U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2012–5024

Prepared in cooperation with the Madison River Fisheries Technical Advisory Committee

Bureau of Land Management, Montana Department of Environmental Quality, 

Montana Fish, Wildlife and Parks, PPL-Montana, U.S. Department of Agriculture 

Forest Service – Gallatin National Forest, U.S. Fish and Wildlife Service

Lateral and Vertical Channel Movement and Potential for 

Bed-Material Movement on the Madison River Downstream 

from Earthquake Lake, Montana
Front cover. U.S. Geological Survey personnel surveying the Madison River downstream from Earthquake Lake, Montana, near 

cross section 600 (photograph by the U.S. Geological Survey, 2006). 

Back cover. Left, Earthquake Lake and the Madison Slide, Montana [photograph by J.R. Stacy, August 1959 (U.S. Geological 

Survey, 2009)]; 

Top right, Madison River downstream from Earthquake Lake, Montana, looking downstream at cross section 1400 

(photograph by the U.S. Geological Survey, 1971); 

Middle right, Madison River downstream from Earthquake Lake, Montana, looking upstream at cross section 800 

(photograph by the U.S. Geological Survey, 1971); 

Bottom right, U.S. Geological Survey personnel surveying the Madison River downstream from Earthquake Lake, 

Montana (photograph by the U.S. Geological Survey, 1971).
Lateral and Vertical Channel Movement 

and Potential for Bed-Material Movement 

on the Madison River Downstream from 

Earthquake Lake, Montana

By Katherine J. Chase and Peter M. McCarthy

Prepared in cooperation with the Madison River Fisheries Technical Advisory 

Committee

Bureau of Land Management

Montana Department of Environmental Quality

Montana Fish, Wildlife and Parks 

PPL-Montana

U.S. Department of Agriculture – Gallatin National Forest

U.S. Fish and Wildlife Service

Scientific Investigations Report 2012–5024

U.S. Department of the Interior

U.S. Geological Survey
ISBN 978-1-4113-3363-5

U.S. Department of the Interior

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

U.S. Geological Survey, Reston, Virginia: 2012

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Chase, K.J., and McCarthy, P.M., 2012, Lateral and vertical channel movement and potential for bed-material movement on the Madison River downstream from Earthquake Lake, Montana: U.S. Geological Survey Scientific Investigations Report 2012–5024, 39 p.
iii

Acknowledgments

The creative assistance of Kevin L. Sattler, Sean M. Lawlor (U.S. Geological Survey), and 

William G. Stotts (U.S. Geological Survey, retired) in surveying the deep and fast parts of 

the Madison River is gratefully acknowledged. Using various techniques such as diving 

and kayaking, they made every effort to survey as much of the channel as safely possible. 

Reviews by Stephen M. Wiele (U.S. Geological Survey) and John G. Elliott (U.S. Geological Survey, retired), are greatly appreciated.

The author also gratefully acknowledges Mark Story, Bruce Roberts, and Scott Barndt 

(U.S. Department of Agriculture Forest Service – Gallatin National Forest), and Brent 

Mabbot (PPL-Montana) for their assistance with reviews.
iv

Contents

Acknowledgments........................................................................................................................................iii

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

Introduction.....................................................................................................................................................2

Purpose and Scope ..............................................................................................................................5

Description of the Study Area ............................................................................................................5

Previous Investigations........................................................................................................................5

Methods..................................................................................................................................................5

Surveys of the Madison River Channel....................................................................................5

HEC-RAS Analysis .......................................................................................................................6

Sediment Sampling......................................................................................................................6

Aerial Photography Analysis .....................................................................................................7

Lateral and Vertical Channel Movement ...................................................................................................8

Lateral Movement.................................................................................................................................9

Vertical Movement by Channel Incision and Aggradation ..........................................................17

Thalweg Elevations ...................................................................................................................17

Water-Surface Elevations ........................................................................................................17

Lateral and Vertical Movement by Channel Subreach.................................................................22

Subreach Between Cross Sections 1400 and 900................................................................22

Subreach Between Cross Sections 900 and 600..................................................................22

Subreach Between Cross Sections 600 and 400..................................................................23

Vertical Channel Changes near Raynolds Pass Bridge................................................................23

Limitations of the Estimates of Lateral and Vertical Channel Movement..................................23

Potential for Bed-Material Movement .....................................................................................................23

Characteristics of Materials In and Near the Madison River Channel .....................................23

Shear Stress and Potential for Bed-Material Movement ............................................................26

Boundary-Shear Stress ............................................................................................................27

Critical Shear Stress .................................................................................................................27

Cross Sections 500–400, Downstream from Spillway.................................................28

Cross Sections 1400–1300, Earthquake Lake Outlet ...................................................33

Limitations of the Estimates for Potential for Bed-Material Movement ...................................33

Summary and Conclusions.........................................................................................................................36

References Cited..........................................................................................................................................37

Appendix 1. Aerial Photographs and Locations of Stream Centerlines and Cross Sections 

of the Madison River Downstream from Earthquake Lake, Montana .......................................

CD-ROM in pocket at back of report and available at http://pubs.usgs.gov/sir/2012/5024/
v

Figures

1. Map showing location of study area.........................................................................................3

2. Map showing location of surveyed cross sections, channel centerline in 2006, 

approximate locations of sediment samples collected in 2006 and 2008, and 

survey reference marks along the Madison River downstream from 

Earthquake Lake, Montana .........................................................................................................4

3. Photograph showing Madison River downstream from Earthquake Lake, 

Montana, looking downstream from right bank at cross section 1100................................9

4. Photographs showing Madison River downstream from Earthquake Lake, 

Montana .......................................................................................................................................12

5. Photographs showing Madison River downstream from Earthquake Lake, 

Montana, looking downstream at cross section 800............................................................13

6. Photograph showing Madison River downstream from Earthquake Lake, 

Montana, looking downstream at cross section 600............................................................14

7. Photographs showing Madison River downstream from Earthquake Lake, 

Montana, upstream from cross section 800...........................................................................15

8. Graph showing lateral channel movement for selected sites along the 

Madison River and annual peak streamflow for the Madison River, Montana................16

9. Graph showing estimated thalweg profiles and calculated width/depth ratios 

of the Madison River downstream from Earthquake Lake, Montana................................18

10. Photographs showing erosion-resistant materials above the Madison River, 

downstream from Earthquake Lake, Montana ......................................................................19

11. Surveyed water-surface profiles, calculated water-surface profile, and 

estimated thalweg profiles of the Madison River downstream from 

Earthquake Lake, Montana .......................................................................................................20

12. Graphs and map showing lateral migration, incision, and aggradation of the 

Madison River channel downstream from Earthquake Lake, Montana between 

1971 and 2006...............................................................................................................................24

13. Cross sections 100, 200, and 300, from 1971 and 2006 surveys on the Madison 

River near Raynolds Pass Bridge downstream from Earthquake Lake, Montana...........26

14. Graph showing distribution of particle sizes of material in and near the 

Madison River downstream from Earthquake Lake, Montana ...........................................30

15. Graph showing calculated mean and point boundary-shear stresses at cross 

section 400 and calculated critical shear stresses for movement of selected 

sediment sizes between cross sections 500 and 400, Madison River downstream from Earthquake Lake, Montana ................................................................................32

16. Graphs showing calculated mean boundary-shear stress at various streamflows and calculated critical shear stresses for selected sediment sizes, 

Madison River downstream from Earthquake Lake, Montana ...........................................34
vi

Conversion Factors, Datum, Acronyms, and Symbols

Inch/Pound to SI

Multiply By To obtain

cubic foot (ft3) 0.02832 cubic meter (m3) 

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

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

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

gallon (gal) 3.785 liter (L)

mile (mi) 1.609 kilometer (km)

pound, avoirdupois (lb) 0.4536 kilogram (kg) 

pound per square foot (lb/ft2) 0.04788 kilopascal (kPa) 

pound per cubic foot (lb/ft3) 16.02 kilogram per cubic meter (kg/m3)

square mile (mi2) 2.590 square kilometer (km2)

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 1983 (NAD 83).

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

Water year, as used in this report, refers to the 12-month period October 1 through 

September 30. It is designated by the calendar year in which it ends.

Tables

1. Recurrence intervals and corresponding annual peak streamflow data for 

two gaging stations near the study area ..................................................................................5

2. Statistics from the digital processing and rectification of aerial photographs 

to the 2006 aerial photograph, Madison River below Earthquake Lake, Montana............8

3. Lateral channel movement and annual peak streamflows for the Madison 

River, Montana ............................................................................................................................10

4. Sediment-size characteristics and calculated critical shear stresses for 

materials in and near the Madison River downstream from Earthquake Lake, 

Montana .......................................................................................................................................28

5. Calculated hydraulic characteristics for selected cross sections on the 

Madison River downstream from Earthquake Lake, Montana ...........................................31
vii

Acronyms used in this report:

CD-ROM Compact Disc–Read-Only Memory

EROS U.S. Geological Survey Earth Resources Observation Systems

GNF Gallatin National Forest

GPS global positioning system

MADTAC Madison River Fisheries Technical Advisory Committee

MDT Montana Department of Transportation

NAD 83 North American Datum of 1983

NAIP National Agriculture Imagery Program

NAPP National Aerial Photography Program

NGVD 29 National Geodetic Datum of 1929

NHAP National High Altitude Photography

NRIS Montana Natural Resources Information System

RM reference mark

RMSE root-mean-square error

USDA U.S. Department of Agriculture

USGS U.S. Geological Survey

USACE U.S. Army Corps of Engineers

Symbols and variables used in this report:

+/- Plus or minus

DX Sediment size for which “x” percent of material is finer by weight or by number, 

in mm or ft

R Hydraulic radius of the stream, or the cross-sectional area divided by the wetted 

perimeter, in ft

S Energy slope, in ft/ft

γ Specific weight of water (62.4 lb/ft3)

γs Specific weight of sediment, assumed to be 2.65 times the specific weight of water, 

in lb/ft3

σg Gradation coefficient, equal to the square root of the ratio D84/D16, dimensionless

τc Critical shear stress, in lb/ft2

τ (DX) Critical shear stress for DX , in lb/ft2

τ*c Dimensionless critical shear stress, or Shields parameter 

τo Mean boundary-shear stress, in lb/ft2

Lateral and Vertical Channel Movement and Potential 

for Bed-Material Movement on the Madison River 

Downstream from Earthquake Lake, Montana

By Katherine J. Chase and Peter M. McCarthy

Abstract

The 1959 Hebgen Lake earthquake caused a massive 

landslide (Madison Slide) that dammed the Madison River and 

formed Earthquake Lake. The U.S. Army Corps of Engineers 

excavated a spillway through the Madison Slide to permit outflow from Earthquake Lake. In June 1970, high streamflows 

on the Madison River severely eroded the spillway channel 

and damaged the roadway embankment along U.S. Highway 

287 downstream from the Madison Slide. Investigations 

undertaken following the 1970 flood events concluded that 

substantial erosion through and downstream from the spillway 

could be expected for streamflows greater than 3,500 cubic 

feet per second (ft3/s). Accordingly, the owners of Hebgen 

Dam, upstream from Earthquake Lake, have tried to manage releases from Hebgen Lake to prevent streamflows from 

exceeding 3,500 ft3/s measured at the U.S. Geological Survey 

(USGS) gaging station 0638800 Madison River at Kirby 

Ranch, near Cameron, Montana.

Management of flow releases from Hebgen Lake to 

avoid exceeding the threshold streamflow at USGS gaging 

station 06038800 is difficult, and has been questioned for two 

reasons. First, no road damage was reported downstream from 

the Earthquake Lake outlet in 1993, 1996, and 1997 when 

streamflows exceeded the 3,500-ft3/s threshold. Second, the 

3,500-ft3/s threshold generally precludes releases of higher 

flows that could be beneficial to the blue-ribbon trout fishery 

downstream in the Madison River.

In response to concerns about minimizing streamflow 

downstream from Earthquake Lake and the possible armoring 

of the spillway, the USGS, in cooperation with the Madison 

River Fisheries Technical Advisory Committee (MADTAC; 

Bureau of Land Management; Montana Department of 

Environmental Quality; Montana Fish, Wildlife and Parks; 

PPL-Montana; U.S. Department of Agriculture Forest Service – Gallatin National Forest; and U.S. Fish and Wildlife 

Service), conducted a study to determine movement of the 

Madison River channel downstream from Earthquake Lake 

and to investigate the potential for bed material movement 

along the same reach. The purpose of this report is to present 

information about the lateral and vertical movement of the 

Madison River from 1970 to 2006 for a 1-mile reach downstream from Earthquake Lake and for Raynolds Pass Bridge, 

and to provide an analysis of the potential for bed-material 

movement so that MADTAC can evaluate the applicability of 

the previously determined threshold streamflow for initiation 

of damaging erosion.

As part of this study channel cross sections originally 

surveyed by the USGS in 1971 were resurveyed in 2006. 

Incremental channel-movement distances were determined by 

comparing the stream centerlines from 14 aerial photographs 

taken between 1970 and 2006. Depths of channel incision and 

aggregation were determined by comparing the 2006 and 1971 

cross-section and water-surface data. Particle sizes of bed and 

bank materials were measured in 2006 and 2008 using the 

pebble-count method and sieve analyses. A one-dimensional 

hydraulic-flow model (HEC-RAS) was used to calculate mean 

boundary-shear stresses for various streamflows; these calculated boundary-shear stresses were compared to calculated 

critical-shear stresses for the bed materials to determine the 

potential for bed-material movement.

A comparison of lateral channel movement distances 

with annual peak streamflows shows that streamflows higher 

than the 3,500-ft3/s threshold were followed by lateral channel 

movement except from 1991 to 1992 and possibly from 1996 

to 1997. However, it was not possible to discern whether the 

channel moved gradually or suddenly, or in response to one 

peak flow, to several peak flows, or to sustained flows. The 

channel moved between 2002 and 2005 even when streamflows were less than the threshold streamflow of 3,500 ft3

/s. 

Comparisons of cross sections and aerial photographs 

show that the channel has moved laterally and incised and 

aggraded to varying degrees. The channel has developed 

meander bends and has incised as much as 5–12 feet (ft) 

through the upstream part of the Madison Slide (cross sections 

1400–800). Near cross section 800, the stream has eroded into 

the steep right bank between the stream and the road where fill 

was mechanically placed after 1970. Channel movement also 

was noted downstream from the Madison Slide. 

Near Raynolds Pass Bridge, about 3 miles (mi) downstream from Earthquake Lake, elevations across the channel 
2 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

have changed by -1.4 ft to +1.9 ft, but these changes were 

local in nature and could represent a few rocks or depressions in the bed. Overall, it does not appear that the materials 

eroded from the Madison Slide are causing aggradation in the 

subreach near the Raynolds Pass Bridge.

Comparisons of critical shear stresses to mean boundaryshear stresses indicate that the D50 particle sizes (median size) 

along the right side of the bed between cross sections 400 and 

500 and along the right side of the bed between cross sections 

1300 and 1400 could move at the threshold streamflow. In 

contrast, most of the D84 particle sizes at those two locations 

probably will not move at the threshold streamflow. This lack 

of movement for the larger particles at the threshold streamflow could lead to further armoring of the bed as the D50 and 

smaller-sized particles are removed from the bed and transported downstream. 

The Shields parameter values from 0.04 to 0.08 that were 

used to calculate critical shear stresses could be conservative for a high-gradient stream such as the Madison. A higher, 

less conservative, Shields parameter would result in higher 

critical shear stresses, meaning that higher streamflows would 

be required to move material than those reported herein. In 

addition, because materials in the channel thalweg are exposed 

to higher boundary-shear stresses than the materials along the 

sides of the channel, larger, more erosion-resistant materials 

likely exist in the deeper parts of the channel where high-flow 

depths and velocities prevented sediment sampling. Movement 

of these materials might require higher critical shear stresses 

than estimated in this report. Characterization of sediment 

sizes in the center of the stream and observation of bedmaterial movement for a range of streamflows could provide 

information to help refine the Shields parameter and criticalshear stress estimates for bed materials in the Madison River 

downstream from Earthquake Lake. Furthermore, resurveying 

cross sections and water-surface elevations more frequently 

(either annually or after high streamflows) could better define 

the relation between streamflow and lateral and vertical channel movement. 

Introduction

On August 17, 1959, a severe earthquake, centered near 

the Madison River north of Hebgen Lake, caused a massive 

landslide (Madison Slide; Hadley, 1964). The Madison Slide 

created an earthen dam that impeded the flow of the Madison River and formed Earthquake Lake (locally referred to 

as Quake Lake, fig. 1). The U.S. Army Corps of Engineers 

(USACE) constructed a relatively straight spillway through 

the Madison Slide to permit outflow from Earthquake Lake. 

The Madison River channel through the Madison Slide 

downstream from Earthquake Lake typically is referred to as 

the “spillway;” the channel just downstream from Earthquake 

Lake is referred to as the “Earthquake Lake outlet.” Since 

1959, the channel sinuosity has increased through the spillway. 

Downstream from the Madison Slide (downstream from cross 

section 700, fig. 2), the channel has migrated both to the right 

and to the left across the valley. 

In June 1970, high streamflows in the Madison River 

severely eroded the spillway and damaged the roadway 

embankment along U.S. Highway 287 north of the channel 

(fig. 1). Flooding in 1971 and 1986 caused additional erosion of the spillway channel and roadway embankment. As a 

result of the flooding and erosional damage in 1970 and 1971, 

several studies were undertaken to assess the stability of the 

Madison Slide area and to mitigate future erosional flood 

damage. Based on these studies, the USACE determined that 

streamflows greater than 3,500 cubic feet per second (ft3/s) 

could result in substantial erosion through and downstream 

from the spillway (U.S. Army Corps of Engineers, 1972). 

Therefore, PPL-Montana, the current (2011) owner of Hebgen 

Dam upstream from Earthquake Lake, has tried to manage 

releases from Hebgen Lake to prevent streamflows [as measured at U.S. Geological Survey (USGS) streamflow-gaging 

station (gaging station) 06038800] from exceeding 3,500 ft3/s. 

Management of flow releases from Hebgen Lake to 

prevent streamflows at USGS gaging station 06038800 from 

exceeding the 3,500-ft3/s threshold streamflow is difficult. 

Flooding of Cabin Creek and Beaver Creek, which enter the 

Madison River between Hebgen Lake and the Earthquake 

Lake outlet, can cause streamflows at the outlet and at gaging 

station 06038800 to exceed the 3,500-ft3/s threshold streamflow even when streamflow releases from Hebgen Lake are 

minimal. 

The 3,500-ft3/s threshold streamflow has been questioned 

for two main reasons. First, no road damage was reported 

downstream from the Earthquake Lake outlet in 1993, 1996, 

and 1997 when streamflows exceeded the 3,500-ft3/s threshold. This lack of road damage during relatively high streamflows might indicate that the channel has become armored 

and is no longer as susceptible to erosion as it was in the 

1970s and 1980s. Secondly, the 3,500-ft3/s threshold generally 

precludes releases of higher flows that could be beneficial to 

the blue-ribbon trout fishery downstream in the Madison River 

(Montana Fish, Wildlife and Parks, 2010). 

In response to the concerns about minimizing streamflows downstream from Earthquake Lake and about the 

possible armoring of the spillway, the USGS, in cooperation 

with the Madison River Fisheries Technical Advisory Committee (MADTAC; Bureau of Land Management; Montana 

Department of Environmental Quality; Montana Fish, Wildlife 

and Parks; PPL-Montana;, U.S. Department of Agriculture 

Forest Service – Gallatin National Forest; and U.S. Fish and 

Wildlife Service), conducted a study to determine the lateral 

and vertical channel movement from 1970 to 2006 for an 

approximately 1-mi reach of the Madison River downstream 

from Earthquake Lake. Channel changes at the bridge on 

State Highway 87 (Raynolds Pass Bridge) also were assessed. 

Furthermore, the potential for moving bed material at various 

streamflows was estimated in order to help MADTAC determine whether the threshold streamflow of 3,500 ft3

/s was still 

applicable for the initiation of damaging erosion. 
111°30' 111°24' 

44°48'44°46'44°50'44°52'

MONTANA

EXPLANATION

Study area

U.S. Geological Survey streamflow-gaging  station and number

Earthquake Lake

Madison River

87

Map area

IDAHO MON

Madison

MadisonSlide

Cabin Beaver 

Cr.

River

Madison 

0 1 2 MILES0 1 2 KILOMETERS

Base from U.S. Geological Survey National Elevation Dataset (NED)raster digital data, 2002, 1:24,000; U.S. Geological Survey National Hydrography Dataset (NHD) digital data, 1999, 1:100,000; and U.S. Census Bureau TIGER digital data, 1990, 1:100,000Lambert Conformal Conic projectionStandard parallels 45°00′N, and 49°00′N, central meridian 109°30′W North American Datum of 1983 (NAD 83).

06038800

060

287

287

06038500

Raynolds

Pass

River

06038800

060385

Figure 1. Location of study area.
500

600 400 700

200

300

100 

111°29' 111°28' 111°27' 111°26'

44°49'30"

44°50'

EXPLANATION

Approximate sediment-sample location (sampled in 2008)Approximate pebble-count location (sampled in 2006)

400 Location and number of surveyed cross section

Channel centerline in 2006Survey control point and identifier

RM1

Base from U.S. Geological Survey Digital Raster Graphic, 1988, 1:24,000Lambert Conformal Conic projection Standard parallels 45°00′N, and 49°00′N, central meridian 109°30′WNorth American Datum of 1983 (NAD 83)

Raynolds Pass Bridge

0 0.5 1 MILE0 0.5 1 KILOMETER

10 EAM P10 PY1097 PID PY1097

Eart

ApAp

Figure 2. Location of surveyed cross sections, channel centerline in 2006, approximate locations of sediment samples collected in 2006 and 2008, analong the Madison River downstream from Earthquake Lake, Montana.
Introduction 5

Purpose and Scope

The purpose of this report is to present information about 

the lateral and vertical movement of the Madison River from 

1970 to 2006 for a 1-mi reach downstream from Earthquake 

Lake and for Raynolds Pass Bridge, and to provide an analysis 

of the potential for bed-material movement so that MADTAC 

can evaluate the applicability of the 3,500-ft3/s threshold 

streamflow for initiation of damaging erosion. Survey data 

from 1960, 1971, 1975 and 2006 and aerial photographs from 

1970 through 2006 were used to quantify lateral and vertical 

channel movement. Particle-size data and hydraulic analyses 

were used to estimate the potential for bed-material movement 

at various streamflows. Supplemental particle-size data were 

collected in 2008. 

Also, the report provides one Compact Disc–Read-Only 

Memory (CD–ROM) that includes appendix 1 at the back of 

this report on the inside back cover. This appendix contains 

aerial photographs (figs. A–1 through A–9) with the locations 

of cross sections and centerlines for the Madison River. 

Description of the Study Area

The Madison River flows westerly from Yellowstone 

National Park into Hebgen Lake, where flow releases are controlled by a dam built in 1915. The Madison Slide is located 

about 6 miles (mi) downstream from Hebgen Lake (fig. 1). 

Earthquake Lake is approximately 4 mi long; its inlet is 

located about 2 mi downstream from Hebgen Lake. Between 

Hebgen Dam and Earthquake Lake, Cabin Creek flows into 

the Madison River from the north. Beaver Creek flows into 

Earthquake Lake from the north. The Madison River flows 

westerly 3 mi from Earthquake Lake and then flows northerly. 

Currently (2011) there is no gaging station at the Earthquake Lake outlet. The USGS operates two gaging stations 

on the Madison River near Earthquake Lake (fig. 1): Madison 

River below Hebgen Lake, near Grayling, Mont., (06038500) 

upstream from Earthquake Lake [“upstream gage,” drainage area 905 square miles (mi2

)], and Madison River at 

Kirby Ranch, near Cameron, Mont., (06038800) downstream 

from Earthquake Lake (“downstream gage,” drainage area 

1,065 mi2). The 3,500-ft3/s threshold streamflow is referenced 

to the downstream gage. The drainage area between the 

upstream gage and the Earthquake Lake outlet is about 90 mi2

(U.S. Army Corps of Engineers, 1972). Therefore the drainage area at the Earthquake Lake outlet is about 995 mi2

, and 

is closer to the drainage area at the downstream gage than the 

drainage area at the upstream gage. Thus the streamflows at 

the downstream gage are assumed to be equal to the streamflows through the Madison Slide downstream from Earthquake Lake for this study. On the basis of the flood-frequency 

information for the downstream gage, the 3,500-ft3/s threshold 

streamflow occurs about every 2 to 5 years within the study 

reach (table 1).

Table 1. Recurrence intervals and corresponding annual peak 

streamflow data for two gaging stations near the study area1.

[Upstream gage, U.S. Geological Survey (USGS) streamflow-gaging station 

06038500, Madison River below Hebgen Lake, near Grayling, Mont.; downstream gage, USGS streamflow-gaging station 06038800, Madison River at 

Kirby Ranch, near Cameron, Mont. Abbreviation: ft3/s, cubic feet per second]

Recurrence 

interval 

(years)

Annual peak streamflow 

upstream gage 

(ft3/s)

Annual peak streamflow 

downstream gage 

(ft3/s)

2 2,510 2,910

5 3,160 4,270

10 3,600 5,180

25 4,160 6,320

1

From Parrett and Johnson (2004).

Previous Investigations

In May and September of 1971, Johnson and Omang 

(1972) surveyed water-surface profiles and 14 cross sections 

along the Madison River downstream from Earthquake Lake. 

They compared these profiles with water-surface profiles surveyed by the USACE in 1960 and determined that the channel 

through the Madison Slide had incised by up to 19 feet (ft). 

Johnson and Omang (1972) further concluded that channel through the spillway had incised by about 8 ft during the 

spring and summer runoff events in 1971. 

The USACE conducted hydraulic studies to determine 

the maximum streamflow that could be discharged downstream from Earthquake Lake without substantially eroding 

the spillway or damaging the highway downstream from the 

slide (U.S. Army Corps of Engineers, 1972). The USACE 

report included sediment-size data for the bed and streambanks downstream from Earthquake Lake and analyses of 

velocities and streamflows necessary for bed-material movement. The USACE estimated that flows of about 3,500 ft3

/s 

could erode the steeper parts of the spillway and produce 

downstream deposition, initiate channel movement and bank 

erosion, and potentially damage highway embankments. 

Methods

Surveys of the Madison River Channel

Data from the 1971 survey (Johnson and Omang, 1972) 

were used to determine the approximate locations of the cross 

sections surveyed for this study. For the 1971 survey, each of 

the 14 cross sections was referenced to a hub. Though northing and easting coordinates for each hub could be calculated 

from data in the survey notes, only distance and elevation data 

were available for the surveyed points along each cross section. Locations of the cross sections were estimated using the 

hub locations, 1970 and 1976 aerial photographs, and sketches 
6 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

from the project files. Of the 14 cross sections, 11 were within 

about 1 mi of the Earthquake Lake outlet, and the other 3 were 

approximately 3.5 mi downstream from the outlet near Raynolds Pass Bridge (fig. 2). 

Cross sections were resurveyed as closely as possible to 

the locations of the 1971 cross sections given that the channel 

changed between 1971 and 2006, and the exact coordinates 

and alignment of the 1971 cross sections were unknown. 

Survey-grade global positioning system (GPS) equipment and 

a total station were used to resurvey location and elevation 

data along the 14 cross sections (fig. 2). Cross sections were 

numbered from downstream to upstream. Cross sections 100, 

200, and 300 are near Raynolds Pass Bridge (fig. 2). Cross 

sections 400, 500, and 600 are downstream from the Madison 

Slide, cross section 700 is near the downstream boundary of 

the Madison Slide (end of the spillway), and cross section 

1400 is at the Earthquake Lake outlet. 

Water-surface elevations were surveyed in 2006 along the 

channel from Earthquake Lake outlet to Raynolds Pass Bridge. 

The 2006 water-surface profiles were compared to 1960 and 

1971 water-surface profiles published in Johnson and Omang 

(1972). In addition, survey notes and drawings containing a 

water-surface profile from 1975 were compiled for this study. 

However, because of turbulence and waves, the water-surface 

elevations through the study reach were difficult to survey. 

During the surveys the water-surface elevations at a single 

location on the Madison River were observed to change by at 

least 0.3 ft several times per minute. 

Cross sections and channel features are described using a 

USGS convention in which features are referenced in a downstream view from left to right. For example, the right bank was 

considered to be on the right-hand side of an observer when 

looking downstream.

Flows through most of the study reach were too deep and 

fast to wade. In 1971 and in 2006, survey personnel waded as 

far into the stream as was safe and then estimated the remaining depths of the cross section. In 2006, the survey personnel 

observed that these estimated thalweg elevations probably 

were within -5 to +2 ft of actual thalweg elevations. Only 

cross sections 100, 200, 300 (near the Raynolds Pass Bridge) 

and 1400 (the most upstream cross section) were entirely 

wadeable. 

The elevations and horizontal coordinates for the 2006 

survey were calculated from three reference marks (RMs) 

along the Madison River used for the 1971 survey. One RM 

is a National Geodetic Survey control point (designation 10 

EAM, PID PY1097) near the Raynolds Pass Bridge. The 

USGS established the other two RMs in 1971: steel posts 

on the right bank of the Madison River just downstream 

from Earthquake Lake (RM 1 and RM 2, fig. 2). A report by 

Foundation and Materials Consultants, Inc. (1972) states that 

between 1959 and 1972 the Madison Slide settled 5 ft. After 

1972, settlement could have affected the elevations of the two 

USGS RMs. However, from examination of the settlement 

curve (Foundation and Materials Consultants, Inc., 1972), 

it appears that minimal (less than 1.5 ft) settlement could be 

expected to occur between 1972 and 2006. Given that no other 

reference elevations or data were available to determine post1972 settlement, the USGS RM elevations established in 1972 

were used for this study. For consistency with the 1971 survey 

and other published data, the 2006 survey was referenced to 

the National Geodetic Vertical Datum of 1929 (NGVD 29).

HEC-RAS Analysis

HEC-RAS version 4.0, a one dimensional, hydraulicflow model developed by the U.S. Army Corps of Engineers 

(2008a, b, c), was used to calculate water-surface elevations 

and other hydraulic variables such as cross-sectional width, 

depth, and area, hydraulic radius, energy slope, and mean 

boundary-shear stress at surveyed cross sections 400 through 

1400 for streamflows that ranged from 400 to 6,000 ft3/s. 

HEC-RAS inputs include streamflow, cross-section geometry, 

distances between cross sections, and Manning’s roughness 

coefficients (Henderson, 1966). First, Manning’s roughness 

coefficients (Henderson, 1966) were estimated for each cross 

section based on channel geometry, vegetation, and bed and 

bank particle sizes observed in the field and in photographs. 

Then, these coefficients were incrementally modified until calculated water-surface elevations were reasonably close to surveyed water-surface elevations for the streamflow at the time 

of the survey (1,040 ft3/s; http://waterdata.usgs.gov/mt/nwis). 

The resulting Manning’s roughness coefficients ranged from 

0.055 to 0.110. These relatively high values were considered 

reasonable due to the large boulders in many locations through 

the study reach. Calculated flow depths at the thalweg for the 

streamflow at the time of the survey (1,040 ft3/s) ranged from 

3 to 8 ft. Differences between calculated and observed watersurface elevations were less than 0.9 ft at all cross sections and 

equal to or less than 0.5 ft at 8 of the 11 cross sections. Given 

the difficulty in surveying the fluctuating water surfaces, these 

differences can be considered reasonable. The similarity of 

the water-surface elevations calculated by HEC-RAS to the 

water-surface elevations that were surveyed indicates that the 

calculation errors attributed to the estimated thalweg elevations for the unwadeable portions of the cross sections did not 

substantially affect the study results.

Sediment Sampling

Sediment-size characteristics were determined for 

surficial bed material, large alluvial bars adjacent to low-flow 

channels, and streambanks by the pebble-count method (Wolman, 1954). Sediment-size distributions of the material below 

the bed and bank surfaces were determined by collecting 

sediment samples in 5-gallon buckets and conducting sieve 

analysis of the samples. The D50 (the median size, or particle 

size for which 50 percent of the sample material is finer) was 

determined by weight from the sieve analyses and by number of particles from the pebble counts. The D16, D65, and D84

(particle sizes for which 16, 65, and 84 percent of the sample 
Introduction 7

materials are finer, respectively) were determined in the same 

manner.

Approximate sample locations are shown on figure 2. 

The pebble counts between cross sections 1300 and 1400 and 

between cross sections 400 and 500 were restricted by high 

flow depths and stream velocities to the right portions of the 

bed; these sampled portions extended approximately 25 percent of the distance across the channel. The pebble count 

between cross sections 100 and 300 was restricted to the left 

and right portions of the bed; the sampled portions of these 

sections extended into the channel approximately 25 percent 

of the distance across the channel. No pebble counts were 

conducted along the bed between cross sections 1200 and 600 

due to high flow depths and stream velocities. 

Aerial Photography Analysis

Aerial photographs taken between 1970 and 2006 were 

obtained from several sources (table 2). Aerial photographs 

from the years 1976, 1981, 1984, and 1986 were not available digitally; thus these photographs were scanned. The 

1970–2005 photographs were transformed and rectified to 

match a common projection and datum. The 2006 digital 

orthophotograph was used as the reference to which the earlier 

photographs were rectified. 

Incremental channel-movement distances were determined from a time series of the 14 aerial photographs taken 

between 1970 and 2006 (table 2, appendix 1). On each aerial 

photograph, two stream centerlines were drawn; one centerline 

corresponded to the stream location shown on the photograph 

for that current time period, and the other centerline corresponded to the stream location from the previous time period. 

In the more braided subreaches downstream from the Madison Slide, centerlines were drawn along the dominant flowconveying channel at the date and streamflow corresponding 

to the aerial photograph. At higher streamflows, more than one 

of the braided channels could be inundated, and the differences between the centerlines would not be as dramatic. For 

example, the channel centerline in 1986, shown on figure A–4, 

was drawn along the stream channel closer to the road because 

that channel appeared larger and was judged to be the dominant flow-conveying channel. However at higher flows much 

of the streamflow also could have been flowing through one 

or more of the multiple channels south of that dominant 

flow-conveying channel. The distance between one of those 

multiple channels and the channel centerline in 1984 could 

be shorter than the distance between the channel centerlines 

shown on figure A–4 (depending on which of those multiple 

channels was chosen for measurement).

To assess the potential error in measuring distances 

between points on aerial photos from different years, test 

points were established at features visible on the aerial photographs. Seven or more test points could be located on 11 of the 

14 aerial photographs. Fewer control points were visible on 

the other three aerial photographs because they did not include 

the entire study area and because some of the structures used 

as test points had not yet been built. The root-mean-square 

error (RMSE) was calculated for the easting (X) and the northing (Y) for the collection of test points on each transformed 

aerial photograph by using the equations:

t t RMSE X X = − ( ( Σ X n r

n

( ) ) ) / 2

1

, and (1)

Y Y t t RMSE( ) = − ( ( Σ Y n r

n

) ) / 2

1 (2)

where

RMSE is the root-mean-square-error;

Xt is the easting coordinate for the test point on 

the transformed image, in feet;

n is the number of control points;

Xr is the easting coordinate for the test point on 

the reference image, in feet;

Yt is the northing coordinate for the test point on 

the transformed image, in feet; and 

Yr is the northing coordinate for the test point on 

the reference image, in feet.

RMSEs for the test points ranged from 0.40 to 14 ft 

(table 2). A stationary object on two aerial photographs 

associated with smaller RMSEs would have about the same 

coordinates, but the stationary object might appear to “move” 

between aerial photographs associated with larger RMSEs. To 

account for the potential error in measuring distances between 

channel centerlines from the aerial photographs, lateral 

distances are reported with an accuracy of plus or minus (+/-) 

30 ft. At the narrowest subreach through cross section 1000, 

this potential +/- 30 ft error is almost equal to the width of the 

channel; in other subreaches the error is about 5–30 percent of 

channel width. If the distance measured between centerlines at 

a certain location along the river was less than 30 ft, channel 

movement was reported as zero at that location.

Aerial photographs from the years 1970, 1976, 1984, 

1986, 1992, 1995, 2000, 2005, and 2006 are included in 

appendix 1 (figs. A–1 through A–9). Aerial photographs from 

the years 1980, 1981, 1987, 1990, and 2002 are not included 

in appendix 1 because substantial channel movement was not 

observed from those photographs, except for the 40 ft (+/- 30 

ft) of movement at cross section 700 and movement towards 

the road about 0.25 mi downstream from cross section 400, 

both observed in the 1987 photograph. 
8 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

Lateral and Vertical Channel 

Movement

The Madison River has moved both laterally (lateral 

migration) and vertically (incision and aggradation) since the 

Madison Slide occurred in 1959. The Madison River through 

the spillway has steep longitudinal slopes [up to 0.046 feet 

per feet (ft/ft)] and, therefore, can transport large quantities of 

material from the bed and banks. Because Earthquake Lake 

tends to trap sediment, the spillway is prone to incision and 

lateral migration. Additionally, the channel banks along the 

spillway are extremely high (about 40 ft high in places; fig. 

3) and bank slopes are almost equal to the angle of repose 

for the bank material. As the river undercuts the bank, large 

Table 2. Statistics from the digital processing and rectification of aerial photographs to the 2006 aerial photograph, Madison River 

below Earthquake Lake, Montana.

[Root-mean-square error, deviation between control-point coordinates on each rectified photograph and the control-point coordinates on the 2006 aerial photograph, calculated for the easting (X) and northing (Y) directions. Abbreviations: ft3

/s, cubic feet per sencond; MDT, Montana Department of Transportation; 

GNF, Gallatin National Forest; EROS, U.S. Geological Survey Earth Resources Observation Systems; NHAP, National High Altitude Photography; NRIS, 

Montana Natural Resources Information System; NAIP, National Agriculture Imagery Program; NAPP, National Aerial Photography Program; USDA, U.S. 

Department of Agriculture; USGS, U.S. Geological Survey]

Photgraphy date Source Format Number of 

control points 

Root-mean-square 

error, easting

(feet)

Root-mean-square 

error, northing

(feet)

Daily mean streamflow 

on date of photograph 

(ft3/s)

6/19/1970 MDT1 Digital 1 0.40 2.5 22,820

6/9/1976 GNF3 Paper copy 7 1.3 1.5 21,040

9/4/1980 EROS NHAP4 Digital 8 1.2 2.6 2719

7/20/1981 GNF3 Paper copy 8 5.8 3.1 5999

7/31/1984 GNF3 Paper copy 3 2.4 4.6 51,680

6/12/1986 GNF3 Paper copy 6 14 9.9 53,400

9/6/1987 EROS NAPP6 Digital 10 11 8.0 21,010

9/10/1990 EROS NAPP6 Digital 10 9.6 6.6 5995

7/29/1992 EROS NAPP6 Digital 10 11 7.5 51,010

8/12/1995 EROS NAPP6 Digital 10 2.5 2.6 21,100

9/7/2000 EROS NAPP6 Digital 10 13 8.6 51,080

9/10/2002 EROS NAPP6 Digital 10 13 9.3 5968

8/20/2005 NRIS7 Digital 10 2.8 5.3 51,110

July or August 2006 USDA NAIP8 Digital 10 0 0 91,030–1,690

1

 Steve Barton, Montana Department of Transportation, written commun., 2008.

2

 Streamflow at USGS streamflow-gaging station Madison River below Hebgen Lake, near Grayling, Montana (06038500; http://waterdata.usgs.gov/mt/nwis).

3

 Jackie Riley, Gallatin National Forest, written commun., 2007.

4

 U.S. Geological Survey, 2007b.

5

 Streamflow at USGS streamflow-gaging station Madison River at Kirby Ranch, near Cameron, Montana (06038800; http://waterdata.usgs.gov/mt/nwis).

6

 U.S. Geological Survey, 2007a.

7

 Montana State Library, 2007.

8

 Laurie Temple, U.S. Geological Survey, written commun., 2008.

9

 Range of streamflows at USGS streamflow-gaging station Madison River at Kirby Ranch, near Cameron, Montana (06038800) for July 1, 2006, to 

August 31, 2006 (http://waterdata.usgs.gov/mt/nwis).

amounts of material are deposited into the channel, further 

contributing to channel instability. In contrast, the longitudinal 

slopes downstream from the spillway are not as steep (about 

0.014 ft/ft). Consequently, much of the material removed from 

the spillway can be deposited downstream, which can lead to 

channel aggradation, widening, and braiding downstream from 

the Madison Slide. 

In this section, lateral movement measured from the timeseries of aerial photographs is discussed. A positive value indicates lateral movement toward the right bank, and a negative 

value indicates lateral movement toward the left bank. Then, 

vertical movement measured and estimated from the channel 

surveys is discussed. Finally, a synopsis of lateral and vertical 

movement on a reach-by-reach basis is presented.
Flow direction

Figure 3. Madison River downstream from Earthquake Lake, 

Montana, looking downstream from right bank at cross section 

1100.

Lateral and Vertical Channel Movement 9

Lateral Movement

Lateral movement (migration) of the Madison River 

channel near the Madison Slide was observed when embankments along U.S. Highway 287 were eroded in 1970. In the 

aerial photograph taken after the highway embankments were 

eroded (fig. A–1), U.S. Highway 287 is washed out from about 

0.05 mi downstream from cross section 600 to about 0.25 mi 

downstream from cross section 400. Also in figure A–1, a 

steep cutbank is apparent above the right bank, just south of 

the road near cross section 800, indicating that the road near 

cross section 800 almost washed out as well. 

Between 1970 and 1976, the aerial photographs show 

channel migration as well as fill placed along the channel. 

Figure A–2 shows that fill was mechanically placed at the 

steep cutbank on the right bank above cross section 800, and 

the channel shifted to the left away from the road. Fill also 

was placed between the channel and the road near cross section 600. Meanders of the main channel near cross sections 

700 and 600 appear to have increased in amplitude and moved 

upstream about 100 ft. The channel generally migrated to the 

left away from the road from cross section 500 downstream 

to cross section 400 (fig. A–2, table 3). A new meander in the 

main channel formed about one-half mile downstream from 

cross section 400 towards the road. 

Lateral migration between 1976 and 1986 is shown on 

figures A–3 and A–4. Between 1976 and 1984, the distances 

measured between the centerlines on the aerial photographs 

(fig. A–3) that were less than the potential rectification error 

(+/-30 ft) are reported as zero in table 3. Between 1984 and 

1986 the river eroded the right bank at cross section 1200 and 

into the left bank at cross section 1100, forming new meander 

bends (fig. A–4, table 3). Comparison of photographs of the 

stream channel upstream from cross section 1100 shows this 

movement to the left (fig. 4). Because the left bank at cross 

section 1100 is high and steep (figs. 3 and 4), large amounts of 

sand, gravel, cobbles, and boulders probably entered the channel and were deposited downstream. Also between 1984 and 

1986, the river eroded into the mechanically placed fill on the 

right bank near cross section 800 (figs. A–4, fig. 5, table 3). 

Between 1984 and 1986, channel movement was more 

substantial downstream from the spillway (fig. A–4, table 3). 

The channel shifted toward the right bank (toward the road) 

downstream from cross section 600. The dead trees in the 

channel downstream from cross section 600 (fig. 6) likely 

grew prior to this 1984–1986 time period, before the channel shifted towards the right bank. The channel moved about 

370 ft (+/- 30 ft) into the right bank between cross sections 

500 and 400 (table 3), damaging the road. 

Lateral migration distances between 1986 and 1992, 

measured between the centerlines in the aerial photographs 

(fig. A–5) were often less than the potential rectification error 

(+/-30 ft) and are reported as zero (table 3). The river generally eroded farther into the right bank downstream from cross 

section 800 (fig. A–5), but this movement occurred between 

cross sections 800 and 700 (not reported in table 3). 

In the 13 years between 1992 and 2005, the Madison 

River channel continued to display considerable mobility. 

First, between 1992 and 1995, the channel shifted into the 

left bank at cross sections 1100, 900, 500, and 400 (fig. A–6, 

table 3). About 0.5 mi downstream from cross section 400, the 

channel moved approximately 530 ft (+/- 30 ft) into the right 

bank, closer to the road (fig. A–6). Then, between 1995 and 

2000, the river moved into the left bank at cross section 400, 

and moved back to the right (towards the road) downstream 

from cross section 400 (table 3, fig. A–7). Between 2000 and 

2005, the channel shifted into the left bank through much 

of the spillway (table 3; fig. A–8). Erosion into the left bank 

upstream from cross section 800 can be seen from the differences in the 1971 and 2006 photographs (fig. 7). Last, between 

2005 and 2006, no changes were determined from the centerlines in the aerial photographs (table 3). 

Centerlines of the Madison River from all of the aerial 

photographs (A–1 through A–8) are shown on the 2006 aerial 

photograph in figure A–9. The maximum lateral migration 

distances of the channel since 1970 (the maximum distances 

between the centerlines from all of the aerial photographs) 

were 560 ft at the downstream end of the study reach, 370 ft 

downstream from the spillway between cross sections 400 

and 500, and 150 ft near the upstream end of the spillway near 

cross section 1100 (all distances are +/- 30 ft). This maximum 

lateral migration is less than the sum of incremental lateral 

migration measured from the aerial photographs because the 

channel did not migrate continuously in one direction throughout this period (1970–2006).
Table 3. Lateral channel movement and annual peak streamflows1 for the Madison River, Montana. [Negative value (-) indicates movement to the left bank (south), positive value indicates movement to the right bank (north). Abbreviations: +/-, plus or minus; ft, feet; USGS, Ucubic feet per second. Symbol: -- data not available or not applicable] Water year Date of photo- graphy Channel movement (+/-30 feet) at or between indicated cross sections, between indicated date and date of previous aerial photograph (ft) Annu

USGS st

Earth- quake Lake outlet Spillway Downstream from spillway Madison River 

Hebgen Lake, 

Grayling, Mo

(06038500

Cross section 1400 Cross section 1300 Cross section 1200 Cross section 1100 Cross section 1000 Cross section 900 Cross section 800 Cross section 700 Cross section 600 Between cross sections 600 and 500 Cross section 500 Between cross sections 500 and 400 Cross section 400 Date of streamflow St

1959 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 8/17/1959 101960 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- 1961 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 7/5/1961 11962 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/22/1961 21963 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/6/1963 21964 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/19/1964 21965 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/29/1965 21966 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/15/1965 21967 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/4/1966 21968 -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- 1969 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 5/28/1969 21970 6/19/1970 -- -- -- -- -- -- -- -- -- -- -- -- -- 6/10/1970 51971 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/28/1971 31972 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 9/21/1972 31973 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/18/1972 21974 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/25/1974 21975 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 10/13/1974 21976 6/9/1976 -- -- -- -- -- -- -56 70 75 -83 -123 -130 -93 10/21/1975 21977 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 10/12/1976 21978 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 3/15/1978 21979 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 10/9/1978 11980 9/4/1980 0 0 0 0 0 0 0 0 0 0 0 0 0 7/3/1980 11981 7/20/1981 0 0 0 0 0 0 0 0 0 0 0 0 0 6/10/1981 21982 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/28/1982 21983 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/19/1982 21984 7/31/1984 0 0 0 0 0 0 -46 0 0 44 0 0 0 11/14/1983 21985 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/21/1984 2
Water 

year

Date of 

photography

Channel movement (+/-30 feet) at or between indicated cross sections, between indicated date and date of previous 

aerial photograph (ft)

Annu

USGS st

Earthquake 

Lake 

outlet

Spillway Downstream from spillway

Madison River 

Hebgen Lake, 

Grayling, Mo

(06038500

Cross 

section 

1400 

Cross 

section 

1300 

Cross 

section 

1200

Cross 

section 

1100

Cross 

section 

1000

Cross 

section 

900

Cross 

section 

800

Cross 

section 

700

Cross 

section 

600

Between 

cross 

sections 

600 and 

500

Cross 

section 

500

Between 

cross 

sections 

500 and 

400

Cross 

section 

400

Date of 

streamflow

St

1986 6/12/1986 0 0 52 -71 68 56 52 0 47 330 110 370 200 6/5/1986 31987 9/6/1987 0 0 0 0 0 0 0 40 0 0 0 0 0 11/8/1986 11988 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 8/5/1988 11989 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 12/13/1988 21990 9/10/1990 0 0 0 0 0 0 0 0 0 0 0 0 0 11/14/1989 21991 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/8/1991 21992 7/29/1992 0 0 0 0 0 0 0 0 0 0 0 0 0 11/18/1991 11993 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 5/27/1993 31994 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 11/3/1993 21995 8/12/1995 0 0 0 -38 0 -42 0 0 73 0 -76 -150 -40 6/11/1995 21996 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/7/1996 31997 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/12/1997 31998 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/27/1998 21999 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 6/13/1999 22000 9/7/2000 0 0 0 0 0 0 0 0 0 94 0 63 -150 5/26/2000 12001 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 7/9/2001 12002 9/10/2002 0 0 0 0 0 0 0 0 0 0 0 0 0 7/16/2002 12003 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 7/21/2003 12004 -- -- -- -- -- -- -- -- -- -- -- -- -- -- 7/7/2004 12005 1/1/2005 0 0 -60 -73 0 -52 -55 0 0 0 0 65 0 6/15/2005 22006 1/1/2006 0 0 0 0 0 0 0 0 0 0 0 0 0 5/25/2006 2

1 From U.S. Geological Survey (2008).

Table 3. Lateral channel movement and annual peak streamflows for the Madison River, Montana.—Continued[Negative value (-) indicates movement to the left bank (south), positive value indicates movement to the right bank (north). Abbreviations: +/-, plus or minus; ft, feet; USGS, Ucubic feet per second. Symbol: -- data not available or not applicable]
Flow direction

Flow direction

A

B

Figure 4. Madison River downstream from Earthquake Lake, Montana. A, Looking upstream from cross 

section 1100, September 1971 [streamflow 400 cubic feet per second at Madison River below Hebgen Lake, 

near Grayling, Montana (06038500)]. B, Looking upstream from farther downstream and slightly south when 

compared to photograph A, September 2008 [streamflow 3,650 cubic feet per second at Madison River at 

Kirby Ranch near Cameron, Montana (06038800)].

12 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana
Flow direction

Flow

direction

Right bank eroded between 1971 

and 2006

A

B

Figure 5. Madison River downstream 

from Earthquake Lake, Montana, looking 

downstream at cross section 800. 

A, September 1971, [streamflow 400 cubic 

feet per second at Madison River below 

Hebgen Lake, near Grayling, Montana 

(06038500)]. B, June 2006, [streamflow 

1,040 cubic feet per second at Madison River 

at Kirby Ranch near Cameron, Montana 

(06038800)].

Lateral and Vertical Channel Movement 13
Flow direction

Figure 6. Madison River downstream from Earthquake Lake, Montana, looking downstream at cross section 600.

14 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

Lateral channel-movement and peak-flow data are shown 

in figure 8. Where more than one year lapsed between aerial 

photographs, it is not possible to discern whether the channel 

moved gradually or all in one year. It also is unclear whether 

the channel moved in response to one peak flow, to several 

peak flows, or to sustained flows. 

Due to the narrow valley through the Madison Slide 

and the steep, high banks, the channel generally has laterally moved less through the spillway (fig. 8, cross sections 

1400–700) than downstream from the spillway (fig. 8, cross 

sections 600–400). In addition, channel movement from about 

cross section 800 to cross section 700 (fig. 8) was less than 

the other portions of the spillway (cross section 1400–900) 

in 1986, 1995, and 2000. Movement from about cross section 800 to cross section 700 was less than the other spillway 

locations except for cross section 1100 in 2005. This subreach 

from about cross section 800 to cross section 700 is locally 

known as the “knickpoint.” A knickpoint is an abrupt drop-off, 

or increase in the longitudinal slope.

Data in figure 8 indicate that streamflows higher than 

the 3,500-ft3/s threshold were followed by lateral channel 

movement except from 1991 to 1992 and possibly from 1996 

to 1997. Flows exceeded the threshold in 1996 and 1997, 

but no aerial photographs were available between 1995 and 

2000; thus, aerial photography data from which to determine 

channel movement between the 1996 and 1997 high flows 

were unavailable. However, the stream moved laterally 120 

to 150 ft between cross sections 500 and 600 during the 

relatively high streamflows in 1996 (Brent Mabbott, PPLMontana, written commun., 2010). Moreover, the channel 

moved between 2002 and 2005 even though streamflows during that period were less than the 3,500-ft3

/s threshold streamflow (fig. 8).
Rock outcrop

A

B

Flow

direction

Flow

direction

Approximate south edge of channel in 2006

Figure 7. Madison River downstream 

from Earthquake Lake, Montana, upstream 

from cross section 800. A, September 1971 

[streamflow 400 cubic feet per second 

at Madison River Hebgen Lake, near 

Grayling, Montana (06038500)]. B, June 2006 

[streamflow 1,040 cubic feet per second 

at Madison River at Kirby Ranch near 

Cameron, Montana (06038800)].

Lateral and Vertical Channel Movement 15
Annual peak flow at upstream gage—Madison River below 

 Hebgen Lake, near Grayling, Montana (06038500)

Annual peak flow at downstream gage—Madison River at 

 Kirby Ranch, near Cameron, Montana (06038800)

Channel movement (plus or minus 30 feet) 

3,500-ft3/s threshold streamflow

400

ANNUAL PEAK STREAMFLOW, IN CUBIC FEET PER SECOND (ft3/s)

0

2,000

1,000

4,000

6,000

8,000

10,000

3,000

5,000

7,000

9,000

11,000

12,000

DISTANCE CHANNEL MOVED BETWEEN INDICATED DATE AND DATE OF PREVIOUS AERIAL PHOTOGRAPH, IN FEET

100

0

200

300

WATER YEAR

1960 1970 1980 1990 2000

No data from 1976 aerial 

photograph are available for 

cross sections 900–1400

Cross section 1200 

Cross section 1100

Cross section 1000

Cross section 900

Cross section 800

Cross section 700

Cross section 600

Between sections 600 and 500

Cross section 500

Between cross sections 500 and 400

Cross section 400

First aerial photograph 

dated June 1970

EXPLANATION

Figure 8. Lateral channel movement for selected sites along the Madison River and annual peak streamflow for the Madison River, 

Montana.

16 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana
Lateral and Vertical Channel Movement 17

Vertical Movement by Channel Incision and 

Aggradation

Between 1971 and 2006, the Madison River channel has 

aggraded and incised to varying degrees throughout the study 

area. Incision and aggradation are reflected in changes in thalweg and water-surface elevations. 

Thalweg Elevations

Using survey notes from 1971 and survey data from 

2006, the vertical changes in the channel thalweg can be 

determined by constructing longitudinal profiles from thalwegelevation data for each cross section (fig. 9). As discussed 

in the section “Study Methods,” the 1971 and 2006 thalweg 

elevations were measured at cross section 1400, but thalweg 

elevations for cross sections 1300–400 were estimated in the 

field. The estimated 2006 thalweg elevations were checked for 

reasonableness by using HEC-RAS calculations. 

At the Earthquake Lake outlet (cross section 1400), the 

channel incised by about 4–5 ft. In addition, a knickpoint 

between cross sections 1000 and 900 that was present in the 

surveyed 1971 thalweg profile was smaller or no longer present in the surveyed 2006 thalweg profile (fig. 9). Foundation 

and Materials Consultants, Inc. (1972) reported that a “massive piece of rock” near cross section 1000 provided resistance 

to erosion. This rock might have moved downstream, or the 

channel could have moved to the side of the rock, causing the 

channel thalweg to lower by about 12 ft at cross section 1000. 

The estimated thalweg surveyed in 2006 at cross section 700 appears to be about 7 ft higher than the thalweg 

estimated during the survey in 1971. This aggradation at 

cross section 700, combined with incision at cross section 

600 (fig. 9), has resulted in a steeper thalweg slope between 

these two cross sections. Between cross sections 800 and 600, 

the Madison River channel is narrower and the water moves 

faster. The channel (about 300 ft upstream from cross section 700) generally has not moved laterally compared to the 

subreaches downstream and upstream (fig. A–9). The materials lining the channel bottom and sides of this subreach are 

larger and more resistant to erosion than the channel materials 

upstream and downstream. Car-sized boulders near cross section 700 were observed (fig.10) in 1971, 2006 and, 2008; these 

large boulders are depicted on the bed and banks in figure 10B. 

Erosion-resistant materials also are visible high above the river 

on each side of the channel. Hadley (1964) and U.S. Army 

Corps of Engineers (1972) describe a large dolomite outcrop 

or buttress between cross sections 700 and 800 high on the left 

bank (fig. 10A and 10B). The two reports also describe a 30-ft 

boulder that was deposited by the Madison Slide on the right 

bank, about 700 ft from the channel (fig. 10C). The subreach 

just downstream from cross section 700 to cross section 600 

has been described as a “pivot point” where incision stops and 

deposition begins (Foundation and Materials Consultants, Inc., 

1972).

At the downstream end of the study reach near cross 

section 400, the 2006 thalweg elevation is slightly higher than 

the 1971 thalweg elevation (fig. 9). The channel has migrated 

substantially between cross sections 600 and 400 (as discussed 

in the section “Lateral Movement”). 

Some of the decreases in thalweg elevations after 1971 

could have been due to settlement of the Madison Slide 

material. Foundation and Materials Consultants, Inc. (1972) 

states that the Madison Slide material settled an average of 

5 ft between 1959 and 1972. However, the settlement curve 

in the 1972 report projects that settling after 1972 would be 

much less than settling before 1972. Based on these data, 

and because no other information regarding Madison Slide 

settlement was available, settling of the materials after 1972 is 

assumed to be negligible for this study.

Water-Surface Elevations

Water-surface elevations are easier to survey than thalweg elevations in rivers like the Madison that are difficult to 

wade due to large depths and velocities. The water-surface 

profiles constructed from water-surface elevations surveyed 

along the Madison River in 1971 and 2006 include many 

more surveyed points than the 11 thalweg points from the 

cross-section surveys. Other water-surface profiles are available from Johnson and Omang (1972) and from project files. 

These water-surface profiles provide some information about 

channel changes from 1960–2006. However, water-surface 

profiles from different dates are difficult to compare because 

water-surface elevations change with streamflow and with the 

geometry of the channel. 

Accordingly, the water-surface profiles from the 1971 and 

2006 data are difficult to compare because streamflows were 

different during the two surveys (400 ft3/s at the upstream gage 

in 1971; 1,040 ft3/s at the downstream gage in 2006). Therefore, a water-surface profile was computed using HEC-RAS to 

represent water-surface elevations (referred to as the calculated 2006 water-surface profile in this report) for a streamflow 

of 400 ft3/s through the study reach for channel conditions in 

2006 (fig. 11). 

The water-surface elevation of the lake has decreased 

along with the elevation of the thalweg at the outlet since 

1971. The lake water-surface elevation in 1971 was 6,387.5 ft 

(above NGVD 29) when streamflow at the upstream gage was 

400 ft3/s (Johnson and Omang, 1972). At cross section 1400 

(the outlet of Earthquake Lake), the calculated water-surface 

elevation for the 400 ft3/s streamflow in 2006 was 6,382.0 ft 

(above NGVD 29), indicating that the water surface of the 

lake (when Earthquake Lake outlet flows are 400 ft3/s) has 

decreased by 5.5 ft since 1971 because of channel incision at 

the Earthquake Lake outlet. 

Comparisons of the water-surface profiles surveyed in 

1960 and 1971 and the calculated 2006 water-surface profile 

indicate that the upper 2,500 ft of the study reach experienced 

the largest decrease in water-surface elevations since 1960, 

and the upper 1,500 ft of the study reach experienced the 
500

600

700

800

900

1000

1100

1300

1400

6,2206,2406,2606,2806,3006,3206,3406,3606,3806,4006,4206,440

0 500 1,000 1,500 2,000 2,500 3,000 3,500 4,000 4,500 5,000 5,500 

ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929 (NGVD 29), IN FEET

DISTANCE DOWNSTREAM FROM EARTHQUAKE LAKE OUTLET, IN FEET

Possible 2006 knickpoint,or oversteepened reach 

Approximate extent of Madison Slide 1971 knickpoint no longer 

apparent in 2006 thalweg 

1200

Spillway crest 

Knickpoint subreach

1971 estimate2006 estimate1971 calculate for 3,500 cu through the 2006 calculate for 3,500 cu through the Cross-section 

500

EXPLANATI

Figure 9. Estimated thalweg profiles and calculated width/depth ratios of the Madison River downstream from Earthquake Lake, Montana.
Dolomite outcrop above left (south) 

bank of Madison River

A

B

C

Large dolomite boulders on streambed and

banks

Flow direction

Figure 10. Erosion-resistant materials 

above the Madison River, downstream from 

Earthquake Lake, Montana. A, Dolomite 

outcrop above left bank of Madison River 

between cross sections 700 and 800, looking 

south from above road, August, 1959. 

B, Portion of same outcrop looking southwest 

from right bank of river, June, 2008. C, Large 

boulder above right bank between cross 

sections 700 and 800, September 1959.

Lateral and Vertical Channel Movement 19
6,2806,3006,3206,3406,3606,3806,2906,3106,3306,3506,3706,3906,400

0 500 1,000 1,500 2,000 2,500 3,000 

DISTANCE DOWNSTREAM FROM EARTHQUAKE LAKE OUTLET, IN FEET

1971 and 1975 knickpoint in water surface no longer apparent in 2006 

800

900

1000

1100

1200

1300

1400

A

No data for 2006 water-surface profil

ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929 (NGVD 29), IN FEET 1960 surveyed water surface for 690 cubic feet per second (ft3/s) at the Earthquake Lake outlet (Johnson and Omang, 1972) 1971 surveyed water surface for 400 ft3/s measured at streamflow-gaging station 06038500, Madison River below Hebgen Lake, near Grayling, Mont. (upstream gage) 1971 estimated thalweg 1975 surveyed water surface for 1,230 ft3/s measured at upstream gage 2006 surveyed water surface with streamflow of 1,040 ft3/s measured at streamflow-gaging station 06038800, Madison River at Kirby Ranch near Cameron, Mont. (downstream gage)

Calculated water surface for 400 ft3/s through the study reach for 

 2006 channel conditions2006 estimated thalweg profile

800 Cross-section number

Knickpoint subreach

Small knickpoints in 2006 surveyed water surface

EXPLANATION

Figure 11. Surveyed water-surface profiles, calculated water-surface profile, and estimated thalweg profiles of the Madison River dEarthquake Lake, Montana. A, Profiles from cross section 1400 to cross section 700. 

B, Profiles from cross section 700 to cross sectio
500

600

700

6,2206,2306,2406,2506,2606,2806,2706,2906,300

6,310

3,000 3,500 4,000 4,500 5,000 5,500 6,000 

ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929 (NGVD 29), IN FEET

DISTANCE DOWNSTREAM FROM EARTHQUAKE LAKE OUTLET, IN FEET

400

Knickpoints in 1971 water-surface profile either not apparent in 2006 profile, or much smaller in 2006 profile 

B

Approximate extent of Madison Slide 1960 surveyed water surface for 690 cubic feet per second (ft3/s) at the Earthquake Lake outlet (Johnson and Omang, 1972)

1971 surveyed water surface for 400 ft3/s measured at 

 streamflow-gaging station 06038500, Madison River below  Hebgen Lake, near Grayling, Mont. (upstream gage)1971 estimated thalweg1975 surveyed water surface for 1,230 ft3/s measured at upstream ga

2006 surveyed water surface with streamflow of 1,040 ft3/s measure

 streamflow-gaging station 06038800, Madison River at Kirby Ranch  near Cameron, Mont. (downstream gage)Calculated water surface for 400 ft3/s through the study reach for 

 2006 channel conditions2006 estimated thalweg profile

600 Cross-section number

EXPLANATION

Figure 11. Surveyed water-surface profiles, calculated water-surface profile, and estimated thalweg profiles of the Madison River downstream from Earthquake Lake, Montana. 

A, Profiles from cross section 1400 to cross section 700. 

B, Profiles from cross section 7

cross section 400.—Continued
22 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

largest decrease since 1971 (fig. 11). The water-surface elevation at cross section 1100 decreased by about 20 ft between 

1960 and 2006. Most of this change occurred between 1960 

and 1971; however, at cross section 1100 the water surface 

elevation decreased as much as 8 ft between 1975 and 2006. 

The 1971 and 1975 water-surface profiles show a knickpoint downstream from cross section 1000. This knickpoint 

was not apparent in the surveyed 2006 water-surface profile, 

possibly due to the undercutting of one or more large boulders 

since the 1971 survey as discussed in the section on “Thalweg 

Elevations.” Instead, smaller knickpoints are evident in the 

surveyed 2006 water-surface profile between cross sections 

1300 and 1200 and between 1100 and 1000 (fig. 11). 

Farther downstream, water-surface elevations decreased 

very little through the knickpoint subreach downstream from 

cross section 800 to cross section 700, where water surfaces 

differ by less than 2.5 ft from 1971 through 2006 (fig. 11A). 

As discussed in the section “Lateral Movement,” the channel 

moved very little laterally through this subreach as well. However, for a short subreach near cross section 700, the calculated 2006 water-surface elevations are slightly higher than the 

1971 water-surface elevations. This change corresponds to the 

aggradation in the same location between 1971 and 2006 as 

discussed in the section “Thalweg Elevations.” 

At cross section 600 (fig. 11B), the calculated 2006 

water-surface elevation is more than 8 ft lower than the surveyed 1971 water-surface elevation. The surveyed 2006 watersurface elevation (streamflow of 1,040 ft3

/s at the downstream 

gage) is almost 6 ft lower than the surveyed 1975 watersurface elevation (streamflow of 1,230 ft3

/s at the upstream 

gage). These comparisons indicate that much of the decrease 

in water surfaces at this location occurred after 1975. 

Between cross section 600 and cross section 500, the 

surveyed 1971 water-surface elevation and the calculated 

2006 water-surface elevations differences ranged from about 

5 to 8 ft. For this same subreach the differences between the 

surveyed 1975 water-surface elevation and the surveyed 2006 

water surface elevation ranged from about 1 to 3 ft, indicating that most of the decrease in water surfaces in the reach 

between cross sections 600 and 500 occurred before 1975. 

Downstream from cross section 500, the surveyed 1971 

water-surface elevations become closer to the calculated 2006 

water-surface elevations, and the surveyed 1975 water-surface 

elevations become closer to the surveyed 2006 water-surface 

elevations, indicating that less incision occurred through 

this part of the channel. Some aggradation is apparent just 

upstream from cross sections 400, where the calculated 2006 

water-surface elevations are slightly higher than the surveyed 

1971 water-surface elevations.

Lateral and Vertical Movement by Channel 

Subreach

The lateral and vertical channel movement at Madison 

River subreaches between 1971 and 2006 can be determined 

from the cross sections in figure 12 and from the width/

depth ratios (calculated for a 3,500-ft3/s streamflow through 

the study reach) in figure 9. Changes in width/depth ratios 

integrate both vertical and lateral channel movement. For 

example, an increased width/depth ratio indicates a channel 

that is widening and/or getting shallower and a decreased 

width/depth ratio indicates a channel that is narrowing and/or 

becoming deeper. 

Subreach Between Cross Sections 1400 and 900

In this subreach that extends from the outlet of Earthquake Lake through the upper one-third of the spillway, 

between 1971 and 2006 the Madison River (generally) eroded 

into the left and right banks and incised (fig. 4, fig. 12, and 

appendix 1). The channel shifted left at cross section 1300, 

right at cross section 1200, left at cross section 1100, and 

right again at 1000. Large amounts of bank material probably 

collapsed into the channel and likely were transported downstream. Instead of aggrading, the channel incised about 5 ft at 

cross section 1400, 4 ft at cross section 1300, 2 ft at cross section 1200, 4 ft at cross section 1100, and 12 ft at cross section 

1000 (figs. 9, 11, and 12). 

The channel shape (fig. 12) and width/depth ratios 

(fig. 9) are fairly similar for cross sections 1400 through 1200, 

and had changed little between 1971 and 2006. However, 

the width/depth ratio at cross section 1100 (figs. 4 and 9) 

increased more than 300 percent between 1971 and 2006 and 

also is larger than the width/depth ratios at cross sections 1200 

and 1000. This increase is a result of the channel eroding into 

the left and right banks, (figs. 4, 12, A–4, A–6, and A–8). 

The knickpoint in the 1971 thalweg profile between cross 

sections 1000 and 900 is not apparent in the 2006 thalweg profile (figs. 9 and 11). The large knickpoint in the water-surface 

profile that was surveyed in 1971 at close to the same location 

as the thalweg knickpoint (fig. 11) is not apparent in the surveyed 2006 water-surface profile. Instead, smaller knickpoints 

are evident in the surveyed 2006 water-surface profile between 

cross sections 1300 and 1200 and between 1100 and 1000. 

Subreach Between Cross Sections 900 and 600

In this subreach that extends from the middle of the spillway to just downstream from the Madison Slide, less lateral 

and vertical movement was detected between 1971 and 2006 

than in the upstream and downstream subreaches. The channel 

has shifted into the right bank (figs. 12 and A–9). The channel 

aggraded at cross section 700 but incised at cross section 600, 

resulting in a flatter thalweg slope between cross sections 800 

and 700 and a steeper thalweg slope between cross sections 
Potential for Bed-Material Movement 23

700 and 600 (fig. 9). Additionally, the width/depth ratios 

increased by 5–10 ft/ft at cross sections 900, 700, and 600 but 

did not change at cross section 800, even though the channel 

at cross section 800 shifted into the right bank between 1971 

and 2006 (figs. 5 and 12). Along the knickpoint portion of the 

subreach, generally from cross section 800 to cross section 

700, the channel has moved very little laterally or vertically, 

perhaps because of large, erosion-resistant rocks in that area as 

discussed in the “Thalweg Elevations” section. 

Subreach Between Cross Sections 600 and 400

In this subreach that begins just below the spillway, the 

channel moved considerably laterally and vertically at cross 

sections 600 and 500, as the river deposited large amounts of 

material into the channel, eroded into the right bank, and then 

incised into a new channel, ultimately lowering the thalweg 

(figs. 9, 12, and A–9). At cross section 400, the river deposited 

material into the right side of the 1971 channel and currently 

(2006) occupies the left side of the 1971 channel, slightly raising the thalweg. 

The channel downstream from the spillway has higher 

width/depth ratios than the upstream channel (fig. 9). By 

2006, the width/depth ratios at cross sections 500 and 400 

had decreased by about 30 to 50 ft/ft since 1971 (fig. 9). At 

these cross sections, the channel seems to be changing from 

a braided channel to a single meandering channel (fig. 12). 

However, this subreach could again become more braided if 

large amounts of material are eroded from the steep upstream 

streambanks and deposited through this area.

Vertical Channel Changes near Raynolds Pass 

Bridge

Three cross sections near Raynolds Pass Bridge about 

3 mi downstream from Earthquake Lake (fig. 2) were surveyed in 1971 and then resurveyed in 2006 to determine if 

materials eroded from the spillway were being deposited near 

the bridge. Comparison of the cross sections from the two 

surveys (1971 and 2006) indicates that the channel was as 

much as 1.4 ft lower in some parts of cross sections 100 and 

200 downstream from the bridge in 1971 than 2006 (fig. 13). 

Additionally, the channel at one location in cross section 300 

was as much as 1.9 ft higher in the 2006 cross section compared to the 1971 cross section. These differences between 

the two surveys were local and could represent a few rocks 

or depressions in the bed. Also at cross section 300, the right 

bank was about 5 ft lower in the 2006 survey than the 1971 

survey. This difference between the right bank elevations from 

the 1971 and 2006 surveys could be due to erosion along the 

right bank just downstream from the bridge or due to the two 

surveys being in slightly different locations. Overall, it does 

not appear that materials eroded from the spillway are causing 

aggradation in this subreach.

Limitations of the Estimates of Lateral and 

Vertical Channel Movement

Channel movement was determined from aerial photographs and sparse survey data. A relation between streamflow 

and channel movement is difficult to determine because more 

than a year passed between most of the aerial photographs and 

more than 30 years passed between the most recent surveys. 

Resurveying cross sections and water-surface elevations more 

frequently (either annually or after high streamflows) could 

better define the relation between streamflow and lateral and 

vertical channel movement.

Potential for Bed-Material Movement

The ability of a river to move its bed material is a function of streamflow, energy slope, flow depth, and bed-material 

characteristics (Shields, 1936). To estimate the potential for 

bed-material movement for selected streamflows along the 

Madison River, materials from in and near the channel were 

measured and shear stresses for selected streamflows were 

calculated. Though several streamflows were analyzed, only 

the 3,500-ft3/s threshold streamflow is discussed in detail.

Characteristics of Materials In and Near the 

Madison River Channel

Hadley (1964) observed that most of the surface of the 

Madison Slide consisted of angular blocks of gneiss, schist, 

and dolomite. The gneiss fragments were 6 to 60 inches (in.) 

long, and the schist fragments were 1 to 12 in. long. Beneath 

the top few feet of the Madison Slide debris, smaller rock 

fragments, as well as sand-, silt-, and clay-sized material 

were present when the USACE excavated the spillway. The 

Madison Slide debris was estimated to be up to 220 ft deep 

between cross sections 700 and 800 (fig. 2) and was estimated 

to thin gradually at the upstream and downstream boundaries 

of the Madison Slide (Hadley, 1964). A drill log showed that 

boulders and cobbles existed down to at least the base of the 

drill hole (50 ft below the surface) on the right bank between 

cross sections 800 and 900 (Foundation and Materials Consultants, Inc., 1972). The right bank is about 50 ft above the bed 

in this subreach; thus, the base of the drill hole probably was 

at or slightly above the elevation of the thalweg.

Data for particle sizes measured in and near the channel 

in 2006 and 2008, as well as particle sizes measured by the 

USACE in 1959 and in 1970 (U.S. Army Corps of Engineers, 

1972), are summarized in table 4 and figure 14. The D50 for all 

of the measurements (not including the rough visual estimate 

for the subreach between cross sections 700 and 800) ranged 

from 3.3 to 170 mm. The largest measured median particle 

sizes (D50 equal to 170 mm) were collected on the surface of 

the bed at the Earthquake Lake outlet (between cross sections 
EXPLANATION

1971 (orientation and horizontal 

 location are approximate)

Channel bottom point

Aggradation

Incision

2006

2006 estimated

Cross section 500

Cross section 400

6,235

6,240

6,245

6,250

6,255

6,260

6,265

6,270

6,220

6,225

6,230

6,235

6,240

6,245

6,250

6,255

6,260

6,265

6,280

6,285

6,290

6,295

6,300

6,305

6,310

6,315

6,320

6,325

Cross section 700

6,260

6,265

6,270

6,275

6,280

6,285

6,290

6,295

6,300

6,305

0 100 200 300 400 500 600 700 800 900 1,000

DISTANCE ACROSS CHANNEL FROM LEFT BANK, IN FEET

0 100 200 300 400 500

DISTANCE ACROSS CHANNEL FROM LEFT BANK, IN FEET

Cross section 800

6,320

6,325

6,330

6,335

6,340

6,345

6,350

6,355

6,360

6,365

Cross section 600

ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929 (NGVD 29), IN FEET ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 

1929 (NGVD 29), IN FEET

Figure 12. Lateral migration, incision, and aggradation of the Madison River channel downstream 

from Earthquake Lake, Montana between 1971 and 2006.

24 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana
Cross section 1000

Cross section 1100

Cross section 900

6,360

6,365

6,370

6,375

6,380

6,385

6,390

6,395

6,400

6,405

6,345

6,350

6,355

6,360

6,365

6,370

6,375

6,380

6,385

6,390

6,340

6,345

6,350

6,355

6,360

6,365

6,370

6,375

6,380

6,385

Cross section 1400

Cross section 1200

Cross section 1300

0 100 200 300 400 500

DISTANCE ACROSS CHANNEL FROM LEFT BANK, IN FEET

6,375

6,380

6,385

6,390

6,395

6,400

6,405

6,410

6,415

6,365

6,370

6,375

6,380

6,385

6,390

6,395

6,400

6,405

6,410

6,375

6,380

6,385

6,390

6,395

6,400

6,405

6,410

6,415

ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929 (NGVD 29), IN FEET

400

500

600

800

900

1000

1100

1200

1300

1400

700

400

500

600

800

1400

700

EXPLANATION

Location and number of 

 surveyed cross section

400

Approximate left and right 

 edges of water in 1971

Dolomite 

outcrop

Flow direction

Approximate

extent of debris from Madison Slide

N

0 100 200 300 METERS

0 500 1,000 FEET

Base from U.S. Department of Agriculture aerial 

photography, 2006

Lambert Conformal Conic projection

Standard parallels 45°00'N and 49°00'N, 

central meridian 109°30'W

North American Datum of 1983 (NAD 83) Earthquake Lake

Cut bank

Location of 

1970 road 

washout

Location of 1986 road washout

Approximate extent of Madison SlideApproximate extent of Madison Slide

Knickpoint subreach

Location of 1986 road washout

Figure 12. Lateral migration, incision, and aggradation of the Madison River channel downstream from Earthquake Lake, Montana 

between 1971 and 2006.—Continued

Lateral and Vertical Channel Movement 25
Figure 13. Cross sections 100, 200, and 300, from 1971 and 2006 surveys on the 

Madison River near Raynolds Pass Bridge downstream from Earthquake Lake, 

Montana.

Cross section 300, approximately 30 feet downstream from Raynolds Pass Bridge

ELEVATION ABOVE NORTH AMERICAN VERTICAL DATUM OF 1929 (NGVD 29), IN FEET

Cross section 100, approximately 1,100 feet downstream from Raynolds Pass Bridge

EXPLANATION

1971

Channel bottom point

2006

0 100 200 300 400 500

DISTANCE ACROSS CHANNEL FROM LEFT BANK, IN FEET

Cross section 200, approximately 450 feet downstream from Raynolds Pass Bridge

6,100

6,105

6,110

6,115

6,120

6,125

6,130

6,135

6,140

6,145

6,110

6,115

6,120

6,125

6,130

6,135

6,140

6,145

6,150

6,155

6,110

6,115

6,120

6,125

6,130

6,135

6,140

6,145

6,150

6,155

26 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

1300 and 1400). However, larger 

particle sizes exist throughout the study 

reach where the deepest parts of the 

channel could not be waded or sampled; car-sized boulders near cross section 700 were observed in 1971, 2006 

and, 2008. Additionally, bed-material 

samples 4, 6, and 7 (fig. 14) and the 

terrace material sample 5 were larger 

than the other measured materials. The 

presence of these larger bed and terrace 

materials probably indicates bed armoring as streamflows have washed finer 

material downstream. 

The gradation coefficient, calculated as the square root of the ratio of 

D84/D16 is a measure of the variability 

of the sediment-size distribution and 

provides some indication of gradation. 

For instance, if the gradation coefficient is about 1, the sediment is poorly 

graded and thus composed of material 

of similar sizes. The gradation coefficient was 1.7 to 2.2 for the bed surface, 

2.2 for the terrace surface, and 4.6 to 

6.5 for the materials sampled from 

the banks and the gravel bar (table 4). 

Unlike the pebble counts for the bed 

and terrace surfaces, the samples from 

the banks and the gravel bar included 

some materials below the surface. The 

bed and terrace surface materials are 

more poorly graded than the material 

on and below the surface on the channel banks and on the gravel bar, probably because of armoring of the bed.

Shear Stress and Potential for 

Bed-Material Movement 

Boundary-shear stress is the force 

per unit area that a river exerts on its 

bed in the direction of flow (Dingman, 

2009). The critical shear stress is the 

shear stress required to initiate movement of sediment of a specific size 

from the bed (Dingman, 2009). If the 

boundary-shear stress is larger than the 

critical shear stress for a given streamflow, the bed material is likely to move, 

potentially resulting in channel adjustments (Elliott, 2002). 
Potential for Bed-Material Movement 27

Boundary-Shear Stress

Mean boundary-shear stress can be approximated by 

the du Bois equation (U.S. Army Corps of Engineers, 2008b, 

p. 12–29):

τo = γRS (3)

where

τo is the mean boundary-shear stress, in pounds 

per square foot;

γ is the specific weight of water (62.4 pounds 

per cubic foot);

R is the hydraulic radius of the stream, or the 

cross-sectional area divided by the wetted 

perimeter, in feet; and

S is the energy slope, in feet per feet.

The mean boundary-shear stress and hydraulic geometry 

variables (cross-sectional area, hydraulic radius, and energy 

slope) were calculated for several streamflows at the surveyed 

cross sections by using HEC-RAS (table 5). Mean boundaryshear stress for the 3,500-ft3

/s threshold streamflow at cross 

section 400 is shown in figure 15. Also shown in figure 15 

are the point boundary-shear stresses, which are calculated by 

substituting streamflow depth for the hydraulic radius in equation 3 at several locations across the cross section, to illustrate 

how the point boundary-shear stresses can vary across the 

channel. The mean boundary-shear stresses are less than the 

point boundary-shear stress at the deepest parts of the channel 

but are greater than the point boundary-shear stress along the 

sides of the channel. 

The mean boundary-shear stresses vary longitudinally 

along the Madison River and generally increase with streamflow (fig. 16). Mean boundary-shear stresses generally are 

higher at cross sections where the thalweg and water-surface 

slopes steepen because the mean boundary-shear stress is 

directly proportional to energy slope (equation 3), and the 

energy slope usually increases as the thalweg and watersurface slopes increase. Mean boundary-shear stresses also 

increase proportionally to depth and velocity (Dingman, 

2009; Elliott, 2002). Mean boundary-shear stresses are high 

at cross section 700 (fig. 16B) where the steepest thalweg 

and water-surface slopes in the study reach occur (figs. 9 and 

11B). Shear stresses are lower downstream from the spillway 

(near cross sections 600 to 400), where thalweg and watersurface slopes are flatter than the spillway. Therefore, many of 

the larger bed materials that could be entrained upstream are 

likely to be deposited through this subreach downstream from 

the spillway. This projected deposition is consistent with the 

thalweg and water-surface profile changes since 1971 and with 

historical observations (U.S. Army Corps of Engineers, 1972; 

Foundation and Materials Consultants, Inc., 1972). 

Critical Shear Stress

Many investigations (Elliott, 2002; Elliott and Hammack, 

2000; Heitmuller and Asquith, 2008) have used the Shields 

(1936) equation to estimate the critical shear stress for movement of the D50 particle size:

τc= τ*

c

 (γs−γ ) D50 (4)

where

τc is the critical shear stress, in pounds per 

square foot;

τ*

c is the dimensionless critical shear stress, or 

Shields parameter;

γs is the specific weight of sediment, assumed to 

be 2.65 times the specific weight of water, 

in pounds per cubic foot;

γ is the specific weight of water (62.4 pound per 

cubic foot); and

D50 is the median particle size, in feet.

Although equation 4 includes a variable for the D50

particle size, for this study critical shear stresses were calculated for the larger particle sizes (D65 and D84) as well as the 

D50. Larger materials in a bed can shield the smaller particles 

from flow, or the smaller particles can be removed from the 

bed leaving a coarser, armored bed. Consequently, a cobbleor boulder-bedded river like the Madison can be considered 

stable until the larger bed materials are in motion (Julien, 

1998). For clarity, only the critical shear stresses for the D50

and D84 particle sizes are discussed in detail in this report.

Use of equation 4 requires an estimated or calculated 

dimensionless critical shear stress or Shields parameter. 

Shields parameter values ranging from 0.01 to 0.11 have been 

used for estimating particle motion (Elliott, 2002; Mueller and 

others, 2005). Elliott and Hammack (2000) determined from 

onsite observations of sediment movement that a value of 

0.03 for the Shields parameter was appropriate for estimating 

movement of material from an alluvial bar along the Gunnison 

River in the Black Canyon, Colo. Elliott (2002) also used a 

Shields parameter value of 0.03 for estimating particle motion 

on the Roaring Fork River in Colo., which is a coarse-bed 

stream with sediment sizes in the same range as the Madison 

River. However, because the materials lining the spillway and 

the channel downstream from the spillway (cross sections 

1400 to 400) were deposited by the Madison Slide, they have 

not been worn into smooth rounded shapes typical of bed 

material in the Gunnison and Roaring Fork Rivers, nor have 

they been reworked by the river over a long time (Hadley, 

1964; figs. 3–7, this report). The bed materials in this part of 

the Madison River are more angular, which could result in a 

larger Shields parameter value (Julien, 1998).
28 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

Table 4. Sediment-size characteristics and calculated critical shear stresses for materials in and near the Madison River downstream 

from Earthquake Lake, Montana.

[Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83). Abbreviations: Dxx, particle size for which xx percent of 

material is finer; σg, gradation coefficient, which equals the square root of the ratio of D84 to D16; τc(Dxx) critical shear stress for given particle size; mm, 

millimeters; lb/ft2, pounds per square foot; USGS, U.S. Geological Survey; ft, feet; USACE, U.S. Army Corps of Engineers. Symbol: -- data not available]

Collecting 

agency

Sample 

number Year Method Approximate easting1

Approximate 

northing1 Description

USGS 1 2008 Sieve analysis 111°26′31′′W 44°49′36′′N Gravel bar along right side of channel between cross 

sections 500 and 400

USGS 2 2008 Sieve analysis 111°27′8′′W 44°49′38′′N Right bank above high water mark near cross 

section 600, along outside bend3

USGS 3 2008 Sieve analysis 111°25′27′′W 44°49′47′′N Right bank between cross sections 1300 and 1200 

USGS 4 2006 Pebble count1,4 111°25′24′′W 44°49′47′′N Bed near spillway between cross sections 1400 and 

1300

USGS 5 2006 Pebble count 111°26′35′′W 44°49′34′′N Terrace on right bank 50 ft upstream from cross 

section 400 

USGS 6 2006 Pebble count1,5 111°29′9′′W 44°49′34′′N Bed between cross sections 300 and 100, near 

Raynolds Pass Bridge

USGS 7 2006 Pebble count1,4 111°26′33′′W 44°49′33′′N Bed between cross sections 500 and 400 

USGS 8 2006 Rough visual 

estimate6

-- -- Bed between cross sections 800 and 700 

USACE 1 1959 Sieve analysis -- -- Spillway, obtained during excavation, exact location 

unknown

USACE 1 1970 Sieve analysis -- -- Mid part of alluvial fan, exact location unknown 

1

 Pebble count samples covered large area of bed, location listed is in vicinity of sample area.

2

 Sediment-size distribution calculated by weight for sieve analysis, by number of particles for pebble-count analysis.

3

 Sample location was 4 feet above the water surface, just above where person was standing in figure 6.

4

 Left and center parts of channel unwadeable. Sampled the right part of the channel bed, which extended into the channel approximately 25 percent of 

distance across the channel.

5

 Center part of the channel unwadable. Sampled the left and right parts of the channel bed, which each extended into the channel approximately 25 percent of 

distance across the channel.

6

 Not sampled or measured.

Because this study did not include observations of 

bed-material movement from which to estimate the Shields 

parameter, a range of values for critical shear stress (τc ) was 

estimated using information from three investigations. First, 

critical shear stress was calculated using a Shields parameter 

of 0.04 for a lower bound because this value was used by the 

USACE for their investigations along the Madison River (U.S. 

Army Corps of Engineers, 1972). Then, based on work by 

Wilcock and McArdell (1993), critical shear stress was calculated using a Shields parameter of 0.08 for an upper bound. 

Wilcock and McArdell (1993) showed that complete motion, 

where enough material is moving to cause incision of the bed, 

occurs at about twice the critical shear stress (equivalent to 

using a Shields parameter of 0.08). Lastly, Shields parameters 

were calculated as a function of particle shape and size 

(variable Shields parameters) as described by Julien (1998). 

Resulting variable Shields parameter values ranged from 0.04 

to 0.06. 

Cross Sections 500–400, Downstream from Spillway

Between cross sections 500 and 400 downstream from 

the spillway, the right part of the channel bed was sampled 

using the pebble-count method (table 4). The critical shear 

stresses calculated using the Shields parameter (0.04) and 

using the variable Shields parameter (0.04–0.06) for the D50

particle size are both smaller than both the mean boundaryshear stress and the point boundary-shear stress calculated 
Potential for Bed-Material Movement 29

Particle size for which indicated percentage of 

bed or bank material is finer2 Gradiation 

coefficient

σg

Critical shear stress for indicated 

particle size, calculated using 

Shields parameter =0.04

Critical shear stress for indicated 

particle size, calculated using 

variable Shields parameter 

(0.04–0.06) from Julien (1998)

D16

(mm)

D50

(mm)

D65

(mm)

D84

(mm)

τc(D50)

(lb/ft2)

τc(D65)

(lb/ft2)

τc(D84)

(lb/ft2)

τc(D50)

(lb/ft2)

τc(D65)

(lb/ft2)

τc(D84)

(lb/ft2)

3.7 18 33 78 4.6 0.24 0.45 1.06 0.26 0.51 1.33

1.0 6.2 13 42 6.4 .084 .18 .56 .080 .18 .65

2.3 22 55 95 6.5 .29 .74 1.3 .37 .94 1.7

110 170 200 300 1.7 2.3 2.7 4.1 3.1 3.7 5.6

32 90 130 160 2.2 1.2 1.8 2.2 1.4 2.2 2.7

38 83 120 180 2.2 1.1 1.6 2.4 1.3 1.9 2.9

64 150 180 280 2.1 2.0 2.4 3.8 2.6 3.1 4.9

-- 1,000 -- -- -- 14 -- -- 19 -- --

.50 3.3 6.0 11 4.7 .045 .081 .15 .043 .085 .16

1.1 4.3 7.0 16 3.8 .058 .094 .22 .059 .099 .25

using equation 3 for cross section 400 for the 3,500-ft3/s 

threshold streamflow (figs. 15 and 16B, table 5). This comparison indicates that some of the D50 particle sizes along the 

right side of the bed near cross section 400 could move at the 

3,500-ft3/s threshold streamflow. However, the critical shear 

stress for the D50 particle size calculated using the Shields 

parameter of 0.08 is larger than both the mean boundary-shear 

stress and the point boundary-shear stress, indicating that 

movement of all of the D50 particle sizes on the bed is unlikely 

at the 3,500-ft3/s threshold streamflow.

The critical shear stresses for the D84 particle size 

calculated using the Shields parameter of 0.04, the variable 

Shields parameter, and the Shields parameter of 0.08 are all 

larger than both the mean boundary-shear stress and the point 

boundary-shear stress calculated for the 3,500-ft3/s threshold 

streamflow, indicating that the larger size fractions along 

the bed near cross section 400 are not likely to move at the 

3,500-ft3/s threshold streamflow. This lack of movement for 

the larger particles could lead to further coarsening or armoring of the bed if the D50 and smaller sizes are removed from 

the bed and transported downstream. However, these smaller 

particles could be replenished by particles eroded from the 

steep banks upstream. 

In summary, some of the D50 particle sizes along the right 

side of the bed between cross sections 500 and 400 could be 

moved by the 3,500-ft3/s threshold streamflow. However, the 

D84 particle sizes probably would not move. 

Table 4. Sediment-size characteristics and calculated critical shear stresses for materials in and near the Madison River downstream 

from Earthquake Lake, Montana.—Continued

[Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83). Abbreviations: Dxx, particle size for which xx percent of 

material is finer; σg, gradation coefficient, which equals the square root of the ratio of D84 to D16; τc(Dxx) critical shear stress for given particle size; mm, 

millimeters; lb/ft2, pounds per square foot; USGS, U.S. Geological Survey; ft, feet; USACE, U.S. Army Corps of Engineers. Symbol: -- data not available]
0

102030405060708090

100

0.1 1 10 100 

CUMULATIVE PERCENT FINER THAN INDICATED SIZE

MATERIAL SIZE, IN MILLIMETERS

 1959—mid part of alluvial fan, exact location unknownU.S. Army Corps of Engineers

EXPLANATION

 1970—spillway, exact location unknown Sample 3—right bank between cross  sections 1300 and 1200 (2008) Sample 1—gravel bar between cross  sections 500 and 400 (2008)U.S. Geological Survey Sample 2—right bank near cross  section 600 (2008) Sample 6—bed between cross  sections 300 and 100 (2006) Sample 7—bed between cross  sections 500 and 400 (2006) 

Gravel Cobble 

 Sample 5—first terrace 50 feet upstream from  cross section 400 on right bank (2006)  Sample 4—bed between cross  sections 1400 and 1300 (2006) 

Sand

Figure 14. Distribution of particle sizes of material in and near the Madison River downstream from Earthquake Lake, Montana.
Potential for Bed-Material Movement 31

Table 5. Calculated hydraulic characteristics for selected cross sections on the Madison River downstream from Earthquake Lake, 

Montana.

[Abbreviations: ft, feet; ; ft2, square feet; ft/ft, foot per foot; lb/ft2 pounds per square foot; ft3/s, cubic feet per second]

Cross-section 

number

Distance downstream 

from Earthquake Lake 

outlet 

(ft)

Mannings roughness 

coefficient 

(dimensionless)

Cross-sectional 

area1

(ft2)

Hydraulic 

radius1

(ft)

Energy slope1

(ft/ft)

Mean boundaryshear stress1

(lb/ft2)

Streamflow through the study reach at the time of the survey (2006) 1,040 ft3/s

1400 0 0.055 255 2.7 0.006 1.0

1300 140 .080 143 2.6 .045 7.3

700 3,347 .110 169 2.2 .077 11

500 5,200 .080 238 3.2 .013 2.6

400 6,232 .075 232 2.4 .017 2.5

2,500 ft3/s

1400 0 0.055 454 4.3 0.005 1.4

1300 140 .080 273 4.1 .034 8.7

700 3,347 .110 276 3.1 .092 18

500 5,200 .080 421 3.1 .013 2.5

400 6,232 .075 397 3.1 .017 3.3

3,000 ft3/s

1400 0 0.055 518 4.7 0.005 1.5

1300 140 .080 314 4.4 .032 8.8

700 3,347 .110 300 3.4 .10 21

500 5,200 .080 488 3.0 .014 2.6

400 6,232 .075 473 2.8 .016 2.8

3,500 ft3/s

1400 0 0.055 534 5.1 0.005 1.6

1300 140 .080 325 4.5 .030 8.4

700 3,347 .110 312 3.5 .12 26

500 5,200 .080 440 3.3 .015 3.1

400 6,232 .075 480 3.1 .015 2.9

4,000 ft3/s

1400 0 0.055 641 5.4 0.005 1.7

1300 140 .080 396 4.9 .029 8.9

700 3,347 .110 352 3.8 .11 26

500 5,200 .080 602 3.6 .015 3.4

400 6,232 .075 624 3.1 .014 2.7

6,000 ft3/s

1400 0 0.055 870 6.7 0.004 1.8

1300 140 .080 541 6.0 .026 9.7

700 3,347 .110 477 4.7 .10 29

500 5,200 .080 799 4.5 .017 4.8

400 6,232 .075 902 3.5 .014 3.1

1

Calculated using HEC-RAS (U.S. Army Corps of Engineers, 2008a, b, c).
6,2206,2256,2306,2356,2406,2456,2506,2556,260

300 350 400 450 500 550 60

ELEVATION ABOVE NATIONAL GEODETIC VERTICAL DATUM OF 1929 (NGVD 29), IN FEET

DISTANCE ACROSS CHANNEL FROM LEFT BANK, IN FEET

EXPLANATION

Estimated ground surfaceCalculated water-surface elevationCalculated mean boundary-shear stressSurveyed ground surfaceCalculated point boundary-shear stress 

Shields parameter = 0.04 for D50 (gray symbol) and D84 (blue symbol) sediment siz

Shields parameter = 0.08 for D50 (gray symbol) and D84 (blue symbol) sediment siz

Critical shear stress for 3,500 cubic feet per second through the study reach calc

Variable Shields parameter (from Julien, 1998) for D50 (gray symbol) and D84 (blue 

 sediment sizes 

Figure 15. Calculated mean and point boundary-shear stresses at cross section 400 and calculated critical shear stresses for movement of sebetween cross sections 500 and 400, Madison River downstream from Earthquake Lake, Montana.
Potential for Bed-Material Movement 33

Cross Sections 1400–1300, Earthquake Lake Outlet

At the upstream end of the spillway, between cross sections 1400 and 1300, the right part of the bed was sampled 

using the pebble-count method (table 4, fig. 14). Through this 

subreach, the mean boundary-shear stresses are difficult to 

compare to the critical shear stresses because the mean boundary-shear stresses increased by about 500 percent between 

cross sections 1400 and 1300 (fig. 16). For the purposes of 

this discussion, it is assumed that the bed sample is representative of the bed material at a midpoint between cross sections 

1400 and 1300, and that the mean-boundary shear stress varies 

linearly between the two cross sections. The critical shear 

stresses for the D50 particle size calculated using all of the 

Shields parameters are smaller than the mean boundary-shear 

stress for the 3,500-ft3/s threshold streamflow (fig. 16A, inset), 

indicating that most of the D50 particles along the right side of 

the bed could move at the 3,500-ft3/s threshold streamflow. 

The critical shear stresses for the D84 particle size calculated using the Shields parameter of 0.04 is smaller than 

the mean boundary-shear stress calculated for the 3,500-ft3/s 

threshold streamflow, indicating that some of these larger 

materials along the right side of the bed could move at the 

3,500-ft3/s threshold streamflow. However, critical shear 

stresses for the D84 particle size calculated using the variable 

Shields parameter and the Shields parameter of 0.08 are both 

larger than the mean boundary-shear stress calculated for 

the 3,500-ft3/s threshold streamflow, indicating that most of 

these larger size fractions along the right part of the bed near 

the outlet are not likely to move at the 3,500-ft3/s threshold 

streamflow. 

In summary, most of the D50 particle sizes along the right 

side of the bed between cross sections 1400 and 1300 could be 

moved by the 3,500-ft3/s threshold streamflow (assuming the 

bed sample is representative of the bed material at a midpoint 

between cross sections 1400 and 1300, and that the meanboundary shear stress varies linearly between cross sections 

1400 and 1300 as depicted in figure 16A). However, most of 

the D84 particle sizes probably would not move. 

Limitations of the Estimates for Potential for 

Bed-Material Movement 

Assumptions for using HEC-RAS to calculate hydraulic 

variables such as water-surface elevation, hydraulic radius, 

streamflow depth, and mean boundary-shear stress (U.S. Army 

Corps of Engineers, 2008b, p. 2–20) include:

1. Steady flow–streamflow does not change with time;

2. Gradually varied flow–depths do not abruptly change 

along the channel; 

3. One-dimensional flow–magnitude and direction of the 

velocity vectors at a cross section are equal—the flow at 

a cross section is all moving in one direction down the 

channel, with no cross-currents or diversions; and 

4. Thalweg slopes that are less than about 0.10 ft/ft. 

Point boundary-shear stresses calculated as a function of 

streamflow depth and energy slope also are affected by these 

assumptions. In addition to the assumptions for using HECRAS to calculate hydraulic variables, use of equation 3 is 

based on the assumption that the channel cross section has a 

regular or trapezoidal shape that is at least 10 times wider than 

it is deep (Elliott, 2002). 

Few natural streams completely satisfy these assumptions 

including the Madison River in the study area. Flow at many 

locations along the study reach, especially near cross section 

700, varies rapidly because large boulders disrupt the flow and 

cross-section shapes (and consequently streamflow depths) 

change substantially from place to place along the channel. 

The Shields parameter used for calculating critical shear 

stress (equation 4) can vary according to energy slope and 

bed-material characteristics such as the sediment-size distribution, shape, orientation, and how tightly particles are packed 

together. As discussed in the section “Critical Shear Stress,” 

investigators have used Shields parameter values ranging from 

0.01 to 0.11. Large Shields parameters have been used to calculate critical shear stresses for high-gradient streams, such as 

the Madison River (Mueller and others, 2005). Therefore, bed 

material in the Madison River might be associated with critical shear stress values at or above the upper ranges of critical 

shear stresses presented in this report. In addition, larger, more 

erosion-resistant materials likely exist in the parts of the channel where high-flow depths and velocities prevented sediment 

sampling. Movement of these materials might require higher 

mean boundary-shear stresses and flow rates than estimated 

in this report. Characterization of sediment sizes in the center 

of the stream and observation of bed-material movement for a 

range of streamflows could provide information to help refine 

the Shields parameter and critical-shear stress estimates for 

bed materials in the Madison River downstream from Earthquake Lake.
0

2468

1012

1400

1300

0 50 100 150 200

DISTANCE FROM EARTHQUAKE LAKE OUTLET, IN FEET

MEAN BOUNDARY SHEAR STRESS, 

IN POUNDS PER SQUARE INCH

Detail showing location of upstream sediment sample 

1400

1300

1200

1100

1000

900

800

05

1015202530

0 500 1,000 1,500 2,000 2,500 3,000 

MEANBOUNDARY-SHEARSTRESS,INPOUNDSPERSQUAREFOOT

DISTANCE FROM EARTHQUAKE LAKE OUTLET, IN FEET

EXPLANATION

1,040 cubic feet per second (ft3/s), 

 2006 survey streamflow 2,500 ft3/s

3,000 ft3/s3,500 ft3/s4,000 ft3/s6,000 ft3/s

Calculated mean boundary-shear stress for:

A

Critical shear stresses for a D50 at cross section 700 that 

was visually estimated 

Approximate extent of Madison Slide

800 Cross-section number

Shields parameter = 0.04 for D50 (gray symbol) and D84 (blue symbol) 

 sediment sizes Shields parameter = 0.08 for D50 (gray symbol) and D84 (blue symbol)  sediment sizes 

Calculated critical shear stress for:

Variable Shields parameter (from Julien, 1998) for D50 (gray symbol) 

 and D84 (blue symbol) sediment sizes 

Figure 16. Calculated mean boundary-shear stress at various streamflows and calculated critical shear stresses for selected sediment siRiver downstream from Earthquake Lake, Montana. A, From cross section 1400 to cross section 700. B, From cross section 700 to cross sec
EXPLANATION

700

600

500

B

Critical shear stresses for a D50

at cross section 700 that wasvisually estimated

1,040 cubic feet per second (ft3/s), 

 2006 survey streamflow 2,500 ft3/s

3,000 ft3/s3,500 ft3/s4,000 ft3/s6,000 ft3/s

Calculated mean boundary-shear stress for:

500 Cross-section number

Shields parameter = 0.04 for D50 (gray symbol) and D84 (blue symbol) 

 sediment sizes Shields parameter = 0.08 for D50 (gray symbol) and D84 (blue symbol)  sediment sizes 

Calculated critical shear stress for:

Variable Shields parameter (from Julien, 1998) for D50 (gray symbol) 

 and D84 (blue symbol) sediment sizes 

05

1015202530

MEANBOUNDARY-SHEARSTRESS,INPOUNDSPERSQUAREFOOT

DISTANCE FROM EARTHQUAKE LAKE OUTLET, IN FEET

3,000 3,500 4,000 4,500 5,000 5,500 6,000 

Approximate extent of Madison Slide

Figure 16. Calculated mean boundary-shear stress at various streamflows and calculated critical shear stresses for selected sediment siMadison River downstream from Earthquake Lake, Montana. A, From cross section 1400 to cross section 700. B, From cross section 700 to section 400.—Continiued
36 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

Summary and Conclusions

The 1959 Hebgen Lake earthquake caused a massive 

landslide (Madison Slide) that dammed the Madison River and 

formed Earthquake Lake. The U.S. Army Corps of Engineers 

excavated a spillway through the Madison Slide to permit outflow from Earthquake Lake. In June 1970, high streamflows in 

the Madison River severely eroded the spillway and damaged 

the roadway embankment along U.S. Highway 287 north of 

the channel. Flooding in 1971 and 1986 caused additional 

erosion of the spillway channel and roadway embankment. 

Investigations undertaken following the 1970 and 1971 flood 

events concluded that substantial erosion through and downstream from the spillway could be expected for streamflows 

greater than 3,500 cubic feet per second (ft3/s). Accordingly, 

PPL-Montana, the current (2011) owner of Hebgen Dam 

upstream from Earthquake Lake, has tried to manage releases 

from Hebgen Lake to prevent streamflows [as measured at 

U.S. Geological Survey (USGS) gaging station 06038800] 

from exceeding 3,500 cubic feet per second (ft3/s). 

Management of flow releases from Hebgen Lake to 

prevent streamflows at USGS gaging station 06038800 from 

exceeding the 3,500-ft3/s threshold streamflow is difficult. 

Flooding of Cabin Creek and Beaver Creek, which enter the 

Madison River between Hebgen Lake and the Earthquake 

Lake outlet, can cause streamflows at the outlet and at gaging 

station 06038800 to exceed the 3,500-ft3/s threshold streamflow even when streamflow releases from Hebgen Lake are 

minimal. 

The 3,500-ft3/s threshold streamflow has been questioned 

for two main reasons. First, no road damage was reported 

downstream from the Earthquake Lake outlet in 1993, 1996, 

and 1997 when streamflows exceeded the 3,500-ft3/s threshold streamflow. This lack of road damage during relatively 

high streamflows might indicate that the channel has become 

armored and is no longer as susceptible to erosion as it was in 

the 1970s and 1980s. Second, the 3,500-ft3/s threshold streamflow generally precludes releases of higher flows that could be 

beneficial to the blue-ribbon trout fishery downstream in the 

Madison River.

In response to concerns about minimizing streamflow 

downstream from Earthquake Lake and the possible armoring 

of the spillway, the USGS, in cooperation with the Madison 

River Fisheries Technical Advisory Committee (MADTAC; 

Bureau of Land Management; Montana Department of 

Environmental Quality; Montana Fish, Wildlife and Parks; 

PPL-Montana; U.S. Department of Agriculture Forest Service 

– Gallatin National Forest; and U.S. Fish and Wildlife Service), conducted a study to determine movement of the Madison River channel downstream from Earthquake Lake and to 

investigate the potential for bed material movement along the 

same reach. The purpose of this report is to present information about the lateral and vertical movement of the Madison 

River from 1970 to 2006 for a 1-mile reach downstream from 

Earthquake Lake and for Raynolds Pass Bridge, and to provide 

an analysis of the potential for bed-material movement so that 

MADTAC can evaluate the applicability of the 3,500-ft3/s 

threshold streamflow for initiation of damaging erosion.

Channel cross sections originally surveyed by the USGS 

in 1971 were resurveyed in 2006. Incremental channelmovement distances were determined by comparing the 

stream centerlines from 14 aerial photographs taken between 

1970 and 2006. Depths of channel incision and aggregation 

were determined by comparing the 2006 and 1971 crosssection and water-surface data. Particle sizes of bed and 

bank materials were measured in 2006 and 2008 using the 

pebble-count method and sieve analyses. A one-dimensional 

hydraulic-flow model (HEC-RAS) was used to calculate mean 

boundary-shear stresses for various streamflows; these calculated boundary-shear stresses were compared to calculated 

critical-shear stresses for the bed materials to determine the 

potential for bed-material movement. 

The Madison River channel through the Madison slide 

downstream from Earthquake Lake (the spillway) has steep 

longitudinal slopes [up to 0.046 feet per feet (ft/ft)] and, 

therefore, can transport large quantities of materials from 

the bed and banks. Because Earthquake Lake tends to trap 

sediment, the spillway is prone to incision and lateral movement. Additionally, the channel banks along the spillway are 

extremely high and the bank slopes are almost equal to the 

angle of repose for the bank material. As the river undercuts 

the banks, large amounts of material are deposited into the 

channel, further contributing to channel instability. In contrast, 

the longitudinal slopes downstream from the spillway are not 

as steep. Consequently, much of the material removed from 

the spillway can be deposited downstream, which can lead to 

channel aggradation, widening, and braiding downstream from 

the Madison Slide. 

Between 1971 and 2006, the Madison River channel 

has moved laterally to varying degrees throughout the study 

area. A comparison of lateral channel movement distances 

to annual peak streamflows shows that streamflows higher 

than 3,500 ft3/s generally were followed by lateral channel 

movement except from 1991 to 1992 and possibly from 1996 

to 1997. Where more than one year lapsed between aerial 

photographs, it is not possible to discern whether the channel 

moved gradually or all in one year. It also is unclear whether 

the channel moved in response to one peak flow, to several 

peak flows, or to sustained flows. The channel moved between 

2002 and 2005 even though streamflows during that period 

were less than the 3,500-ft3/s threshold streamflow.

The channel has incised to varying degrees through the 

Madison Slide. Between 1971 and 2006, the channel bed 

incised by as much as 5 feet (ft) at the Earthquake Lake outlet 

(cross section 1400) and as much as 12 ft at cross section 

1000. Near cross section 800, the stream has eroded into fill 

that was mechanically placed between 1970 and 1975 along 

the steep right bank between the stream and the road.

The channel appears to have changed the least at the 

downstream end of the Madison Slide, along a subreach from 

near cross section 800 to cross section 700. The stream in this 

subreach could be composed of erosion-resistant materials 
References Cited 37

similar to the large dolomite boulder on the right bank that 

was deposited by the Madison Slide and the dolomite outcrop 

on the left bank. 

Channel movement also was noted downstream from the 

Madison Slide. The channel has aggraded, moved laterally, 

and incised a new lower channel between cross sections 600 

and 500. The channel has moved laterally and aggraded at 

cross section 400. 

Near Raynolds Pass Bridge, about 3 mile (mi) downstream from Earthquake Lake, elevations across the channel 

have changed by -1.4 ft to +1.9 ft, but these changes were 

local in nature and could represent a few rocks or depressions 

in the bed. The right bank at cross section 300 was about 5 ft 

lower in the 2006 survey than the 1971 survey; this difference 

could indicate erosion at the right back or could be due to the 

two surveys being in slightly different locations. Overall, it 

does not appear that the materials eroded from the Madison 

Slide are causing aggradation near the Raynolds Pass Bridge.

Maximum lateral-movement distances of the channel 

between 1970 and 2006 (the maximum distances between 

the centerlines from all of the aerial photographs) were 150 ft 

near the upstream end of the spillway near cross section 1100, 

370 ft downstream from the spillway between cross sections 

400 and 500, and 560 ft about 1 mile downstream from the 

Madison Slide. All channel movement-distances are plus or 

minus (+/-) 30 ft due to potential errors in rectifying the aerial 

photographs. 

Channel movement was determined from aerial photographs and sparse survey data. A relation between streamflow 

and channel movement is difficult to determine because more 

than a year passed between most of the aerial photographs and 

more than 30 years passed between the most recent surveys. 

Resurveying cross sections and water-surface elevations more 

frequently (either annually or after high streamflows) could 

better define the relation between streamflow and lateral and 

vertical channel movement. 

The ability of a river to move particles on the bed is a 

function of the boundary shear stress or the force per unit 

area that a river exerts on its bed in the direction of flow. 

The critical shear stress is the shear stress required to initiate 

movement of sediment of a specific size from the bed. If the 

boundary shear stress is larger than the critical shear stress for 

a given streamflow, the bed material is likely to move, potentially resulting in channel adjustments. Critical shear stresses 

were calculated for the D50, D65, and D84 sediment sizes at two 

locations: near the upstream end of the Madison Slide and 

downstream from the Madison Slide. 

Some of the critical shear stresses calculated for the D50

particle sizes along the right side of the bed between cross sections 500 and 400, and all of the critical shear stresses calculated for the D50 particle sizes along the right side of the bed 

between cross sections 1400 and 1300 are less than the mean 

boundary-shear stress generated by the 3,500-ft3/s threshold 

streamflow. These comparisons indicate that these median 

particle sizes could move at the 3,500-ft3/s threshold streamflow. In contrast, all of the critical shear stresses calculated for 

the D84 particle sizes along the right side of the bed at between 

cross sections 500 and 400 and most of the critical shear 

stresses calculated for the D84 particle sizes along the right side 

of the bed between cross sections 1400 and 1300 are greater 

than the mean boundary-shear stress generated by a streamflow of 3,500 ft3

/s. These comparisons indicate that most of 

these larger particles probably will not move at the 3,500-ft3/s 

threshold streamflow. This lack of movement for the larger 

particles at the 3,500-ft3/s threshold streamflow could lead to 

further armoring of the bed as the D50 and smaller-sized particles are removed from the bed and transported downstream. 

However, these smaller particles could be replenished by 

particles eroded from the steep spillway banks. 

The Shields parameter values from 0.04 to 0.08 that were 

used to calculate critical shear stresses could be conservative for a high-gradient stream such as the Madison River. A 

higher, less conservative, Shields parameter would result in 

higher critical-shear stresses, meaning that higher streamflows 

would be required to move material than those reported herein. 

In addition, larger, more erosion-resistant materials likely 

exist in the parts of the channel where high-flow depths and 

velocities prevented sediment sampling. Movement of these 

materials might require higher mean boundary-shear stresses 

and flow rates than estimated in this report. Characterization 

of sediment sizes in the center of the stream and observation 

of bed-material movement for a range of streamflows could 

provide information to help refine the Shields parameter and 

critical-shear stress estimates for bed materials in the Madison 

River downstream from Earthquake Lake. 

References Cited

Dingman, S.L., 2009, Fluvial Hydraulics: New York, Oxford 

University Press, 559 p.

Elliott, J.G., and Hammack, L.A., 2000, Entrainment of 

riparian gravel and cobbles in an alluvial reach of a regulated river: Regulated Rivers–Research and Management, 

v. 16, no. 1, p. 37–50. (Also available at http://dx.doi.

org/10.1002/(SICI)1099-1646(200001/02)16:1<37::AIDRRR564>3.0.CO;2-V.)

Elliott, J.G., 2002, Bed-material entrainment potential, Roaring Fork River at Basalt, Colorado: U.S. Geological Survey 

Water-Resources Investigations Report 02–4223, 33 p.

Foundation and Materials Consultants, Inc., 1972, Report on 

preliminary foundation investigation, Quake Lake Dam, 

Madison County, Montana: Missoula, Mont., Foundation 

and Materials Consultants, Inc. [prepared for U.S. Department of Agriculture Forest Service–Northern Region, Missoula, Mont., variously paged].
38 Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana

Hadley, J.B., 1964, Landslides and related phenomena accompanying the Hebgen Lake Earthquake of August 17, 1959: 

U.S. Geological Survey Professional Paper 435-K, 31 p.

Heitmuller, F.T., and Asquith, W.H., 2008, Potential for bedmaterial entrainment in selected streams of the Edwards 

Plateau—Edwards, Kimble, and Real Counties, Texas, and 

vicinity: U.S. Geological Survey Scientific Investigations 

Report 2008–5017, 76 p.

Henderson, F.M., 1966, Open channel flow: New York, MacMillan, 522 p.

Hughes, M.L., McDowell, W.A., and Marcus, W.A., 2006, 

Accuracy assessment of georectified aerial photographs–

Implications for measuring lateral channel movement in 

a GIS: Geomorphology, v. 74, p. 1–16. (Also available at 

http://dx.doi.org/10.1016/j.geomorph.2005.07.001.)

Johnson, M.V., and Omang, R.J., 1972, Degradation of the 

Earthquake Lake outflow channel, southwestern Montana: 

U.S. Geological Survey Professional Paper 800-C, 4 p.

Julien, P.Y., 1998, Erosion and sedimentation: Cambridge, 

United Kingdom, Cambridge University Press, 280 p.

Montana Fish, Wildlife and Parks, 2010, Metadata for Montana Blue and Red Ribbon Streams, accessed January 30, 

2010, at http://fwp.mt.gov/doingBusiness/reference/gisData/

metadata/blueredstreams.htm.

Montana State Library, 2007, Metadata for Montana 2005 

color NAIP orthophotos, 12-kilometer tiles: Montana Natural Resources Information System, accessed January 29, 

2007, at http://gisportal.msl.mt.gov/GPT9/catalog/search/

viewMetadataDetails.page?uuid={539F25E9-36E3-4F94-

A174-FF609D8192CC}.

Mueller, E.R., Nelson, J.M., and Pitlick, John, 2005, Variation in the reference Shields stress for bed load transport in 

gravel-bed streams and rivers: Water Resources Research, 

v. 41, W04006, 10 p. (Also available at http://dx.doi.

org/10.1029/2004WR003692.)

Parrett, C.P., and Johnson, D.R, 2004, 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. 

Shields, A.F., 1936, Application of similarity principles and 

turbulence research to bedload movement: translated from

Anwendung der Aehnlichkeitsmechanik und der Turbulenzforschung auf die Geschiebewegung: Mitteilung Preussischen Versuchanstalt für Wasserbau und Schiffbau, Berlin, 

No. 26, by Ott, W.P., and van Uchelen, J.C., California Institute of Technology, Hydrodynamics Laboratory, Publication 

number 176, Pasadena, Calif., 167, 43 p.

U.S. Army Corps of Engineers, 1972, Report on Quake Lake 

Project, Madison River, Montana: Omaha, Nebr., U.S. 

Army Corps of Engineers [variously paged].

U.S. Army Corps of Engineers, Hydrologic Engineering Center, 2008a, HEC-RAS, River analysis system user’s manual, 

version 4.0: Hydrologic Engineering Center, Davis, Calif., 

733 p.

U.S. Army Corps of Engineers, Hydrologic Engineering 

Center, 2008b, HEC-RAS, River analysis system hydraulic 

reference manual, version 4.0: Davis, Calif., 411 p.

U.S. Army Corps of Engineers, Hydrologic Engineering Center, 2008c, HEC-RAS, River analysis system applications 

guide, version 4.0:, Davis, Calif., 351 p.

U.S. Geological Survey, 2007a, National Aerial Photography 

Program (NAPP), [U.S. Geological Survey Center for Earth 

Resources Observation & Science (EROS)], accessed January 1, 2007, at http://eros.usgs.gov/#/Find_Data/Products_

and_Data_Available/NAPP.

U.S. Geological Survey, 2007b, National High Altitude 

Photography (NHAP), [U.S. Geological Survey Center for 

Earth Resources Observation & Science (EROS)], accessed 

January 1, 2007, at http://eros.usgs.gov/#/Find_Data/

Products_and_Data_Available/NHAP.

U.S. Geological Survey, 2008, Peak streamflow for Montana, 

accessed June 11, 2008, at http://nwis.waterdata.usgs.gov/

mt/nwis/peak.

U.S. Geological Survey, 2009, U.S. Geological Survey 

Photographic Library, accessed February 12, 2009, 

at http://libraryphoto.cr.usgs.gov/cgi-bin/search.

cgi?search_mode=noPunct&free_form=Madison&free_

form=Slide&free_form=dolomite&free_form=.

Wilcock, P.R., and McArdell, B.W., 1993, Surface-based 

fractional transport rates–Mobilization thresholds and 

partial transport of a sand-gravel sediment: Water Resources 

Research v. 29, no. 4, p. 1297–1312. (Also available at 

http://dx.doi.org/10.1029/92WR02748.)

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

material: American Geophysical Union Transactions, v. 35, 

p. 951–956.
Appendix 1 39

Appendix 1. Aerial Photographs and Locations of Stream Centerlines and Cross 

Sections of the Madison River Downstream from Earthquake Lake, Montana.

Incremental-channel movement was determined from 

14 aerial photographs taken between 1970 and 2006. Aerial 

photographs from the years 1980, 1981, 1987, 1990, and 2002 

are not included in this appendix because substantial channel movement was not observed from those photographs, 

except for the 40 ft (plus or minus 30 ft) of movement at cross 

section 700 and movement towards the road about 0.25 mi 

downstream from cross section 400, both observed in the 1987 

photograph. The 2006 digital orthophotograph was used as a 

reference to which the earlier photographs were rectified. On 

each aerial photograph, two stream centerlines were drawn: 

one centerline corresponded to the stream location shown on 

the photograph, and the other centerline corresponded to the 

stream location from the previous aerial photograph. In the 

more braided subreaches downstream from the Madison Slide, 

centerlines were drawn along the dominant flow-conveying 

channel at the date and streamflow corresponding to the 

aerial photograph. At higher streamflows, more than one of 

the braided channels could be inundated, and the differences 

between the centerlines would not be as dramatic. As discussed in the section “Methods,” channel-movement distances 

measured between centerlines on the aerial photographs are 

plus or minus 30 ft, due to potential errors in rectification of 

the photographs.

The nine aerial photographs (figs. A–1 to A–9) are 

located in the CD–ROM on the inside back cover of this 

report. This appendix also can be downloaded from http://

pubs.usgs.gov/sir/2012/5024/.
Publishing support provided by the: 

Denver and Rolla Publishing Service Centers

For more information concerning this publication, contact: 

Director, Montana Water Science Center 

U.S. Geological Survey 

3162 Bozeman Ave. 

Helena, MT 59601 

(406) 457–5900

Or visit the Montana Water Science Center Web site at: 

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

Chase and McCarthy— Lateral and Vertical Channel Movement and Potential for Bed-Material Movement on the Madison River, Montana—SIR 2012–5024

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