Determination of Channel-Morphology Characteristics,

Bankfull Discharge, and Various Design-Peak Discharges 

in Western Montana

In cooperation with the Montana Department of Transportation and the

U.S. Department of Agriculture-Forest Service

 Lolo National Forest

Scientific Investigations Report 2004-5263

U.S. Department of the Interior

U.S. Geological Survey
COVER PHOTOGRAPH: Flower Creek near Libby, Montana (station 12303100). Photograph by Sean M. Lawlor, 

U.S. Geological Survey, taken in 2002.
Determination of Channel-Morphology 

Characteristics, Bankfull Discharge, and 

Various Design-Peak Discharges in 

Western Montana

By Sean M. Lawlor

U.S. Department of the Interior

U.S. Geological Survey

In cooperation with the 

Montana Department of Transportation and the 

U.S. Department of Agriculture-Forest Service

 Lolo National Forest

Scientific Investigations Report 2004-5263
U.S. Department of the Interior

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Reston, Virginia: 2004

For sale by U.S. Geological Survey, Information Services

Box 25286, Denver Federal Center

Denver, CO 80225

For more information about the USGS and its products:

Telephone: 1-888-ASK-USGS

World Wide Web: http://www.usgs.gov/

For additional information write to:

District Chief

U.S. Geological Survey

3162 Bozeman Avenue

Helena, Montana 59601

Any use of trade, product, or firm names in this publication is for descriptive purposes only and does not imply 

endorsement by the U.S. Government.

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

reproduce any copyrighted materials contained within this report.
 iii

Contents

Glossary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .iv

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

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

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

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

Determination of Channel-Morphology Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

Determination of Bankfull Discharge at Gaged Sites. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Determination of Various Design-Peak Discharges at Ungaged Sites . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

Regression Relations between Various Design-Peak Discharges and Channel Morphology . . . . . . . . . . . 8

Use of Existing Flood-Frequency Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

Regression Relations between Channel Morphology and Drainage Area and Bankfull Discharge

and Drainage Area . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

References Cited. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

Data. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

Figures

Figure 1. Map showing location of the study area, measurement sites, and two flood regions . . . . . . . . . . . 3

2. Schematic diagram showing typical channel reach and cross section for measurement

of channel features. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3. Photographs showing site and cross-section locations on South Crow Creek

and Mill Creek, western Montana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4. Graph showing longitudinal profiles for Boulder Creek at Maxville and Eightmile Creek near 

Florence, Montana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7

5. Boxplot showing variation in recurrence interval of bankfull discharge at 41 selected sites,

western Montana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

6. Boxplot showing variation of ratio of bankfull discharge to the 2-year design-peak discharge

at 41 selected sites, western Montana. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

7. Graphs showing regional relations of bankfull-channel dimensions and bankfull 

discharge to drainage area for different ranges of mean annual precipitation . . . . . . . . . . . . . . . . . . . . . 11

Tables

Table 1. Channel-morphology characteristics and design-peak-discharge data for selected

streamflow-gaging stations, western Montana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

2. Basin and climatic characteristics for selected streamflow-gaging stations, western

Montana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3. Three sets of regression equations for estimation of design-peak discharge in western

Montana . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
iv 

Conversion Factors, Datum, and Acronyms

Vertical coordinate information is referenced to the National Geodetic Vertical Datum of 1929 

(NGVD 29). Horizontal coordinate information is referenced to the North American Datum of 1927 

(NAD 27).

Acronyms used in this report:

OLS Ordinary Least Squares

SEP Standard error of prediction

USGS U.S. Geological Survey

Glossary

active-channel width The width of the active channel measured perpendicular to streamflow. The active-channel, a 

short-term geomorphic feature formed by prevailing stream discharges, is narrower than the bankfull channel and is 

defined by a break in bank slope that also typically is the edge of permanent vegetation.

bankfull cross-sectional area The cross-sectional area of a stream channel at bankfull stage measured 

perpendicular to streamflow.

bankfull discharge The stream discharge generally considered to be the single discharge that is most effective for 

moving sediment, forming or removing bars, and forming or changing bends and meanders, all of which result in the 

average morphological characteristics of channels (Dunne and Leopold, 1978).

bankfull-recurrence interval The average interval, in years, between annual peak discharges that exceed bankfull 

discharge.

bankfull stage The elevation above gage datum of the water surface corresponding to bankfull discharge.

bankfull-wetted perimeter The length, in feet, of the contact between the stream of flowing water and its containing 

channel, measured at a section perpendicular to streamflow at bankfull discharge.

bankfull width The width of the bankfull channel measured at a section perpendicular to streamflow at bankfull 

discharge.

D50 The median size of streambed particles as determined by measuring the intermediate axis of numerous particles 

Multiply By To obtain

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

foot (ft) 0.3048 meter (m)

foot per foot (ft/ft) 1.0 meter per meter (m/m)

inch (in.) 25.4 millimeter (mm)

square foot (ft2) 0.09290 square meter (m2)

square mile (mi2) 2.590 square kilometer (km2)
 v

on the streambed surface selected at random.

drainage area The horizontal projection of the area upstream from a specific location that has a common outlet at the 

site for its surface runoff from precipitation that normally drains by gravity into a stream.

entrenchment ratio The vertical containment of the river described as the ratio of the flood-prone width to the bankfull 

width (Rosgen, 1996).

flood-prone width The width across the flood plain, measured at a section perpendicular to the streamflow, at a 

water-surface elevation corresponding to twice the maximum depth of the bankfull channel (Rosgen, 1996).

Manning’s roughness coefficient (n) A dimensionless measure of the frictional resistance to flow, or roughness, 

of a stream channel.

maximum bankfull depth The maximum depth of the bankfull channel measured at a section perpendicular to 

streamflow.

mean annual precipitation The basin average value for annual precipitation.

mean bankfull depth The mean depth of the bankfull channel measured at a section perpendicular to streamflow.

percent of basin covered by forest That portion of the drainage area of a stream shown in green on a 7.5-minute 

U.S. Geological Survey topographic map, divided by the total drainage area, and multiplied by 100.

recurrence interval The average interval, in years, between exceedances of a particular annual peak discharge.

Rosgen classification A system of describing river channels based on channel geometry, stream plan-view patterns, 

and streambed material (Rosgen, 1996).

sinuosity The ratio of the measured channel distance divided by the straight-line distance of the valley from the 

beginning of the channel reach to the end of the channel reach.

thalweg The lowest point in a stream channel.

width/depth ratio The ratio of bankfull width to mean bankfull depth measured at a section perpendicular to 

streamflow.
Determination of Channel-Morphology Characteristics, 

Bankfull Discharge, and Various Design-Peak Discharges 

in Western Montana

By Sean M. Lawlor

Abstract

Stream-restoration projects using natural stream designs 

typically are based on channel configurations that can accommodate a wide range of streamflow and sediment-transport conditions without excessive erosion or deposition. Bankfull discharge is an index of streamflow considered to be closely 

related to channel shape, size, and slope (channel morphology). 

Because of the need for more information about the relation 

between channel morphology and bankfull discharge, the U.S. 

Geological Survey (USGS), in cooperation with the Montana 

Department of Transportation and the U.S. Department of Agriculture-Lolo National Forest, conducted a study to collect channel-morphology and bankfull-discharge data at gaged sites and 

use these data to improve current (2004) methods of estimation 

of bankfull discharge and various design-peak discharges at 

ungaged sites. This report presents channel-morphology characteristics, bankfull discharge, and various design-peak discharges for 41 sites in western Montana.

Channel shape, size, and slope and bankfull discharge 

were determined at 41 active or discontinued USGS streamflow-gaging sites in western Montana. The recurrence interval 

for the bankfull discharge for this study ranged from 1.0 to 4.4 

years with a median value of 1.5 years.

The relations between channel-morphology characteristics 

and various design-peak discharges were examined using 

regression analysis. The analyses showed that the only characteristics that were significant for all peak discharges were either 

bankfull width or bankfull cross-sectional area.

Bankfull discharge at ungaged sites in most of the study 

area can be estimated by application of a multiplier after determining the 2-year peak discharge at the ungaged site. The multiplier, which is the ratio of bankfull discharge to the 2-year 

peak discharge determined at the 41 sites, ranged from 0.21 to 

3.7 with a median value of 0.84. 

Regression relations between bankfull discharge and 

drainage area and between bankfull width and drainage area 

were examined for three ranges of mean annual precipitation. 

The results of the regression analyses indicated that both drainage area and mean annual precipitation were significantly 

related (p values less than 0.05) to bankfull discharge.

Introduction

Stream alterations in western Montana have resulted in 

adverse habitat changes for many fish and wildlife species and 

have contributed to declines in native fish populations (Peters, 

1990). Projects to restore stream channels to their original and 

natural condition are increasingly being undertaken to reverse 

those declines. Successful restoration of altered stream channels to a more stable and natural condition requires information 

about the relation between channel morphology and streamflow 

under natural conditions.

Over the past 10 years, methods have been developed 

(Rosgen, 1996) that use channel morphology to assess relative 

stream stability and to design stable channel configurations. A 

key to proper use of these methods is the determination of bankfull discharge—an index of streamflow that is considered to be 

closely related to channel shape, size, and slope. Currently 

(2004), bankfull discharge at ungaged sites commonly is 

approximated using regression equations that relate peak discharge having a 2-year recurrence interval to various basin and 

climatic characteristics or using regression equations that relate 

a 2-year peak discharge to active-channel or bankfull width 

(Parrett and Johnson, 2004). Estimates from existing regression 

equations may have significant error, however, because the 

assumption that bankfull discharge is equal to peak discharge 

having a 2-year recurrence interval may not be valid for many 

sites. Previous studies have indicated that the recurrence interval for bankfull discharge at some sites is less than 2 years 

(Leopold and others, 1964; Rosgen, 1996; Moody and Odem, 

1999).

A recent study in southwestern Montana (Bass, 1999) indicated that regression equations for estimation of 2-year peak 

discharge based on channel width might be improved by the 

inclusion of bankfull depth, cross-sectional area, or other channel-morphology characteristics as additional explanatory variables. Because the 2-year peak discharge generally is highly 

correlated with other annual peak discharges (flood discharges), 

results presented by Bass (1999) suggest that inclusion of other 

channel-morphology characteristics in a regression analysis 

might result in improved estimates of other annual peak discharges ranging from the 2-year flood to the 500-year flood.

Studies by Dunne and Leopold (1978), White (2001), and 

Cinotto (2003) showed a strong relation between bankfull discharge and drainage area. This relation was used on a recon-
2 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

naissance level to infer some channel-morphology characteristics at sites not having onsite channel measurements within 

regions with similar runoff characteristics. Regional relations 

between other channel-morphology characteristics—such as 

bankfull width, mean bankfull depth, bankfull cross-sectional 

area—and drainage area also can be useful for reconnaissancelevel studies.

Because of the need for more information about the relation between channel morphology and stream discharge, the 

U.S. Geological Survey (USGS), in cooperation with the Montana Department of Transportation and the U.S. Department of 

Agriculture Forest Service-Lolo National Forest, conducted a 

study to collect channel-morphology and bankfull-discharge 

data at gaged sites. These data then were used to try to improve 

methods for estimation of bankfull discharge and other flood 

discharges—annual peak discharges having recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years (various designpeak discharges)—at ungaged sites and to develop relations 

between bankfull discharge and drainage area and channel-morphology characteristics and drainage area.

Purpose and Scope

This report presents channel-morphology characteristics, 

bankfull discharge, and various design-peak discharges for 41 

sites in western Montana. Specifically, the report describes: (1) 

determination of key channel-morphology characteristics at 

selected streamflow-gaging sites, (2) determination of bankfull 

discharge and its recurrence interval at each streamflow-gaging 

site, (3) development of a multiplier to apply to existing floodfrequency equations, (4) determination of the relation of various 

design-peak discharges for selected recurrence intervals to measured morphologic characteristics, and (5) analysis of regional 

relations between bankfull channel width, bankfull mean depth, 

bankfull cross-sectional area, and bankfull discharge to drainage area.

Channel-morphology data were collected at 41 sites in 

western Montana during 2001-03. At each site, a reach of 

stream was selected for detailed measurements of water-surface, streambed, and bankfull elevations. Within each reach, 

one to three cross sections were surveyed to estimate bankfull 

widths, mean bankfull depths, cross-sectional area, wetted 

perimeter, and flood-prone width. Stream discharge, particlesize distribution, and Manning’s roughness coefficients (n values) were determined at each site (Barnes, 1967). These measurements also were used to estimate a Rosgen Level II stream 

classification (Rosgen, 1996) for each site. In some instances, 

stream reaches did not readily fit all parameters of the Rosgen 

stream classification. Stream profiles were surveyed and calculations made to determine bankfull discharge and its recurrence 

interval for each site. Regression analysis was used to determine whether relations between various peak discharges (recurrence intervals ranging from 2 to 500 years) and bankfull width 

might be improved by inclusion of channel-morphology data. 

Bankfull width, bankfull depth, bankfull cross-sectional area, 

and bankfull discharge were related to drainage area using 

regression analysis. The relations were developed for three 

ranges of mean annual precipitation.

Description of the Study Area

The study area consists of about 25,140 mi2 in the Clark 

Fork and Kootenai River drainage basins in western Montana 

(fig. 1). In the northwestern part of the study area, mountain 

ranges typically are separated by narrow, steep-sided valleys 

that have little to no basin-fill deposits. These valleys primarily 

were the result of erosion by glaciers and streams. In contrast, 

much of the remainder of the study area consists of mountain 

ranges separated by larger valleys that are wide, deep, and can 

be filled with thousands of feet of basin-fill deposits (Kendy and 

Tresch, 1996).

Cold winters and mild summers characterize the climate of 

the study area. Winters are cold, and thick snow pack accumulates in the mountains. Summers generally are warm and dry in 

the valleys and cool in the surrounding mountains. The growing season typically extends from May to September or October, but in some basins is as short as July to August (National 

Oceanic and Atmospheric Administration, 1992). Following 

periods of extreme cold, mountainous areas commonly warm 

up more rapidly than valleys causing pronounced temperature 

inversions. The prevailing wind in most of the study area is 

from the west, and strong, gusty winds are common year round.

Precipitation in the study area primarily accompanies winter and spring frontal systems and summer convection storms. 

Annual precipitation can range from about 10 in. in the southwestern part of the study area to about 100 in. in the mountains 

of northwestern Montana (National Oceanic and Atmospheric 

Administration, 1992). Most of the valleys receive between 10 

and 30 in. of precipitation per year, with more than one-half 

falling in winter and spring. Large winter snowpacks in the 

mountains gradually release their water content as snowmelt 

that helps maintain streamflow well into summer.

Determination of Channel-Morphology 

Characteristics

Channel-morphology data were collected at 41 sites near 

active or discontinued streamflow-gaging stations during 2000-

03. All gaged sites in western Montana were initially considered for study. However, many sites were eliminated from further study because they were in urban areas or areas affected by 

dams, bridges, or other man-made structures; the annual peakdischarge record was less than 10 years; they were located in 

non-dynamic bedrock channels; or they were in areas with substantial recent land-use changes in the watershed. Other sites 

along large streams were eliminated from further study because 

their large widths and depths precluded efficient and economical data collection.
Determination of Channel-Morphology Characteristics 3

Figure 1. Location of the study area, measurement sites, and two flood regions (from Parrett and Johnson, 2004).

0 10 20 30 40 50 MILES

0 10 20 30 40 50 KILOMETERS

12304120

12301999

12391100

12339900

12387450

12342950

12375900

12346500

12302400

12301997

12388400

12324100

12369650

12335500

12338600

12377150

12374250

12332000

12340200

12352000

12350500

12352200

12303100

12329500

12351400

12331700

12353850

12353820 12339300

12300800

12339450

12324700

12300400

12344300

12330000

12304060

12383500

12355350

12304040

46O

12388400

M O N T A N A

EXPLANATION

U.S. GEOLOGICAL SURVEY 

STREAMFLOW-GAGING 

STATION AND NUMBER

Clark

Fork

Clark

Fork

Clark

Fork

Base modified from U.S. Geological Survey

digital data, 1:100,000, 1994. North American 

Datum of 1927 (NAD 27)

CONTINENTAL

DIVIDE

Flathead

 Lake

Study

 area

12302500

Missoula

Butte

Kalispell

Yaak

Fortine

Trego

Swan 

Lake

Columbia 

 Falls Libby

Trout 

Creek

Niarada

Ronan

St. 

Ignatius

Dixon

Haugan

Superior

Arlee Seely Lake

Ovando

Clearwater

Helmville

Drummond

Garrison

Maxville

Philipsburg

Anaconda

Hamilton

Darby

Conner

Stevensville

Florence

Lolo

Bonner

Blacktail Cr

Basin

Cr Zulu 

 Cr

Deep Cr

Cayuse

Cr Big

Richards

 Cr Flower Cr

Granite 

 Cr

Shaughnessy 

Cr

White

 Pine Cr

East Fork

 Timber Cr

North

 Fork

 Lost Cr

Mission 

Cr

Revais 

 Cr

Valley Cr

Big Knife Cr

Dry Cr

Deer 

Cr

West

 Twin

 Cr Marshall Cr

Eightmile Cr

Kootenai

 Cr

Monture 

Cr

Clearwater

Cr

Lolo

Blackfoot

Hayes Cr

Edwards 

 Gulch

Flint

Cr

Boulder 

 Cr

Cr Racetrack

Rock

Creek

M

Fork

Trapper

Cr

Burke

Cr

Cr

R

Little

Nevada

Wolf

Cr

Cr

Rock

Cr

R

Hungry

Reservoir

Horse

Lake

Koocanusa

Gulch

Skalkaho

CANADA

IDAHO

12324590

Mill Cr

S. Crow

Cr

Northern Rocky

Mtns

NORTHWEST

REGION

WEST

REGION

470

48O

49O 116O 115O

114O

113O

Kootenai

River

ACTIVE (2000-03)

DISCONTINUED 12353820
4 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

A suitable reach near the gaging station was identified at 

each site. In general, the selected reach was about 20 bankfullchannel widths in length and, whenever possible, the gaging 

station was located in the selected reach. Within the selected 

reach, water-surface, streambed (thalweg), and bankfull-channel elevations were measured at a minimum of seven locations 

along the channel using a survey level or an electronic-surveying instrument (total station). Reaches with flow obstructions 

such as bridge abutments, diversion structures, culverts, and 

bridges were avoided, if possible. Within each selected reach, 

one to three representative stream-channel (reference) cross 

sections were identified. Elevations and distances were

measured at each cross section using a survey level and a fiberglass tape or a total station. The reference cross sections generally were located in stable subreaches between channel bends 

(fig. 2) as described by Parrett and others (1987), Leopold 

(1994), and Rosgen (1996). If a reach had more than one reference cross section, data from the cross sections were averaged 

to provide reach-representative values of bankfull width, mean 

bankfull depth, bankfull cross-sectional area, bankfull-wetted 

perimeter, width/depth ratio, and entrenchment ratio. Site and 

cross-section locations on South Crow Creek and Mill Creek in 

western Montana are shown on figure 3. 

Figure 2. Typical channel reach and cross section for measurement of channel features.

Thalweg

Water surface

Bankfull stage

Bankfull width

Outer bend

(may be eroding)

Outer bend

(may be eroding)

Flow

 Point bar

 (sediment may

 be depositing) Riffle

Cross section

Cross section

Riffle

Cross section

Streamflow-gaging station

Outer bend

(may be eroding)

Riffle

Point bar

(sediment may

 be depositing)

Point bar

(sediment may

 be depositing)

TYPICAL CHANNEL REACH 

FOR MEASUREMENT OF CHANNEL-FEATURE

ELEVATIONS AND CROSS SECTIONS

TYPICAL STREAM CHANNEL CROSS SECTION

Vertical bank to

horizontal flood plain
Determination of Channel-Morphology Characteristics 5

Figure 3. Site and cross-section locations on South Crow Creek (top) and Mill Creek (bottom), western Montana.

12375900

Mill

Creek

Bassoo

Creek

Little Bitterroot

River

12374250

0 1 MILE

0 1 KILOMETER

Base modified from U.S. Geological Survey

Mill Pocket Creek quadrangle, 1:24,000, 1964

South

Crow

Creek

0

0

1 MILE

1 KILOMETER

Kicking

Horse

Reservoir

N

Base modified from U.S. Geological Survey

Ft. Connah quadrangle, 1:24,000, 1964

Crow Creek

Crow N.

Cr

SITE LOCATION MAP

SITE LOCATION MAP

N

A survey level and fiberglass tape or total station were 

used to survey channel distance and elevation. Channel distance and elevation were used to construct longitudinal profiles 

of the water-surface, thalweg, and bankfull elevations. The 

USGS gaging-station datum at each site, referenced to NGVD 

29, was used for vertical control during the surveys.

The bankfull stage was readily identified at most sites by 

topographic features (bankfull indicators), such as a change 

from a vertical bank to a horizontal flood plain (fig. 2). At many 

of the sites, bankfull stage also was marked by a change in the 

size distribution of materials along the bank. Occasionally, 

vegetation was used as an indicator; however, topographic features generally were more reliable indicators of bankfull stage.

Bankfull widths, bankfull depths, flood-prone widths,

streambed-material sizes, and channel roughness were determined at each site; bankfull cross-sectional area, bankfullwetted perimeters, entrenchment ratio, and sinuosity were then 

calculated. The flood-prone width was estimated by first determining the maximum depth of the bankfull channel at the cross 

section. Then a range-finder was set at the elevation corresponding to twice the maximum bankfull depth to measure the 

horizontal distance to the ground surface (perpendicular to the 

flow) on each side of the stream at that elevation, and the two 

distances were summed. The entrenchment ratio was calculated 

by dividing flood-prone width by bankfull width. In some 

instances, flood-prone width and sinuosity (needed to determine a Rosgen Level II stream classification; Rosgen, 1996) 

were difficult to measure because of thick vegetation on the 

flood plain. Aerial photographs and USGS 7.5-minute topographic maps were used in these instances to estimate floodprone width and sinuosity. In instances where sinuosity was 

determined from the ratios of channel length to valley length 

from aerial photographs and topographic maps, and from the 

ratios of valley slope to channel slope, the sinuosity values 

shown in table 1 (at back of report) may not be consistent with 

sinuosity values determined by any one method.
6 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

Streambed particle-size distribution was determined from 

a pebble count through the selected stream reach using methods 

described by Wolman (1954). The Manning roughness coefficient (n value) at each cross section was estimated by visual 

inspection and comparison with n values from photographs 

(Barnes, 1967). Channel-morphology data together with various design-peak discharge data (Parrett and Johnson, 2004) for 

each site are shown in table 1; selected basin and climatic variables for each site are shown in table 2 (at back of report). 

Additional data were collected during the site visit. Discharge was either determined from the most recent stage-discharge relation or measured with a current meter. Currentmeter measurements were made in accordance with methods 

described by Rantz and others (1982). 

Determination of Bankfull Discharge at 

Gaged Sites

Bankfull discharge and its associated recurrence interval 

were determined at each of the 41 gaged sites. For each study 

reach, the bankfull-stage, water-surface, and thalweg elevations, along with associated channel-distance data, were used to 

construct longitudinal profiles. Under the hydraulic condition 

of gradually varied flow, which is the most common hydraulic 

condition in natural streams (Jobson and Froehlich, 1988), 

bankfull-stage, water-surface, and thalweg profiles tend to be 

parallel. For example, figure 4 shows the longitudinal profiles 

and a best-fit line through the bankfull-stage data for two typical 

study reaches (Boulder Creek at Maxville and Eightmile Creek 

near Florence). In both examples, the left and right bankfullstage profiles closely parallel the best-fit line with little pointto-point variability between the elevations and the line. In addition, the best-fit line through the left and right bankfull-stage 

profiles closely parallel the water-surface profiles. At some 

sites, both bankfull-stage profiles did not vary consistently 

(generally because of natural changes in streambed gradient) 

which caused both the bankfull-stage profiles to be segmented, 

rather than straight lines. In some instances, water-surface profiles were used as a guide in drawing the bankfull-stage profiles 

because the water-surface profiles were more uniform. The longitudinal profiles, together with the stage-discharge relation 

derived from data from the gaging station, were used to determine bankfull discharge if possible. 

At 20 sites (table 1) where a gaging station was located 

within the selected reach, the bankfull discharge at the gage was 

determined from the bankfull stage-discharge relation. For 11 

of the sites with active gages, the most recent stage-discharge 

relation was used to determine bankfull discharge (table 1). For 

seven of the sites with discontinued gages, the most recent 

stage-discharge relation was used to determine bankfull discharge. For two other sites with discontinued gages, the most 

recent stage-discharge relation did not provide reliable values 

for bankfull discharge, and the stage-discharge relation was 

adjusted on the basis of the discharge measured at the time of 

the site visit. 

At 19 sites where the stage-discharge relation was not reliable (even after adjustment) or where the gage was not located 

within the study reach, a computer program for calculation of 

water-surface profiles (HEC-RAS version 3.0, U.S. Army 

Corps of Engineers, 2001a,b,c) based on the standard-step 

method (Davidian, 1984) was used to calculate a water-surface 

profile for bankfull discharge. The HEC-RAS model used 

cross-section and channel-distance data and estimated Manning’s roughness coefficients to calculate water-surface elevation at each cross section for a selected discharge and an initial 

water-surface elevation at the most downstream cross section. 

For this analysis, the starting downstream water-surface elevation was the bankfull stage, and the discharge was varied until 

the simulated water-surface elevations at the remaining cross 

sections in the reach closely matched the surveyed bankfullstage elevations. The discharge that resulted in the closest 

match of water-surface elevation to bankfull-stage elevation at 

all cross sections was determined to be the bankfull discharge 

(table 1). 

At two sites, the stage-discharge relation and the simulations from HEC-RAS did not produce reliable information to 

determine bankfull discharge. In these two instances, the Manning equation for uniform flow (Henderson, 1966) was used to 

determine the bankfull discharge at one cross section for each 

site using cross-sectional area, average water-surface slope in 

the reach, and the Manning’s roughness coefficient as input 

variables (table 1).

Finally, the bankfull discharge for each site was plotted on 

the most recent flood-frequency curve (Parrett and Johnson, 

2004) to determine the recurrence interval for the bankfull discharge. The recurrence interval for bankfull discharge at the 41 

sites in western Montana was somewhat variable from site to 

site and ranged from 1.0 to 4.4 years (table 1). The median 

value of recurrence interval was 1.5 years (fig. 5), which is similar to the recurrence interval for bankfull discharge determined 

in other studies (Rosgen, 1996; Moody and Odem, 1999; Castro 

and Jackson, 2001; White, 2001; and Cinotto, 2003). 

Determination of Various Design-Peak 

Discharges at Ungaged Sites

One of the key goals of this study was to determine 

whether measured channel-morphology characteristics at

gaged sites could be used to improve existing methods for estimation of bankfull discharge and various design-peak discharges at ungaged sites. Accordingly, regression analysis was 

used to examine the relation between various design-peak discharges and channel morphology at the 41 gaged sites in the 

current study.

 
Determination of Various Design-Peak Discharges at Ungaged Sites 7

Figure 4. Longitudinal profiles for Boulder Creek at Maxville (station 12330000, top) and Eightmile Creek 

near Florence (station 12351400, bottom), Montana. MEASURED ELEVATIONS REFERENCED TO GAGE DATUM (NGVD 29), IN FEET

DISTANCE, IN FEET

0 50 100 150 200 250 300

190

186

192

196

194

188

184

Left bankfull-stage

Left water-surface

Best-fit line for bankfull stage

Streambed (thalweg)

Right water-surface

Right bankfull-stage

4,742

4,744

4,746

4,748

4,750

4,752

4,754

4,756

4,758

0 100 200 300 400 500

DISTANCE, IN FEET

Left bankfull-stage

Left water-surface

Best-fit line for bankfull stage

Streambed (thalweg)

Right water-surface

Right bankfull-stage

198

200
8 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

Figure 5. Variation in recurrence interval of bankfull discharge at 41 selected

sites, western Montana. RECURRENCE INTERVAL, IN YEARS

25th percentile

Median

75th percentile

90th percentile

10th percentile

95th percentile

Minimum (and 5th percentile)

3.8

3.1

2.2

1.5

1.2

1.1

1.0

4.4 Maximum

1.9 Mean

Regression Relations between Various Design-Peak 

Discharges and Channel Morphology

Multiple regression analyses were performed to determine 

whether equations used to estimate design-peak discharges 

(based on bankfull width as the only explanatory variable, table 

3, at back of report) might be improved by the inclusion of other 

measured channel-morphology characteristics. Regression 

analysis also was used to develop an estimation equation for 

bankfull discharge. To help ensure that relations between the 

various design-peak discharges and the channel-morphology 

characteristics would be linear, all variables were converted to 

base 10 logarithms (log), so that the regression equations were 

of the following linear form:

 log QT or BF = log K + a1 log x1 + a2 log x2 + ... ap log xp, (1)

where

QT or BF is the design-peak discharge or the bankfull (BF) discharge (in cubic feet per second), with a recurrence interval of T years,

K is the regression constant,

a1 through ap are regression coefficients, and

x1 through xp are channel-morphology characteristics.

Equation 1 can be expressed without logarithms in the following non-linear form:

 QT or BF = K’ x1

a1 x2a2 ... xpap , (2)

where

K’ is the anti log (10K) of the linear regression constant K,

and all other terms are as previously defined.

Channel-morphology characteristics that were used as 

potential explanatory variables in the multiple regression analyses were bankfull width, mean bankfull depth, bankfull crosssectional area, width/depth ratio, flood-prone width, entrenchment ratio, the D50 streambed-particle size, water-surface slope 

(determined from the water-surface profiles), and an index 

number ranging from 1 to 7, corresponding to the seven different values of the Rosgen stream classification of the 41 sites 

(table 1). Two additional variables, site latitude and site longitude, also were used in the regression analyses to determine 

whether regression results might vary by location within the 

study area (table 2).

An Ordinary Least Squares (OLS) stepwise-regression 

analysis using the method of all possible regressions was conducted using a computer program (Steppan and others, 1998). 

The regression analysis indicated that the only explanatory variables that were significant (p value less than 0.05) for all QT 

(2-, 5-, 10-, 25-, 50-, 100-, 200-, and 500-year recurrence intervals) and QBF were either bankfull width or bankfull crosssectional area. For all QT and QBF, the equations based on bankfull cross-sectional area had slightly greater coefficients of
Determination of Various Design-Peak Discharges at Ungaged Sites 9

determination (r

2

) and slightly smaller standard errors of estimate than the equations based on bankfull width. Equations 

based on bankfull cross-sectional area thus can be considered to 

be slightly more reliable than those based on bankfull width, but 

field measurement of bankfull cross-sectional area is more complicated than measurement of bankfull width. Accordingly, 

equations for estimation of QT or QBF based on bankfull width 

might be considered preferable to those based on bankfull 

cross-sectional area.

Use of Existing Flood-Frequency Equations

Parrett and Johnson (2004) recently developed three sets 

of regression equations relating annual peak discharges (designpeak discharges) with recurrence intervals of 2, 5, 10, 25, 50, 

100, 200, and 500 years to various basin characteristics, activechannel width, and bankfull width for eight regions in Montana. 

As defined in the glossary, active-channel width is a measure of 

a geomorphic feature similar to, but narrower than, the bankfull 

channel. One of the regions (West Region) lies wholly within 

the study area of this report, and one (Northwest Region) lies 

partly within the study area (fig. 1). The regression equations 

and measures of their predictive reliability (standard error of 

prediction, SEP) for the West and Northwest Regions are shown 

in table 3. Parrett and Johnson (2004) also provided methods 

for weighting estimates from any two or more of the three sets 

of regression equations based on their standard error of prediction and degree of correlation.

The regression equations developed by Parrett and 

Johnson (2004) are based on data from 90 to 96 gaged sites in 

the West Region and 29 to 35 gaged sites in the Northwest 

Region (table 3). The regression equations relating the various 

design-peak discharges to bankfull width based on data from 

only the 41 gaged sites in this study are not necessarily consistent with or comparable to the regression equations based on 

more data developed by Parrett and Johnson (2004). Accordingly, the equations developed by Parrett and Johnson (2004) 

for estimation of design-peak discharges are considered to be 

more reliable than those developed for this study. 

Although Parrett and Johnson (2004) did not develop a 

regression equation for estimation of bankfull discharge, a 

method was developed for estimation of bankfull discharge at 

ungaged sites based on data collected during this study that is 

consistent with the design-peak discharge equations developed 

by Parrett and Johnson (2004). The method is based on use of 

a multiplier applied to estimates of the 2-year peak discharge 

from equations from Parrett and Johnson (2004). The multiplier 

was calculated by using the median value of the ratios of bankfull discharge to the 2-year peak discharge at the 41 sites used 

in this study. The variability of the ratios of bankfull discharge 

to the 2-year peak discharge at the 41 sites is shown by the boxplot in figure 6. The values of the ratios ranged from 0.21 to 3.7, 

Figure 6. Variation of ratio of bankfull discharge to the 2-year 

design-peak discharge at 41 selected sites, western Montana. MULTIPLIER

1.5 95th percentile

1.4 90th percentile

1.1 75th percentile

0.84 Median

0.61 25th percentile

0.51 10th percentile

0.36 5th percentile

0.21 Minimum

3.7 Maximum

0.89 Mean
10 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

with a median value of 0.84 and a mean value of 0.89. Thus, 

bankfull discharge at an ungaged site in western Montana can 

be calculated by first using one of the applicable equations, or a 

weighted combination of two or three of the applicable equations, developed by Parrett and Johnson (2004) for estimation of 

the 2-year peak discharge and then multiplying that estimate by 

0.84. For example, if the equation from Parrett and Johnson 

(2004) for estimation of the 2-year peak discharge based on 

basin characteristics yields an estimate for 2-year peak discharge of 120 ft3/s for an ungaged site in western Montana, the 

estimated bankfull discharge would be 120 ft3/s x 0.84, or 101 

ft3

/s. The reliability of estimates for bankfull discharge at 

ungaged sites based on use of the median multiplier together 

with estimated values of the 2-year peak discharge (table 3) is 

believed to be about the same as the reliability of the estimates 

for the 2-year peak discharge indicated by Parrett and Johnson 

(2004, table 2) for the West Region (Charles Parrett, U.S. Geological Survey, oral commun., 2003) because they are based on 

the same equations. The reliability of estimates for bankfull 

discharge based on use of the median multiplier for ungaged 

sites in the Northwest Region is unknown because none of the 

41 sites used to develop the average multiplier were located in 

the Northwest Region.

Generally, the use of estimation equations based on regression has limitations because regression analyses do not define 

actual physical relations among variables; thus, regression 

equations might not provide reliable results when the bankfull 

widths are outside the range of values used to develop the equations. Meaningful relations between bankfull width and various 

design-peak discharges require stable conditions so that the 

channel is fully adjusted to the prevailing conditions of water 

and sediment discharge. Therefore, the equations in table 3 

probably are not applicable to stream reaches having the following conditions: 

1. Channels that are braided or unstable.

2. Channels largely composed of bedrock. 

3. Channel reaches having long pools or steep slopes.

4. Channels altered by recent floods or human activities.

5. Small streams with poorly defined channels that are 

highly vegetated.

6. Streams with recent changes in streamflow regimen, such 

as those resulting from the construction of upstream 

diversion or regulation structures.

An additional constraint on the use of estimation equations 

based on bankfull width in table 3 is that the site needs to be

visited and the width needs to be measured. Properly identifying bankfull width requires training and experience and, even 

among individuals experienced in making channel-geometry 

measurements, the variability in measured widths can be large. 

Both Wahl (1977) and Hammer (1981) reported that errors in 

geomorphic measurements could be as large as 30 percent even 

for experienced hydrographers. Equations based on bankfull 

and active-channel width (table 3) have measurement error 

described by Wahl (1977) included in the standard error of prediction (Parrett and Johnson, 2004).

Regression Relations between Channel 

Morphology and Drainage Area and 

Bankfull Discharge and Drainage Area

Studies by Emmett (1975) and Dunne and Leopold (1978) 

have shown that the bankfull-channel dimensions of width, 

mean depth, and cross-sectional area and bankfull discharge are 

related to the size of drainage area within regions where hydrologic processes and climate are similar. Regression analysis of 

the relation between these channel-morphology characteristics 

and drainage area and bankfull discharge and drainage area for 

gaged streams can provide a means of estimating channel morphology and bankfull discharge for ungaged streams when the 

drainage area is known. Plots of these relations have been 

termed regional curves (Dunne and Leopold, 1978); these 

curves can be used as a means of validating bankfull indicators 

observed in the field. However, according to Moody and Odem 

(1999), these curves should not be used as the primary means of 

estimating channel geometry or bankfull discharge.

To help ensure that climate would be similar for all sites 

used to develop regional relations between channel morphology 

and drainage area and between bankfull discharge and drainage 

area, mean annual precipitation was used as an additional potential explanatory variable in a regression analysis. To determine 

whether the relations might vary with location within the study 

area, site latitude and site longitude also were used as additional 

potential explanatory variables. 

An OLS stepwise-regression analysis (Steppan and others, 

1998) was used to relate the logarithms of bankfull width, mean 

bankfull depth, bankfull cross-sectional area, and bankfull discharge to the logarithms of drainage area, mean annual precipitation, and site latitude and longitude at all of the 41 gaged sites. 

The results of each of the four regression analyses indicated that 

both drainage area and mean annual precipitation were significant (p values less than 0.05) explanatory variables for estimation of bankfull discharge. However, the results of each of the 

four regression analyses also indicated that site latitude and site 

longitude were not significant (p values greater than 0.05) 

explanatory variables for estimation of bankfull discharge. 

To ensure that regional curves relating channel morphology and bankfull discharge to drainage area alone would 

include the effects of mean annual precipitation, each gaged site 

was assigned an index number of 1, 2, or 3, depending upon the 

value of mean annual precipitation at the site. All gaged sites 

having a mean annual precipitation of less than 30 in. were 

given an index number of 1, all sites having mean annual precipitation between 30 to 45 in. were given an index number of 

2, and all sites having mean annual precipitation greater than 45 

in. were given an index number of 3. Regression analyses using 

drainage area and index number as the only explanatory variables were used to develop equations of the following form:
Regression Relations between Channel Morphology and Drainage Area and Bankfull Discharge and Drainage Area 11

log Y = log K + a1 log DA + a2 log Index (i), (3)

where

Y is either bankfull width (in feet), mean 

bankfull depth (in feet), bankfull crosssectional area (in square feet), or bankfull 

discharge (in cubic feet per second),

K is the regression constant,

a1 and a2 are regression coefficients,

DA is drainage area (in square miles), and

Index(i) is the index number (1, 2, or 3) for mean 

annual precipitation (in inches) at the site.

Because a2 log Index(i) is a constant that can have only 

three values, depending upon whether Index(i) = 1, 2, or 3, 

equation 3 can be simplified to:

 log Y = Ci

 + a1 log DA, (4)

where

Ci

 = a2 log Index(i). 

Using equation 4, three regional curves were drawn that 

relate Y to drainage area. Each curve has the same slope (a1), 

but a different intercept (anti log Ci

) depending upon the value 

of the Index(i) for the mean annual precipitation. The resultant 

regional curves relating bankfull width, mean bankfull depth, 

bankfull cross-sectional area, and bankfull discharge to drainage area within the study area are shown in figure 7. The

Figure 7. Regional relations of bankfull-channel dimensions and bankfull discharge to drainage area for different ranges of mean 

annual precipitation.

10 100 1,000

1

10

100

1,000

DRAINAGE AREA, IN SQUARE MILES

BANKFULL CROSS-SECTIONAL AREA, IN SQUARE FEET

0.1 1

y = 7.86 x (0.523)

r = 0.42 (for all three curves) 2

10 100 1,000

1

10

100

1,000

DRAINAGE AREA, IN SQUARE MILES

BANKFULL WIDTH, IN FEET

0.1 1

y = 7.70 x(0.441)

r = 0.83 (for all three curves) 2

10 100 1,000

1

10

DRAINAGE AREA, IN SQUARE MILES

BANKFULL DISCHARGE, IN CUBIC FEET PER SECOND

0.1 1

10,000

1,000

100

y = 16.4 x (0.851)

r = 0.82 (for all three curves) 2

100 1,000

1

10

DRAINAGE AREA, IN SQUARE MILES

MEAN BANKFULL DEPTH, IN FEET

0.1 1 10

0.1

y = 0.869 x (0.221)

r = 0.53 (for all three curves) 2

y = 6.04 x(0.441)

y = 3.99 x(0.441)

y = 3.69 x (0.523)

y = 5.94 x (0.523)

y = 4.59 x (0.851)

y = 10.2 x (0.851)

y = 0.573 x (0.221)

y = 0.745 x (0.221)

EXPLANATION

RANGE OF MEAN ANNUAL PRECIPITATION, IN INCHES

Less than 30 30-45 Greater than 45
12 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

regional curves can be used on a reconnaissance level (without 

a site visit for measurement) to estimate channel morphology 

and bankfull discharge for ungaged sites in western Montana. 

Mean annual precipitation at an ungaged site in western Montana can be determined from Parrett and Johnson (2004).

The curves developed for this study are based on sparse, 

highly variable data. The relatively small number of streamflow-measurement stations used in the regression analysis

limits the strength of the regional curves presented in this 

report. More detailed climatic data might further enhance the 

results from this study and possibly allow further stratification 

by climatic zones or ecoregions. For parts of Montana east of 

the Continental Divide with different basin and climatic characteristics, new data collection and analysis would be beneficial in 

estimating bankfull and other flood discharges.

Summary

Channel-morphology data were collected at 41 active or 

discontinued streamflow-gaging sites in western Montana. A 

suitable reach near the gaging station was identified at each site. 

In general, the selected reach was about 20 bankfull widths in 

length and, whenever possible, the gaging station was located 

within this reach. Within the selected reach, water-surface, 

streambed (thalweg), and bankfull-channel elevations were 

measured as well as bankfull widths and bankfull depths. 

Bankfull cross-sectional areas, bankfull-wetted perimeters, and 

width/depth ratio were determined from the elevation and location data. Furthermore, the flood-prone width, entrenchment 

ratio, sinuosity, streambed-material sizes, and channel roughness were determined at each site. 

Bankfull discharge and its associated recurrence interval 

were determined at each of the 41 gaged sites. For each study 

reach, the bankfull-stage, water surface, and thalweg elevations, 

and associated channel-distance data were used to construct 

longitudinal profiles. At 11 sites with active gages, the recent 

stage-discharge relation was used to determine bankfull discharge. For seven sites with discontinued gages, the most 

recent stage-discharge relation was used to determine bankfull 

discharge. For two other sites with discontinued gages, the 

stage-discharge relation was adjusted on the basis of the discharge measured at the time of the site visit. At 19 sites, where 

the stage-discharge relation was not reliable or where the gage 

was not located within the study reach, a computer program for 

calculation of water-surface profiles was used to calculate a 

water-surface profile for bankfull discharge. At two sites, the 

Manning equation for uniform flow was used to determine the 

bankfull discharge at one cross section for each site. Finally, 

the bankfull discharge for each site was plotted on the most 

recent flood-frequency curve to determine the recurrence interval for the bankfull discharge. The recurrence interval for bankfull discharge ranged from 1.0 to 4.4 years. The median value 

of the recurrence interval was 1.5 years. 

Regression analysis was used to examine the relation 

between various design-peak discharges and channelmorphology at the 41 gaged sites. Channel morphology characteristics that were used as potential explanatory variables in 

the multiple regression analyses were bankfull width, bankfull 

cross-sectional area, mean bankfull depth, the median

streambed-particle size (D50), water-surface slope, width/depth 

ratio, flood-prone width, entrenchment ratio, and an index number ranging from 1 to 7, corresponding to the seven different 

values of the Rosgen stream classification of the 41 sites. An 

Ordinary Least Squares (OLS) stepwise-regression analysis 

indicated that the only explanatory variables that were significant for all design-peak and bankfull discharges were either 

bankfull width or bankfull cross-sectional area. Equations for 

estimation of design-peak or bankfull discharge based on bankfull width might be considered preferable to those based on 

bankfull cross-sectional area, because bankfull width is less 

complicated to measure than bankfull cross-sectional area. 

Bankfull discharge at ungaged sites in most of the study 

area can be estimated by application of a multiplier after determining the 2-year peak discharge at the ungaged site. The multiplier, which is the ratio of bankfull discharge to the 2-year 

peak discharge determined at the 41 sites, ranged from 0.21 to 

3.7 with a median value of 0.84. The reliability of estimates for 

bankfull discharge at ungaged sites based on the multiplier of 

0.84 together with estimated values of the 2-year peak discharge 

is believed to be about the same as the reliability of the estimates for the 2-year peak discharge for the West Region. The 

reliability of estimates for bankfull discharge based on the use 

of the multiplier for ungaged sites in the Northwest Region

is unknown. 

Regression analysis of the relation between channel-morphology characteristics and drainage area and bankfull discharge to drainage area can provide a means of estimating channel morphology and bankfull discharge for ungaged streams 

when the drainage area is known. An OLS stepwise-regression 

analysis was used to relate the logarithms of bankfull width, 

mean bankfull depth, bankfull cross-sectional area, and bankfull discharge to the logarithms of drainage area, mean annual 

precipitation, and site latitude and longitude for all 41 sites. The 

results of each of the four regression analyses indicated that 

both drainage area and mean annual precipitation were significant explanatory variables for estimation of bankfull discharge. 

To ensure that regional curves relating channel morphology and 

bankfull discharge to drainage area alone would include the 

effects of mean annual precipitation, each site was assigned an 

index number (equal to a specific range of the mean annual precipitation). The regional curves developed for the study area 

can be used on a reconnaissance level to estimate channel morphology and bankfull discharge for ungaged sites in western 

Montana.
References Cited 13

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geocities.com/SiliconValley/Network/1900/

ERPref.html#Homepage

U.S. Army Corps of Engineers, 2001a, HEC-RAS, River analysis system user’s manual, version 3.0: Davis, Calif., Hydrologic Engineering Center, 320 p.

U.S. Army Corps of Engineers, 2001b, HEC-RAS, River analysis system hydraulic reference manual, version 3.0: Davis, 

Calif., Hydrologic Engineering Center, 262 p.

U.S. Army Corps of Engineers, 2001c, HEC-RAS, River analysis system applications guide, version 3.0: Davis, Calif., 

Hydrologic Engineering Center, 344 p.

U.S. Geological Survey, 2004, Montana flood-frequency and 

basin characteristics data, accessed November 22, 2004,

at http://mt.water.usgs.gov/freq

Wahl, K.L., 1977, Accuracy of channel measurements and 

implications in estimating streamflow characteristics: U.S. 

Geological Survey Journal of Research, v. 5, no. 6,

p. 811-814.

White, K.E., 2001, Regional curve development and selection 

of a reference reach in the non-urban, lowland sections of the 

Piedmont Physiographic Province, Pennsylvania and Maryland: U.S. Geological Survey Water-Resources Investigations Report 01-4146, 20 p.

Wolman, M.G., 1954, A method of sampling coarse river-bed 

material: Transactions of the American Geophysical Union, 

v. 35, p. 951-956.
14 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana
DATA 15

DATA
16 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

Table 1. Channel-morphology characteristics and design-peak-discharge data for selected streamflow-gaging stations, western

Montana

[Location of streamflow-gaging stations shown in figure 1. All sites are in Montana. Bold text denotes only those stations that were active during data collection 

(2000-03). Drainage area, bankfull width, mean bankfull depth, maximum bankfull depth, bankfull cross-sectional area, width/depth ratio, flood-prone width,

entrenchment ratio, sinuosity, D50, recurrence interval, and Rosgen classification defined in the glossary; measured characteristics are averages except entrenchment ratio, valley and channel slope, and sinuosity. Abbreviations: ft, foot; ft/ft, foot per foot; ft2, square foot; mm, millimeter; ft3/s, cubic feet per second. Symbol: <, less than] 

Station 

number

(fig. 1)

Station name

Bankfull 

width

(ft)

Mean 

bankfull 

depth 

(ft)

Maximum 

bankfull 

depth

(ft)

Bankfull 

crosssectional 

area

(ft2

) 

Width/ 

depth 

ratio1

 

Floodprone 

width 

(ft)

Entrenchment

ratio

Valley 

slope

(ft/ft)

Channel 

slope

(ft/ft) 

12300400 Cayuse Creek near Trego 8.9 0.53 0.86 4.6 18.7 19 2.2 0.036 0.035

12300800 Deep Creek near Fortine 14 1.6 2.4 22.2 8.8 26 1.9 .012 .011

12301997 Richards Creek near Libby 8.7 .63 .75 5.4 13.8 16 1.9 .035 .033

12301999 Wolf Creek near Libby 34 1.5 2.2 50.9 24.1 44 1.3 .011 .010

12302400 Shaughnessy Creek near Libby 10 .85 1.2 8.8 12.2 13 1.4 .052 .049

12302500 Granite Creek near Libby 34 1.9 2.6 61.6 19.7 50 1.5 .025 .024

12303100 Flower Creek near Libby 25 1.8 2.7 43.8 14.5 38 1.6 .047 .042

12304040 Basin Creek near Yaak 30 2.2 3.4 64.2 13.6 112 3.7 .014 .008

12304060 Blacktail Creek near Yaak 21 1.2 1.8 24.6 17.5 65 3.1 .030 .026

12304120 Zulu Creek near Yaak 14 .94 1.6 12.7 14.9 61 4.5 .023 .022

12324100 Racetrack Creek below Granite Creek, near 

Anaconda

 25 2.2 2.9 53.4 11.4 57 2.3 .007 .007

12324590 Little Blackfoot River near Garrison 57 2.7 3.7 150 21.1 140 2.6 .004 .003

12324700 Clark Fork tributary near Drummond 8.9 .39 .59 3.5 22.8 20 2.2 .013 .012

12329500 Flint Creek at Maxville 45 2.7 3.9 119 17.5 110 2.4 .003 .003

12330000 Boulder Creek at Maxville 33 1.8 2.5 56.7 18.3 45 1.4 .022 .018

12331700 Edwards Gulch at Drummond 6.1 .79 1.5 4.9 9.9 23 3.9 .035 .031

12332000 Middle Fork Rock Creek near Philipsburg 75 1.9 2.7 144 38.5 100 1.3 .010 .010

12335500 Nevada Creek above Reservoir, near Helmville 38 1.5 2.2 55.0 26.0 90 2.4 .005 .004

12338600 Monture Creek at Lolo National Forest boundary, 

near Ovando 

 73 2.1 2.9 152 36.8 370 5.0 .005 .004

12339300 Deer Creek near Seely Lake 21 .97 1.5 20.6 22.4 61 2.7 .008 .008

12339450 Clearwater River near Clearwater 120 2.2 3.5 261 56.2 362 3.1 .003 .003

12339900 West Twin Creek near Bonner 19 2.2 3.1 40.2 8.5 36 2.0 .054 .050

12340200 Marshall Creek near Missoula 4.4 .52 .74 2.3 8.9 10 2.6 .060 .060

12342950 Trapper Creek near Conner 49 2.0 2.8 95.5 25.2 268 4.9 .015 .015

12344300 Burke Gulch near Darby 8.1 1.2 1.5 9.9 6.8 16 1.9 .050 .050

12346500 Skalkaho Creek near Hamilton 33 2.0 2.9 65.2 16.3 41 1.3 .021 .020

12350500 Kootenai Creek near Stevensville 30 1.3 2.6 38.1 25.1 42 1.5 .048 .047

12351400 Eightmile Creek near Florence 14 2.0 2.6 27.0 6.8 65 4.8 .013 .010

12352000 Lolo Creek above Sleeman Creek, near Lolo 57 1.8 2.7 103 31.9 77 1.4 .005 .004

12352200 Hayes Creek near Missoula 8.3 1.1 1.2 9.0 8.2 28 3.3 .053 .051

12353820 Dry Creek near Superior 24 1.3 2.0 31.4 18.8 37 1.6 .014 .013

12353850 East Fork Timber Creek near Haugan 9.8 .76 1.4 7.9 13.7 32 3.2 .014 .014

12355350 Big Creek at Big Creek Ranger Station, near 

Columbia Falls

 45 2.5 3.1 112 18.3 70 1.6 .013 .012

12369650 North Fork Lost Creek near Swan Lake 26 2.7 3.9 71.5 9.6 55 2.1 .010 .010

12374250 Mill Creek above Bassoo Creek, near Niarada 19 1.0 1.7 19.2 18.2 50 2.7 .028 .028

12375900 South Crow Creek near Ronan 18 1.6 2.9 29.3 11.7 33 1.8 .057 .053

12377150 Mission Creek above reservoir, near St. Ignatius 39 2.4 3.7 94.7 16.8 59 1.5 .016 .016

12383500 Big Knife Creek near Arlee 15 1.2 2.6 18.1 13.0 33 2.2 .033 .028

12387450 Valley Creek near Arlee 15 1.7 20.5 24.6 9.0 36 2.4 .032 .030

12388400 Revais Creek below West Fork, near Dixon 22 1.7 2.6 37.0 12.8 46 2.1 .035 .035

12391100 White Pine Creek near Trout Creek 26 1.4 2.4 37.3 18.5 42 1.6 .029 .028

1Data from individual cross-section values are not averages of bankfull width and mean bankfull depth. 2From Parrett and Johnson (2004).

3

Determined from stage-discharge relation.

4Determined from water-surface profile model (U.S. Army Corps of Engineers, 2001a,b,c). 5Determined from uniform-flow equation (Henderson, 1966).
TABLE 1 17

Table 1. Channel-morphology characteristics and design-peak-discharge data for selected streamflow-gaging stations, western

Montana—Continued

Station 

number

(fig. 1)

Sinuosity

(ft/ft)

D50 

(mm)

Estimated 

Manning’s 

roughness 

coefficient 

(n)

Recurrence 

interval 

(bankfull 

discharge, 

in years)

Rosgen 

classification

Bankfull discharge

(ft3

/s)

Design-peak discharge2 (Q), in cubic feet per second, for indicated 

recurrence interval (in years)

2 5 10 25 50 100 200 500

12300400 1.09 31.0 0.063 1.1 B4 317 51 89 120 162 197 235 276 334

12300800 1.03 28.0 .040 1.1 C4 3

73 130 169 197 233 261 291 321 365

12301997 1.06 60.0 .045 1.4 C4 4

13 24 50 71 100 123 148 173 207

12301999 1.10 105 .075 1.3 B3 4

617 617 1,270 1,750 2,390 2,860 3,320 3,780 4,350

12302400 1.06 14.0 .043 4.3 A4 4

28 11 30 52 94 141 203 287 439

12302500 1.08 110 .075 2.0 B3 4

260 250 1,100 1,320 1,800 2,120 2,660 3,500 5,070

12303100 1.10 100 .070 1.2 B3 4

130 250 320 390 490 610 840 1,200 1,730

12304040 1.02 21.0 .045 1.2 C4 3

191 260 369 443 537 607 677 748 844

12304060 1.15 70.0 .065 2.2 B3 5

80 73 128 169 227 275 325 378 454

12304120 1.05 39.0 .055 2.1 C4 5

44 42 72 98 137 173 214 262 337

12324100 1.03 5.2 .035 1.3 C4 4

275 366 485 556 637 693 745 794 855

12324590 1.03 27.0 .035 1.5 C4 3917 1,250 2,540 3,620 5,230 6,600 8,100 9,740 12,100

12324700 1.04 <.062 .032 2.4 C6 3

60 47 100 147 221 287 361 446 574

12329500 1.36 28.0 .050 1.4 B4 4

345 451 691 862 1,090 1,270 1,450 1,650 1,910

12330000 1.22 105 .065 1.7 B3 3335 372 570 726 953 1,150 1,360 1,600 1,950

12331700 1.11 <.062 .030 1.6 C6 4

14 20 63 113 209 311 443 610 897

12332000 1.05 65.0 .065 1.2 C3 3

554 906 1,240 1,430 1,640 1,790 1,920 2,040 2,190

12335500 1.14 9.0 .035 1.4 C4 4195 504 937 1,270 1,720 2,080 2,440 2,830 3,350

12338600 1.19 40.0 .073 1.3 C4 41,130 1,350 1,650 1,820 2,020 2,160 2,290 2,410 2,560

12339300 1.02 32.5 .036 1.0 C4 3

124 244 321 372 438 487 537 588 657

12339450 1.27 50.0 .030 1.6 C4 41,400 1,600 2,200 2,630 3,210 3,670 4,160 4,680 5,410

12339900 1.08 80.0 .055 1.9 B3 4

95 97 167 223 304 372 446 527 646

12340200 1.00 45.0 .043 1.2 C4 49 17 27 35 48 59 71 85 106

12342950 1.04 60.0 .046 2.0 B4 4

440 450 589 688 824 931 1,050 1,170 1,340

12344300 1.27 6.0 .075 4.4 B4 3

14 9 15 19 24 28 31 35 40

12346500 1.07 160 .073 1.1 B3 3375 672 872 986 1,120 1,200 1,280 1,350 1,440

12350500 1.02 165 .075 1.4 A4 3

670 814 1,060 1,200 1,360 1,470 1,570 1,660 1,770

12351400 1.27 5.7 .075 2.3 E4 4

55 50 73 89 110 126 142 159 181

12352000 1.20 80.0 .035 1.1 C3 31,140 1,460 1,760 1,960 2,210 2,410 2,610 2,810 3,090

12352200 1.04 15.0 .040 2.4 B4 4

15 11 26 40 62 82 104 129 166

12353820 1.05 52.0 .045 1.2 C2 4

140 386 462 508 561 599 635 670 714

12353850 1.03 5.0 .035 1.1 C4 48 39 60 74 91 104 117 130 147

12355350 1.05 89.0 .035 1.0 C3 3

719 1,140 1,440 1,650 1,940 2,160 2,390 2,640 2,980

12369650 1.03 215 .070 1.5 B3 3

240 260 310 344 386 417 448 480 523

12374250 1.14 58.0 .052 3.1 C4 3

66 43 82 116 170 220 279 348 458

12375900 1.14 110 .065 2.5 B3 3

197 168 251 303 367 413 456 498 552

12377150 1.04 35.0 .045 3.0 B4 3

480 420 531 598 675 729 780 828 890

12383500 1.18 22.6 .055 3.7 B3 3

51 38 55 67 82 94 106 118 135

12387450 1.07 60.0 .057 2.1 B4 3

59 57 79 93 112 127 142 157 177

12388400 1.03 100 .070 3.8 B3 3

210 156 224 272 336 386 439 493 570

12391100 1.04 58.0 .065 1.2 B4 4

130 212 340 442 591 717 858 1,010 1,250
18 Determination of Channel-Morphology Characteristics, Bankfull Discharge, and Various Design-Peak Discharges in Western Montana

Table 2. Basin and climatic characteristics for selected streamflow-gaging stations, western Montana1

[Location of streamflow-gaging stations shown in figure 1. All sites are in Montana. Latitude and longitude reported in

degrees, minutes, and seconds; North American Datum of 1927 (NAD 27). Drainage area, mean annual precipitation, and

percentage of basin covered by forest defined in the glossary. Abbreviations: mi2, square miles; in., inches]

Station 

number

(fig. 1)

Station name Latitude Longitude

Drainage

area

 (mi2)

Mean 

annual 

precipitation

(in.)

Percentage 

of basin 

covered by 

forest

12300400 Cayuse Creek near Trego 483633 1150142 5.29 28 95

12300800 Deep Creek near Fortine 484600 1145300 18.9 50 92

12301997 Richards Creek near Libby 481531 1151157 9.50 29 90

12301999 Wolf Creek near Libby 481401 1151702 216 27 100

12302400 Shaughnessy Creek near Libby 481800 1153600 1.16 60 97

12302500 Granite Creek near Libby 481807 1153529 23.6 67 88

12303100 Flower Creek near Libby 482041 1153620 11.1 67 96

12304040 Basin Creek near Yaak 485549 1152856 27.4 235 2

96

12304060 Blacktail Creek near Yaak 485703 1153227 8.66 35 93

12304120 Zulu Creek near Yaak 484349 1153830 5.27 34 94

12324100 Racetrack Creek below Granite Creek, near 

Anaconda

461644 1125507 39.5 35 95

12324590 Little Blackfoot River near Garrison 463111 1124733 407 20 65

12324700 Clark Fork tributary near Drummond 463700 1130200 4.61 15 15

12329500 Flint Creek at Maxville 462750 1131420 208 20 68

12330000 Boulder Creek at Maxville 462820 1131359 71.3 31 98

12331700 Edwards Gulch at Drummond 464025 1130831 4.69 16 35

12332000 Middle Fork Rock Creek near Philipsburg 461142 1133000 123 35 93

12335500 Nevada Creek above Reservoir, near Helmville 464642 1124600 116 23 74

12338600 Monture Creek at Lolo National Forest boundary, 

near Ovando 

470537 1130910 105 41 75

12339300 Deer Creek near Seely Lake 471237 1133227 19.8 39 82

12339450 Clearwater River near Clearwater 470109 1132312 345 37 81

12339900 West Twin Creek near Bonner 465500 1134300 7.33 25 62

12340200 Marshall Creek near Missoula 465300 1135500 5.63 23 84

12342950 Trapper Creek near Conner 455343 1141051 28.5 66 67

12344300 Burke Gulch near Darby 460200 1140900 6.50 22 80

12346500 Skalkaho Creek near Hamilton 460940 1135652 87.8 36 99

12350500 Kootenai Creek near Stevensville 463214 1140931 28.9 64 69

12351400 Eightmile Creek near Florence 463910 1135730 19.5 21 87

12352000 Lolo Creek above Sleeman Creek, near Lolo 464500 1140900 250 52 98

12352200 Hayes Creek near Missoula 464900 1140600 4.16 33 79

12353820 Dry Creek near Superior 471317 1145819 46.3 254 280

12353850 East Fork Timber Creek near Haugan 472500 1152500 2.72 58 89

12355350 Big Creek at Big Creek Ranger Station, near 

Columbia Falls

483607 1140955 82.1 48 74

12369650 North Fork Lost Creek near Swan Lake 475306 1134753 13.0 2

57 288

12374250 Mill Creek above Bassoo Creek, near Niarada 474949 1144145 19.6 225 2

97

12375900 South Crow Creek near Ronan 472930 1140133 7.57 67 48

12377150 Mission Creek above reservoir, near St. Ignatius 471923 1135843 12.4 74 33

12383500 Big Knife Creek near Arlee 470851 1135824 6.88 241 2

95

12387450 Valley Creek near Arlee 471013 1141347 15.3 232 2

93

12388400 Revais Creek below West Fork, near Dixon 471559 1142421 23.4 236 2

88

12391100 White Pine Creek near Trout Creek 474419 1154027 8.75 58 86

1U.S. Geological Survey (2004).

2William Stotts (U.S. Geological Survey, written commun., 2004).
TABLE 3 19

Table 3. Three sets of regression equations for estimation of design-peak discharge in western Montana1

[Abbreviations: n, number of stations used in the regression analysis; SEP, standard error of prediction; QT, annual peak discharge, in cubic feet per second, for 

recurrence interval T, in years; A, drainage area, in square miles; P, mean annual precipitation, in inches; F, percentage of basin covered by forest; Wac, width of 

active channel, in feet; Wbf, width of bankfull channel, in feet]

Regression equation

Average

SEP,

in log units

Average

SEP,

in percent

Regression equation

Average

SEP,

in log units

Average

SEP,

in percent

(1) Based on basin characteristics

West Region (n = 96) Northwest Region (n = 35)

Q2 = 0.268 A0.927 P1.60 (F+1)-0.508 0.242 60.5 Q2 = 0.128 A0.918 P1.33 0.202 49.2

Q5 = 1.54 A0.884 P1.36 (F+1)-0.577 .224 55.4 Q5 = 1.19 A0.846 P0.954 .164 39.2

Q10 = 3.63 A0.86 P1.25 (F+1)-0.605 .221 54.3 Q10 = 4.10 A0.807 P0.72 .161 38.4

Q25 = 8.50 A0.835 P1.14 (F+1)-0.639 .222 54.6 Q25 = 15.8 A0.76 P0.51 .161 38.4

Q50 = 13.2 A0.823 P1.09 (F+1)-0.652 .227 56.0 Q50 = 31.2 A0.733 P0.445 .157 37.4

Q100 = 18.7 A0.812 P1.06 (F+1)-0.664 .235 58.5 Q100 = 56.4 A0.71 P0.403 .168 40.2

Q200 = 24.7 A 0.804 P1.04 (F+1)-0.674 .248 62.2 Q200 = 97.0 A0.694 P0.364 .190 46.0

Q500 = 35.4 A 0.792 P1.02 (F+1)-0.69 .267 67.9 Q500 = 175 A0.674 P0.347 .230 56.9

(2) Based on active-channel width

West Region (n = 93) Northwest Region (n = 29)

Q2 = 1.11 Wac1.74 .252 63.5 Q2 = 1.57 Wac1.67 .318 84.3

Q5 = 2.46 Wac1.63 .244 61.1 Q5 = 5.04 Wac1.50 .294 76.4

Q10 = 3.75 Wac1.58 .245 61.4 Q10 = 9.68 Wac1.40 .297 77.3

Q25 = 5.81 Wac1.51 .252 63.4 Q25 = 21.3 Wac1.30 .302 79.1

Q50 = 7.61 Wac1.48 .261 66.2 Q50 = 36.1 Wac1.24 .312 82.3

Q100 = 9.57 Wac1.45 .272 69.6 Q100 = 60.0 Wac1.19 .325 86.7

Q200 = 11.8 Wac1.43 .286 73.8 Q200 = 92.7 Wac1.16 .342 92.9

Q500 = 15.0 Wac1.41 .304 79.8 Q500 = 164 Wac1.12 .370 103.4

(3) Based on bankfull width

West Region (n = 90) Northwest Region (n = 29)

Q2 = 0.281 Wbf

1.98 .281 72.3 Q2 = 0.527 Wbf

1.82 .348 95.1

Q5 = 0.678 Wbf

1.86 .266 67.5 Q5 = 1.93 Wbf1.63 .324 86.6

Q10 = 1.08 Wbf

1.79 .263 66.6 Q10 = 4.00 Wbf1.52 .326 87.3

Q25 = 1.75 Wbf

1.72 .266 67.5 Q25 = 9.46 Wbf

1.40 .329 88.0

Q50 = 2.34 Wbf

1.69 .272 69.5 Q50 = 16.6 Wbf1.34 .334 90.1

Q100 = 2.99 Wbf

1.66 .281 72.3 Q100 = 28.4 Wbf

1.29 .345 94.1

Q200 = 3.72 Wbf

1.64 .293 76.1 Q200 = 45.0 Wbf

1.26 .360 99.6

Q500 = 4.82 Wbf

1.61 .310 81.7 Q500 = 81.6 Wbf1.21 .386 109.9

1

From Parrett and Johnson (2004).