In cooperation with the

Maine Atlantic Salmon Commission and

U.S. Fish and Wildlife Service

Hydraulic-Geometry Relations for Rivers in Coastal and 

Central Maine

Scientific Investigations Report 2004-5042

U.S. Department of the Interior

U.S. Geological Survey
Cover Photograph: Piscataquis River at Dover-Foxcroft, Maine, October 18, 2000. (Photography by Laura Flight, 

U.S. Geological Survey)
Hydraulic-Geometry Relations for Rivers in Coastal 

and Central Maine

By Robert W. Dudley

In Cooperation with the

Maine Atlantic Salmon Commission and U

.S. Fish and Wildlife Service

Scientific Investigations Report 2004-5042

U.S. Department of the Interior

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

Gale A. Norton, Secretary

U.S. Geological Survey

Charles G. Groat, Director

U.S. Geological Survey, Augusta, Maine: 2004

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

Box 25286, Denver Federal Center

Denver, CO 80225

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endorsement by the U.S. Government.

Although this report is in the public domain, permission must be secured from the individual copyright owners to reproduce any copyrighted materials contained within this report.
 iii

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

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

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

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

Physiography and Hydrogeology............................................................................................................................2

Land Use.................................................................................................................................................................4

Climate ...................................................................................................................................................................5

Methods of Data Collection and Analysis.................................................................................................................................5

Streamflow.....................................................................................................................................................................5

Bankfull Streamflow.......................................................................................................................................................6

Stream-Channel Geometry.............................................................................................................................................6

Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine..................................................................................8

Bankfull Streamflow.......................................................................................................................................................8

At-a-Station Hydraulic-Geometry Relations ..................................................................................................................9

Regional Hydraulic-Geometry Relations ......................................................................................................................10

Summary and Conclusions ......................................................................................................................................................11

References Cited .....................................................................................................................................................................18

Figures

1. Map showing locations of U.S. Geological Survey streamflow-gaging stations and Instream Flow

Incremental Methodology sites in coastal and central Maine used in this study................................................ 3

2. Schematic diagram showing measures of channel geometry ................................................................................... 7

3. Relation of bankfull streamflow to mean annual streamflow for rivers in coastal and central Maine.....................11

4. Regional relation of bankfull streamflow to drainage area for rivers in coastal and central Maine.........................13

5. Regional relation of bankfull channel width to drainage area for rivers in coastal and central Maine. ...................14

6. Regional relation of bankfull mean channel depth to drainage area for rivers in coastal and central Maine ..........15

7. Regional relation of bankfull channel cross-sectional area to drainage area for rivers in coastal and 

central Maine........................................................................................................................................................16

Tables

1. U.S. Geological Survey streamflow-gaging stations and Instream Flow Incremental Methodology 

sites in coastal and central Maine used in this study.......................................................................................... 4

2. Climatological data, 1971-2000, for National Weather Service stations in coastal and central Maine................... 5

3. Mean annual, 1.5-year peak, and bankfull streamflows, and flow duration of bankfull streamflow for

rivers in coastal and central Maine...................................................................................................................... 9

4. Coefficients and exponents for the at-a-station hydraulic-geometry equations for selected U.S. 

Geological Survey streamflow-gaging stations in coastal and central Maine....................................................10

5. Regional regression equations for estimating bankfull channel width, channel depth, and 

streamflow velocity as functions of bankfull streamflow for rivers in coastal and central Maine.....................12

6 Regional regression equations for estimating bankfull streamflow, channel width, channel depth, and 

channel cross-sectional area as functions of drainage area for rivers in coastal and central Maine ................12

7. Regional regression equations for estimating bankfull streamflow, bankfull channel width, 

mean bankfull channel depth, and bankfull channel cross-sectional area for various regions 

in the eastern United States.................................................................................................................................17

CONTENTS
iv 

Appendix 1: Descriptions of U.S. Geological Survey Streamflow-Gaging Stations

A1. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the West

Branch Union River at Amherst, Maine (USGS streamflow-gaging station number 01023000) .........................21

A2. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for 

Garland Brook near Mariaville, Maine (USGS streamflow-gaging station number 01024200) ..........................22

A3. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the 

Piscataquis River near Dover-Foxcroft, Maine (USGS streamflow-gaging station number 01031500) ..............23

A4. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for 

Passadumkeag River at Lowell, Maine (USGS streamflow-gaging station number 01035000)..........................24

A5. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the

Sheepscot River at North Whitefield, Maine (USGS streamflow-gaging station number 01038000) ................25

A6. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for 

Johnson Brook at South Albion, Maine (USGS streamflow-gaging station number 01049130).........................26

A7. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the

Togus River at Togus, Maine (USGS streamflow-gaging station number 01049550) .........................................27

A8. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the 

Swift River near Roxbury, Maine (USGS streamflow-gaging station number 01055000)...................................28

A9. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the

Nezinscot River at Turner Center, Maine (USGS streamflow-gaging station number 01055500).......................29

A10. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the 

Royal River at Yarmouth, Maine (USGS streamflow-gaging station number 01060000)....................................30

Conversion Factors

To convert temperature in degrees Fahrenheit (°F) to degrees Celsius (°C) use the following equation:

°C = 5/9 * (°F - 32)

Multiply By To obtain

gallon per minute (gal/min) 3.785 liter per minute

inch (in.) 25.4 millimeter

foot (ft) 0.3048 meter

mile (mi) 1.609 kilometer

square mile (mi2) 2.589 square kilometer

foot per second (ft/s) 0.3048 meter per second

cubic foot per second (ft3/s) 0.02832 cubic meter per second
Hydraulic-Geometry Relations for Rivers in Coastal and 

Central Maine

By Robert W. Dudley

Abstract

Hydraulic-geometry relations (curves) were 

derived for 15 sites on 12 rivers in coastal and central 

Maine on the basis of site-specific (at-a-station) 

hydraulic-geometry relations and hydraulic models. Ata-station hydraulic-geometry curves, expressed as wellestablished power functions, describe the relations 

between channel geometry, velocity, and flow at a 

given point on a river. The derived at-a-station 

hydraulic-geometry curves indicate that, on average, a 

given increase in flow at a given river cross section in 

the study area will be nearly equally conveyed by 

increases in velocity and channel cross-sectional area.

Regional curves describing the bankfull streamflow and associated channel geometry as functions of 

drainage area were derived for use in stream-channel 

assessment and restoration projects specific to coastal 

and central Maine. Regional hydraulic-geometry curves 

were derived by combining hydraulic-geometry information for 15 river cross sections using bankfull flow as 

the common reference streamflow. The exponents of 

the derived regional hydraulic-geometry relations indicate that, in the downstream direction, most of the 

conveyance of increasing contribution of flow is 

accommodated by an increase in cross-sectional 

area—with about 50 percent of the increase in flow 

accommodated by an increase in channel width, and 32 

percent by an increase in depth. The remaining 18 

percent is accommodated by an increase in streamflow 

velocity.

On an annual-peak-series basis, results of this 

study indicate that the occurrence of bankfull streamflow for rivers in Maine is more frequent than the 1.5-

year streamflow. On a flow-duration basis, bankfull 

streamflow for rivers in coastal and central Maine is 

equaled or exceeded approximately 8.1 percent of the 

time on mean—or about 30 days a year. Bankfull 

streamflow is roughly three times that of the mean 

annual streamflow for the sites investigated in this 

study. Regional climate, snowmelt hydrology, and 

glacial geology may play important roles in dictating 

the magnitude and frequency of occurrence of bankfull 

streamflows observed for rivers in coastal and central 

Maine.

Introduction

Understanding the physical processes that 

control the dimension, plan, profile, and function of 

natural, self-maintaining river channels is critical to 

understanding river conditions favorable for stable and 

productive fish habitat. Although biologists have a 

good understanding of the physical characteristics of 

favorable habitat for Atlantic salmon, less information 

is available on the form and function of natural, selfmaintaining river channels in Maine. Improved understanding of the relation of river-channel geometry to 

streamflow (also referred to as discharge), watershed 

characteristics, and productivity of salmon habitat can 

assist regulatory agencies in evaluating the effects of 

anthropogenic disturbance on habitat productivity and 

can guide the restoration of such sites (Jowett, 1998). 

The dimensions of a river channel are a result of 

the ability of the water to erode the land surface 

opposed by the ability of land surface to resist that 

erosion. A river’s ability to erode sediment is a function 

of the magnitude and frequency of streamflow and 

suspended-sediment load in the system. Farming and 

forestry practices, residential and urban development 

(filling in wetlands, paving surfaces, constructing 

bridges and culverts), and water management 

(damming, withdrawing, and diverting) can affect the 

amount, location, and timing of water movement 

through a watershed. Physical alteration of a watershed 

can introduce hydraulic instability in the system and 

cause the river to adjust its ability to transport water and 

sediment at the point of the activity; these changes can, 
2 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

in turn, propagate upstream and (or) downstream. Such 

changes can include increased deposition (aggradation), 

increased erosion (degradation), bank slumping, overwidening, and the abandonment of existing channels for 

new ones (Dunne and Leopold, 1978; Rosgen, 1996). A 

river channel affected by changes that compromise the 

stream’s ability to be self-maintaining is described as 

“disturbed.”

With growing public interest in instream restoration projects in Maine, the number and extent of disturbed 

river reaches needs to be objectively quantified—requiring a baseline knowledge of the characteristics of relatively undisturbed river channels in the region. 

Hydraulic geometry has been used for half a century to 

help assess the physical and hydraulic variables in natural 

channel stability (Leopold and Maddock, 1953). Stable, 

self-maintaining, natural channels conform to a crosssectional geometry, plan, and profile proportional to the 

size of the upstream watershed, streamflow, and sediment 

load (Dunne and Leopold, 1978). Within a region of 

homogenous geology and climate, the mean characteristics describing the shape of the channel are sufficiently 

consistent for the degree of deviation from what is 

commonly observed in the region to be interpreted as the 

magnitude of the effect of disturbance (Dunne and 

Leopold, 1978). Regional statistical models or curves that 

relate river-channel geometry to drainage area and 

streamflow make use of this concept and are a valuable 

tool used to characterize disturbed river reaches and to 

help water-resources managers ensure the efficacy and 

longevity of restoration projects. To develop these 

regional statistical curves for rivers in Maine, the U.S. 

Geological Survey (USGS) entered into a cooperative 

agreement with the Maine Atlantic Salmon Commission 

(ASC), and U.S. Fish and Wildlife Service (USFWS) in 

2001.

Purpose and Scope

This report presents the data, methods, and results 

of a cooperative study (from 2001 to 2003) to collect 

hydraulic-geometry data at 15 sites on 12 streams in 

coastal and central Maine, and to derive regional 

hydraulic-geometry curves based on those data. Regional 

hydraulic-geometry curves relate river-channel hydraulic 

geometry (morphology) to explanatory characteristics of 

a drainage basin, such as drainage area, for rivers in a 

particular region of study (region of similar geology and 

climate). The regional hydraulic-geometry curves, based 

on the USGS streamflow-measurement and stagedischarge relation data, as well as data obtained from 

Instream Flow Incremental Methodology (IFIM) studies, 

were developed to assist the cooperating agencies and 

other natural-resources managers with river morphology 

and habitat assessment, and river restoration projects in 

coastal and central Maine. The scope of this investigation 

was confined to rivers in coastal and central Maine that 

have USGS streamflow measurement and stagedischarge relation data available or were investigated in 

an earlier IFIM study for the ASC, and (or) contain 

Atlantic salmon habitat. The regional curves developed 

here are compared to regional curves that have been 

developed for the States of North Carolina, Maryland, 

Vermont, and Pennsylvania (Sweet and Geratz, 2003; 

McCandless and Everett, 2002; Harman and others, 

2001; Jaquith and Kline, 2001; White, 2001; Harman and 

others, 1999).

Description of the Study Area

The study area includes 15 sites on 12 rivers in 

coastal and central Maine. Ten sites currently are or 

historically have been gaged by the USGS (table 1; fig. 

1). The five other site are IFIM sites on the Pleasant 

River (2 sites) and Narraguagus River (3 sites) (table 1; 

fig. 1). Sites were selected in coastal and central Maine 

to minimize variations in the hydraulic-geometry curves 

caused by differences in physiographic setting, including 

but not limited to rivers that contain known Atlantic 

salmon habitat. 

Physiography and Hydrogeology

Continental glaciers intermittently covered Maine 

from about 1.5 million to 10,000 years ago. As the 

glaciers slowly moved across the land they altered the 

landscape by eroding, transporting, and depositing rock 

debris for miles. The surficial geology of present-day 

Maine largely consists of sand, gravel, and other unconsolidated sediments produced by this erosion, transport, 

and deposition by glaciers (Marvinney and Thompson, 

2000; Johnson, 1925). The surficial material for all the 

watersheds in this study is predominantly glacial till (a 

heterogeneous, unsorted mix of material ranging in size 

from fine sand to boulders, with generally low permeability) and stratified drift, which occasionally includes 

glaciomarine deposits and eskers (Thompson and Borns, 

1985). Sand and gravel deposits and fractured bedrock 

serve as ground-water aquifers throughout the State. 

The five IFIM sites P3, P11, N11, N12a, and N12b 

and USGS stations 01038000, 01049130, 01049550, and 

01060000 (table 1; fig. 1) are in coastal and near-coastal
Introduction 3

Figure 1. U.S. Geological Survey streamflow-gaging stations and Instream Flow Incremental Methodology sites in coastal and central Maine 

used in this study.

70o

71o

45o

44o

43o

69o 68o

67o

01023000

01024200

01031500 01035000

01038000

01049130

01049550

01054300

01055000

01055500

01060000

EXPLANATION

U.S. Geological Survey streamflowgaging station and identifier

Instream Flow Incremental

Methodology site and identifier

National Weather Service station

County boundary

SCALE

0

0

20 MILES

30 KILOMETERS

Base from U.S. Geological Survey

digital files, scale 1:2,000,000,

projection UTM, zone 19

Atlantic Ocean

YORK

CUMBERLAND

ANDROSCOGGIN

OXFORD

FRANKLIN

KENNEBEC

KNOX

WALDO

SOMERSET

PENOBSCOT

PISCATAQUIS

WASHINGTON

SAGADAHOC

LINCOLN

HANCOCK

Dover-Foxcroft

Eastport

Grand Lake Stream

Portland

Augusta

Rumford

River

Penobscot

Kennebec

Androscoggin River

River

River

Piscataquis

0

0

40

50

80 MILES

100 KILOMETERS

45

71o

70 o

69 o 68 o

67 o

44 o

47 o

46 o

43 o

West Branch

Union River

River

Royal

Sheepscot r Rive

Swift River

Togus Stream

Garland Brook

River

Nezinscot

Pl R easa e nt iv r Narraguagus

River

River

Passadumkeag

P3

P3

N11, N12a, N12b

P11

STUDY AREA
4 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

Table 1. U.S. Geological Survey streamflow-gaging stations and Instream Flow Incremental Methodology sites in coastal and 

central Maine used in this study.

U.S. Geological Survey streamflow-gaging station

Latitude 

(north, 

decimal 

degrees)

Longitude 

(west, 

decimal 

degrees)

Drainage 

area 

(square 

miles)

Period of record for 

streamflow data

Number Name

01023000 West Branch Union River at Amherst, Maine 44.840 68.372 148 1910-1919, 1929-1979

01024200 Garland Brook near Mariaville, Maine 44.721 68.411 9.79 1964-1982

01031500 Piscataquis River near Dover-Foxcroft, Maine 45.175 69.315 298 1903-2001

01035000 Passadumkeag River at Lowell, Maine 45.185 68.474 297 1916-1979

01038000 Sheepscot River at North Whitefield, Maine 44.223 69.593 145 1938-2001

01049130 Johnson Brook at South Albion, Maine 44.498 69.486 2.92 1980-1991

01049550 Togus Stream at Togus, Maine 44.266 69.698 23.7 1982-1995

01055000 Swift River near Roxbury, Maine 44.642 70.588 96.9 1929-2001

01055500 Nezinscot River at Turner Center, Maine 44.270 70.230 169 1941-1996

01060000 Royal River at Yarmouth, Maine 43.799 70.179 141 1950-2001

Instream Flow Incremental Methodology site

Number Name

P3 Pleasant River Transect Number 3 44.67 67.74 94.0 --

P11 Pleasant River Transect Number 11 44.78 67.92 22.5 --

N11 Narraguagus River Transect Number 11 44.74 68.01 93.6 --

N12a Narraguagus River Transect Number 12a 44.84 68.07 65.0 --

N12b Narraguagus River Transect Number 12b 44.85 68.07 65.0 --

river watersheds. These watersheds are in a physiographic region of broad lowlands that were inundated by 

the ocean during deglaciation. Randall (2001) describes 

this region as composed of sparse and scattered coarsegrained stratified drift deposited early during deglaciation with some fine-grained stratified drift generally at or 

close to land surface.

The remaining six USGS sites are in a formerly 

glaciated region that generally sloped away (south to 

south-east) from the ice. Stations 01024200 and 

01055500 are in a region with abundant coarse-grained 

stratified drift in the stream valleys. Stations 01023000 

and 01035000 are in a region with sparser coarse-grained 

stratified drift deposited mostly in eskers. Stations 

01031500 and 01055000 are in a high-relief area with 

coarse stratified drift commonly perched above the 

modern stream grade on the valley sides. The valley-fill 

material in this region is capped by alluvium and there 

are scattered bedrock outcrops (Randall, 2001).

Land Use

The 15 sites are in counties that are 70- to 97-

percent forested and characterized by rolling topography 

with no urban development (Irland, 1998). The greatest 

changes in land use in Maine have occurred with the 

replacement of agriculture and pasture lands by forest 

during the past century. The State’s overall forest cover, 
Methods of Data Collection and Analysis 5

estimated at about 70 percent in 1900, increased to 

approximately 90 percent by 1995 (Irland, 1998). Six of 

the 12 study watersheds (Pleasant, Narraguagus, Garland, 

West Branch Union, Passadumkeag, and Piscataquis) are 

in the sparsely populated counties of Washington, 

Hancock, southern Penobscot and southern Piscataquis 

counties (fig. 1). During 1880-1995, the increase in forest 

cover in these counties has been relatively minor, ranging 

from about 11 to 22 percent (Irland, 1998). Four of the 

watersheds (Sheepscot, Johnson, Togus, and Royal) are 

in the historically more populated counties of Lincoln, 

Androscoggin, Cumberland, Kennebec, and Waldo (fig. 

1). These counties were historically more heavily deforested and have seen increases in forest cover ranging 

from approximately 100 to 186 percent during 1880-1995 

(Irland, 1998). The remaining two watersheds (Swift and 

Nezinscot) are in western Maine in Franklin, Oxford, and 

western Androscoggin counties. Since 1880, these three 

counties have seen mean increases in forest area of 33, 

67, and 100 percent, respectively (Irland, 1998).

Climate

The climate of coastal and central Maine is typified 

as temperate and humid with mild summers and cold 

winters with little spatial variability (table 2). Records 

from National Weather Service (NWS) stations in Portland, Rumford, Augusta, Dover-Foxcroft, Grand Lake 

Stream, and Eastport (fig. 1) indicate a mean normal 

annual temperature, based on the 30-year period 1971-

2000, of 44 oF (table 2). Mean monthly temperatures 

range from 18 oF in January to 67 oF in July. The mean 

annual precipitation is about 44 in., and is fairly evenly 

distributed throughout the year (National Oceanic and 

Atmospheric Administration, 2002). High streamflows in 

coastal and central Maine typically occur in the spring 

due to snowmelt, which largely determines the relative 

magnitude and frequency of high streamflows.

Methods of Data Collection and Analysis

Streamflow

The 10 USGS streamflow-gaging stations used in 

this study were selected on the basis of several criteria: 

(1) only unregulated, nonurban rivers gaged by the USGS 

with 10 or more years of continuous-streamflow record 

were considered; (2) only sites in coastal and central 

Maine were eligible for consideration; (3) rivers with 

known Atlantic salmon habitat and similar channel 

substrate based on regional surficial geology were 

included where possible (all the rivers in this study have 

channels composed of gravel, cobbles, boulders, and 

bedrock); and (4) only USGS streamflow-gaging stations 

with measurements available at natural, stable cross 

sections were used. Stations with streamflow measurements at or near bridges or other hydraulic structures that 

could represent an unnatural cross-sectional geometry 

were not included.

Daily mean streamflow data for the 10 USGS 

streamflow-gaging stations (table 1; fig. 1) were obtained 

from the USGS National Water Information System 

(U.S. Geological Survey, 1998). The stations had periods 

of record ranging from 12 to 99 years in length with a 

mean of 51 years. For each of the streamflow-gaging

Table 2. Climatological data, 1971-2000, for National Weather Service stations in coastal and central Maine.

National Weather 

Service station locations

Mean annual 

temperature (oF)

Mean monthly 

January 

temperature (o

F)

Mean monthly 

July temperature 

(

oF)

Annual 

precipitation 

(in.)

Portland 45.7 21.7 68.7 45.8

Rumford 43.9 17.1 68.2 44.9

Augusta 45.8 19.5 70.1 42.3

Dover-Foxcroft 40.3 12.1 66.0 44.0

Grand Lake Stream 42.3 15.3 67.3 44.8

Eastport 44.1 22.1 64.0 44.8

Mean 43.7 18.0 67.4 44.4
6 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

stations used in this study, continuous records of streamflow were computed by applying the relation between 

the continuously recorded height of the gaged water 

surface relative to an established datum plane (stage) 

and the flow of the river (discharge) (Rantz and others, 

1982). The river channel or structure (riffle, bedrock 

falls, bridge opening, culvert opening) that controls the 

level of the gaged water surface is called the hydraulic 

control for the station. The stage-discharge relation is a 

function of the geometry of the river channel or structure and can vary over time as the channel fills and (or) 

scours. The historical stage-discharge relations for each 

station were obtained from station-analysis files 

archived at the USGS Maine District office. These 

historical stage-discharge relations were qualitatively 

evaluated for systematic trends over time to determine if 

the river channels near the stations were systematically 

aggrading or degrading. All stations evaluated appeared 

to be stable and self-maintaining with regard to the variability observed in the stage-discharge relations.

A range of streamflow measurements was made 

at each IFIM site as part of the IFIM studies. Streamflows were measured using standard streamflow 

measurement techniques (Rantz and others, 1982) with 

a Marsh-McBirney Model 2000 Flowmate electronic 

current meter attached to a top-setting wading rod 

(Kleinschmidt Associates, 1999a, 1999b). The streamflow measurements were used to calibrate a hydraulic 

model at each of the IFIM cross sections. Once calibrated, the hydraulic models provide a method for estimating streamflow at the IFIM cross section given a 

surveyed water-surface elevation.

Bankfull Streamflow

A common reference flow with a specific recurrence interval is used to integrate the hydraulic-geometry data for a variety of rivers in a region. Regional 

hydraulic-geometry curves often are calibrated to a 

reference flow known as bankfull flow (Qbkf). Bankfull 

flow is the flow that completely fills the channel up to 

the elevation of the floodplain, without overtopping the 

channel banks. Bankfull flow is a useful reference flow 

because it can be estimated at ungaged sites based on 

observable, physical channel features and does not 

require knowledge of flow frequency in the river. 

Furthermore, bankfull flow is generally thought to be 

the flow that determines the dominant morphological 

characteristics of river channels. Dunne and Leopold 

(1978) describe bankfull flow as the “discharge at 

which channel maintenance is the most effective, that is, 

the discharge at which moving sediment, forming or 

removing bars, forming or changing bends and meanders, and generally doing work that results in the mean 

morphologic characteristics of channels.”

The elevation of the bankfull streamflow at each 

USGS streamflow-gaging station and IFIM site was 

determined by surveying the elevation of nearby bankfull morphological features. Morphological features 

defining the extent of the “active channel” (U.S. 

Geological Survey, 1975) include: (1) tops of point 

bars—composed of sediment deposited on the insides of 

meander bends; (2) changes in vegetation—the low 

limit of upland, perennial vegetation on the bank, or 

sharp breaks in vegetation density and (or) type; (3) 

changes in channel-bank slope—the change from a 

vertical bank to a horizontal surface (floodplain); and 

(4) changes in bank materials—clear changes in sediment-particle sizes that may be associated with changes 

in bank slope (McCandless and Everett, 2002; Brunner, 

1999; Rosgen, 1996). Change in channel-bank slope 

was the most common bankfull feature used to identify 

bankfull stage in this study. Bankfull streamflow at each 

USGS streamflow-gaging station was determined by 

applying the most recent stage-discharge relation (rating 

curve) for that site to determine the streamflow that 

corresponded to the surveyed bankfull elevation. The 

surveyed bankfull elevation at each IFIM cross section 

was applied to the calibrated hydraulic model for that 

cross section to compute the corresponding bankfull 

streamflow.

Stream-Channel Geometry

When making measurements at streamflowgaging stations, hydrographers measure streamflow 

velocity, channel width, and channel depth. Streamflow-measurement notes provide the quantitative data 

used to develop the at-a-station curves that describe the 

manner in which width, depth, and velocity change with 

streamflow at the 10 USGS streamflow-gaging stations. 

Hydraulic-geometry curves that reflect the most recent 

watershed land use (primarily reforestation since the 

early 20th century) were developed using measurement 

notes from the most recent available date backwards 

until a minimum of nine measurements, representing a 

wide range of streamflows, were identified. 
Methods of Data Collection and Analysis 7

The flow of a river may be measured in different 

locations depending on the flow conditions; for example, 

low flows may be measured at a wading cross section and 

high flows may be measured from a bridge at a different 

cross section nearby. For each USGS streamflow-gaging 

station, measurements that represent a single, naturalchannel cross section were selected. This selection 

process required careful review of the streamflowmeasurement notes to determine the location of each 

measurement. Several stations offered ideal naturalchannel cross sections equipped with cableways that 

enabled hydrographers to measure a range of flows at a 

single, repeatable location. Conversely, some sites had 

measurements at a number of different locations, making 

it difficult to select a group of at least 9 to 10 measurements that represented a single cross section. For the 

IFIM sites, cross-sectional geometry data were surveyed 

in the field at one location for each site.

The fundamental relations between channel-geometry dimensions, velocity, and flow can be expressed as 

the following well-established power functions (Leopold 

and Maddock, 1953; Dunne and Leopold, 1978; 

Osterkamp and others, 1983; Leopold and others, 1992):

w=aQb, (1)

d=cQf, (2)

v=kQm (3)

Where Q is streamflow in ft3/s, w is cross section 

width in ft, d is mean cross section depth in ft (crosssectional area, A, in ft2

, divided by w), v is the mean 

cross-sectional velocity in ft/s (Q divided by A), b, f, and 

m are derived exponents, and a, c, and k are derived coefficients (fig. 2). 

Because flow is the product of velocity and area,

Q = Av (4)

From the equations above:

Q = (aQb)(cQf)(kQm) (5)

Then,

b + f + m = l (6)

a * c * k = l (7)

The power relations for each site are referred to as 

“at-a-station curves” and describe how the river channel 

accommodates changes in flow at a particular point in the 

river (for example, see Emmett’s (1975) at-a-station analyses for the Upper Salmon River Area, Idaho). The at-astation curves were derived for each of the 10 USGS 

streamflow-gaging stations by linear regression of the 

base-10 logarithms of w, d, and v against the base-10 

logarithm of Q.

Hydraulic-geometry data used to derive the 

regional curves were computed by substituting the bankfull streamflow (Qbkf) determined for each of the 10 

USGS streamflow-gaging stations into the derived at-astation curves for that site. For the IFIM sites, bankfull 

hydraulic-geometry data were computed from surveyed 

cross-section data used to develop the hydraulic models 

for each site (Kleinschmidt Associates, 1999a, 1999b).

Figure 2. Schematic diagram showing measures of channel geometry.

channel width, w

mean depth, d=A/w

cross-sectional area, A
8 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

 The base-10 logarithms of the bankfull w, d, and v

(denoted wbkf, dbkf, vbkf) were individually regressed 

against the base-10 logarithm of Qbkf for all 15 stations to 

derive regional curves as a function of bankfull streamflow. These resulting regression lines are also referred to 

as “downstream curves” because they describe the 

manner in which a river conveys increasing contribution 

of flow in a downstream direction by changes in width, 

depth, and velocity. 

A fundamental condition for regional curves is that 

they are derived from data representative of stable, selfmaintaining reaches whose form is not systematically 

changing over time. To quantitatively ensure that this 

condition is met, temporal trends were analyzed for the 

cross-sectional-area data for each site using the nonparametric Mann-Kendall test (Helsel and Hirsch, 1992). 

None of the sites had a significant (p<0.1) temporal trend 

in cross-sectional area.

Hydraulic-Geometry Relations for Rivers in 

Coastal and Central Maine

Bankfull Streamflow

Based on regional curve analyses in many regions 

outside Maine, bankfull streamflow occurs, in general, 

every 1 to 2 years, averaging about every 1.5 years 

(Dunne and Leopold, 1978; Emmett, 1975; Leopold and 

others, 1992). The cited recurrence intervals are 

computed on the basis of an annual-peak-series analysis 

(Interagency Advisory Committee on Water Data, 1982). 

McCandless and Everett (2002), Jaquith and Kline 

(2001), and Emmett (1975) found that bankfull streamflows for their sites had mean recurrence intervals of 

about 1.5 years. Harman and others (1999) and White 

(2001) found bankfull streamflows for sites in the Piedmont regions of North Carolina, Pennsylvania and Maryland had a mean recurrence interval of 1.4 years. Harman 

and others (2001) found bankfull streamflows for sites in 

the North Carolina Blue Ridge region had a mean recurrence interval of 1.3 years. Emmett (1975) stated that the 

occurrence of bankfull flow in the Upper Salmon River 

area of Idaho was approximately four times that of the 

mean annual flow. On average, on a flow-duration basis, 

Emmett (1975) noted that bankfull streamflow was 

equaled or exceeded about 4 percent of the time.

Results of this study indicate that, on an annualpeak-series basis, the occurrence of bankfull streamflow 

for rivers in Maine is more frequent than the occurrence 

of bankfull flow observed in other regions. All the bankfull streamflows in this study were of lesser magnitude 

than the corresponding 1.5-year peak-flow event (table 

3). Sweet and Geratz (2003) also found that the occurrence of bankfull streamflows in the Coastal Plain of 

North Carolina to be much shorter than the 1.5-year 

interval estimated by other national and North Carolina 

studies. A derived linear-regression relation between 

bankfull and mean annual streamflows in Maine indicates 

that bankfull streamflow is roughly three times that of the 

mean annual streamflow (fig. 3). In comparison, Dunne 

and Leopold (1978) observed that rivers in Pennsylvania, 

where peak flows are typically caused by heavy rain 

events, had bankfull to mean-annual flow ratios 2 to 4 

times higher than ratios for rivers in Wyoming, where 

peak flows typically result from mountain snowmelt.

Although the occurrence of bankfull flows in 

coastal and central Maine, on an annual-peak-series 

basis, is more frequent than the 1.5-year peak-flow event, 

bankfull streamflows are equaled or exceeded approximately 8.1 percent of the time on mean—or about 30 days 

a year on a flow-duration basis (table 3). The flow-duration occurrence of bankfull streamflow in coastal and 

central Maine is similar to the 4-percent flow-duration 

exceedance probability (15 days a year) computed by 

Emmett (1975) for bankfull flows in the Upper Salmon 

River watershed in Idaho.

At the high-frequency end of an annual-peak series 

(streamflows approaching the 1-year recurrence 

interval), flows of equal flow-duration exceedance probability on different streams will occur more frequently in 

streams for which the rainfall-runoff response is quicker. 

Streams will have a quick rainfall-runoff response if they 

have characteristics such as steep basin slopes, little to no 

surface-water storage, and (or) impervious or low-permeability basin areas. For example, the drainage areas for 

the stations on the Passadumkeag River at Lowell, Maine 

(USGS station 01035000) and Togus Stream at Togus, 

Maine (USGS station 01049550) have more than 20 

percent surface-water storage in the form of lakes, pond, 

and wetlands. The 1.5-year flood streamflows (computed 

on an annual-peak-series basis) for these two streams 

have flow-duration exceedance probabilities of 2.8 

percent and 0.6 percent, respectively. By contrast, the 

Swift River near Roxbury, Maine (USGS station 

01055000), and the Wild River at Gilead, Maine (USGS 

station 01054200), have quicker rainfall-runoff 

responses, because each has less than 4 percent of their 

drainage area as surface-water storage. Consequently, the 

1.5-year-flood streamflows at these streams have flowduration exceedance probabilities of 0.07 percent
Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine 9

Table 3. Mean annual, 1.5-year peak, and bankfull streamflows, and flow duration of bankfull streamflow for rivers in coastal and central 

Maine.

[ft3/s, cubic feet per second]

U.S. Geological Survey streamflow-gaging station Mean annual 

streamflow 

(ft3

/s)

1.5-year peak 

streamflow 

(ft3

/s)

Bankfull 

streamflow 

(ft3

/s)

Flow duration

 of bankfull 

streamflow 

Number Name (percent)

01023000 West Branch Union River at Amherst, Maine 270 1,500 943 4.7

01024200 Garland Brook near Mariaville, Maine 22 324 41 14.3

01031500 Piscataquis River near Dover-Foxcroft, Maine 600 6,770 3,260 2.8

01035000 Passadumkeag River at Lowell, Maine 506 1,760 924 15.3

01038000 Sheepscot River at North Whitefield, Maine 248 1,630 582 11.3

01049130 Johnson Brook at South Albion, Maine 4.7 58 16 6.0

01049550 Togus Stream at Togus, Maine 41 339 94 10.7

01055000 Swift River near Roxbury, Maine 202 4,760 688 6.2

01055500 Nezinscot River at Turner Center, Maine 301 2,670 883 7.4

01060000 Royal River at Yarmouth, Maine 271 3,120 1,460 2.6

 Mean: 8.1

and 0.02 percent respectively. Compared to streams in 

the western and southern United States, where other 

regional curves have been derived, Maine streams could 

be considered to have a quicker rainfall-runoff response 

due to the effects of hydrogeology and climate.

The glacial geology of Maine may play a role in 

dictating the magnitude and frequency of occurrence of 

bankfull streamflows in Maine. Given the relatively 

recent glacial activity, the river systems in coastal and 

central Maine are relatively young compared to those in 

other regions of the United States. Coastal and central 

Maine stream-channel beds typically contain bedrock 

and large boulders. The boulders are typically of such 

size that they are not regularly transported downstream 

except during extreme high-flow events with flow magnitudes much greater than bankfull flows. In other regions 

of the United States, where the surficial material is 

homogenous, fine-grained sediment, river systems that 

are unregulated and self-maintaining are free to form 

meandering patterns and channel slopes according to 

their drainage-area sizes, and water and sediment 

supplies. In comparison, streams in coastal and central 

Maine examined in this study appear to carry little 

suspended fine-grained sediment load and their meanders 

and slopes are commonly controlled by bedrock outcrops 

and fissures (Stephen M. Dickson, Maine Geological 

Survey, oral commun., 2003; Johnson, 1925).

At-a-Station Hydraulic-Geometry Relations 

The derived at-a-station hydraulic-geometry relations indicate that, on average, a given increase in flow at 

a given river cross section in the study area will be nearly 

equally conveyed by increases in velocity and crosssectional area (table 4). Based on the mean derived at-astation hydraulic-geometry-equation exponents, about 48 

percent of the increase in flow is accommodated by an 

increase in velocity, 33 percent by an increase in depth, 

and 19 percent by an increase in width.

Comparison of the exponent values derived for 

rivers in coastal and central Maine (table 4) to those 

derived for other regions illustrates the variability in 

these relations due to climate and physiographic setting. 

Williams (1978) graphically computed hydraulic exponents for 165 streams across the United States, representing many physiographic regions, resulting in 

exponent ranges of 0.00 < b < 0.82, 0.10 < f < 0.78, and 

0.03 < m < 0.81. Mackey and others (1998) derived mean 

at-a-station exponents of b = 0.16, f = 0.30, and m = 0.55 

for 24 river sites in Massachusetts as part of a hydraulic-
10 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

General forms of hydraulic-geometry equations: w=aQb; d=cQf; v=kQm

Table 4. Coefficients and exponents for the at-a-station hydraulic-geometry equations for selected U.S. Geological Survey streamflow-gaging 

stations in coastal and central Maine.

[w, channel width in feet; d, mean channel depth in feet; v, mean streamflow velocity in feet per second; Q, streamflow in cubic feet per second; a, c, k, coefficients of hydraulic-geometry 

curves; b, f, m, exponents of hydraulic-geometry curves; equations defined in table footer]

USGS streamflow-gaging station Coefficients Exponents

Number Name a c k Product b f m Sum

01023000 West Branch Union River at Amherst, Maine 28.7 0.342 0.102 1.00 0.164 0.321 0.515 1.00

01024200 Garland Brook near Mariaville, Maine 5.89 0.311 0.545 1.00 0.314 0.411 0.275 1.00

01031500 Piscataquis River near Dover-Foxcroft, Maine 32.8 0.319 0.096 1.00 0.200 0.320 0.480 1.00

01035000 Passadumkeag River at Lowell, Maine 31.8 0.199 0.158 1.00 0.159 0.388 0.453 1.00

01038000 Sheepscot River at North Whitefield, Maine 35.2 0.498 0.057 1.00 0.103 0.281 0.617 1.00

01049130 Johnson Brook at South Albion, Maine 3.22 0.310 1.002 1.00 0.509 0.399 0.093 1.00

01049550 Togus Stream at Togus, Maine 13.5 0.250 0.297 1.00 0.224 0.378 0.398 1.00

01055000 Swift River near Roxbury, Maine 95.1 0.731 0.014 0.99 0.046 0.272 0.681 1.00

01055500 Nezinscot River at Turner Center, Maine 42.0 0.504 0.047 1.00 0.106 0.290 0.604 1.00

01060000 Royal River at Yarmouth, Maine 90.4 0.653 0.017 1.00 0.068 0.272 0.660 1.00

 Mean 0.189 0.333 0.478

geometry investigation. Emmett (1975) derived at-astation curves for 39 sites in the upper Salmon River area 

in Idaho as part of a hydrologic evaluation of the area. The 

resulting mean at-a-station exponent values were b = 

0.14, f = 0.40, and m = 0.46. Leopold and Maddock 

(1953) derived mean exponent values of b = 0.26, f = 

0.40, and m = 0.34 for 20 semiarid river sites in the Great 

Plains and southwestern United States. 

The USGS cross sections used to derive the at-astation hydraulic relations at each streamflow-gaging 

station in Maine are described by station in appendix 1. 

Regional Hydraulic-Geometry Relations 

Regional hydraulic-geometry curves were derived 

by combining at-a-station relation information for the 10 

USGS stations and hydraulic-geometry information from 

the 5 IFIM sites, referenced to bankfull streamflow. The 

Qbkf specific to each USGS streamflow-gaging-station, 

determined from field surveys of bankfull geomorphic 

features, was input to the derived at-a-station power functions, and their associated widths, depths, and mean 

velocities (wbkf, dbkf, vbkf) were computed. For the IFIM 

sites, bankfull hydraulic-geometry data were computed 

from the calibrated cross-sectional hydraulic model for 

each site. The base-10 logarithms of these bankfull flow, 

velocity, and geometry data were used in linear regression 

analyses to derive regional curves with Qbkf as the 

explanatory variable (table 5). 

The exponents of the derived regional hydraulicgeometry relations indicate that, in the downstream direction, most of the conveyance of increasing flow is accommodated by an increase in cross-sectional area—about 50 

percent of the increase in flow is accommodated by an 

increase in channel width, and 32 percent by an increase 

in depth. The remaining 18 percent is accommodated by 

an increase in streamflow velocity. These exponents 

agree closely with other field-derived exponents 

presented by Cao and Knight (1996), who report results 

from 10 studies in Canada, China, United Kingdom, and 

the United States. The mean exponents are 0.51, 0.34, and 

0.15 for width, mean depth, and mean flow velocity, 

respectively. In the same paper, Cao and Knight (1996) 

derive theoretical exponents of 0.50, 0.33, and 0.17 

(width, mean depth, and mean flow velocity, respectively) based on the concepts of stream power and fluvial 

process probability.

To make these regional relations more directly 

field-applicable to stream assessment, the bankfull
Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine 11

Figure 3. Relation of bankfull streamflow to mean annual streamflow for rivers in coastal and central Maine. [Qbkf, bankfull streamflow; Qann, 

mean annual streamflow; R2

, fraction of variance explained by regression].

1 10 100 1,000

MEAN ANNUAL STREAMFLOW, IN CUBIC FEET PER SECOND

1

10

100

1,000

10,000

BANKFULL STREAMFLOW, IN CUBIC FEET PER SECOND

EXPLANATION

Regression line

Qbkf = 2.27 Qann1.06

R2 = 0.95

streamflow and its associated channel geometry are 

commonly derived as a function of drainage area (for 

examples, see: McCandless and Everett, 2002; Harman 

and others, 2001; White, 2001; Harman and others, 

1999). In particular, the relation of bankfull channel 

width to drainage area is a commonly used assessment 

tool because the width is easily measured in the field, 

assuming the river stage of the bankfull streamflow is 

known or can be otherwise identified by morphological 

features. Similarly, the drainage area is commonly 

derived using topographic maps or a Geographic Information System (GIS). Thus, the measured channel width 

can be compared to the range of regional values expected 

for a drainage basin of that size as described by the 

regional curve derived for the appropriate reference flow, 

climate, and physiographic region of interest. 

Regional curves describing the bankfull streamflow and associated channel geometry as functions of 

drainage area were derived for the sites used in this study 

(table 6, figs. 4 to 7). The derived regression exponents 

agree reasonably well with exponents derived by other 

studies in the eastern United States (table 7) (Sweet and 

Geratz, 2003; McCandless and Everett, 2002; Harman 

and others, 2001; Jaquith and Kline, 2001; White, 2001; 

Harman and others, 1999). 

Summary and Conclusions

Baseline knowledge of the characteristics of 

natural river channels in central and coastal Maine will 

assist water-resources managers with instream-restoration projects. Stable, self-maintaining, natural channels 

conform to a cross-sectional geometry, plan, and profile 

proportional to the size of the upstream watershed, 

streamflow, and sediment load. Within a region of similar 

hydrogeology and climate, the mean characteristics 

describing the shape of the channel are sufficiently
12 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

Table 5. Regional regression equations for estimating bankfull channel width, channel depth, and streamflow velocity as functions of 

bankfull streamflow for rivers in coastal and central Maine.

[Qbkf, bankfull streamflow in cubic feet per second; wbkf, bankfull channel width, in feet; dbkf, bankfull mean channel depth, in feet; vbkf, bankfull mean streamflow velocity, 

in feet per second; R2

, fraction of variance explained by regression] 

Regression equation Average standard error 

of estimate R2

wbkf =3.36Qbkf

0.50 +21.2 to -17.5 0.94

dbkf =0.361Qbkf

0.32 +24.5 to -19.7 0.82

vbkf =0.825Qbkf

0.18 +43.3 to -30.2 0.37

consistent that the degree of deviation from what is 

commonly observed in the region can be interpreted as 

the magnitude of the effect of disturbance. Regional 

statistical models or curves that relate river-channel 

geometry to drainage area and streamflow make use of 

this concept and are a valuable tool used to characterize 

disturbed river reaches and to help water-resources 

managers ensure the efficacy and longevity of restoration projects. 

This report presents the data, methods, and results 

of a cooperative study (from 2001 to 2003) between the 

U.S. Geological Survey (USGS), Maine Atlantic 

Salmon Commission (ASC), and U.S. Fish and Wildlife 

Service to collect hydraulic-geometry data for rivers in 

coastal and central Maine and derive regional hydraulicgeometry curves calibrated to the bankfull reference 

flow. Bankfull flow is the flow that completely fills the 

channel up to the elevation of the floodplain, without 

overtopping the banks. Bankfull flow is a useful reference flow because it can be estimated at ungaged sites 

based on observable, physical channel features and does 

not require knowledge of flow frequency in the river. In 

addition, bankfull flow is generally thought to be the 

flow that determines the dominant morphological characteristics of river channels. The regional curves, based 

on the USGS streamflow-measurement data and data 

obtained from Instream Flow Incremental Methodology 

(IFIM) studies, were developed to assist the cooperating 

agencies and other natural-resources managers incorporate river morphology with habitat assessment in riverrestoration projects in coastal and central Maine. 

This investigation was confined to rivers in 

coastal and central Maine that had USGS streamflowmeasurement and stage-discharge relation data available 

or had been investigated previously as part of an IFIM 

study by the ASC. The 15 sites used in this study are in 

heavily forested watersheds that are characterized by 

rolling topography and no urban development. All the 

selected sites are in coastal and central Maine to minimize variations caused by differences in physiographic 

setting. Only channel-geometry data available at 

natural, stable cross sections were used.

On an annual-peak-series basis, results of this 

study indicate that the occurrence of bankfull streamflow for rivers in Maine is more frequent than the occurrence of bankfull streamflow observed in other regions. 

On a flow-duration basis, bankfull streamflow for rivers

Table 6. Regional regression equations for estimating bankfull streamflow, channel width, channel depth, and channel cross-sectional 

area as functions of drainage area for rivers in coastal and central Maine.

[Qbkf, bankfull streamflow in cubic feet per second; wbkf, bankfull channel width, in feet; dbkf, bankfull mean channel depth, in feet; Abkf, bankfull cross-sectional area, in 

square feet ; DA, drainage area in square miles; R2

, fraction of variance explained by regression] 

Regression equation Average standard error of estimate R2

Qbkf =5.19DA1.05 +66.0 to -39.8 0.88

wbkf =7.67DA0.52 +37.9 to -27.5 0.82

dbkf =0.594DA0.34 +29.4 to -22.7 0.76

Abkf =4.55DA0.86 +70.5 to -41.3 0.82
Figure 4. Regional relation of bankfull streamflow to drainage area for rivers in coastal and central Maine. [Qbkf, bankfull streamflow; DA, drainage area; R2, fr

explained by regression]. 1 10 100 1,000 DRAINAGE AREA, IN SQUARE MILES 110 100

1,000

10,000

BANKFULL STREAMFLOW, IN CUBIC FEET PER SECOND EXPLANATIONRegression line Qbkf = 5.19 DA1.05 R2 = 0.88

95-percent confidence bound95-percent prediction bound
Figure 5. Regional relation of bankfull channel width to drainage area for rivers in coastal and central Maine. [wbkf, channel width associated with the bankfu

area; R2, fraction of variance explained by regression].

1 10 100 1,0

DRAINAGE AREA, IN SQUARE MILES

1

10

100

1,000

BANKFULL CHANNEL WIDTH, IN FEET EXPLANATIONRegression line

wbkf = 7.67 DA0.52

R2 = 0.8295-percent confidence bound95-percent prediction bound
Figure 6. Regional relation of bankfull mean channel depth to drainage area for rivers in coastal and central Maine. [dbkf, mean channel depth associated with 

DA, drainage area; R2, fraction of variance explained by regression]. 1 10 100 1,000 DRAINAGE AREA, IN SQUARE MILES 0.1 1.0

10.0

BANKFULL MEAN CHANNEL DEPTH, IN FEET EXPLANATIONRegression line dbkf = 0.594 DA0.34

R2 = 0.7695-percent confidence bound95-percent prediction bound

BANKFULL AVERAGE CHANNEL DEPTH, IN FEET
Figure 7. Regional relation of bankfull channel cross-sectional area to drainage area for rivers in coastal and central Maine. [Abkf, channel cross-sectional area 

streamflow; DA, drainage area; R2, fraction of variance explained by regression].

1 10 100 1,0

DRAINAGE AREA, IN SQUARE MILES

1

10

100

1,000

BANKFULL CHANNEL CROSS-SECTIONAL AREA, IN SQUARE FEET EXPLANATIONRegression line

Abkf = 4.55 DA0.86

R2 = 0.8295-percent confidence bound95-percent prediction bound
Table 7. Regional regression equations for estimating bankfull streamflow, bankfull channel width, mean bankfull channel depth, and bankfull channel cross-se

regions in the eastern United States.

[Qbkf, bankfull streamflow in cubic feet per second; wbkf, bankfull channel width, in feet; dbkf, bankfull mean channel depth, in feet; Abkf, bankfull channel cross-sectional area, in square feet; DA, drain

Investigators Region studied 

Bankful

streamflow

Banfull

channel width

Average bankfull

channel depth

Bank

cross-s

This study (2004) Central and coastal Maine Qbkf =5.19DA1.05 wbkf =7.67DA0.52 dbkf =0.594DA0.34 Abkf =4.

Sweet and Geratz (2003) North Carolina Coastal Plain Qbkf =8.79DA0.76 wbkf =9.64DA0.38 dbkf =0.98DA0.36 Abkf =9.McCandless and Everett (2002) Maryland Piedmont Qbkf =84.6DA0.76 wbkf =14.8DA0.39 dbkf =1.18DA0.34 Abkf =17Harman and others (2001) North Carolina Blue Ridge Qbkf =115.7DA0.73 wbkf =19.9DA0.36 dbkf =1.10DA0.31 Abkf =22Jaquith and Kline (2001) Vermont (statewide) Qbkf =17.7DA1.07 wbkf =10.2DA0.50 dbkf =1.22DA0.25 Abkf =12White (2001) Pennsylvania and Maryland Piedmont Qbkf =69.6DA0.79 wbkf =14.8DA0.46 dbkf =0.780DA0.39 Abkf =11

Harman and others (1999) North Carolina Piedmont Qbkf =66.6DA0.89 wbkf =11.9DA0.43 dbkf =1.50DA0.32 Abkf =21
18 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

in coastal and central Maine is equaled or exceeded 

approximately 8.1 percent of the time on average—or 

about 30 days a year. Bankfull streamflow is roughly 

three times that of the mean annual streamflow for the 

sites investigated in this study. Regional climate, snowmelt hydrology, and glacial geology may play important 

roles in dictating the magnitude and frequency of occurrence of bankfull streamflows observed for rivers in 

coastal and central Maine.

The fundamental relations between channel-geometry dimensions, velocity, and flow can be expressed as 

well-established power functions, also referred to as “ata-station curves.” The derived at-a-station hydraulicgeometry relations indicate that, on average, a given 

increase in flow at a given river cross section in the study 

area, will be nearly equally accommodated by increases 

in velocity and cross-sectional area. Based on the mean 

derived at-a-station hydraulic-geometry equation exponents, about 48 percent of the increase in flow is accommodated by an increase in velocity, 33 percent by an 

increase in depth, and 19 percent by an increase in width.

Regional hydraulic-geometry curves were derived 

by combining at-a-station relation information from the 

10 USGS sites and hydraulic-geometry information from 

the 5 IFIM sites, referenced to bankfull streamflow. The 

exponents of the derived regional hydraulic-geometry 

relations indicate that, in the downstream direction, most 

of the conveyance of increasing contribution of flow is 

accommodated by an increase in cross-sectional 

area—about 50 percent of the increase in flow is accommodated by an increase in channel width, and 32 percent 

by an increase in depth. The remaining 18 percent is 

accommodated by an increase in streamflow velocity.

Regional curves describing the bankfull streamflow and associated channel geometry as functions of 

drainage area also were derived for the sites in this study. 

The derived regression exponents agree reasonably well 

with exponents derived in other studies in the eastern 

United States.

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Augusta, Maine, Maine Geological Survey, p.1-8. 

McCandless, T.L. and Everett, R., 2002, Maryland river survey—Bankfull discharge and channel characteristics of 

streams in the Piedmont hydrologic region: U.S. Fish and 

Wildlife Service Chesapeake Bay Field Office Report, 

CBFO-S02-01, 175 p.

National Oceanic and Atmospheric Administration, 2002, Climatography of the United States, no. 81, Monthly station 

normals of temperature, precipitation, and heating and 

cooling degree days, 1971-2000—Region 17, Maine: 

Asheville, N.C., National Oceanic and Atmospheric 

Administration,16 p. 

Osterkamp, W.R., Lane, L.J., and Foster, G.R., 1983, An analytic treatment of channel-morphology relations: U.S. 

Geological Survey Professional Paper 1288, 21 p.

Randall, A.D., 2001, Hydrogeologic framework of stratified 

drift aquifers in the glaciated northeastern United States: 

U.S. Geological Survey Professional Paper 1415-B, 179 

p., 1 plate showing hydrophysiographic regions in the glaciated northeastern United States, scale 1:2,500,000.

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

of streamflow (2 volumes): U.S. Geological Survey 

Water-Supply Paper 2175, 631 p. 

Rosgen, D.L., 1996, Applied River Morphology, Pagosa 

Springs, Colorado, Wildland Hydrology Books, 390 p.

Sweet, W.V. and Geratz, J.W., 2003, Bankfull hydraulicgeometry relationships and recurrence intervals for North 

Carolina’s Coastal Plain: Journal of the American Water 

Resources Association, v. 39, no. 4, p. 861-871.

Thompson, W.B. and Borns, H.W., 1985, Surficial geologic 

map of Maine: Maine Geological Survey, Department of 

Conservation, scale 1:5,000,000.

U.S. Geological Survey, 1975, Estimating flow characteristics 

from channel size: U.S. Geological Survey SurfaceWater Technical Memorandum no. 75.16, 6 p.

U.S. Geological Survey, 1998, National Water Information 

System (NWIS). U.S. Geological Survey Fact Sheet FS027-98. Reston, Virginia, 2 p.

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

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

the Piedmont Physiographic Province, Pennsylvania and 

Maryland: U.S. Geological Survey Water-Resources 

Investigations Report 01-4146, 20 p.

Williams, G.P., 1978, Hydraulic-geometry of river cross sections—Theory of minimum variance: U.S. Geological 

Survey Professional Paper 1029, 47 p.
20 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

Appendix 1: Descriptions of U.S. Geological Survey Streamflow-Gaging Stations

References to left and right side of the river correspond to one’s left and right when facing downstream.
Appendix 21

01023000 West Branch Union River at Amherst, Maine (Period of record: 1910-19, 1929-79)

The West Branch Union River streamflow-gaging station was located on the right bank, about 1 mi upstream 

from State Route 9 bridge in Amherst. Bedrock falls serve as the hydraulic control for the station. The cross section 

where the data used to derive the hydraulic-geometry relations were collected is approximately 0.25 mi downstream 

from the station. The river channel at the cross section is characterized as rocky, composed of bedrock, cobbles, and 

gravel, with some silt. All the measurement data are from wading measurements (fig. A1).

Figure A1. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the West Branch Union River at Amherst, 

Maine (USGS streamflow-gaging station number 01023000).

1 10 100 1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
22 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

01024200 Garland Brook near Mariaville, Maine (Period of record: 1964-82)

The Garland Brook streamflow-gaging station was located on the left bank, about 22 ft upstream from State 

Route 18 in Mariaville. The State Route 18 culvert serves as the hydraulic control for the station. The cross section 

where the data used to derive the hydraulic-geometry relations were collected is approximately at the station. The river 

channel at the cross section is characterized as rocky, composed of sand, gravel, cobbles, and some bedrock. All the 

measurement data are from wading measurements (fig. A2).

Figure A2. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for Garland Brook near Mariaville, Maine

(USGS streamflow-gaging station number 01024200).

0.1 1.0 10.0 100.0 1,000.0

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
Appendix 23

01031500 Piscataquis River near Dover-Foxcroft, Maine (Period of record: 1902-present)

The Piscataquis River streamflow-gaging station is currently (2004) active and is on the left bank about 30 ft 

downstream from Lows Bridge in Dover-Foxcroft. Bedrock and boulders 200 ft downstream from the station serve as 

the hydraulic control for the station at low and medium flows. At high flows, the channel becomes the hydraulic 

control. The cross section where the data used to derive the hydraulic-geometry relations were collected is approximately 400 ft downstream from the station. The river channel at the cross section is characterized as rocky, composed 

of gravel, cobbles, and some boulders. All the measurement data are from wading measurements except for one boat 

measurement at high flow (fig. A3).

Figure A3. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Piscataquis River near DoverFoxcroft, Maine (USGS streamflow-gaging station number 01031500).

10 100 1,000 10,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

1,000.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

1,000.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
24 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

01035000 Passadumkeag River at Lowell, Maine (Period of record: 1916-79)

The Passadumkeag River streamflow-gaging station was on the right bank about 0.5 mi downstream from Fogg 

Brook Road Bridge and the dam in Lowell. Coarse gravel rips serve as the hydraulic control for the station. During the 

years the river was gaged, the streamflow was not regulated by the dam. The cross section where the data used to derive 

the hydraulic-geometry relations were collected is approximately 100 ft downstream from the station at a cableway. 

The river channel at the cross section is characterized as rocky, composed of coarse gravel, cobbles, and some bedrock. 

All measurement data are from wading and cable measurements made at or beneath the cableway providing a data set 

with very little variability (fig. A4).

Figure A4. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Passadumkeag River at Lowell, 

Maine (USGS streamflow-gaging station number 01035000).

100 1,000 10,000

STREAMFLOW, IN CUBIC FEET PER SECOND

1

10

100

1,000

Width

Velocity

Depth

EXPLANATION

1

10

100

1,000

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
Appendix 25

01038000 Sheepscot River at North Whitefield, Maine (Period of record: 1939-present)

The Sheepscot River streamflow-gaging station is currently (2004) active and is on the left bank about 50 ft 

upstream from the State Route 126 bridge in North Whitefield. A bedrock outcrop 50 ft downstream from the station 

serves as the hydraulic control for the station. The bridge opening acts as the high-water hydraulic control only at 

stages exceeding 5.0 ft—well above the bankfull flow. The cross section where the data used to derive the hydraulicgeometry relations were collected is at a cableway between the station and the bridge. The river channel at the cross 

section is characterized as rocky, composed of cobbles, boulders, and bedrock. All measurement data are from wading 

and cable measurements made at or beneath the cableway providing a data set with very little variability (fig. A5).

Figure A5. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Sheepscot River at North Whitefield, 

Maine (USGS streamflow-gaging station number 01038000).

10 100 1,000 10,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
26 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

01049130 Johnson Brook at South Albion, Maine (Period of record: 1980-91)

The Johnson Brook streamflow-gaging station was on the right bank upstream from the Dutton Road culvert, 

about 0.2 mi south of State Highway 9 and 202 in South Albion. A v-notch weir in the culvert served as the hydraulic 

control for the station. The cross section where the data used to derive the hydraulic-geometry relations were collected 

is approximately 200 ft upstream from the station, though locations of measurement at this site were highly variable. 

The river channel at the cross section is characterized as gravelly, composed of sand, gravel, and cobbles. All the 

measurement data are from wading measurements (fig. A6).

Figure A6. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for Johnson Brook at South Albion, Maine

(USGS streamflow-gaging station number 01049130).

1 10 100

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
Appendix 27

01049550 Togus River at Togus, Maine (Period of record: 1982-95)

The Togus River streamflow-gaging station was located on the right bank about 600 ft downstream from the 

State Route 226 Bridge. A concrete broad-crested weir 50 ft downstream from the station served as the hydraulic 

control for the station. The cross section where the data used to derive the hydraulic-geometry relations were collected 

is at a cableway approximately 100 ft downstream from the station. The river channel at the cross section is characterized as rocky, composed of cobbles and bedrock. All measurement data are from wading and cable measurements 

made at or beneath the cableway providing a data set with little variability (fig. A7).

Figure A7. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Togus River at Togus, Maine (USGS 

streamflow-gaging station number 01049550).

1 10 100 1,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
28 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

01055000 Swift River near Roxbury, Maine (Period of record: 1929-present)

The Swift River streamflow-gaging station is currently (2004) active and is on the left bank at Swift River Falls, 

about 7.2 mi upstream from the confluence of the Swift River with the Androscoggin River. The bedrock falls 50 ft 

downstream from the station serve as the hydraulic control for the station. The cross section where the data used to 

derive the hydraulic-geometry relations were collected is at a cableway approximately 400 ft upstream from the station. 

The river channel at the cross section is characterized as rocky, composed of gravel, cobbles, and boulders. All 

measurement data are from cableway measurements providing a data set with very little variability (fig. A8).

Figure A8. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Swift River near Roxbury, Maine 

(USGS streamflow-gaging station number 01055000).

10 100 1,000 10,000 100,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

1,000.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

1,000.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
Appendix 29

01055500 Nezinscot River at Turner Center, Maine (Period of record: 1941-96, 2001-present)

The Nezinscot River streamflow-gaging station is currently (2004) active and is on the left bank 500 ft upstream 

from State Route 117 Bridge in Turner. Bedrock, cobble, and boulder rips 300 ft downstream from the station serve 

as the hydraulic control for the station. The cross section where the data used to derive the hydraulic-geometry relations were collected is at a cableway at the station. The river channel at the cross section is characterized as rocky, 

composed of cobbles and boulders. All the measurement data are from measurements made at or beneath the cableway 

providing a data set with very little variability (fig. A9).

Figure A9. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Nezinscot River at Turner Center, 

Maine (USGS streamflow-gaging station number 01055500).

100 1,000 10,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

1,000.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

1,000.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
30 Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine

01060000 Royal River at Yarmouth, Maine (Period of record: 1950-present)

The Royal River streamflow-gaging station is currently (2004) active and is on the right bank about 150 ft 

upstream from the East Main Street bridge in Yarmouth. Bedrock falls 50 ft downstream from the station serve as the 

hydraulic control for the station. The cross section where the data used to derive the hydraulic-geometry relations were 

collected is at a cableway approximately 300 ft upstream from the station. The river channel at the cross section is characterized as rocky, composed of cobbles, bedrock, and some silt. All the measurement data are from cableway 

measurements providing a data set with very little variability (fig. A10).

Figure A10. At-a-station relations of channel width, mean depth, and mean velocity to streamflow for the Royal River at Yarmouth, Maine 

(USGS streamflow-gaging station number 01060000).

100 1,000 10,000

STREAMFLOW, IN CUBIC FEET PER SECOND

0.1

1.0

10.0

100.0

1,000.0

Width

Velocity

Depth

EXPLANATION

0.1

1.0

10.0

100.0

1,000.0

WIDTH AND DEPTH, IN FEET

VELOCITY, IN FEET PER SECOND
Dudley, Robert W. —Hydraulic-Geometry Relations for Rivers in Coastal and Central Maine—USGS Scientific Investigations Report 2004-5042

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