72 72 69 67 68 70 72 73 73 72 72 72 66Q.90 .00 .00 .00 .00 .00 .63 .50 .21 .18 .02 .00 .00 .63Q.80 .02 .03 .01 .00 .02 2.0 .9 .37 .34 .05 .00 .00 1.0Q.50 .11 .11 .10 .06 .53 17 2.9 1.4 1.6 .28 .06 .07 5.7Q.20 .35 .34 .26 .37 17 109 10 5.5 19 8.2 1.5 .31 21QM .51 .36 .43 .35 15 71 17 3.6 14 11 2.0 2.3 11

44 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 3. Long-term monthly and annual streamflow characteristics (calculated by using period-of-record data through water year 2005) for selected gaging stations 

used to develop regression equations.—Continued[The gaging stations presented in this table are stations that have 10 or more years of streamflow records and were used to develop regression equations that estimate monthly and annual streamflow characteristics for ungaged sites in or near Charles M. Russell National Wildlife Refuge. Streamflow values are in cubic feet per second. Abbreviations: Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow]

Indicated 

characteristic October November December January February March April May June July August September Annual

Site 45 (Burns Creek near Savage)

Long-term monthly and annual streamflow characteristics (water years 1958–67, 1975–84, 1986)

Years of record 21 21 21 20 20 20 20 20 20 20 20 20 20Q.90 .19 .53 .26 .06 .00 1.1 1.9 .82 1.7 .14 .00 .00 1.2Q.80 .22 .63 .45 .14 .24 1.7 2.3 1.1 2.0 .55 .01 .00 1.4Q.50 1.0 .91 .66 .40 .79 15 4.8 3.0 4.4 1.8 .25 .21 5.3Q.20 2.3 1.5 1.1 1.0 27 93 9.2 7.2 11 5.3 1.1 1.3 11QM 1.5 1.1 .81 .76 13 38 12 4.4 6.1 4.3 .56 1.1 7.0

Supplemental Data 45
Supplement 4. Selected basin and climatic characteristics for gaging stations used in various analyses to estimate streamflow characteristics.—Continued

[Elevation information is referenced to the North American Vertical Datum of 1988. Abbreviation: GIS, geographic information system. Symbol: --, no data]

Site

number

(fig. 1)

Station 

number Station name

Drainage area,

in square miles

Basinwide mean elevation,

in feet

Maximum elevation,

in feet

Manually 

determined1

GIS

determined2, 3

Manually 

determined1

GIS

determined2

Manually 

determined1

GIS

determined1

1 06114900 Taffy Creek tributary near Winifred 3.0 2.9 3,290 3,295 -- 3,4502 06115270 Armells Creek near Landusky -- 397 -- 3,339 -- 6,4273 06115300 Duval Creek near Landusky 3.3 3.9 3,110 3,101 -- 3,2644 06115350 Rock Creek near Landusky -- 75 -- 3,398 -- 5,5285 06127520 Home Creek near Sumatra 2.0 2.3 3,190 3,183 -- 3,3286 06127570 Butts Coulee near Melstone 6.7 6.8 3,000 3,008 -- 3,2227 06128900 Box Elder Creek tributary near Winnett 16 16 2,900 2,913 -- 3,1818 06129000 Box Elder Creek near Winnett 684 690 3,470 3,440 -- 6,3829 06129500 McDonald Creek at Winnett 421 428 4,140 4,003 -- 6,078

10 06129700 Gorman Coulee near Cat Creek 2.3 2.4 2,910 2,931 -- 3,00511 06130600 Cat Creek near Cat Creek 37 35 2,870 2,900 -- 3,17612 06130610 Bair Coulee near Mosby 1.8 1.8 3,130 3,152 -- 3,36113 06130620 Blood Creek tributary near Valentine 2.0 2.0 3,100 3,093 -- 3,29314 06130650 Hell Creek near Jordan 71 70 -- 2,779 -- 3,11515 06130700 Sand Creek near Jordan 317 315 3,050 3,036 -- 3,65016 06130850 Second Creek tributary No. 2 near Jordan 2.1 2.1 2,830 2,794 -- 2,92817 06130915 Russian Coulee near Jordan 3.5 3.4 2,660 2,658 -- 2,77718 06130940 Spring Creek tributary near Van Norman 1.4 1.3 2,570 2,596 -- 2,74819 06130950 Little Dry Creek near Van Norman 1,224 1,222 2,860 2,853 -- 3,62120 06131000 Big Dry Creek near Van Norman 2,554 2,551 2,870 2,874 -- 3,65021 06131200 Nelson Creek near Van Norman 100 110 2,620 2,593 -- 2,90422 06137400 Big Sandy Creek at reservation boundary, near Rocky Boy 25 25 4,860 4,776 -- 6,35923 06154400 Peoples Creek near Hays 220 226 3,570 3,588 -- 5,97824 06154410 Little Peoples Creek near Hays 13 13 4,640 4,547 -- 5,69225 06154550 Peoples Creek below Kuhr Coulee, near Dodson 675 697 3,500 3,218 -- 5,97826 06155100 Black Coulee near Malta 6.6 12 2,550 2,564 -- 2,67927 06155200 Alkali Creek near Malta 162 184 2,470 2,508 -- 2,80928 06155300 Disjardin Coulee near Malta 4.8 3.9 2,470 2,521 -- 2,664

46 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 4. Selected basin and climatic characteristics for gaging stations used in various analyses to estimate streamflow characteristics.—Continued

[Elevation information is referenced to the North American Vertical Datum of 1988. Abbreviation: GIS, geographic information system. Symbol: --, no data]

Site

number

(fig. 1)

Station 

number Station name

Drainage area,

in square miles

Basinwide mean elevation,

in feet

Maximum elevation,

in feet

Manually 

determined1

GIS

determined2, 3

Manually 

determined1

GIS

determined2

Manually 

determined1

GIS

determined1

29 06164600 Beaver Creek tributary near Zortman 3.9 3.8 3,260 3,255 -- 3,73430 06164800 Beaver Creek above Dix Creek, near Malta 929 920 2,730 2,710 -- 5,60731 06173300 Willow Creek tributary near Fort Peck 0.9 0.9 2,360 2,357 -- 2,45832 06175540 Prairie Elk Creek near Oswego 352 340 2,460 2,398 -- 2,84833 06175550 East Fork Sand Creek near Vida 8.5 8.7 2,440 2,432 -- 2,66634 06177050 East Fork Duck Creek near Brockway 12 15 2,910 2,932 -- 3,38735 06177100 Duck Creek near Brockway 54 55 2,910 2,951 -- 3,59936 06177150 Redwater River at Brockway 216 217 2,810 2,844 -- 3,61037 06177200 Tusler Creek near Brockway 90 89 2,980 2,953 -- 3,52638 06177500 Redwater River at Circle 547 550 2,810 2,813 -- 3,61039 06177700 Cow Creek tributary near Vida 1.7 1.9 2,490 2,494 -- 2,61540 06181000 Poplar River near Poplar 3,174 -- 2,730 2,625 -- 3,30641 06183450 Big Muddy Creek near Antelope 967 -- 2,380 2,384 -- 2,84242 06294900 Middle Fork Froze to Death Creek tributary near Ingomar 1.4 1.4 3,220 3,201 -- 3,42843 06309020 Rock Springs Creek tributary at Rock Springs 1.0 1.1 3,000 3,011 -- 3,07844 06309040 Dry House Creek near Angela 39 37 2,940 2,932 -- 3,12845 06329200 Burns Creek near Savage 233 234 2,600 2,586 -- 3,098

1Basin or climatic characteristic not used in final regression models for any annual streamflow or peak-flow characteristics; provided for informational purposes only.2Basin characteristic used in final regression models for estimating peak-flow characteristics.3Basin characteristic used in final regression models for estimating annual streamflow characteristics.

Supplemental Data 47
Supplement 5. Selected peak-flow characteristics (calculated by using period-of-record data through water year 2005) for selected 

gaging stations used to develop regression equations.

[The gaging stations presented in this table are stations that have 10 or more years of annual peak-flow records and were used to develop regression equations 

that estimate peak-flow characteristics for ungaged sites. Streamflow values are in cubic feet per second. Abbreviations: PK1.5, 1.5-year recurrence interval 

peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year recurrence interval peak flow]

Site 

number 

(fig. 1)

Station 

number Station name

Years of 

annual peak 

records

PK1.5 PK2 PK2.33

1 06114900 Taffy Creek tributary near Winifred 29 29 48 58

3 06115300 Duval Creek near Landusky 43 31 62 82

5 06127520 Home Creek near Sumatra 33 13 26 34

6 06127570 Butts Coulee near Melstone 43 54 84 100

7 06128900 Box Elder Creek tributary near Winnett 19 81 124 147

8 06129000 Box Elder Creek near Winnett 20 867 1,270 1,490

9 06129500 McDonald Creek at Winnett 36 223 338 401

10 06129700 Gorman Coulee near Cat Creek 33 32 71 98

11 06130600 Cat Creek near Cat Creek 18 60 93 111

12 06130610 Bair Coulee near Mosby 32 7.4 16 22

13 06130620 Blood Creek tributary near Valentine 32 4.1 8.2 11

15 06130700 Sand Creek near Jordan 11 414 647 780

16 06130850 Second Creek tributary No. 2 near Jordan 33 12 24 31

17 06130915 Russian Coulee near Jordan 32 21 36 46

18 06130940 Spring Creek tributary near Van Norman 32 22 39 49

19 06130950 Little Dry Creek near Van Norman 20 1,510 2,130 2,450

20 06131000 Big Dry Creek near Van Norman 66 1,180 2,240 2,900

21 06131200 Nelson Creek near Van Norman 17 259 432 529

23 06154400 Peoples Creek near Hays 39 72 148 199

24 06154410 Little Peoples Creek near Hays 33 25 42 53

25 06154550 Peoples Creek below Kuhr Coulee, near Dodson 45 320 558 700

26 06155100 Black Coulee near Malta 13 49 73 88

27 06155200 Alkali Creek near Malta 18 66 149 209

28 06155300 Disjardin Coulee near Malta 47 17 27 33

29 06164600 Beaver Creek tributary near Zortman 32 31 55 70

30 06164800 Beaver Creek above Dix Creek, near Malta 12 355 831 1,170

31 06173300 Willow Creek tributary near Fort Peck 19 24 47 62

32 06175540 Prairie Elk Creek near Oswego 10 690 1,050 1,250

33 06175550 East Fork Sand Creek near Vida 15 112 178 216

34 06177050 East Fork Duck Creek near Brockway 48 44 75 94

35 06177100 Duck Creek near Brockway 17 77 164 222

36 06177150 Redwater River at Brockway 18 315 558 701

37 06177200 Tusler Creek near Brockway 16 82 140 173

38 06177500 Redwater River at Circle 73 304 628 842

39 06177700 Cow Creek tributary near Vida 43 32 65 87

42 06294900 Middle Fork Froze to Death Creek tributary near Ingomar 15 50 69 79

43 06309020 Rock Springs Creek tributary at Rock Springs 17 6.1 10 12

44 06309040 Dry House Creek near Angela 16 73 144 190

45 06329200 Burns Creek near Savage 21 158 311 409

48 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 6. Selected basin and climatic characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife Refuge.—Continued

[All basin and climatic characteristics determined by using geographic information system (GIS). Elevation information is referenced to the North American Vertical Datum of 1988. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir]

Stream name

Site 

map 

number

Location on stream

Drainage 

area, 

in square 

miles1, 2

Mean 

elevation, 

in feet1

Maximum 

elevation, 

in feet3

Minimum 

elevation, 

in feet4

Relief, 

in feet2

Basinwide 

mean slope, 

in feet per mile4

Mean annual 

precipitation, 

in inches4

Two Calf Creek T1 at CMR boundary 93 3,003 3,556 2,350 1,206 11.2 14.3

T2 at confluence with FPR 122 2,973 3,556 2,253 1,302 11.8 14.3

Armells Creek T3 at CMR boundary 335 3,430 6,427 2,436 3,991 10.1 15.2

T4 at confluence with FPR 399 3,336 6,427 2,244 4,183 10.8 15.1

Siparyann Creek T5 at CMR boundary 41 3,256 5,164 2,641 2,523 8.4 13.9

T6 at confluence with FPR 58 3,086 5,164 2,268 2,896 11.1 13.8

Rock Creek T7 at CMR boundary 75 3,398 5,528 2,670 2,858 10.8 14.6

T8 at confluence with FPR 98 3,236 5,528 2,249 3,279 12.0 14.3

C K Creek T9 at CMR boundary 82 3,398 5,725 2,656 3,070 9.4 15.0

T10 at confluence with FPR 122 3,180 5,725 2,250 3,475 10.2 14.4

Beauchamp Creek T11 at CMR boundary 141 2,865 4,044 2,381 1,662 6.7 13.2

T12 at confluence with FPR 162 2,829 4,044 2,252 1,792 7.6 13.2

Sacajawea River T13 at CMR boundary 372 2,866 3,505 2,281 1,223 6.6 13.7

T14 at confluence with FPR 387 2,855 3,505 2,263 1,241 6.9 13.6

Squaw Creek T15 at CMR boundary 191 2,851 3,397 2,283 1,114 12.1 13.1

T16 at confluence with FPR 194 2,845 3,397 2,260 1,137 12.2 13.1

Fourchette Creek T17 at CMR boundary 69 2,636 2,845 2,342 503 3.9 12.6

T18 at confluence with FPR 350 2,583 3,232 2,252 980 4.4 12.7

Supplemental Data 49
Supplement 6. Selected basin and climatic characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife Refuge.—Continued

[All basin and climatic characteristics determined by using geographic information system (GIS). Elevation information is referenced to the North American Vertical Datum of 1988. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir]

Stream name

Site 

map 

number

Location on stream

Drainage 

area, 

in square 

miles1, 2

Mean 

elevation, 

in feet1

Maximum 

elevation, 

in feet3

Minimum 

elevation, 

in feet4

Relief, 

in feet2

Basinwide 

mean slope, 

in feet per mile4

Mean annual 

precipitation, 

in inches4

Telegraph Creek T19 at CMR boundary 169 2,631 3,232 2,282 950 4.7 12.8

T20 at confluence with 

Fourchette Creek

207 2,611 3,232 2,261 971 4.6 12.8

Seven Blackfoot Creek T21 at CMR boundary 86 3,066 3,406 2,298 1,108 14.5 13.3

T22 at confluence with FPR 90 3,048 3,406 2,253 1,153 15.0 13.3

Timber Creek (north of 

the Missouri River)

T23 at CMR boundary 147 2,714 3,346 2,264 1,082 10.4 12.9T24 at confluence with FPR 147 2,713 3,346 2,264 1,082 10.4 12.9

Hell Creek T25 at CMR boundary 64 2,799 3,115 2,325 791 9.0 13.1

T26 at confluence with FPR 73 2,771 3,115 2,242 873 10.0 13.1

Big Dry Creek T27 at CMR boundary 2,761 2,852 3,650 997 2,653 5.5 12.8

T28 at confluence with FPR 2,830 2,843 3,650 997 2,653 5.5 12.8

Timber Creek (south of 

the Missouri River)

T29 at CMR boundary 329 2,663 3,406 2,276 1,131 5.3 12.5T30 at confluence with FPR 331 2,661 3,406 2,257 1,149 5.4 12.5

Nelson Creek T31 at CMR boundary 118 2,584 2,904 2,285 619 7.5 12.6

T32 at confluence with FPR 122 2,578 2,904 2,247 656 7.6 12.6

1Basin characteristic used in final regression models for estimating peak-flow characteristics.2Basin characteristic used in final regression models for estimating annual streamflow characteristics.3Basin characteristic not used in final regression models for any annual streamflow or peak-flow characteristic; however, basin characteristic was used to determine applicable estimation coefficients for 

monthly streamflow characteristics.

4Basin or climatic characteristic not used in final regression models for any annual streamflow or peak-flow characteristic; provided for informational purposes only.

50 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Two Calf 

Creek

T1 at CMR 

boundary

Q.90 0.03 0.06 0.02 <0.01 0.01 0.55 0.43 0.2 0.34 0.1 0.01 <0.01 0.77

Q.80 .04 .09 .05 .02 .06 1.1 .63 .36 .47 .22 .03 .01 1.1Q.50 .20 .18 .14 .08 .48 7.8 1.6 1.2 1.8 .96 .24 .10 3.2Q.20 .54 .39 .27 .40 10 47 6.2 3.9 7.7 6.6 1.8 .48 8.6

QM .51 .30 .27 .51 7.9 31 9.4 3.2 6.7 5.4 1.7 1.7 5.7

T2 at confluence 

with FPR

Q.90 .03 .07 .03 <.01 .02 .66 .51 .24 .41 .12 .02 <.01 0.92

Q.80 .05 .10 .06 .02 .07 1.3 .75 .43 .56 .26 .04 .01 1.3Q.50 .24 .21 .16 .09 .57 9.3 1.9 1.4 2.1 1.1 .29 .12 3.8Q.20 .64 .47 .33 .48 12 56 7.4 4.6 9.1 7.8 2.2 .57 10

QM .61 .35 .32 .61 9.4 37 11 3.8 8.0 6.4 2.0 2.0 6.8

Armells 

Creek

T3 at CMR 

boundary

Q.90 <.01 <.01 <.01 <.01 <.01 1.2 .12 .05 1.4 .02 <.01 <.01 4.4

Q.80 <.01 <.01 <.01 <.01 <.01 2.1 1.0 .63 2.3 .09 <.01 <.01 8.3Q.50 <.01 .04 .04 <.01 .20 25 5.5 12 20 2.2 .41 <.01 12Q.20 .03 .18 .22 .28 19 129 12 111 115 22 6.2 .25 39

QM .34 .12 .20 .28 24 60 12 57 86 15 2.9 .10 22

T4 at confluence 

with FPR

Q.90 <.01 <.01 <.01 <.01 <.01 1.3 .14 .06 1.6 .02 <.01 <.01 5.0

Q.80 <.01 <.01 <.01 <.01 <.01 2.4 1.1 .70 2.6 .11 <.01 <.01 9.3Q.50 <.01 .04 .04 <.01 .22 28 6.2 13 22 2.4 .46 <.01 13Q.20 .04 .20 .24 .31 21 144 14 124 128 25 6.9 .28 44

QM .38 .13 .22 .31 27 67 14 64 97 17 3.3 .12 24

Supplemental Data 51
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Siparyann 

Creek

T51 at CMR 

boundary

Q.90 <0.01 <0.01 <0.01 0.02 0.10 1.2 0.67 0.39 0.31 <0.01 <0.01 <0.01 0.75

Q.80 <.01 .01 .02 .04 .15 2.2 1.1 1.2 .59 .28 <.01 <.01 1.3Q.50 .18 .35 .30 .22 1.2 8.4 4.8 4.0 4.1 1.2 .16 .04 3.2Q.20 2.1 2.5 2.0 1.7 6.8 27 14 12 13 7.9 1.0 .96 9.5

QM 1.6 1.4 1.2 1.4 5.5 20 11 13 9.4 4.4 .91 2.6 6.0

T61 at confluence 

with FPR

Q.90 <.01 <.01 .01 .02 .13 1.5 .87 .50 .40 <.01 <.01 <.01 .97

Q.80 <.01 .01 .02 .06 .20 2.8 1.4 1.5 .76 .36 <.01 <.01 1.7Q.50 .24 .46 .39 .28 1.5 11 6.2 5.1 5.2 1.6 .20 .05 4.1Q.20 2.7 3.2 2.5 2.2 8.8 35 18 15 17 10 1.4 1.2 13

QM 2.1 1.8 1.5 1.8 7.0 25 14 16 12 5.7 1.2 3.3 7.7

Rock Creek T7 at CMR 

boundary

Q.90 <.01 <.01 .01 .02 .15 1.7 .97 .56 .45 <.01 <.01 <.01 1.1

Q.80 <.01 .02 .02 .06 .22 3.2 1.6 1.6 .85 .40 <.01 <.01 1.9Q.50 .26 .51 .43 .31 1.7 12 6.9 5.7 5.8 1.8 .23 .05 4.6Q.20 3.0 3.6 2.8 2.5 9.8 39 20 17 19 11 1.5 1.4 14

QM 2.4 2.0 1.7 2.0 7.9 28 16 18 14 6.3 1.3 3.7 8.6

T8 at confluence 

with FPR

Q.90 <.01 <.01 .01 .03 .19 2.0 1.2 .69 .55 <.01 <.01 <.01 1.3

Q.80 <.01 .02 .03 .08 .27 3.9 1.9 2.0 1.0 .49 <.01 <.01 2.4Q.50 .33 .63 .53 .38 2.1 15 8.5 7.0 7.2 2.2 .28 .06 5.7Q.20 3.7 4.4 3.5 3.1 12 48 24 21 23 14 1.9 1.7 18

QM 2.9 2.5 2.0 2.5 9.7 35 19 23 17 7.8 1.6 4.6 11

52 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

C K Creek T9 at CMR 

boundary

Q.90 <0.01 <0.01 0.01 0.03 0.16 1.8 1.1 0.61 0.49 <0.01 <0.01 <0.01 1.2

Q.80 <.01 .02 .02 .07 .24 3.5 1.7 1.8 .92 .44 <.01 <.01 2.1Q.50 .29 .56 .47 .34 1.9 13 7.5 6.2 6.4 2.0 .25 .06 5.1Q.20 3.3 3.9 3.1 2.7 11 42 21 19 21 12 1.6 1.5 16

QM 2.6 2.2 1.8 2.2 8.6 31 17 20 15 6.9 1.4 4.0 9.4

T10 at confluence 

with FPR

Q.90 <.01 <.01 .02 .03 .21 2.4 1.4 .80 .64 <.01 <.01 <.01 1.6

Q.80 <.01 .02 .03 .09 .31 4.5 2.2 2.4 1.2 .57 <.01 <.01 2.7Q.50 .37 .73 .61 .44 2.4 17 9.8 8.1 8.3 2.6 .32 .07 6.6Q.20 4.3 5.0 4.0 3.6 14 55 28 24 27 16 2.2 2.0 21

QM 3.4 2.8 2.4 2.8 11 40 22 26 19 9.0 1.9 5.2 12

Beauchamp 

Creek

T11 at CMR 

boundary

Q.90 .04 .09 .04 <.01 .02 .82 .63 .29 .50 .15 .02 <.01 1.1

Q.80 .06 .13 .08 .02 .09 1.6 .93 .53 .70 .32 .04 .02 1.6Q.50 .29 .26 .20 .11 .70 12 2.4 1.8 2.6 1.4 .36 .14 4.7Q.20 .79 .58 .40 .59 15 69 9.1 5.7 11 9.7 2.7 .70 13

QM .75 .44 .40 .75 12 46 14 4.8 9.9 7.9 2.5 2.4 8.5

T12 at confluence 

with FPR

Q.90 .04 .10 .04 <.01 .02 .92 .70 .33 .56 .17 .02 <.01 1.3

Q.80 .07 .14 .09 .03 .10 1.8 1.0 .59 .78 .36 .05 .02 1.8Q.50 .33 .29 .22 .12 .79 13 2.6 2.0 2.9 1.6 .40 .16 5.3Q.20 .89 .64 .45 .66 17 78 10 6.4 13 11 3.0 .79 15

QM .84 .49 .45 .84 13 52 15 5.3 11 8.9 2.8 2.7 9.5

Supplemental Data 53
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Sacajawea 

River

T13 at CMR 

boundary

Q.90 0.05 0.12 0.05 0.01 0.02 1.1 0.84 0.39 0.67 0.20 0.03 <0.01 1.5

Q.80 .09 .17 .10 .03 .11 2.1 1.2 .70 .93 .43 .06 .02 2.2Q.50 .39 .35 .27 .15 .94 15 3.1 2.4 3.5 1.9 .48 .19 6.4Q.20 1.1 .77 .54 .79 20 93 12 7.6 15 13 3.6 .94 18

QM 1.0 .58 .53 1.0 16 62 18 6.3 13 11 3.3 3.3 11

T14 at confluence 

with FPR

Q.90 .05 .12 .05 .01 .03 1.1 .86 .40 .69 .20 .03 <.01 1.6

Q.80 .09 .18 .10 .03 .12 2.2 1.3 .72 .95 .44 .06 .02 2.2Q.50 .40 .36 .27 .15 .96 16 3.2 2.4 3.6 1.9 .49 .19 6.6Q.20 1.1 .79 .55 .81 21 95 12 7.8 15 13 3.7 .96 18

QM 1.0 .60 .55 1.0 16 63 19 6.5 14 11 3.4 3.4 12

Squaw 

Creek

T15 at CMR 

boundary

Q.90 .03 .08 .03 <.01 .02 .75 .58 .27 .46 .14 .02 <.01 1.0

Q.80 .06 .12 .07 .02 .08 1.4 .85 .48 .64 .3 .04 .01 1.5Q.50 .27 .24 .18 .10 .64 11 2.2 1.6 2.4 1.3 .33 .13 4.4Q.20 .72 .53 .37 .54 14 64 8.3 5.2 10 8.9 2.5 .64 12

QM .69 .40 .36 .68 11 42 13 4.4 9.0 7.2 2.3 2.2 7.7

T16 at confluence 

with FPR

Q.90 .03 .08 .03 <.01 .02 .76 .59 .27 .47 .14 .02 <.01 1.1

Q.80 .06 .12 .07 .02 .08 1.5 .87 .49 .65 .30 .04 .02 1.5Q.50 .27 .25 .19 .10 .65 11 2.2 1.7 2.4 1.3 .34 .13 4.5Q.20 .74 .54 .37 .55 14 65 8.5 5.3 11 9.0 2.5 .66 12

QM .70 .41 .37 .70 11 43 13 4.4 9.2 7.4 2.3 2.3 7.9

54 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Fourchette 

Creek

T171 at CMR 

boundary

Q.90 0.01 0.03 0.01 <0.01 <0.01 0.29 0.22 0.10 0.18 0.05 <0.01 <0.01 0.40Q.80 .02 .05 .03 <.01 .03 .55 .33 .19 .24 .11 .02 <.01 .57Q.50 .10 .09 .07 .04 .25 4.0 .82 .62 .91 .49 .13 .05 1.7Q.20 .28 .20 .14 .21 5.3 24 3.2 2.0 4.0 3.4 .95 .25 4.0

QM .26 .15 .14 .26 4.1 16 4.8 1.7 3.5 2.8 .87 .86 3.0

T18 at confluence 

with FPR

Q.90 .04 .10 .04 <.01 .02 .93 .71 .33 .57 .17 .03 <.01 1.3

Q.80 .07 .15 .09 .03 .10 1.8 1.1 .60 .79 .37 .05 .02 1.8Q.50 .33 .30 .23 .13 .80 13 2.7 2.0 3.0 1.6 .41 .16 5.5Q.20 .90 .65 .46 .67 17 79 10 6.5 13 11 3.1 .80 15

QM .85 .49 .45 .85 13 52 16 5.4 11 9.0 2.8 2.8 9.6

Telegraph 

Creek

T19 at CMR 

boundary

Q.90 .03 .07 .03 <.01 .01 .64 .49 .23 .40 .12 .02 <.01 .90

Q.80 .05 .10 .06 .02 .07 1.2 .73 .42 .55 .26 .04 .01 1.3Q.50 .23 .21 .16 .09 .55 9.0 1.8 1.4 2.1 1.1 .28 .11 3.8Q.20 .62 .45 .32 .47 12 55 7.2 4.5 8.9 7.6 2.1 .55 10

QM .59 .34 .31 .59 9.2 36 11 3.7 7.8 6.2 2.0 1.9 6.6

T20 at confluence 

with Fourchette Creek

Q.90 .03 .08 .03 <.01 .02 .72 .55 .26 .44 .13 .02 <.01 1.0

Q.80 .06 .11 .07 .02 .08 1.4 .82 .46 .61 .28 .04 .01 1.4Q.50 .26 .23 .18 .10 .62 10 2.1 1.6 2.3 1.2 .32 .12 4.2Q.20 .70 .51 .35 .52 13 61 8.0 5.0 9.9 8.5 2.4 .62 11

QM .66 .38 .35 .66 10 41 12 4.2 8.7 7.0 2.2 2.2 7.4

Supplemental Data 55
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Seven 

Blackfoot Creek

T21 at CMR 

boundary

Q.90 0.02 0.05 0.02 <0.01 0.01 0.51 0.39 0.18 0.31 0.09 0.01 <0.01 0.71

Q.80 .04 .08 .05 .01 .05 .98 .58 .33 .43 .20 .03 .01 1.0Q.50 .18 .16 .12 .07 .44 7.2 1.5 1.1 1.6 .88 .22 .09 3.0Q.20 .49 .36 .25 .37 9.5 43 5.7 3.6 7.0 6.0 1.7 .44 7.8

QM .47 .27 .25 .47 7.2 29 8.6 3.0 6.2 4.9 1.6 1.5 5.3

T22 at confluence 

with FPR

Q.90 .02 .06 .02 <.01 .01 .53 .41 .19 .33 .10 .01 <.01 .74

Q.80 .04 .08 .05 .02 .06 1.0 .61 .34 .45 .21 .03 .01 1.0Q.50 .19 .17 .13 .07 .46 7.5 1.5 1.2 1.7 .92 .24 .09 3.1Q.20 .52 .38 .26 .39 9.9 45 5.9 3.7 7.4 6.3 1.8 .46 8.2

QM .49 .28 .26 .49 7.6 30 9.0 3.1 6.4 5.2 1.6 1.6 5.5

Timber 

Creek (north of the Missouri River)

T23 at CMR 

boundary

Q.90 .03 .07 .03 <.01 .01 .65 .50 .23 .40 .12 .02 <.01 .90

Q.80 .05 .10 .06 .02 .07 1.2 .74 .42 .55 .26 .04 .01 1.3Q.50 .23 .21 .16 .09 .56 9.1 1.9 1.4 2.1 1.1 .29 .11 3.8Q.20 .63 .46 .32 .47 12 55 7.2 4.5 9.0 7.7 2.1 .56 10

QM .59 .35 .32 .59 9.2 37 11 3.8 7.8 6.3 2.0 1.9 6.7

T24 at confluence 

with FPR

Q.90 .03 .07 .03 <.01 .01 .65 .50 .23 .40 .12 .02 <.01 .90

Q.80 .05 .10 .06 .02 .07 1.2 .74 .42 .55 .26 .04 .01 1.3Q.50 .23 .21 .16 .09 .56 9.1 1.9 1.4 2.1 1.1 .29 .11 3.8Q.20 .63 .46 .32 .47 12 55 7.2 4.5 9.0 7.7 2.2 .56 10

QM .60 .35 .32 .59 9.2 37 11 3.8 7.9 6.3 2.0 1.9 6.7

56 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Hell Creek T251 at CMR 

boundary

Q.90 0.02 0.04 0.02 <0.01 <0.01 0.36 0.28 0.13 0.22 0.07 <0.01 <0.01 0.50

Q.80 .03 .06 .03 .01 .04 .70 .41 .23 .31 .14 .02 <.01 .71Q.50 .13 .12 .09 .05 .31 5.1 1.0 .79 1.2 .62 .16 .06 2.1Q.20 .35 .25 .18 .26 6.7 31 4.0 2.5 5.0 4.3 1.2 .31 5.3

QM .33 .19 .18 .33 5.2 20 6.1 2.1 4.4 3.5 1.1 1.1 3.7

T26 at confluence 

with FPR

Q.90 .02 .04 .02 <.01 <.01 .41 .31 .15 .25 .07 .01 <.01 .57

Q.80 .03 .06 .04 .01 .04 .79 .46 .26 .35 .16 .02 <.01 .81Q.50 .15 .13 .10 .06 .35 5.7 1.2 .89 1.3 .70 .18 .07 2.4Q.20 .40 .29 .20 .30 7.6 35 4.6 2.9 5.6 4.8 1.4 .35 6.0

QM .37 .22 .20 .37 5.8 23 6.9 2.4 4.9 4.0 1.2 1.2 4.2

Big Dry 

Creek

T271 at CMR 

boundary

Q.90 .20 .48 .20 .05 .10 4.5 3.5 1.6 2.8 .82 .12 .02 6.3

Q.80 .36 .71 .42 .13 .47 8.7 5.1 2.9 3.8 1.8 .25 .09 8.9Q.50 1.6 1.4 1.1 .61 3.9 63 13 9.8 14 7.8 2.0 .78 26Q.20 4.4 3.2 2.2 3.3 84 382 50 32 62 53 15 3.9 88

QM 4.1 2.4 2.2 4.1 64 255 76 26 54 44 14 13 47

T281 at confluence 

with FPR

Q.90 .21 .49 .20 .05 .10 4.6 3.5 1.6 2.8 .83 .12 .02 6.4

Q.80 .36 .72 .43 .13 .48 8.8 5.2 3.0 3.9 1.8 .25 .09 9.0Q.50 1.6 1.5 1.1 .62 3.9 64 13 9.9 15 7.9 2.0 .79 27Q.20 4.4 3.2 2.2 3.3 85 387 51 32 63 54 15 3.9 89

QM 4.2 2.4 2.2 4.2 65 258 77 26 55 44 14 14 47

Supplemental Data 57
Supplement 7. Estimates of long-term monthly and annual streamflow characteristics for selected ungaged sites on tributaries that cross Charles M. Russell National Wildlife 

Refuge.—Continued[Estimates determined by using regression equations (table 8, shaded values) and estimation coefficients (table 3, unshaded values). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; Q.90, 90-percent exceedance streamflow; Q.80, 80-percent exceedance streamflow; Q.50, 50-percent exceedance streamflow; Q.20, 20-percent exceedance streamflow; QM, mean streamflow. Symbol: <, less than]

Stream 

name

Site 

number

Location on 

stream

Streamflow 

characteristic

October

November

December

January

February

March

April

May

June

July

August

September

Annual

Timber 

Creek (south of the Missouri River)

T29 at CMR 

boundary

Q.90 0.04 0.11 0.04 <0.01 0.02 0.98 0.75 0.35 0.6 0.18 0.03 <0.01 1.4

Q.80 .08 .16 .09 .03 .10 1.9 1.1 .63 .83 .39 .05 .02 1.9Q.50 .35 .32 .24 .13 .84 14 2.8 2.1 3.1 1.7 .43 .17 5.8Q.20 .95 .69 .48 .71 18 83 11 6.9 14 12 3.2 .84 16

QM .90 .52 .48 .90 14 55 17 5.7 12 9.5 3.0 2.9 10

T30 at confluence 

with FPR

Q.90 .05 .11 .04 .01 .02 .99 .76 .36 .61 .18 .03 <.01 1.4

Q.80 .08 .16 .09 .03 .10 1.9 1.1 .64 .84 .39 .05 .02 2.0Q.50 .36 .32 .24 .13 .85 14 2.8 2.2 3.2 1.7 .44 .17 5.8Q.20 .96 .70 .49 .72 18 84 11 7.0 14 12 3.3 .85 16

QM .91 .53 .48 .91 14 56 17 5.8 12 9.6 3.0 3.0 10

Nelson 

Creek

T31 at CMR 

boundary

Q.90 .02 .04 .02 <.01 <.01 .42 .32 .15 .26 .08 .01 <.01 .58

Q.80 .03 .07 .04 .01 .04 .81 .48 .27 .36 .17 .02 <.01 .83Q.50 .15 .14 .10 .06 .36 5.9 1.2 .91 1.3 .72 .19 .07 2.5Q.20 .41 .30 .21 .30 7.8 36 4.7 2.9 5.8 5.0 1.4 .36 6.1

QM .38 .22 .20 .38 6.0 24 7.1 2.4 5.1 4.1 1.3 1.2 4.3

T32 at confluence 

with FPR

Q.90 .02 .05 .02 <.01 .01 .44 .34 .16 .27 .08 .01 <.01 .61

Q.80 .03 .07 .04 .01 .05 .85 .50 .29 .38 .18 .02 <.01 .87Q.50 .16 .14 .11 .06 .38 6.2 1.3 .96 1.4 .76 .19 .08 2.6Q.20 .43 .31 .22 .32 8.2 37 4.9 3.1 6.1 5.2 1.5 .38 6.4

QM .40 .24 .21 .40 6.3 25 7.4 2.6 5.3 4.3 1.3 1.3 4.6

1This site has values of one or more basin characteristics that are outside the range of values used in developing regression equations. Estimates of streamflow characteristics for this site should be used with 

caution.

58 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana
Supplement 8. Estimates of selected peak-flow characteristics for selected ungaged sites on tributaries 

that cross Charles M. Russell National Wildlife Refuge.—Continued

[Estimates determined by using regression equations (table 9). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; PK1.5, 1.5-year recurrence interval 

peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year recurrence interval peak flow. Streamflow values 

are in cubic feet per second]

Stream name Site 

number Region Location on stream PK1.5 PK2 PK2.33

Two Calf Creek T1 South at CMR boundary 173 297 369

T2 at confluence with FPR 208 357 443

Armells Creek T3 South at CMR boundary 301 497 606

T4 at confluence with FPR 353 582 709

Siparyann Creek T5 North at CMR boundary 72 138 183

T6 at confluence with FPR 83 160 214

Rock Creek T7 North at CMR boundary 92 178 238

T8 at confluence with FPR 102 200 267

C K Creek T9 North at CMR boundary 95 186 248

T10 at confluence with FPR 111 219 294

Beauchamp Creek T11 North at CMR boundary 118 233 312

T12 at confluence with FPR 124 247 332

Sacajawea River T13 South at CMR boundary 445 748 919

T14 at confluence with FPR 459 772 947

Squaw Creek T15 South at CMR boundary 296 506 626

T16 at confluence with FPR 301 513 635

Fourchette Creek T17 North at CMR boundary 89 172 229

T18 at confluence with FPR 168 341 462

Telegraph Creek T19 North at CMR boundary 126 252 339

T20 at confluence with 

Fourchette Creek

137 274 369

Seven Blackfoot Creek T21 South at CMR boundary 159 273 339

T22 at confluence with FPR 165 284 352

Timber Creek (north of 

the Missouri River)

T23 North at CMR boundary 120 237 319

T24 at confluence with FPR 120 237 319

Supplemental Data 59
Supplement 8. Estimates of selected peak-flow characteristics for selected ungaged sites on tributaries 

that cross Charles M. Russell National Wildlife Refuge.—Continued

[Estimates determined by using regression equations (table 9). Streamflow values are in cubic feet per second. Abbreviations: CMR, Charles M. Russell National Wildlife Refuge; FPR, Fort Peck Reservoir; PK1.5, 1.5-year recurrence interval 

peak flow; PK2, 2-year recurrence interval peak flow; PK2.33, 2.33-year recurrence interval peak flow. Streamflow values 

are in cubic feet per second]

Stream name Site 

number Region Location on stream PK1.5 PK2 PK2.33

Hell Creek T25 South at CMR boundary 156 272 340

T26 at confluence with FPR 172 300 375

Big Dry Creek T27 South at CMR boundary 1,550 2,510 3,020

T28 at confluence with FPR 1,590 2,560 3,090

Timber Creek (south of 

the Missouri River)

T29 South at CMR boundary 470 800 987

T30 at confluence with FPR 472 804 992

Nelson Creek T31 South at CMR boundary 262 457 571

T32 at confluence with FPR 269 468 585

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Helena Publishing Service Center

For more information concerning this publication, contact:

Director, USGS Montana Water Science Center

3162 Bozeman Ave.

Helena, MT 59601

(406) 457–5900

Or visit the Montana Water Science Center Web site at:

http://mt.water.usgs.gov

60 Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana

Sando and others—Estimation of Streamflow Characteristics for Charles M. Russell National Wildlife Refuge, Northeastern Montana—SIR 2008–5009

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