Scientific Investigations Report 2013–5155

U.S. Department of the Interior

U.S. Geological Survey

Prepared in cooperation with the

Massachusetts Department of Environmental Protection

Bureau of Resource Protection

Wetlands and Waterways Program and

Massachusetts Environmental Trust

Equations for Estimating Bankfull Channel Geometry 

and Discharge for Streams in Massachusetts
Front cover. Photograph of bankfull conditions on the Green River near Great Barrington, Massachusetts (USGS streamgage 

01198000), looking upstream of Hurlburt Street on March 5, 2008.

Back cover. Photograph of bankfull survey at cross section #6 looking downstream on Cadwell Creek near Belchertown, 

Massachusetts (USGS streamgage 01174900), on December 9, 2004.
Equations for Estimating Bankfull Channel 

Geometry and Discharge for Streams in 

Massachusetts

By Gardner C. Bent and Andrew M. Waite

Prepared in cooperation with the 

Massachusetts Department of Environmental Protection

Bureau of Resource Protection 

Wetlands and Waterways Program and 

Massachusetts Environmental Trust

Scientific Investigations Report 2013–5155

U.S. Department of the Interior

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

SALLY JEWELL, Secretary

U.S. Geological Survey

Suzette M. Kimball, Acting Director

U.S. Geological Survey, Reston, Virginia: 2013

For more information on the USGS—the Federal source for science about the Earth, its natural and living 

resources, natural hazards, and the environment, visit http://www.usgs.gov or call 1–888–ASK–USGS.

For an overview of USGS information products, including maps, imagery, and publications, 

visit http://www.usgs.gov/pubprod

To order this and other USGS information products, visit http://store.usgs.gov

Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the 

U.S. Government.

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

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

Suggested citation:

Bent, G.C., and Waite, A.M., 2013, Equations for estimating bankfull channel geometry and discharge for streams in 

Massachusetts: U.S. Geological Survey Scientific Investigations Report 2013–5155, 62 p., http://dx.doi.org/10.3133/

sir20135155.

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

ISBN 978-1-4113-3693-3
iii

Acknowledgments

The authors thank Barry Baldigo and Jeff Chaplin of the U.S. Geological Survey (USGS) for 

valuable input and training on field methods in bankfull studies. The authors also thank Pete 

Cinotto, USGS, for use of a spreadsheet developed for bankfull data entry and calculations; 

Thomas Garday and Dennis Verdi of the U.S. Department of Agriculture, Natural Resources 

Conservation Service, for sharing data collected for bankfull assessments at two USGS 

streamgages in Massachusetts; and Mickey Marcus, New England Environmental, Inc., 

Amherst, Massachusetts, for hosting a bankfull workshop in Amherst, Mass., during May 2004. 

Special thanks and appreciation go to Heidi Davis, Massachusetts Department of Environmental 

Protection, for field assistance.
THIS PAGE INTENTIONALLY LEFT BLANK
v

Contents

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

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

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

Description of Study Area ...................................................................................................................3

Methods of Data Collection and Analysis .................................................................................................3

Site Selection.........................................................................................................................................6

Bankfull Stage Indicators....................................................................................................................6

Bankfull Channel Geometry ................................................................................................................6

Bankfull Discharge ...............................................................................................................................7

Development of Equations for Estimating Bankfull Geometry and Discharge ..................................11

Factors Affecting Bankfull Channel Geometry and Discharge ...................................................12

Bankfull Channel Geometry and Discharge at Study Sites .........................................................12

Equations..............................................................................................................................................16

Confidence- and Prediction-Interval Estimation ...........................................................................31

Application...........................................................................................................................................32

Comparison to Other Studies in the Eastern United States and Southeastern Canada ..................35

Limitations of the Regional Curves and Regression Equations and Areas for Further Study.........41

Summary and Conclusions.........................................................................................................................42

References Cited..........................................................................................................................................43

Appendix 1. Information on the Starting and Ending Locations of Surveyed Stream Reaches 

and Locations of the Two Surveyed Cross Sections for Study Sites in and Near 

Massachusetts ...............................................................................................................................48

Appendix 2. Bankfull Data Collected at the Two Surveyed Cross Sections and Stream 

Reach for Study Sites in and Near Massachusetts .................................................................51

Appendix 3. Results of Analyses of Simple and Multiple Regression Equations to Estimate 

Bankfull Width, Mean Depth, Cross-Sectional Area, and Discharge for Streams in 

and near Massachusetts ..............................................................................................................60

Appendix 4. Summary Statistics, Confidence and Prediction Interval Parameters, and 

Results of Analyses of Simple Regression Equations for Estimating the Bankfull Width, 

Mean Depth, Cross-Sectional Area, and Discharge for Streams in the Northeastern 

United States...................................................................................................................................61
vi

Figures

1. Map showing location of U.S. Geological Survey streamgage and crest-stage gage 

study sites used in the development of bankfull channel geometry and discharge 

equations for streams in and near Massachusetts ................................................................4

2. Map showing locations of the physiographic provinces and U.S. Environmental 

Protection Agency Level III ecoregions in and near Massachusetts .................................5

3. Graphs showing simple regression equation residuals in relation to drainage area 

for bankfull: A, width, B, mean depth, C, cross-sectional area, and D, discharge for 

streams in and near Massachusetts.......................................................................................24

4. Map showing geographic distribution of bankfull width simple regression equation 

residuals for study sites in and near Massachusetts...........................................................25

5. Graphs showing regional curves of the relation between bankfull: A, width, B, mean 

depth, C, cross-sectional area, and D, discharge and drainage area for streams in 

and near Massachusetts...........................................................................................................26

6. Graphs showing multiple regression equation residuals in relation to drainage area 

for bankfull: A, width, B, mean depth, C, cross-sectional area, and D, discharge and 

in relation to mean basin slope for bankfull: E, width, F, mean depth, G, crosssectional area, and H, discharge for streams in and near Massachusetts......................28

7. Map showing geographic distribution of bankfull width multiple regression equation 

residuals for study sites in and near Massachusetts...........................................................30

8. Graph showing regression lines for bankfull width in relation to drainage area for 

selected studies in the northeastern United States .............................................................40

Tables

1. Description of U.S. Geological Survey streamgage and crest-stage gage study sites 

used in development of bankfull channel geometry and discharge equations for 

streams in and near Massachusetts.........................................................................................8

2. Estimated peak discharge for the 1.01, 1.05, 1.11, 1.25, 1.5, 2, 2.33, 5, and 10-year 

recurrence intervals for the study sites used in development of bankfull channel 

geometry and discharge equations for streams in and near Massachusetts .................10

3. Bankfull channel geometry and discharge for study sites in and near 

Massachusetts............................................................................................................................13

4. Estimated bankfull discharge using equations by Limerinos (1970) and Jarrett (1984) 

for study sites in and near Massachusetts ............................................................................17

5. Basin and land-use characteristics of the study sites used in development of 

bankfull channel geometry and discharge equations for streams in and near 

Massachusetts............................................................................................................................20

6. Statistical summary of simple and multiple regression equations for estimating 

bankfull stream width, mean depth, cross-sectional area, and discharge for streams 

in and near Massachusetts ......................................................................................................22

7. Simple and multiple regression equation confidence and prediction interval 

parameters for estimating the bankfull width, mean depth, cross-sectional area, 

and discharge for streams in and near Massachusetts ......................................................33

8. Equation parameters used for estimating bankfull channel geometry and discharge 

by drainage area for selected hydrologic regions or physiographic provinces and 

states in the eastern United States and southeastern Canada. .........................................36
vii

Conversion Factors, Datum, and Abbreviations

Inch/Pound to SI

Multiply By To obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

Area

square mile (mi2) 2.590 square kilometer (km2)

Volume

cubic foot (ft3) 0.02832 cubic meter (m3)

Flow rate

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

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

 °F=(1.8×°C)+32

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

 °C=(°F–32)/1.8

Vertical coordinate information is referenced to the North American Vertical Datum of 1988 

(NAVD 88).

Horizontal coordinate information is referenced to the North American Datum of 1983 (NAD 83).

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

Abbreviations

GIS Geographic Information Systems

MAGIC University of Connecticut Map and Geography Information Center

MassGIS Massachusetts Office of Geographic Information

MDEP Massachusetts Department of Environmental Protection

NED National Elevation Dataset

NHD National Hydrography Dataset

NH GANIT New Hampshire Geographical Information System

NYSGIS New York State Geographical Information System

RIGIS Rhode Island Geographic Information System

USEPA U.S. Environmental Protection Agency

USGS U.S. Geological Survey

VCGI Vermont Center for Geographic Information
THIS PAGE INTENTIONALLY LEFT BLANK
Equations for Estimating Bankfull Channel Geometry and 

Discharge for Streams in Massachusetts

By Gardner C. Bent and Andrew M. Waite

Abstract

Regression equations were developed for estimating 

bankfull geometry—width, mean depth, cross-sectional area—

and discharge for streams in Massachusetts. The equations 

provide water-resource and conservation managers with 

methods for estimating bankfull characteristics at specific 

stream sites in Massachusetts. This information can be used 

for the adminstration of the Commonwealth of Massachusetts 

Rivers Protection Act of 1996, which establishes a protected 

riverfront area extending from the mean annual high-water 

line corresponding to the elevation of bankfull discharge along 

each side of a perennial stream. Additionally, information 

on bankfull channel geometry and discharge are important 

to Federal, State, and local government agencies and 

private organizations involved in stream assessment and 

restoration projects.

Regression equations are based on data from stream 

surveys at 33 sites (32 streamgages and 1 crest-stage 

gage operated by the U.S. Geological Survey) in and near 

Massachusetts. Drainage areas of the 33 sites ranged from 

0.60 to 329 square miles (mi2). At 27 of the 33 sites, field 

data were collected and analyses were done to determine 

bankfull channel geometry and discharge as part of the 

present study. For 6 of the 33 sites, data on bankfull channel 

geometry and discharge were compiled from other studies 

done by the U.S. Geological Survey, Natural Resources 

Conservation Service of the U.S. Department of Agriculture, 

and the Vermont Department of Environmental Conservation. 

Similar techniques were used for field data collection and 

analysis for bankfull channel geometry and discharge at all 

33 sites. Recurrence intervals of the bankfull discharge, which 

represent the frequency with which a stream fills its channel, 

averaged 1.53 years (median value 1.34 years) at the 33 sites. 

Simple regression equations were developed for bankfull 

width, mean depth, cross-sectional area, and discharge using 

drainage area, which is the most significant explanatory 

variable in estimating these bankfull characteristics. The 

use of drainage area as an explanatory variable is also the 

most commonly published method for estimating these 

bankfull characteristics. Regional curves (graphic plots) of 

bankfull channel geometry and discharge by drainage area 

are presented. The regional curves are based on the simple 

regression equations and can be used to estimate bankfull 

characteristics from drainage area. Multiple regression 

analysis, which includes basin characteristics in addition to 

drainage area, also was used to develop equations. Variability 

in bankfull width, mean depth, cross-sectional area, and 

discharge was more fully explained by the multiple regression 

equations that include mean-basin slope and drainage area 

than was explained by equations based on drainage area 

alone. The Massachusetts regional curves and equations 

developed in this study are similar, in terms of values of 

slopes and intercepts, to those developed for other parts of the 

northeastern United States.

Limitations associated with site selection and 

development of the equations resulted in some constraints for 

the application of equations and regional curves presented in 

this report. The curves and equations are applicable to stream 

sites that have (1) less than about 25 percent of their drainage 

basin area occupied by urban land use (commercial, industrial, 

transportation, and high-density residential), (2) little to 

no streamflow regulation, especially from flood-control 

structures, (3) drainage basin areas greater than 0.60 mi2 and 

less than 329 mi2, and (4) a mean basin slope greater than 

2.2 percent and less than 23.9 percent. The equations may not 

be applicable where streams flow through extensive wetlands. 

The equations also may not apply in areas of Cape Cod and 

the Islands and the area of southeastern Massachusetts close 

to Cape Cod with extensive areas of coarse-grained glacial 

deposits where none of the study sites are located. Regardless 

of the setting, the regression equations are not intended for 

use as the sole method of estimating bankfull characteristics; 

however, they may supplement field identification of the 

bankfull channel when used in conjunction with field verified 

bankfull indicators, flood-frequency analysis, or other 

supporting evidence.

Introduction

Information about the channel geometry and discharge 

of streams under bankfull conditions is important for many 

hydrologic applications. Bankfull discharge is the streamflow 

that occurs when the stream fills its channel and any additional 

discharge will result in the stream overflowing its banks. 
2 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Bankfull geometry (width, cross-sectional area, mean depth) 

defines the physical extent of the stream when the stream is 

bankfull. The geometry of a stream and the location of the 

water’s edge at bankfull conditions are fundamental measures 

of the size and location of the stream. 

Information about bankfull channel geometry is 

important for the application of the Commonwealth of 

Massachusetts Rivers Protection Act of 1996–310 Code of 

Massachusetts Regulations (CMR) 10.00–Section 10.58 

(The Commonwealth of Massachusetts, 2009). This Act 

specifies that riverfront areas of all perennial streams be 

protected, where the riverfront area is defined as a 200-footwide strip (25-foot-wide strip in selected densely developed 

areas) of land on each side of a stream that starts at the mean 

annual high-water line of perennial streams. The Act states 

that the mean annual high-water line is best represented by 

bankfull field indicators, such as change in slope, changes 

in vegetation, stain lines, top of point bars, changes in 

bank material, or bank undercuts along streambanks that 

correspond to the elevation of the water surface of the stream 

when the stream fills its banks and establishes the bankfull 

stream width. Town and city conservation commissions and 

the Massachusetts Department of Environmental Protection 

(MDEP) are charged with enforcing the Riverfront Protection 

Act by regulating work in the riverfront areas and, thus, must 

be able to accurately determine the bankfull stream width of 

perennial streams.

In Massachusetts, bankfull data are being used in the 

design of bridges and culverts for stream crossings, such 

that they can accommodate fish and wildlife passage and 

avoid adverse effects on ecological systems (Massachusetts 

Department of Transportation, 2010; Massachusetts Executive 

Office of Energy and Environmental Affairs, 2012). State and 

Federal regulations required that the new and replacement 

structures span the stream channel width by a minimum of 

1.2 times the bankfull width. The River and Stream Continuity 

Partnership (2011) developed revised river and stream 

crossing standards for Massachusetts using the same standard 

of 1.2 times the bankfull width. Additionally, the U.S. Army 

Corps of Engineers–New England District is using these 

same river and stream crossing standards for its State General 

Permit (http://www.nae.usace.army.mil/Regulatory/SGP/

ma.htm) in Massachusetts.

Information about bankfull channel geometry and discharge is important to Federal, State, and local governments 

and private organizations involved in stream assessment and 

restoration projects. Stream-restoration projects during the last 

two decades have focused on using a natural-channel design 

approach that depends on estimates of natural bankfull channel geometry and discharge rather than traditional engineering 

practices that may involve straightening, widening, deepening, 

or hardening banks and channels.

Bankfull channel geometry and discharge are commonly 

estimated using equations and graphical plots that relate 

bankfull width, mean depth, cross-sectional area, and 

discharge to drainage area; the graphical plots are referred to 

as “regional curves.” In Massachusetts and throughout the 

eastern United States where sub-regional or statewide regional 

curves are not available, regional curves published by Dunne 

and Leopold (1978) are used by Federal, State, and local 

governments and private organizations to estimate bankfull 

geometry and discharge. Though widely used, the curves 

developed by Dunne and Leopold (1978) for the eastern 

United States were developed from sites of unknown locations 

(Emmett, 2004), and the accuracy of these curves when 

applied to streams in Massachusetts is unknown. Moreover, 

regional curves such as these are based on simple regression 

equations and use one explanatory variable, drainage area, to 

estimate the response variables of bankfull width, mean depth, 

cross-sectional area, and bankfull discharge. However, much 

variability is present in relations between drainage area and 

bankfull geometry and discharge. These simple regression 

equations for bankfull channel geometry and discharge cannot 

account for the variance that may result from other factors 

such as basin slope, basin elevation, surficial geology, soil 

type, the presence of water bodies and wetlands, and land use 

in the basin. These factors could be incorporated in multiple 

regression equations that could provide better estimates of 

bankfull geometry and discharge than the commonly used 

regional curves. Improved methods of estimating bankfull 

geometry and discharge are needed to support implementation 

of the Riverfront Protection Act of 1996 and other hydrologic 

applications in Massachusetts than are currently available 

with the generalized regional curves for the eastern United 

States or other field-based approaches. To address this need, 

the U.S. Geological Survey (USGS), in cooperation with 

the MDEP, Bureau of Resource Protection, Wetlands and 

Waterways Program and Massachusetts Environmental 

Trust, conducted a study to develop equations for estimating 

bankfull geometry and discharge from data collected at stream 

sites in and near Massachusetts, using simple and multiple 

regression techniques. 

Purpose and Scope

This report describes the methods used, data collected, 

and equations developed for estimating bankfull channel 

geometry and discharge for streams in Massachusetts. 

As a part of this study, bankfull channel geometry data 

were collected and analyzed for 27 sites—20 streams in 

Massachusetts, 3 streams in northern Connecticut, 2 streams 

in southern New Hampshire, and 2 streams in northern Rhode 

Island—during July through December 2004. Bankfull 

channel geometry and discharge data for six other streams 

in or near Massachusetts collected as part of other studies 

were also used in the development of equations. The six 

additional sites include two in Massachusetts, three in New 

York, and one in Vermont. The simple regression equations 

were developed by relating bankfull width, mean depth, crosssectional area, and discharge to drainage area at these 33 sites 

in and near Massachusetts. Multiple regression with additional 
Methods of Data Collection and Analysis 3

basin characteristics also was used to develop equations. The 

simple regression equations developed for Massachusetts 

are compared to equations developed for other areas in the 

eastern United States and southeastern Canada. Limitations 

of the regional curves, methods used in data collection, and 

estimation of the bankfull discharge are discussed.

Description of Study Area

The bankfull geometry and discharge at a stream location 

can be greatly affected by the geography, climate, and surficial 

geology upstream from that location. In Massachusetts, these 

factors, particularly the extent and type of surficial deposits, 

could affect stream channel and flow characteristics. 

Massachusetts encompasses 8,093 square miles (mi2) 

in the northeastern United States (fig. 1). Elevations range 

from sea level in coastal areas to about 3,500 feet (ft) above 

sea level (NAVD 88) in the northwest. Elevations generally 

increase from eastern to western Massachusetts. The 

climate in Massachusetts is humid with average annual precipitation ranging from about 40 to 45 inches (in.) in eastern 

Massachusetts to about 40 to 50 in. in western Massachusetts, 

where higher elevations may cause orographic effects. Average 

annual temperature is about 50 degrees Fahrenheit (°F) in eastern Massachusetts and about 45 °

F in western Massachusetts. 

Surficial deposits that overlie bedrock in most of 

Massachusetts were deposited mainly during the last glacial 

period but can include areas of recent floodplain alluvium 

deposits. In this report, these surficial deposits are classified 

as either till (which includes till, till with bedrock outcrops, 

sandy till over sand, and end-moraine deposits) or stratified 

deposits (which include sand and gravel, coarse sand, finegrained sand, and floodplain alluvium deposits). Till (also 

known as ground moraine) is an unsorted, unstratified mixture 

of clay, silt, sand, gravel, cobbles, and boulders, typically 

deposited by glaciers on top of bedrock throughout much of 

the State. Till is primarily found in upland areas but can also 

be found at depth in river valleys. Stratified deposits include 

sorted and layered glaciofluvial and glaciolacustrine deposits. 

Glaciofluvial deposits are material of all grain sizes (clay, 

silt, sand, gravel, and cobbles) deposited by glacial meltwater 

streams in outwash plains and river valleys. Glaciolacustrine 

deposits generally consist of clay, silt, and fine sand deposited 

in temporary lakes that formed after the retreat of the glacial 

ice sheet. Stratified deposits are more widespread in eastern 

Massachusetts than in western Massachusetts. In eastern 

Massachusetts, stratified deposits can be extensive outwash 

plains, particularly in the southeast. In other areas of the State, 

stratified deposits are more likely to be found in river valleys. 

On Cape Cod and the Islands and the area of southeastern 

Massachusetts close to Cape Cod, the surficial geology is 

almost entirely stratified deposits (Simcox, 1992, p. 47, 

51, and 52) (area labeled as U.S. Environmental Protection 

Agency (USEPA) Level III ecoregion–Atlantic Coastal 

Pine Barrens in fig. 2). In these areas, precipitation mainly 

percolates into the soil and through the unsaturated zone to 

the groundwater table (reducing surface runoff) and later 

discharges to the stream as base flow. Thus, runoff peaks can 

be greatly diminished in magnitude, which may also affect the 

streamflows that form bankfull channel discharges. 

The geomorphic and hydrologic variability associated 

with different physiographic provinces can be an important 

factor in determining bankfull characteristics. Denny (1982) 

identifies seven physiographic provinces within the study area. 

From eastern to western Massachusetts, the physiographic 

provinces are the Coastal Plain, Coastal Lowlands, Central 

Highlands, Connecticut Valley, Hudson-Green-Notre Dame 

Highlands, Vermont Valley, and the Taconic Highlands (fig. 2). 

Additionally, the USEPA has divided the United States into 

ecological regions (U.S. Environmental Protection Agency, 

2006). These regions are based on ecosystems that generally 

are similar and have been identified through the analysis 

of the patterns and the composition of biotic and abiotic 

features. These features include geology, physiography, 

vegetation, climate, soils, land use, wildlife, and hydrology. 

The study area includes four Level III ecoregions (U.S. 

Environmental Protection Agency, 2006). From eastern to 

western Massachusetts, the USEPA Level III ecoregions are 

Atlantic Coastal Pine Barrens, Northeastern Coastal Zone, 

Northeastern Highlands, and Eastern Great Lakes and Hudson 

Lowlands (fig. 2).

Methods of Data Collection and 

Analysis

The methods used for site selection, data collection for 

bankfull channel geometry, and data analysis to determine 

bankfull discharge and recurrence interval are similar to those 

used in other studies of bankfull characteristics of streams 

in the eastern United States. As in the other studies, the data 

collection and analyses were based on surveys done at USGS 

streamgages and associated stream reaches using methods 

outlined by Leopold (1994) and Rosgen (1994, 1996). Field 

data were collected between July and December 2004. The 

methods described in this section were used at the 27 sites 

for which data were collected and analyzed as part of the 

current study, unless otherwise indicated. Methods of data 

collection and analysis for the six additional sites are similar 

and are described in other reports. Methods for the two sites 

in Massachusetts are described by the U.S. Department of 

Agriculture, Natural Resources Conservation Service (Thomas 

Garday, U.S. Department of Agriculture, written commun., 

2005). The three sites in eastern New York studied by the 

USGS are described in Mulvihill and Baldigo (2007). The 

one site in Vermont is described in Jaquith and Kline (2006) 

for the Vermont Department of Environmental Conservation, 

Water Quality Division, River Management Program.
4 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

0 25 50 MILES

0 25 50 KILOMETERS

ATLANTIC OCEAN

LONG ISLAND SOUND

01198000

01184100

01174900

01193800

01163200

01111500 01109000

01109070

01100600

01103500

01199050

01187300

01181000 01176000

01175670

01111300

01096000

01101000

01171500

01169900

01169000

01170100 01162500

01105600

01105870

01333000

010965852

01334000

01360640

01361000

01362100

01174600

01174000

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

VERMONT NEW HAMPSHIRE

NEW

YORK

U.S. Geological Survey streamgage and identifier

Base from U.S. Geological Survey Digital Line Graphs, 1989

Universal Transverse Mercator, 1:100,000 scale

Other coverages from MAGIC, MassGIS, NH GANIT, NYSGIS, RIGIS, and VCGI

Study basin

01174900

U.S. Geological Survey crest-stage gage and identifier

01362100

EXPLANATION

73°00' 72°00' 71°00' 70°00'

42°00'

42°30'

41°30'

Figure 1. Location of U.S. Geological Survey streamgage and crest-stage gage study sites used in the development of bankfull channel 

geometry and discharge equations for streams in and near Massachusetts.
Methods of Data Collection and Analysis 5

COASTAL LOWLANDS

CENTRAL HIGHLANDS

CONNECTICUT VALLEY

HUDSON-GREEN-NOTRE DAME HIGHLANDS 

VERMONT VALLEY

TACONIC HIGHLANDS

HUDSON-ST. LAWRENCE LOWLANDS

HUDSONST. LAWRENCE

LOWLANDS

COASTAL PLAIN

01111500

01093800

01333000

01181000 01175670

01170100

01169900

01169000

01162500

01105600

01096000

01199050

01111300

01198000

01174900 01171500

01163200

01109000

01105870

01103500

01101000

01187400 01184100

010965852

01100600

01109070

01176000

01334000

01360640

01361000

01362100

01174600

01174000

0 25 50 MILES

0 25 50 KILOMETERS

73° 72° 71° 70°

41°

42°

43°

EXPLANATION

Level III ecoregions (U.S. Environmental Portection Agency, 2006)

 Eastern Great Lakes and Hudson Lowlands

 Northeastern Highlands

 Northeastern Coastal Zone

 Atlantic Coastal Pine Barrens

01109070

Study basin

Physiographic province boundary (Denny, 1982)

U.S. Geological Survey streamgage and identifier

01362100 U.S. Geological Survey crest-stage gage and identifier

Modified from Denny, 1992 Base from U.S. Geological Survey Digital Line Graphs, 1989

Universal Transverse Mercator, 1:100,000 scale

Other coverages from MAGIC, MassGIS, NH GANIT, NYSGIS, RIGIS, and VCGI

Figure 2. Locations of the physiographic provinces and U.S. Environmental Protection Agency Level III ecoregions in and near 

Massachusetts.
6 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Site Selection

The stream sites that were used in this study met a number of general selection criteria that are similar to the criteria 

used in other bankfull studies in the eastern United States. 

These criteria are

1. the site is at a continuous or recently discontinued USGS 

streamgage or crest-stage gage in or near Massachusetts;

2. the streamgage or crest-stage gage at the site has a minimum of 10 years of streamflow record;

3. streamflow at the site is relatively naturally flowing with 

little to no high-flow regulation by dams, diversions, or 

other features;

4. the drainage area contains less than 25 percent urban 

land use, where urban land use includes commercial, 

industrial, transportation, and high-density residential 

(MassGIS, 2009);

5. the site is wadeable for surveying; and

6. identifiable bankfull indicators are present.

Additionally, sites with differing drainage areas were included 

to develop equations that would be applicable throughout the 

State.

All current and discontinuous streamgages in and 

near Massachusetts with data in the USGS National Water 

Information System (NWIS) were reviewed in terms of these 

selection criteria. Twenty-seven streamgages were identified in 

NWIS that met the criteria (table 1 and fig. 1). 

Bankfull Stage Indicators

Bankfull stage is the elevation of the streamwater surface 

when the stream fills its channel; it can be recognized in the 

field by a number of physical indicators and characteristics 

along the stream’s banks. Identification of bankfull-stage 

indicators (henceforth “bankfull indicators”) generally 

followed procedures discussed in Harrelson and others 

(1994), Leopold (1994), U.S. Department of Agriculture, 

Forest Service (1995, 2003, and 2004), Rosgen (1996), and 

Powell and others (2004). For this study the emphasis was on 

the following bankfull indicators in this order: (1) the active 

floodplain (a flat depositional surface adjacent to the stream 

channel) where the stream overtops its banks, (2) depositional 

features (such as point bars), (3) changes in the bank slope, 

(4) changes in the particle size of bank material, (5) undercuts 

or scour lines in the bank, and (6) changes in vegetation on 

the bank (for example, an area with no trees, transitioning to 

an area with trees). The most common feature used for the 

identification of the bankfull stage was the active floodplain 

where the stream overtopped its banks. 

As a guide to field investigations and for comparison 

with field observations, the stream stages of peak discharges 

with recurrence intervals of 1 to 10 years were estimated from 

discharge data at the streamgage associated with each site 

(table 2). Previous studies have shown that bankfull conditions 

are associated with peak discharges that recur, on average, 

every 1.5 years (Dunne and Leopold, 1978; Harrelson and 

others, 1994; Rogen, 1996). The stages associated with the 

1- to 2-year recurrence interval peak discharges were used 

in the field to help identify the general areas along streambanks to be examined for bankfull indicators. Recurrence 

intervals of annual peak discharges were calculated using a 

Log-Pearson Type III analysis following procedures outlined 

by the Interagency Advisory Committee on Water Data (1982) 

for the associated streamgage at each site for the period of 

record. The estimated peak discharges for the 1- to 2-year 

recurrence intervals then were used with the 2004 water year1

stage-discharge rating curve for active streamgages to determine the corresponding stream stage of these peak discharges; 

the most recent stage-discharge rating curve available for the 

time period when the streamgage was in operation was used 

for discontinued streamgages. In the field, the elevations on 

the streambank of water levels (stage) that would be associated with these peak discharges were determined using the 

difference between the elevation (stage) of water surface at the 

time of the field survey and the peak discharge stage values. 

Generally field bankfull indicators were found to fall within 

the range of elevations (stage) associated with the 1- to 2-year 

recurrence interval peak discharges at each site. In all cases, 

however, the best field bankfull indictor was used, even if it 

was above or below the range of elevations (stage) estimated 

from peak discharges. 

Bankfull Channel Geometry

The procedures for determining bankfull channelgeometry characteristics generally followed the methodologies 

presented in a number of widely used publications. Bankfullstage indicators were identified at 14 to 25 locations (averaged 

20 locations) along the stream channel, separated by a 

distance equivalent to approximately one bankfull width, at 

each of the 27 sites. The latitude and longitude of the most 

upstream location and the most downstream location at each 

of the 27 sites are presented in appendix 1. The total length 

of stream surveyed at each site averaged about 1,384 feet (ft) 

(range 552–2,661 ft). At the 14 to 25 locations at each site, the 

bankfull indicators were flagged on the left and right stream 

banks (looking downstream). The best indicators (right and 

left banks) were identified, and any other likely indicators 

at higher or lower elevations were also identified. The type 

of bankfull indicator generally was noted, and generally, a 

relative rating of good, fair, or poor was noted. 

1

A water year is the 12-month period beginning October 1 and ending 

September 30. It is designated by the calendar year in which it ends.
Methods of Data Collection and Analysis 7

The elevations of bankfull indicators, the water surface, and the stream thalweg were determined relative to the 

established datum at the streamgage at each site using standard 

surveying techniques (Harrelson and others, 1994; Leopold, 

1994; U.S. Department of Agriculture, 1995, 2003, and 2004; 

Rosgen, 1996; and Powell and others, 2004). The accuracy 

of the elevation points surveyed was recorded to the nearest 

0.01 ft, and all loops within the survey closed within 0.02 ft 

of the starting elevations. The horizontal distances between 

the locations were measured, generally along the thalweg of 

the stream.

Detailed cross sections to define bankfull channel geometry (width, mean depth, and cross-sectional area) were surveyed at two of the locations where bankfull indicators were 

flagged at each site. These detailed cross-sectional surveys 

were made at riffle sections at the two locations that were most 

representative of the bankfull channel geometry of the entire 

stream reach. The detailed cross-sectional survey consisted 

of 20 to 25 points in a section across the stream at which the 

elevation of the stream channel bottom and streambanks were 

determined; points along the cross sections were more closely 

spaced where changes in the elevation of the stream channel 

bottom and streambanks were greatest. Additional data on 

streambed materials were collected at the two riffle locations, 

using methods described by Wolman (1954) (appendix 2). The 

data included measurements of the intermediate particle-size 

diameter at 50 locations across each of the two cross sections.

The elevations of the bankfull indicators, water surface, 

and thalweg and the distance along the stream reach were 

entered into a Microsoft EXCEL spreadsheet template developed for bankfull stream reach surveys (Peter Cinotto, U.S. 

Geological Survey, written commun., 2004). The spreadsheet 

plotted a profile of the bankfull indicators, water surface, and 

thalweg of the stream reach and the surveyed cross section at 

the two selected riffle locations. The spreadsheet calculated 

the bankfull and water-surface slopes. The spreadsheet also 

calculated bankfull width, mean depth, cross-sectional area, 

and the particle-size distribution of the streambed material at 

the two detailed cross sections.

Bankfull Discharge

Bankfull discharge for each of the 27 sites was calculated 

using the elevations of bankfull indicators at locations that 

were in the gage pool of the streamgage. This method was 

the primary method of calculating bankfull discharge for the 

present study, and the values of bankfull discharge calculated 

in this way were used to develop the equations. The gage 

pool is the area of the stream reach in which the stream stage 

is recorded and for which the existing stage-discharge relation (rating curve) is determined. Only locations within the 

gage pool could be used because the elevations needed to be 

related to the elevation of the water surface in the gage pool 

in order to use the stage-discharge relation developed for the 

streamgage to calculate bankfull discharge. In most cases, only 

one of the locations where bankfull indicators were flagged 

along the stream reach at each site was located in the gage 

pool. In those cases, the elevations of the bankfull indicators 

from the right and left banks were averaged to determine the 

bankfull elevation at the streamgage. In cases where more than 

one location was in the gage pool, the elevations of the bankfull indicators from right and left banks for all those locations 

were averaged. The bankfull stage then was used with the 

stage-discharge rating curve that was applicable when the data 

were collected (water year 2004) for that streamgage to estimate the bankfull discharge. For discontinuous streamgages, 

the most recent stage-discharge rating curve that was available for the time period when the streamgage was operating 

was used. 

The recurrence interval of the bankfull discharge at 

each of the 33 sites was determined from an analysis of the 

annual instantaneous peak discharges for the period of record 

through water year 2009 at each site. The Log-Pearson Type 

III method (Interagency Advisory Committee on Water Data, 

1982) was used to determine flood frequency (recurrence 

interval of specific flood discharges) from the streamflow 

record. The number of water years of record analyzed for 

the 33 sites ranged from 19 to 97 with an average of about 

54 years and a median of 49 years (table 2). A minimum of 

10 years of record is typically used for a peak-flow analysis. 

The recurrence intervals of bankfull discharges were taken 

as equal to the recurrence interval of the equivalent annual 

instantaneous peak discharge (table 2). For those sites with 

bankfull discharges between recurrence intervals of the computed peak discharges in table 2, the bankfull discharge recurrence intervals were estimated by interpolation. 

Bankfull discharge was also estimated for each of the 

27 sites using two alternative methods that use data collected 

at the two riffle locations at each site where detailed cross 

sections were surveyed. These methods were considered 

check methods of the primary method of estimating bankfull 

discharge, which was done using the elevation of bankfull 

indicators in the gage pool of each site and the corresponding 

stage-discharge rating curve. Detailed data used in the two 

alternative check methods are provided in appendix 2. 

The first alternative check method, which is the more 

common method, uses the Manning’s equation.

2 1

3 2 1.49 Q AR S

n = , (1)

where

Q = discharge, in cubic feet per second; 

n = Manning’s roughness coefficient;

A = cross-sectional area of channel, in square 

feet;

R = hydraulic radius, in feet; and

S = energy gradient or friction slope, in feet per 

foot.
8 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Table 1. Description of U.S. Geological Survey streamgage and crest-stage gage study sites used in development of bankfull channel geometry and discharge equations for streams in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; °, degrees; ʹ, minutes; ′′, seconds; p, present; --, none; CSG, crest-stage gage] USGS station no. Station name Station latitude Station longitude Major river basin Drain- age area (mi2

)

Period of record Remarks

Data collected for this study

01093800 Stony Brook Tributary near Temple, NH 42° 51ʹ 36′′ 71° 50ʹ 00′′ Merrimack 3.6 1963–2004 --01096000 Squannacook River near West Groton, MA 42° 38ʹ 03′′ 71° 39ʹ 30′′ Nashua 63.7 1949–p Occasional regulation at low flow by mill 

upstream; regulation greater prior to 1961.

010965852 Beaver Brook at North Pelham, NH 42° 46ʹ 58′′ 71° 21ʹ 15′′ Merrimack 47.8 1986–p Some regulation at low and medium flows.01100600 Shawsheen River near Wilmington, MA 42° 34ʹ 05′′ 71° 12ʹ 55′′ Shawsheen 36.5 1963–p Diversions at times since 1973 for municipal 

supply.

01101000 Parker River at Byfield, MA 42° 45ʹ 10′′ 70° 56ʹ 46′′ Parker 21.3 1945–p Occasional regulation by mill and ponds.01103500 Charles River at Dover, MA 42° 15ʹ 22′′ 71° 15ʹ 38′′ Charles 183 1937–p Flow affected by diversions to and from basin 

for municipal supply.

01105600 Old Swamp River near South Weymouth, MA 42° 11ʹ 25′′ 70° 56ʹ 43′′ Boston 

Harbor

4.5 1966–p --

01105870 Jones River at Kingston, MA 41° 59ʹ 27′′ 70° 44ʹ 03′′ South 

Coastal

15.7 1966–p Flow regulated by pond upstream.

01109000 Wading River near Norton, MA 41° 56ʹ 51′′ 71° 10ʹ 38′′ Taunton 43.3 1925–p Flow regulated to some extent by lakes and 

reservoirs and diversions to and from basin for municipal supplies.

01109070 Segreganset River near Dighton, MA 41° 50ʹ 25′′ 71° 08ʹ 36′′ Taunton 10.6 1966–p Occasional regulation by ponds and diversion 

for municipal supply.

01111300 Nipmuc River near Harrisville, RI 41° 58ʹ 52′′ 71° 41ʹ 11′′ Blackstone 16.0 1964–1991, 

1993–p

--

01111500 Branch River at Forestdale, RI 41° 59ʹ 47′′ 71° 33ʹ 47′′ Blackstone 91.2 1909–1913, 

1940–p

Occasional regulation by pond, and prior 

to 1957 greater regulation by mills and reservoirs.

01162500 Priest Brook near Winchendon, MA 42° 40ʹ 57′′ 72° 06ʹ 56′′ Millers 19.4 1916–p Prior to 1962, occasional diurnal fluctuation 

at low flow by mill.

01163200 Otter River at Otter River, MA 42° 35ʹ 18′′ 72° 02ʹ 29′′ Millers 34.1 1964–p --01169000 North River at Shattuckville, MA 42° 38ʹ 18′′ 72° 43ʹ 32′′ Deerfield 89.0 1939–p Diurnal fluctuation at times caused by mill.01169900 South River near Conway, MA 42° 32ʹ 31′′ 72° 41ʹ 39′′ Deerfield 24.1 1966–p Diurnal fluctuation by small powerplant since 

April 1982.

01170100 Green River near Colrain, MA 42° 42ʹ 12′′ 72° 40ʹ 16′′ Deerfield 41.4 1967–p --01171500 Mill River at Northampton, MA 42° 19ʹ 05′′ 72° 39ʹ 21′′ Connecticut 52.6 1938–p Flow regulated by mill.
Methods of Data Collection and Analysis 

9

Table 1. Description of U.S. Geological Survey streamgage and crest-stage gage study sites used in development of bankfull channel geometry and discharge equations for streams in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; °, degrees; ʹ, minutes; ′′, seconds; p, present; --, none; CSG, crest-stage gage]

USGS 

station no. Station name Station latitude Station longitude Major river basin Drain- age area (mi2) Period of record Remarks

Data collected for this study—Continued

01174900 Cadwell Creek near Belchertown, MA 42° 20ʹ 08′′ 72° 22ʹ 12′′ Chicopee 2.55 1961–1997 --01175670 Sevenmile River near Spencer, MA 42° 15ʹ 54′′ 72° 00ʹ 19′′ Chicopee 8.81 1960–p Occasional regulation by ponds since 1971.01176000 Quaboag River at West Brimfield, MA 42° 10ʹ 56′′ 72° 15ʹ 51′′ Chicopee 150 1912–p Slight diurnal fluctuation at low flow caused 

by mill prior to 1956; regulation much greater prior to 1938.

01181000 West Branch Westfield River at Huntington, MA 42° 14ʹ 14′′ 72° 53ʹ 46′′ Westfield 94.0 1935–p Prior to 1950, some diurnal fluctuation at low 

flow caused by mill.

01184100 Stony Brook near West Suffield, CT 41° 57ʹ 38′′ 72° 42ʹ 39′′ Connecticut 10.4 1960–1981 (CSG), 

1981–p

--

01187300 Hubbard Brook near West Hartland, CT 42° 02ʹ 14′′ 72° 56ʹ 22′′ Connecticut 19.9 1938–55, 1956–p --01198000 Green River near Great Barrington, MA 42° 11ʹ 31′′ 73° 23ʹ 28′′ Housatonic 51.0 1951–1971, 

1994–1996, and 2007–p

--

01199050 Salmon Creek at Lime Rock, CT 41° 56ʹ 32′′ 73° 23ʹ 29′′ Housatonic 29.4 1961–p --01333000 Green River at Williamstown, MA 42° 42ʹ 32′′ 73° 11ʹ 50′′ Hudson 42.6 1949–p Slight diurnal fluctuation at times caused by 

mill.

Data collected for other studies

101174000 Hop Brook near New Salem, MA 42° 28ʹ 42′′ 72° 20ʹ 05′′ Chicopee 3.39 1947–82 --101174600 Cadwell Creek near Pelham, MA 42° 21ʹ 16′′ 72° 23ʹ 18′′ Chicopee 0.60 1961–94 --201334000 Walloomsac River near North Bennington, VT 42° 54ʹ 46′′ 73° 15ʹ 25′′ Hudson 111 1931–p Occasional diurnal fluctuation at low flow 

caused by mills upstream; diurnal fluctuation greater prior to 1960.

301360640 Valatie Kill near Nassau, NY 42° 33ʹ 07′′ 73° 35ʹ 31′′ Hudson 9.48 1990–p --301361000 Kinderhook Creek at Rossman, NY 42° 19ʹ 50′′ 73° 44ʹ 40′′ Hudson 329 1906–15, 1928, 

1984, and 1988–p (CSG); and 1929–68

--

301362100 Roeliff Jansen Kill near Hillsdale, NY 42° 09ʹ 14′′ 73° 31ʹ 14′′ Hudson 27.5 1957–59 and 

1960–p (CSG)

--

1Data from Thomas Garday, U.S. Department of Agriculture, Natural Resources Conservation Service, written commun., 2005.2Data from Jaquith and Kline, 2006.3Date from Mulvihill and Baldigo, 2007.
10 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Table 2. Estimated peak discharge for the 1.01, 1.05, 1.11, 1.25, 1.5, 2, 2.33, 5, and 10-year recurrence intervals for the study sites used in development of bankfull channel geometry and discharge equations for streams in and near Massachusetts.[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft3/s, cubic foot per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; --, no data]

USGS

station no. Station name

Drainage 

area

(mi2

)

Water years analyzed

Number 

of water 

years 

analyzed

Recurrence intervals

(years)

1.005 1.01 1.05 1.11 1.25 1.50 2 2.33 5 10

Peak discharge

(ft3/s)

01093800 Stony Brook Tributary near Temple, NH 3.6 1964–2004 41 54 60 81 96 120 148 188 208 308 40701096000 Squannacook River near West Groton, MA 63.7 1950–2009 60 343 394 574 703 900 1,136 1,452 1,608 2,357 3,044010965852 Beaver Brook at North Pelham, NH 47.8 1987–2009 23 222 246 332 396 496 620 796 887 1,357 1,83801100600 Shawsheen River near Wilmington, MA 36.5 1964–2009 46 175 193 258 304 374 459 574 632 917 1,19101101000 Parker River at Byfield, MA 21.3 1946–2009 64 70 76 98 115 140 171 215 237 352 46901103500 Charles River at Dover, MA 183 1938–2009 72 511 550 682 772 903 1,056 1,254 1,350 1,803 2,21201105600 Old Swamp River near South Weymouth, MA 4.5 1967–2009 43 41 48 71 87 113 145 188 210 317 41901105870 Jones River at Kingston, MA 15.7 1967–2009 43 78 86 110 126 149 175 207 223 293 35301109000 Wading River near Norton, MA 43.3 1926–2009 84 175 191 245 281 335 397 478 517 700 86401109070 Segreganset River near Dighton, MA 10.6 1967–2009 43 -- -- 186 214 255 301 360 388 518 63201111300 Nipmuc River near Harrisville, RI 16 1965–1991, 1994–2009 43 111 127 186 229 298 382 500 560 865 1,16401111500 Branch River at Forestdale, RI 91.2 1940–2000 70 511 566 762 901 1,113 1,369 1,718 1,892 2,752 3,57501162500 Priest Brook near Winchendon, MA 19.4 1917, 1919–2009 92 120 130 164 189 228 277 346 381 566 75701163200 Otter River at Otter River, MA 34.1 1965–2009 45 -- -- 258 291 337 389 456 487 630 75301169000 North River at Shattuckville, MA 89 1940–2009 70 1,376 1,538 2,111 2,517 3,139 3,885 4,895 5,399 7,866 10,20001169900 South River near Conway, MA 24.1 1967–2009 43 650 704 900 1,042 1,266 1,545 1,937 2,139 3,185 4,25801170100 Green River near Colrain, MA 41.4 1968–2009 42 -- -- 1,395 1,568 1,816 2,095 2,450 2,619 3,388 4,05501171500 Mill River at Northampton, MA 52.6 1939–2009 71 -- -- 1,000 1,201 1,496 1,831 2,259 2,462 3,377 4,15101174900 Cadwell Creek near Belchertown, MA 2.55 1962–1997 36 35 39 54 65 80 97 119 129 178 21901175670 Sevenmile River near Spencer, MA 8.81 1961–2009 49 -- -- 82 97 119 146 182 200 287 37001176000 Quaboag River at West Brimfield, MA 150 1913–2009 97 624 640 711 768 865 994 1,185 1,287 1,848 2,46901181000 West Branch Westfield River at Huntington, MA 94 1936–2009 74 1,280 1,436 2,016 2,449 3,145 4,026 5,296 5,959 9,459 13,12001184100 Stony Brook near West Suffield, CT 10.4 1960–2009 50 90 102 148 183 238 308 407 459 726 1,00101187300 Hubbard Brook near West Hartland, CT 19.9 1938–55, 1957–2009 71 171 200 314 402 545 730 999 1,140 1,883 2,65201198000 Green River near Great Barrington, MA 51.0 1952–71, 1994–1996, 

and 2008–09

25 -- -- 645 742 899 1,102 1,398 1,556 2,413 3,355

01199050 Salmon Creek at Lime Rock, CT 29.4 1962–2009 48 150 170 242 296 380 483 628 702 1,076 1,44601333000 Green River at Williamstown, MA 42.6 1950–2009 60 -- -- 737 846 1,006 1,191 1,430 1,545 2,083 2,563101174000 Hop Brook near New Salem, MA 3.39 1948–82 35 -- -- 73 86 104 125 151 163 217 261101174600 Cadwell Creek near Pelham, MA 0.60 1962–94 33 -- -- 18 21 24 28 33 35 46 55201334000 Walloomsac River near North Bennington, VT 111 1932–2009 78 1,121 1,244 1,657 1,934 2,337 2,793 3,374 3,650 4,904 5,980301360640 Valatie Kill near Nassau, NY 9.48 1991–2009 19 135 153 214 255 316 384 471 512 698 854301361000 Kinderhook Creek at Rossman, NY 329 1909, 1928–68, and 

1988–2009

64 2,110 2,274 2,870 3,305 3,989 4,839 6,038 6,656 9,863 13,160

301362100 Roeliff Jansen Kill near Hillsdale, NY 27.5 1958–2009 52 -- -- 359 430 536 661 826 906 1,287 1,631

1Study site from Thomas Garday, U.S. Department of Agriculture, Natural Resources Conservation Service, written commun., 2005.2Study site from Jaquith and Kline, 2006.3Study site from Mulvihill and Baldigo, 2007.
Development of Equations for Estimating Bankfull Geometry and Discharge 11

For this study, the variable S was approximated using the 

estimated water-surface slope at the riffle cross section. Jarrett 

(1984) reports that the use of the water-surface slope in place 

of the energy or friction slope, S, is a common practice. The 

water-surface slope was estimated using the slope of a best-fit 

line through the water-surface elevations at the surveyed location one bankfull width upstream from the riffle section, at the 

riffle section, and at the surveyed location one bankfull width 

downstream from the riffle section.

The Manning’s roughness coefficient “n” was calculated 

using four equations developed by Limerinos (1970) using 

the d16, d50, d84, and dw of the streambed material. For this 

study, the particle-size distributions of the streambed material 

at the d16, d50, and d84 [intermediate particle diameter that 

equals or exceeds that of 16, 50, and 84 percent of the particle 

diameters, respectively, determined by methods described by 

Wolman (1954)] were determined from the 50-point pebble 

count of the intermediate particle-size diameter at each of 

the two riffle cross sections. The dw (weighted particle-size 

distribution) was determined from the following equation that 

weights the d16, d50, and d84.

dddd w = ++ ((0.1 0.3 0.6 16 ) ( 50 ) ( 84 )) (2)

Manning’s roughness coefficient “n” using the d16 was

16

0.0926

0.10 1.60log

, (3)

using the d50, the equation was

1

6

50

0.0926

0.35 2.0

R

n R log d=

+

, (4)

using the d84, the equation was

1

6

84

0.0926

1.16 2.0

R

n R log d=

+

, and (5)

using the dw, the equation was

1

6 0.0926

0.90 2.0

w

R

n R log d=

+

, (6)

where

n = Manning’s roughness coefficient;

R = hydraulic radius, in feet;

d16 = 16th percentile particle diameter of bed 

material, in feet;

d50 = 50th percentile (median) particle diameter 

of bed material, in feet;

d84 = 84th percentile particle diameter of bed 

material, in feet; and

dw = weighted particle diameter of bed material, 

in feet (see equation 2).

With a second alternative check method, bankfull discharge also was calculated using an equation developed by 

Jarrett (1984) for high-gradient streams.

0.83 0.12 Q AR S = 3.8 , (7)

where

Q = discharge, in cubic feet per second; 

A = cross-sectional area of channel, in square 

feet;

R = hydraulic radius, in feet; and

S = energy gradient or friction slope, in feet 

per foot.

Jarrett (1986, p. 15) notes that S (the energy gradient or 

friction slope) is the slope of the energy line of a body of flowing water. Also, Jarrett (1986) states that, on the basis of data 

from 21 streams used to develop equation 7 (Jarrett, 1984), the 

friction slope and water-surface slope can be used interchangeably. The major limitation of the equation is that the watersurface slope of the stream channel must be between 0.002 to 

0.04 ft/ft. Other limitations are discussed by Jarrett (1984) in 

greater detail.

Development of Equations for 

Estimating Bankfull Geometry and 

Discharge

The common method of estimating bankfull channel 

geometry and discharge is to relate bankfull width, mean 

depth, cross-sectional area, and discharge to drainage area 

through regression equations and graphic plots. The plots of 

the regression equations for bankfull channel geometry and 

discharge are commonly referred to as “regional curves.” 

Regional curves are based on simple regression equations, 

which use one explanatory variable, drainage area, to estimate 

the response variables of bankfull width, mean depth, crosssectional area, and bankfull discharge. Multiple regression 

equations have more than one explanatory variable, such as 

factors and basin characteristics other than drainage area, that 

may affect bankfull geometry and discharge. 
12 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Factors Affecting Bankfull Channel Geometry 

and Discharge

Drainage area of a basin is the main factor affecting 

bankfull channel geometry and discharge. However, physical, 

hydrologic, land-use, and climatic characteristics of a drainage 

basin can affect bankfull channel geometry and discharge. 

For example, bankfull studies in Pennsylvania (Chaplin, 

2005) and Virginia (Keaton and others, 2005) found that the 

presence of carbonate bedrock was inversely related to values 

of bankfull discharge, width, mean depth, and cross-sectional 

area. Sherwood and Hutiger (2005) found that main-channel 

slope and elevation were related (positive and negative, 

respectively) to bankfull channel geometry and discharge. 

Anthropogenic factors, such as flood control dams or major 

diversions, also can affect bankfull channel geometry and 

discharge, but because the present study used naturally flowing 

streams with little to no peak-flow regulations, anthropogenic 

factors were not considered here.

Characteristics that could affect bankfull channel geometry and discharge were summarized by reviewing peak-flow 

studies in states in northeastern United States: Connecticut 

(Ahearn, 2004), Maine (Hodgkins, 1999), Massachusetts 

(Wandle, 1983; Murphy, 2001), New Hampshire (Olson, 

2009), New York (Lumia and others, 2006), Rhode Island 

(Zarriello and others, 2012), and Vermont (Olson, 2002). 

All of these studies found drainage area to be a significant 

variable, along with characteristics of the basin such as areal 

percentage of lakes and ponds (Olson, 2002), areal percentage of wetlands (Hodgkins, 1999 and Olson, 2009), areal 

percentage of basin storage (lakes, ponds, and swamps) 

(Wandle, 1983; Lumia and others, 2006; and Zarriello and 

others, 2012), areal percentage of forest land (Lumia and 

others, 2006), main-channel slope (Wandle, 1983; Lumia and 

others, 2006; and Olson, 2009), ratio of main-channel slope 

to basin slope (Lumia and others, 2006), percent of a basin 

above a set elevation (Olson, 2002 and Lumia and others, 

2006), mean basin elevation (Wandle, 1983; Ahearn, 2004), 

difference between the mean and minimum basin elevations 

(Murphy, 2001), basin lag factor (Lumia and others, 2006), 

drainage density (Zarriello and others, 2012), mean-annual 

runoff (Lumia and others, 2006), maximum snow depth 

(Lumia and others, 2006), mean annual precipitation (Lumia 

and others, 2006), mean April precipitation (Olson, 2009), 

and the recurrence interval associated with 24-hour rainfall 

amounts (Ahearn, 2004). Characteristics that were shown by 

these studies to have positive effects on peak flow are drainage 

area, main-channel slope, percent of a basin higher than a set 

elevation, mean basin elevation, mean annual precipitation, 

and the recurrence interval of 24-hour rainfall amounts. Characteristics shown to have negative effects on peak flows are 

basin storage, percentage of lakes and ponds, areal percentage 

of wetlands, percentage of forest land, average main-channel 

elevation, and basin shape.

Bankfull Channel Geometry and Discharge at 

Study Sites

Bankfull geometry (width, mean depth, and crosssectional area) and discharge are presented in table 3 for the 

27 sites at which data were collected as part of the present 

study and for the 6 sites for which data were compiled from 

other studies. Data from all 33 sites were used to develop the 

equations and regional curves.

Bankfull width, mean depth, and cross-sectional area 

were determined from the two surveyed cross sections at riffle 

locations at the 27 sites at which data were collected as part of 

this study; values from the two cross sections were averaged 

for use in developing the equations. Bankfull geometry for 

the 6 additional sites was determined as the average of values 

from 1 to 7 cross sections per site (table 3). Average values for 

all 33 sites used in developing equations ranged from 13.5 to 

148 ft for bankfull width, 0.73 to 5.8 ft for bankfull mean 

depth, and 9.77 to 858.5 ft2 for bankfull cross-sectional area. 

Estimates of bankfull discharge were made at the 

27 sites using three methods—one primary method and two 

alternative check methods. Bankfull discharge calculated from 

the elevation of bankfull indicators and the stage-discharge 

rating curve at the streamgage was the primary method, and 

the values that were calculated from this method were used 

in developing equations (table 3). This method was used as 

the primary method because the stage-discharge rating curve 

is based on physical measurements of discharge and stage 

at the site. It also is the simplest method, requires the fewest 

assumptions, and requires estimation of the fewest number of 

variables. The two alternative methods for estimating bankfull 

discharge provided checks on the results of the bankfull 

indicator-stage method for comparison of the 27 sites where 

data were collected for this study. The two alternative check 

methods were based on data collected at the two surveyed 

riffle cross-section locations. 

Bankfull discharge at the 27 study sites, based on the 

primary bankfull indicator-stage method for comparison with 

values determined using the other two check methods, ranged 

from 46 to 3,470 cubic feet per second (ft3/s) (table 3). The 

recurrence intervals of bankfull discharges for the 27 study 

sites ranged from 1.03 to 3.48 years (table 3) with an average of 1.58 years and a median of 1.34 years. For all 33 sites 

that provided the data used to develop the equations, bankfull 

discharge ranged from 24 to 5,640 ft3/s, and the recurrence 

intervals ranged from 1.03 to 3.48 years with an average of 

1.53 years and a median of 1.34 years. 

The average bankfull discharges calculated using the 

Limerinos dw equation (equation 6) (1970) and the Manning’s 

equation (equation 1) for each of the 27 sites ranged from 

132 to 3,302 ft3/s (table 4); that range compares well with 

the range of estimated bankfull discharges using the bankfull 

indicator elevations and the stage-discharge rating curve 

(primary) method for the 27 sites (table 3). Evaluation of the 

percent difference between the two methods found that the 

average and median difference was about 25 and 21 percent 
Development of Equations for Estimating Bankfull Geometry and Discharge 13

Table 3. Bankfull channel geometry and discharge for study sites in and near Massachusetts.—Continued

[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; 

ft3/s, cubic foot per second; yr, year; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; --, unknown]

USGS 

station no. Station name

Drainage 

area 

(mi2)

Bankfull 

discharge 

(ft3/s)

Discharge 

recurrence 

interval 

(yr)

Crosssection 

no.

Bankfull 

width 

(ft)

Bankfull 

mean 

depth 

(ft)

Bankfull 

crosssectional 

area 

(ft2)

Data collected for this study

01093800 Stony Brook Tributary near Temple, NH 3.60 211 2.41 9 24.00 1.65 39.54

17 25.00 1.50 37.42

Average 24.50 1.58 38.48

01096000 Squannacook River near West Groton, MA 63.7 742 1.14 3 81.50 3.52 286.89

16 65.90 3.01 198.36

Average 73.70 3.27 242.63

010965852 Beaver Brook at North Pelham, NH 47.8 433 1.16 3 57.00 3.91 223.05

14 43.80 2.82 123.47

Average 50.40 3.37 173.26

01100600 Shawsheen River near Wilmington, MA 36.5 295 1.10 6 57.80 3.59 207.46

10 74.30 2.47 183.59

Average 66.05 3.03 195.53

01101000 Parker River at Byfield, MA 21.3 273 3.16 1 43.50 3.08 133.79

2 49.40 2.47 121.93

Average 46.45 2.78 127.86

01103500 Charles River at Dover, MA 183 954 1.33 11 98.50 3.96 390.01

17 98.80 3.97 392.00

Average 98.65 3.97 391.01

01105600 Old Swamp River near South Weymouth, MA 4.50 226 2.73 8 40.30 1.28 51.47

14 30.80 1.34 41.29

Average 35.55 1.31 46.38

01105870 Jones River at Kingston, MA 15.7 253 3.48 6 42.50 2.00 85.00

13 34.80 2.16 75.05

Average 38.65 2.08 80.03

01109000 Wading River near Norton, MA 43.3 295 1.15 5 40.00 2.13 85.06

10 41.30 2.56 105.60

Average 40.65 2.35 95.33

01109070 Segreganset River at Dighton, MA 10.6 193 1.07 8 31.30 2.28 71.42

14 33.80 1.62 54.66

Average 32.55 1.95 63.04

01111300 Nipmuc River near Harrisville, RI 16.0 318 1.31 9 46.00 2.24 103.07

13 57.50 2.03 116.63

Average 51.75 2.14 109.85

01111500 Branch River at Forestdale, RI 91.2 1,210 1.34 7 87.00 3.67 319.58

9 79.80 3.18 253.39

Average 83.40 3.43 286.49
14 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Table 3. Bankfull channel geometry and discharge for study sites in and near Massachusetts.—Continued

[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; 

ft3/s, cubic foot per second; yr, year; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; --, unknown]

USGS 

station no. Station name

Drainage 

area 

(mi2)

Bankfull 

discharge 

(ft3/s)

Discharge 

recurrence 

interval 

(yr)

Crosssection 

no.

Bankfull 

width 

(ft)

Bankfull 

mean 

depth 

(ft)

Bankfull 

crosssectional 

area 

(ft2)

Data collected for this study—Continued

01162500 Priest Brook near Winchendon, MA 19.4 182 1.10 6 59.60 1.59 94.98

9 51.50 2.48 127.82

Average 55.55 2.04 111.40

01163200 Otter River at Otter River, MA 34.1 374 1.43 6 66.50 1.61 107.34

13 52.90 1.93 102.18

Average 59.70 1.77 104.76

01169000 North River at Shattuckville, MA 89.0 3,070 1.23 2 108.80 4.91 534.10

17 103.80 4.80 497.87

Average 106.30 4.86 515.99

01169900 South River near Conway, MA 24.1 1,710 1.71 9 61.10 4.09 249.68

18 70.00 3.98 278.68

Average 65.55 4.04 264.18

01170100 Green River near Colrain, MA 41.4 2,110 1.52 3 109.00 2.86 311.70

15 100.50 3.52 353.37

Average 104.75 3.19 332.54

01171500 Mill River at Northampton, MA 52.6 1,600 1.33 2 86.00 3.53 303.51

6 83.00 3.60 298.96

Average 84.50 3.57 301.24

01174900 Cadwell Creek near Belchertown, MA 2.55 46 1.03 6 20.30 1.28 26.05

11 16.90 1.33 22.48

Average 18.60 1.31 24.27

01175670 Sevenmile River near Spencer, MA 8.81 163 1.74 20 37.90 1.49 56.43

13 25.50 1.80 45.99

Average 31.70 1.65 51.21

01176000 Quaboag River at West Brimfield, MA 150 1,010 1.54 4 143.90 2.67 384.51

20 121.00 2.71 327.46

Average 132.45 2.69 355.99

01181000 West Branch Westfield River at Huntington, MA 94.0 3,470 1.34 2 112.50 3.14 353.66

11 135.80 3.17 430.09

Average 124.15 3.16 391.88

01184100 Stony Brook near West Suffield, CT 10.4 274 1.38 18 48.00 1.74 83.40

22 39.50 1.58 62.26

Average 43.75 1.66 72.83

01187300 Hubbard River near West Hartland, CT 19.9 507 1.21 6 72.00 2.38 171.40

16 74.50 2.20 164.03

Average 73.25 2.29 167.72
Development of Equations for Estimating Bankfull Geometry and Discharge 15

Table 3. Bankfull channel geometry and discharge for study sites in and near Massachusetts.—Continued

[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; 

ft3/s, cubic foot per second; yr, year; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; --, unknown]

USGS 

station no. Station name

Drainage 

area 

(mi2)

Bankfull 

discharge 

(ft3/s)

Discharge 

recurrence 

interval 

(yr)

Crosssection 

no.

Bankfull 

width 

(ft)

Bankfull 

mean 

depth 

(ft)

Bankfull 

crosssectional 

area 

(ft2)

Data collected for this study—Continued

01198000 Green River near Great Barrington, MA 51.0 1,150 1.56 7 75.30 2.76 207.61

20 62.80 3.25 204.40

Average 69.05 3.01 206.01

01199050 Salmon Creek at Lime Rock, CT 29.4 490 1.52 14 49.00 2.14 104.75

21 43.50 2.78 121.03

Average 46.25 2.46 112.89

01333000 Green River at Williamstown, MA 42.6 1,220 1.56 8 84.00 2.84 241.38

15 74.00 3.34 246.86

Average 79.00 3.09 244.12

Data collected for other studies 1

01174000 Hop Brook near New Salem, MA 3.39 80 1.09 1 16.41 1.10 17.54

2 17.93 1.40 25.54

6 19.70 1.40 27.21

8 27.73 0.90 25.98

Average 20.44 1.20 24.07

1

01174600 Cadwell Creek near Pelham, MA 0.60 24 1.24 3 17.0 0.77 13.23

4 10.8 0.86 9.29

5 18.0 0.72 12.96

8 10.5 0.56 5.86

9 13.6 0.79 10.78

10 6.7 0.85 5.66

11 18.2 0.58 10.59

Average 13.5 0.73 9.77

2

01334000 Walloomsac River near North Bennington, VT 111 1,879 1.10 -- 110 3.7 410

3

01360640 Valatie Kill near Nassau, NY 9.48 227 41.07 -- 38.3 2.3 89.0

-- 34.5 2.2 76.8

-- 42.7 2.1 87.6

-- 38.7 1.8 69.6

Average 38.55 2.1 80.75

3

01362100 Kinderhook Creek at Rossman, NY 329 5,640 41.83 -- 139.6 5.8 806.5

-- 156.4 5.8 910.5

Average 148.0 5.8 858.5

3

01361000 Roeliff Jansen Kill near Hillsdale, NY 27.5 690 41.59 -- 54.4 3.5 189.1

-- 55.8 3.8 213.8

-- 60.4 3.1 185.2

Average 56.87 3.47 196.03

1

Data from Thomas Garday, U.S. Department of Agriculture, Natural Resources Conservation Service, written commun., 2005.

2

Data from Jaquith and Kline, 2006.

3

Data from Mulvihill and Baldigo, 2007.

4

Recurrence interval published as 1.16, 2.1, and 1.8 years for stations 01360640, 01362100, and 01361000, respectively, by Mulvihill and Baldigo, 2007.
16 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

higher, respectively, for the Limerinos method than for the 

primary method. The estimated bankfull discharge using 

the Jarrett equation (equation 7) (1984) ranged from 69 to 

3,678 ft3/s (table 4); that range compares well with the range 

of estimated bankfull discharges from the primary method in 

table 3. A comparison of percent differences between these 

two methods found that the average and median differences 

were about 22 and 17 percent higher, respectively, for the 

Jarrett method than for the primary method. The Limerinos 

and Jarrett methods compared well with each other, as 

comparison of the percent difference found on average that 

Jarrett is about 3 percent higher than Limerinos, but the 

median is 4 percent lower for Jarrett (1984) than Limerinos 

(1970) (table 4). 

The average bankfull width, mean depth, cross-sectional 

area, and discharge generally appear to be greater at the 

sites in and near western Massachusetts than at the sites in 

and near eastern Massachusetts. Specifically, these bankfull 

characteristics appear to be greater in the Hudson-GreenNotre Dame Highlands between the Connecticut Valley 

(east) and the Vermont Valley (west) physiographic provinces 

(fig. 2) defined by Denny (1982). These sites include North 

River at Shattuckville, Mass. (01169000), South River near 

Conway, Mass. (01169900), Green River near Colrain, Mass. 

(01170100), West Branch Westfield River at Huntington, 

Mass. (01181000), Hubbard River near West Hartland, 

Conn. (01187300), and Green River at Williamstown, Mass. 

(01333000). Although bankfull characteristics at these six 

sites appear to be slightly different from the others in and near 

western Massachusetts, comparison of selected basin and landuse characteristics (table 5), peak discharges for recurrence 

intervals ranging from about 1 to 10 years (table 2) on a per 

unit area basis, annual precipitation characteristics, and annual 

runoff characteristics did not find any notable differences from 

other sites in and near the region. 

Equations

Simple and multiple regression equations for bankfull 

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

presented in table 6. All equations were developed using base10 log-transformed bankfull channel geometry, discharge, 

and basin characteristic data (table 5) for all 33 study sites. 

The transforming of data is a common procedure that makes 

the data more symmetric, linear, and constant in variance 

(homoscedasticity) (Helsel and Hirsch, 2002). Detailed results 

for the simple and multiple regression analyses for bankfull 

channel geometry and discharge are shown in appendix 3. 

Although the equations were developed using log-transformed 

data, the equations are shown in table 6 in forms that allow the 

use of non-transformed data. 

The simple regression analyses used the automated 

procedures in the statistical software package Minitab (2003). 

The standard techniques of simple regression analyses were 

followed as discussed in Helsel and Hirsch (2002). The 

bankfull channel geometry and discharge simple regression 

equations using drainage area as the explanatory variable 

were evaluated by reviewing the adjusted R2 (coefficient of 

determination), predicted R2, plots of residuals, and other 

statistical indicators of model fit/validity. The predicted R2 for 

bankfull width (0.8635), mean depth (0.7995), cross-sectional 

area (0.9028), and discharge (0.7428) were all acceptable 

(table 6). Plots of the residuals were evaluated to verify that 

the residuals had no outliers, curvature, or heteroscedasticity 

(absence of homoscedasticity). Figures 3A–D show that the 

residuals of the simple regression equation for the bankfull 

channel geometry and discharge, by drainage area, have no 

outliers, curvature, or heteroscedasticity. The residuals are 

equally distributed on both the postitive and negative side 

of the zero line. The regression equation residuals were also 

reviewed spatially to make sure that no clear geographic trends 

were observed. Figure 4 shows the geographic distribution 

of the residuals for the bankfull width equation. There are six 

sites in western Massachusetts where residuals had higher 

positive values (regression equation is under predicting 

the actual value) than other sites in and near western 

Massachusetts. Four sites in southeastern Massachusetts 

had higher negative values (regression equation is over 

predicting the actual value) than other sites in and near eastern 

Massachusetts. All other areas of the State show a fairly even 

distribution of positive and negative residuals at the study sites 

with no clear pattern; overall, figure 4 shows a fairly even 

distribution of the residuals over the study area. More detailed 

output from the simple regression equations are presented in 

appendix 3. Graphic plots of the simple regression equations 

(equations 8–11 in table 6), which relate bankfull width, mean 

depth, cross-sectional area, and discharge to drainage area, 

are shown in figures 5A–D, respectively. These plots also 

serve as regional curves for Massachusetts and allow users to 

easily estimate bankfull geometry and discharge from a known 

drainage area for any site within the range of drainage areas 

shown. The graphs are plotted using logarithmic scales for “x” 

and “y” axes, which is common practice for regional curves.

In the multiple regression analysis, the basin 

characteristics listed in table 5 were investigated for their 

potential relation to bankfull width, mean depth, cross 

sectional area, and discharge. The automated statistical 

selection procedures “best subsets” and “stepwise” were 

used in Minitab (2003) to evaluate the basin characteristics 

as potential explanatory variables. Both selection procedures 

determined the statistical contribution of the explanatory 

variables (basin characteristics) that were entered into the 

equation, and variables were retained or deleted on the basis 

of their statistical importance. A statistical significance level 

of 0.05 for p-values of explanatory variables was generally 

used for entry or retention in the equations. Additionally, 

potential multiple regression equations were evaluated using 

the adjusted R2, predicted R2 plots of residuals, and so forth 

in determining the best possible equations. The standard 

techniques of multiple regression analyses were followed, as 

discussed in Helsel and Hirsch (2002). 
Development of Equations for Estimating Bankfull Geometry and Discharge 17

Table 4. Estimated bankfull discharge using equations by Limerinos (1970) and Jarrett (1984) for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/s, cubic foot per second; yr, year; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name

Drainage 

area 

(mi2

)

Crosssection 

no.

Limerios (1970) Jarrett (1984) From table 3

Estimated bankfull 

discharge 

(ft3/s) 

(based on dw)

Recurrence 

interval of average discharge 

(based on dw)

Estimated 

bankfull 

discharge 

(ft3/s)

Recurrence 

interval of 

average 

discharge

Estimated 

bankfull 

discharge 

(ft3/s)

Discharge 

recurrence 

interval 

(yr)

01093800 Stony Brook Tributary near Temple, NH 3.60 9 213 133

17 169 111

Average 191 2.05 122 1.27 211 2.41

01096000 Squannacook River near West Groton, MA 63.7 3 1,120 1,588

16 1,760 1,198

Average 1,440 1.98 1,393 1.90 742 1.14

010965852 Beaver Brook at North Pelham, NH 47.8 3 652 11,013

14 627 581

Average 639 1.55 797 2.00 433 1.16

01100600 Shawsheen River near Wilmington, MA 36.5 6 489 1830

10 419 1551

Average 454 1.48 690 2.85 295 1.1

01101000 Parker River at Byfield, MA 21.3 1 221 1449

2 112 1362

Average 167 1.47 406 7.22 273 3.16

01103500 Charles River at Dover, MA 183 11 1,143 11,918

17 1,065 12,017

Average 1,104 1.62 1,968 6.94 954 1.33

01105600 Old Swamp River near South Weymouth, MA 4.50 8 198 134

14 133 104

Average 166 1.74 119 1.29 226 2.73

01105870 Jones River at Kingston, MA 15.7 6 276 1255

13 285 249

Average 281 4.55 252 3.40 253 3.48

01109000 Wading River near Norton, MA 43.3 5 352 304

10 360 1413

Average 356 1.33 358 1.34 295 1.15

01109070 Segreganset River at Dighton, MA 10.6 8 254 292

14 2234 178

Average 244 1.21 235 1.18 193 1.07
18 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Table 4. Estimated bankfull discharge using equations by Limerinos (1970) and Jarrett (1984) for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; dw, weighted particle-size distribution—equation 2 in report (Lim- erinos, 1970); ft3/s, cubic foot per second; yr, year; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island] USGS station no. Station name Drainage area (mi2

)

Crosssection 

no.

Limerios (1970) Jarrett (1984) From table 3

Estimated bankfull 

discharge 

(ft3/s) 

(based on dw)

Recurrence 

interval of average discharge 

(based on dw)

Estimated 

bankfull 

discharge 

(ft3/s)

Recurrence 

interval of 

average 

discharge

Estimated 

bankfull 

discharge 

(ft3/s)

Discharge 

recurrence 

interval 

(yr)

01111300 Nipmuc River near Harrisville, RI 16.0 9 536 406

13 324 1342

Average 430 1.70 374 1.47 318 1.31

01111500 Branch River at Forestdale, RI 91.2 7 1,640 1,824

9 31,414 1,308

Average 1,527 1.65 1,566 1.78 1,210 1.34

01162500 Priest Brook near Winchendon, MA 19.4 6 402 262

9 368 1460

Average 385 2.38 361 2.13 182 1.1

01163200 Otter River at Otter River, MA 34.1 6 375 322

13 569 384

Average 472 2.17 353 1.32 374 1.43

01169000 North River at Shattuckville, MA 89.0 2 3,047 3,589

17 3,558 3,767

Average 3,302 1.30 3,678 1.43 3,070 1.23

01169900 South River near Conway, MA 24.1 9 1,863 1,605

18 1,619 1,533

Average 1,741 1.75 1,569 1.53 1,710 1.71

01170100 Green River near Colrain, MA 41.4 3 2,010 1,632

15 2,123 1,978

Average 2,066 1.47 1,805 1.24 2,110 1.52

01171500 Mill River at Northampton, MA 52.6 2 2,176 1,708

6 1,740 1,558

Average 1,958 1.65 1,633 1.35 1,600 1.33

01174900 Cadwell Creek near Belchertown, MA 2.55 6 150 74

11 138 65

Average 144 3.15 69 1.15 46 1.03

01175670 Sevenmile River near Spencer, MA 8.81 20 150 154

13 113 1135

Average 132 1.37 144 1.48 163 1.74
Development of Equations for Estimating Bankfull Geometry and Discharge 19

Table 4. Estimated bankfull discharge using equations by Limerinos (1970) and Jarrett (1984) for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/s, cubic foot per second; yr, year; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name

Drainage 

area 

(mi2

)

Crosssection 

no.

Limerios (1970) Jarrett (1984) From table 3

Estimated bankfull 

discharge 

(ft3/s) 

(based on dw)

Recurrence 

interval of average discharge 

(based on dw)

Estimated 

bankfull 

discharge 

(ft3/s)

Recurrence 

interval of 

average 

discharge

Estimated 

bankfull 

discharge 

(ft3/s)

Discharge 

recurrence 

interval 

(yr)

01176000 Quaboag River at West Brimfield, MA 150 4 1,410 1,629

20 1,629 1,521

Average 1,519 3.43 1,575 3.68 1,010 1.54

01181000 W. Branch Westfield River at Huntington, MA 94.0 2 2,622 2,037

11 2,345 2,110

Average 2,484 1.12 2,073 1.06 3,470 1.34

01184100 Stony Brook near West Suffield, CT 10.4 18 4335 294

22 4186 203

Average 260 1.22 248 1.29 274 1.38

01187300 Hubbard River near West Hartland, CT 19.9 6 1,257 815

16 709 638

Average 983 1.97 726 1.49 507 1.21

01198000 Green River near Great Barrington, MA 51.0 7 682 1750

20 964 1920

Average 823 1.18 835 1.19 1,150 1.56

01199050 Salmon Creek at Lime Rock, CT 29.4 14 457 415

21 5265 509

Average 361 1.22 462 1.45 490 1.52

01333000 Green River at Williamstown, MA 42.6 8 1,919 1,236

15 1,275 1,094

Average 1,597 2.59 1,165 1.46 1,220 1.56

1For the cross-sections, the Jarrett (1984) calculation of discharge had water-surface slopes less than 0.002 ft/ft.2For cross-section 14 at streamgage 01109070 Segreganset River at Dighton, MA, 12 of 50 Wolman (1954) pebble count samples were classified as bedrock and not used in calculation of the Manning’s 

roughness coefficient (Limerinos, 1970) using the dw (equations 2 and 6 in this report).

3For cross-section 9 at streamgage 01111500 Branch River at Forestdale, RI, 27 of 50 Wolman (1954) pebble count samples were classified as bedrock and not used in calculation of the Manning’s roughness coefficient (Limerinos, 1970) using the dw (equations 2 and 6 in this report).4For cross-sections 18 and 22 at streamgage 01184100 Stony Brook near West Suffield, CT, 30 of 50 and 44 of 50, respectively, Wolman (1954) pebble count samples were classified as bedrock and not 

used in calculation of the Manning’s roughness coefficient (Limerinos, 1970) using the dw (equations 2 and 6 in this report).

5For cross-section 21 at streamgage 01199050 Salmon Creek at Lime Rock, CT, 3 of 50 Wolman (1954) pebble count samples were classified as bedrock and not used in calculation of the Manning’s 

roughness coefficient (Limerinos, 1970) using the dw (equations 2 and 6 in this report).
20 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Table 5. Basin and land-use characteristics of the study sites used in development of bankfull channel geometry and discharge equations for streams in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; ft, foot; %, percent; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; --, no data] USGS station no. Station name Drain- age area (mi2

)

Mean 

basin 

elevation1

(ft)

Maximum 

basin 

elevation2

(ft)

Minimum 

basin 

elevation2

(ft)

Basin 

relief3

(ft)

Mean 

basin 

slope4 

(%)

Area of 

water 

bodies1

(%)

Area 

of wetlands1

(%)

Area of 

forest 

land1

(%)

Area of 

urban 

land1 

(%)

Area of 

agricultural land1

(%)

Area of 

sand and 

gravel 

deposits1

(%)

01093800 Stony Brook Tributary near Temple, NH 3.60 21,379 2,266 913 1,353 16.967 50.0 50.4 592.9 50.0 54.3 20.8

01096000 Squannacook River near West Groton, MA 63.7 622 1,492 249 1,243 8.129 0.9 2.2 82.0 1.3 6.0 27.0010965852 Beaver Brook at North Pelham, NH 47.8 2348 635 149 486 5.510 50.8 57.2 548.5 51.0 56.8 27.2

01100600 Shawsheen River near Wilmington, MA 36.5 5161 5358 582 274 4.414 0.5 4.0 29.0 24.0 2.5 39.001101000 Parker River at Byfield, MA 21.3 5116 5354 530 325 6.084 2.4 10.0 58.0 1.4 8.2 43.001103500 Charles River at Dover, MA 183 5225 5581 589 492 5.325 2.3 7.1 47.0 6.4 6.2 46.001105600 Old Swamp River near South Weymouth, MA 4.50 2142 199 74 125 3.384 0.2 6.0 40.6 8.2 0.0 33.001105870 Jones River at Kingston, MA 15.7 582 5210 513 215 4.189 7.3 14.0 55.0 1.0 7.7 96.001109000 Wading River near Norton, MA 43.3 179 435 62 373 3.845 2.7 9.2 57.0 6.7 4.4 58.001109070 Segreganset River at Dighton, MA 10.6 5112 5243 526 212 3.144 0.4 6.9 75.0 1.6 6.1 16.001111300 Nipmuc River near Harrisville, RI 16.0 531 771 346 425 5.635 0.5 3.6 83.0 1.4 3.9 0.501111500 Branch River at Forestdale, RI 91.2 495 818 193 625 7.058 5.8 4.6 67.0 4.1 4.5 5.801162500 Priest Brook near Winchendon, MA 19.4 1,095 1,871 849 1,022 6.948 1.7 3.0 88.0 0.7 4.3 10.001163200 Otter River at Otter River, MA 34.1 51,075 51,335 5896 445 6.630 3.6 5.3 67.0 9.3 2.8 26.001169000 North River at Shattuckville, MA 89.0 1,425 2,322 433 1,889 15.139 0.4 0.6 86.0 0.3 10.0 5.901169900 South River near Conway, MA 24.1 1,126 1,819 475 1,344 15.611 0.4 0.3 78.0 0.3 15.0 13.001170100 Green River near Colrain, MA 41.4 1,352 2,410 465 1,945 17.141 0.5 0.5 91.0 0.1 5.6 0.501171500 Mill River at Northampton, MA 52.6 841 1,692 170 1,522 12.138 1.0 0.9 81.0 3.1 6.8 16.001174900 Cadwell Creek near Belchertown, MA 2.55 2923 51,132 5541 621 7.231 50.0 56.2 589.9 50.0 56.6 20.7

01175670 Sevenmile River near Spencer, MA 8.81 871 1,072 651 421 8.587 2.3 3.7 73.0 0.2 14.0 13.001176000 Quaboag River at West Brimfield, MA 150 808 1,227 385 842 8.558 3.3 5.5 67.0 1.8 15.0 21.001181000 West Branch Westfield River at Huntington, MA 94.0 1,422 2,236 393 1,843 14.012 1.3 1.3 91.0 0.4 2.3 4.001184100 Stony Brook near Suffield, CT 10.5 2261 680 158 509 7.542 50.6 511.8 551.2 51.5 525.3 236.0

01187300 Hubbard Brook near West Hartland, CT 19.9 21,287 1,643 603 1,017 8.754 52.1 54.7 589.5 50.0 50.9 20.3

01198000 Green River near Great Barrington, MA 51.0 21,183 2,058 691 1,367 8.336 0.8 3.4 79.4 0.2 13.7 29.8
Development of Equations for Estimating Bankfull Geometry and Discharge 21

Table 5. Basin and land-use characteristics of the study sites used in development of bankfull channel geometry and discharge equations for streams in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square miles; ft, foot; %, percent; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; NY, New York; RI, Rhode Island; VT, Vermont; --, no data]

USGS 

station no. Station name

Drainage 

area 

(mi2

)

Mean 

basin 

elevation1

(ft)

Maximum 

basin 

elevation2

(ft)

Minimum 

basin 

elevation2

(ft)

Basin 

relief3

(ft)

Mean 

basin 

slope4 

(%)

Area of 

water 

bodies1

(%)

Area 

of wetlands1

(%)

Area of 

forest 

land1

(%)

Area of 

urban 

land1 

(%)

Area of 

agricultural land1

(%)

Area of 

sand and 

gravel 

deposits1

(%)

01199050 Salmon Creek at Lime Rock, CT 29.4 21,170 2,445 618 1,818 613.186 53.9 53.7 667.1 50.4 511.4 215

01333000 Green River at Williamstown, MA 42.6 1,554 3,476 615 2,861 24.519 0.1 0.0 79.0 0.5 15.0 11.0901174000 Hop Brook near New Salem, MA 3.39 21,030 51,302 5735 570 10.786 50.0 51.3 584.6 50.0 56.0 22.1

901174600 Cadwell Creek near Pelham, MA 0.60 51,014 51,132 5873 259 10.081 50.0 516.0 573.7 50.0 51.6 --

1001334000 Walloomsac River near North Bennington, VT 111 51,604 53,737 5509 3,228 615.512 50.3 54.6 675.3 50.4 510.6 --

1101360640 Valatie Kill near Nassau, NY 9.48 5751 51,342 5436 906 611.218 50.5 52.2 681.9 50.1 512.5 --

1101361000 Kinderhook Creek at Rossman, NY 329 5897 52,653 540 2,613 614.417 -- -- 675.3 -- -- --

1101362100 Roeliff Jansen Kill near Hillsdale, NY 27.5 71,040 81,960 8590 1,370 612.384 -- -- 672.6 -- -- --

1From Zarriello and Socolow (2003), unless otherwise footnoted.2From Armstrong and others (2008), unless otherwise footnoted.3Basin relief is the maximum basin elevation minus the minimum basin elevation.4From 1:24,000 scale digital elevation models (DEMs) (U.S. Geological Survey, 2007a), unless otherwise footnoted.5From Falcone (2011).6From Lumia and others (2006).7From Wandle (1983).8From U.S. Geological Survey topographic maps.9Study site from Thomas Garday, U.S. Department of Agriculture, Natural Resources Conservation Service, written commun., 2005.10Study site from Jaquith and Kline (2006).11Study site from Mulvihill and Baldigo (2007).
22 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Table 6. Statistical summary of simple and multiple regression equations for estimating bankfull stream width, mean depth, cross-sectional area, and discharge for streams in and near Massachusetts. [n, number; R2, coefficient of determination; Se, standard error of the estimate; Sp, standard error of the prediction; ft, foot; mi2, square miles; ft2, square foot; ft3/s, cubic foot per second; log, base-10 logarithm; %, percent] Equa- tion num- ber Equation n R2 Ad- justed 

R2

Predicted R2

Se

(log)

Se

(%)

Sp

(log)

Sp

(%)

Simple regression equation

8 Bankfull width (ft) = 15.0418 [Drainage area (mi2)]0.4038 33 0.877 0.873 0.8635 0.0903 21.02 0.0950 22.149 Bankfull mean depth (ft) = 0.9502 [Drainage area (mi2)]0.2960 33 0.820 0.814 0.7995 0.0826 19.19 0.0873 20.30

10 Bankfull cross-sectional area (ft2) = 14.1156 [Drainage area (mi2)]0.7026 33 0.911 0.908 0.9028 0.1308 30.81 0.1369 32.31

11 Bankfull discharge (ft3/s) = 37.1364 [Drainage area (mi2)]0.7996 33 0.770 0.762 0.7428 0.2608 65.89 0.2757 70.43

Multiple regression equation

12 Bankfull width (ft) = 10.6640 [Drainage area (mi2)]0.3935 [Mean basin slope (%)]0.1751 33 0.900 0.894 0.8780 0.0825 19.17 0.0913 21.2613 Bankfull mean depth (ft) = 0.7295 [Drainage area (mi2)]0.2880 [Mean basin slope (%)]0.1346 33 0.845 0.834 0.8159 0.0781 18.13 0.0850 19.7614 Bankfull cross-sectional area (ft2) = 7.6711 [Drainage area (mi2)]0.6842 [Mean basin slope (%)]0.3105 33 0.937 0.932 0.9320 0.1123 26.30 0.1234 29.0015 Bankfull discharge (ft3/s) = 8.2490 [Drainage area (mi2)]0.7545 [Mean basin slope (%)]0.7659 33 0.871 0.862 0.8366 0.1986 48.23 0.2234 55.02
Development of Equations for Estimating Bankfull Geometry and Discharge 23

The result of the multiple regression analyses was that 

drainage area was the most significant variable in explaining 

the variability of bankfull width, mean depth, cross-sectional 

area, and discharge. Evaluation of the other potential 

explanatory variables (basin and land-use characteristics) 

(table 5) found that mean basin slope [1:24,000 scale digital 

elevation models (DEMs); (U.S. Geological Survey, 2007a)] 

was a significant variable in the equations for bankfull 

width, mean depth, cross-sectional area, and discharge at a 

statistical significance level of 0.05 for p-values (appendix 3). 

The predicted R2 for bankfull width (0.8780), mean depth 

(0.8159), cross-sectional area (0.9320), and discharge (0.8366) 

regression equations were all acceptable (table 6). Plots 

of the residuals were evaluated to verify that the residuals 

had no outliers, curvature, or heteroscedasticity (absence of 

homoscedasticity). Figures 6A–H show that the residuals 

of the multiple regression equation for the bankfull channel 

geometry and discharge in relation to drainage area and mean 

basin slope have no outliers, curvature, or heteroscedasticity. 

The residuals are equally distributed on both on the postitive 

and negative side of the zero line. Additionally, the residuals 

by drainage area for the multiple regression equations 

(figs. 6A, B, C, and D) are smaller (closer to zero) than those 

for each of the simple regression equations in figures 3A–D. 

Figure 7 shows the geographic distribution of the residuals 

for the bankfull width multiple regression equation. The 

distribution of positive and negative residuals across the 

State shows no clear geographic pattern. Clusters of sites 

with positive residuals in western Massachusetts and with 

negative residuals in southeastern Massachusetts, which 

occurred for the residuals of the simple regression equation for 

bankfull width (fig. 4), do not appear in the geographic plot 

of residuals for the multiple regression equation (fig. 6). More 

detailed output from the analyses of the multiple regression 

equations is presented in appendix 3. Multiple regression 

equations for bankfull width, mean depth, cross-sectional area, 

and discharge are shown as equations 12–15, respectively, 

in table 6.

Inclusion of mean basin slope as an explanatory 

variable in the multiple regression equations helps account 

for a significant amount of the variance that cannot be 

accounted for by drainage area alone. Statistical results 

for the simple and multiple regression equations in table 6 

show that the R2 statistics increased and that the standard 

error of the estimate and prediction decreased from the 

simple to multiple regression equations. These results show 

that the multiple regression equations for bankfull channel 

geometry and discharge equations are an improvement over 

the simple regression equations, which use only drainage 

area as the explanatory variable. Generally, mean basin slope 

is higher in basins in western Massachusetts than in eastern 

Massachusetts, the significance of which in the regression 

equations may be related to a number of factors that differ 

regionally across Massachusetts, such as topography, geology, 

and climate.

The significance of mean basin slope in the multiple 

regression equation, and the differences in geographic patterns 

between residuals of the single regression equation (without 

basin slope) and those of the multiple regression equation, 

indicate there may be regional patterns in bankfull geometry 

and discharge across Massachusetts. An alternative to representing these possible regional patterns in bankfull geometry 

and discharge across Massachusetts would be to develop separate equations for regions within the State. This approach has 

been followed in several recent studies with regional equations 

for bankfull geometry and discharge developed at statewide 

scales. For example, in Maryland, Pennsylvania, Virginia, and 

West Virginia, physiographic provinces were used as regions 

for the development of separate sets of equations for these 

states. Hydrologic regions, based on analyses of peak-flow 

characteristics, were used to delineate regions for bankfull 

equations in New York. In the present study, several possible 

types of regions were considered for use in developing separate sets of equations for different parts of Massachusetts—

physiographic provinces (Denney, 1982; 6 provinces) (fig. 2), 

flood regions based on peak-flow analyses (Wandle, 1983; 

3 regions—eastern, central, and western), and USEPA Level 

III ecoregions (U.S. Environmental Protection Agency, 2006; 

4 regions) (fig. 2). All of these regional schemes generally 

divide the State longitudinally from west to east. Thus, they 

generally reflect patterns of topography, climate/precipitation, 

and to some extent, surficial geology. However, separate sets 

of equations were not developed for regions within 

Massachusetts in the present study because such equations 

would be based on small numbers of sites. In equations based 

on small numbers of sites, any one individual site, which 

may be anomalous in some way, has a larger influence on 

the equation parameters than in equations based on larger 

numbers of sites. Confidence and prediction intervals also are 

larger for equations that are based on smaller sample sizes. 

The approach of a single set of equations for Massachusetts 

is consistent with the approach taken in recent studies for the 

adjacent New England States of New Hampshire and Vermont.

The multiple regression equations that include mean basin 

slope, a factor that represents regional differences, to some 

extent provide a function similar to separate sets of regional 

regression equations.
24 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.1 1 10 100 1,000

Bankfull width regression residuals,

in base-10 logarithms

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.1 1 10 100 1,000

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0.1 1 10 100 1,000

Drainage area, in square miles

Bankfull cross-sectional area regression residuals,

in base-10 logarithms

Bankfull mean depth regression residuals,

in base-10 logarithms

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.1 1 10 100 1,000

Bankfull discharge regression residuals,

in base-10 logarithms

Drainage area, in square miles

A B

C D

Figure 3. Simple regression equation residuals in relation to drainage area for bankfull: A, width, B, mean depth, C, cross-sectional 

area, and D, discharge for streams in and near Massachusetts.
Development of Equations for Estimating Bankfull Geometry and Discharge 25

0 25 50 MILES

0 25 50 KILOMETERS

ATLANTIC OCEAN

LONG ISLAND SOUND

01198000

01184100

01174900

01193800

01163200

01111500

01109000

01109070

01100600

01103500

01199050

01187300

01181000 01176000

01175670

01111300

01096000

01101000

01171500

01169900

01169000

01170100 01162500

01105600

01105870

01333000

010965852

01334000

01360640

01361000

01362100

01174600

01174000

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

VERMONT NEW HAMPSHIRE

NEW

YORK

Base from U.S. Geological Survey Digital Line Graphs, 1989

Universal Transverse Mercator, 1:100,000 scale

Other coverages from MAGIC, MassGIS, NH GANIT, NYSGIS, RIGIS, and VCGI

Study basin

EXPLANATION

72°00' 71°00' 70°00' 73°00'

42°00'

42°30'

41°30'

Residual of simple regression equation

 at study site and identifier

+0.060 to +0.19

0.000 to +0.059

-0.001 to -0.059

-0.060 to -0.230

Figure 4. Geographic distribution of bankfull width simple regression equation residuals for study sites in and near Massachusetts.
26 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Study site

Lower 90-percent prediction interval

Lower 90-percent confidence interval

Upper 90-percent confidence interval

Upper 90-percent prediction interval

Bankfull width regression line

EXPLANATION

B

Bankfull Width = 

15.0418(Drainage Area)0.4038

R2 = 0.877

1

10

100

1,000

0.1 1 10 100 1,000

Bankfull width, in feet

Bankfull Mean Depth = 

0.9502(Drainage Area) 0.2960

R2 = 0.820

0.1

1

10

0.1 1 10 100 1,000

Bankfull mean depth, in feet

Drainage area, square miles

A

Figure 5. Regional curves of the relation between bankfull: A, width, B, mean 

depth, C, cross-sectional area, and D, discharge and drainage area for streams in 

and near Massachusetts.
Development of Equations for Estimating Bankfull Geometry and Discharge 27

1

10

100

1,000

10,000

100,000

0.1 1 10 100 1,000

C

Study site

Lower 90-percent prediction interval

Lower 90-percent confidence interval

Upper 90-percent confidence interval

Upper 90-percent prediction interval

Regression line

EXPLANATION

D

1

10

100

1,000

10,000

0.1 1 10 100 1,000

Bankfull cross-sectional area, in square feet

Bankfull Cross-Sectional Area = 

14.1156(Drainage Area) 0.7026

R2 = 0.911

Bankfull discharge, in cubic feet per second

Drainage area, square miles

Study site

Lower 90-percent prediction interval

Lower 90-percent confidence interval

Upper 90-percent confidence interval

Upper 90-percent prediction interval

Regression line

EXPLANATION

Bankfull Discharge = 

37.1364(Drainage Area) 0.7996

R2 = 0.770

Figure 5. Regional curves of the relation between bankfull: A, width, B, mean depth, 

C, cross-sectional area, and D, discharge and drainage area for streams in and near 

Massachusetts.—Continued
28 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.1 1 10 100 1,000

Bankfull wdith regression residuals,

in base-10 logarithms

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

0.1 1 10 100 1,000

Bankfull mean depth regression residuals,

in base-10 logarithms

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

Bankfull cross-sectional area regression residuals,

0.1 1 10 100 1,000

in base-10 logarithms

Drainage area, in square miles

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.1 1 10 100 1,000

Bankfull discharge regression residuals,

in base-10 logarithms

Drainage area, in square miles

A B

C D

Figure 6. Multiple regression equation residuals in relation to drainage area for bankfull: A, width, B, mean depth, C, cross-sectional 

area, and D, discharge and in relation to mean basin slope for bankfull: E, width, F, mean depth, G, cross-sectional area, and H,

discharge for streams in and near Massachusetts.
Development of Equations for Estimating Bankfull Geometry and Discharge 29

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

1 10 100

Bankfull width regression residuals,

in base-10 logarithms

-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

0.25

1 10 100

Bankfull mean depth regression residuals,

in base-10 logarithms

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

1 10 100

Mean basin slope, in percent

Bankfull cross-sectional area regression residuals,

in base-10 logarithms

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

1 10 100

Bankfull discharge regression residuals,

in base-10 logarithms

Mean basin slope, in percent

E F

G H

Figure 6. Multiple regression equation residuals in relation to drainage area for bankfull: A, width, B, mean depth, C, cross-sectional 

area, and D, discharge and in relation to mean basin slope for bankfull: E, width, F, mean depth, G, cross-sectional area, and H,

discharge for streams in and near Massachusetts.—Continued
30 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

0 25 50 MILES

0 25 50 KILOMETERS

ATLANTIC OCEAN

LONG ISLAND SOUND

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

VERMONT NEW HAMPSHIRE

NEW

YORK

Base from U.S. Geological Survey Digital Line Graphs, 1989

Universal Transverse Mercator, 1:100,000 scale

Other coverages from MAGIC, MassGIS, NH GANIT, NYSGIS, RIGIS, and VCGI

Study basin

EXPLANATION

73°00' 72°00' 71°00' 70°00'

42°00'

42°30'

41°30'

Residual of multiple regression equation

 at study site and identifier

+0.050 to +0.180

0.000 to +0.049

-0.001 to -0.049

-0.050 to -0.170

01198000

01184100

01174900

01193800

01163200

01111500 01109000

01109070

01100600

01103500

01199050

01187300

01181000 01176000

01175670

01111300

01096000

01101000

01171500

01169900

01169000

01170100 01162500

01105600

01105870

01333000

010965852

01334000

01360640

01361000

01362100

01174600

01174000

Figure 7. Geographic distribution of bankfull width multiple regression equation residuals for study sites in and near Massachusetts.
Development of Equations for Estimating Bankfull Geometry and Discharge 31

Confidence- and Prediction-Interval Estimation

An important adjunct to the estimation of bankfull 

discharge and channel geometry using the equations is the 

estimation of the confidence and prediction intervals of each 

value. The confidence interval provides an estimate for the 

mean of the response variable “y” (bankfull channel geometry 

and discharge) given any value of the independent explanatory variable “x” (drainage area and mean basin slope) (Helsel 

and Hirsch, 2002, p. 240–241, 300). The confidence intervals provide estimates of the lower and upper limits for the 

estimates of the bankfull channel geometry and discharge 

from the equations. For example, the 90-percent confidence 

interval for an estimated value (mean) of the response variable 

(“y” or bankfull channel geometry and discharge) defines the 

lower and upper limits between which the true estimate has a 

90-percent chance of being found. In contrast, the prediction 

interval provides the confidence interval for an estimate of an 

individual response variable “y” (not the mean of the response 

variable “y”) (Helsel and Hirsch, 2002, p. 241–242, 300). The 

prediction interval is different from the confidence interval 

in that it incorporates an additional term for the unexplained 

variability of the estimate and the slope and intercept of the 

equation. The lower and upper 90-percent confidence and 

prediction intervals are included on the plots of the regression 

equations (figs. 5A–D). The prediction interval is much wider 

than the confidence interval, and the lines appear to be parallel 

to the simple regression line, whereas the confidence interval 

is bowed. 

Equations 16–19 were used to calculate the lower 

and upper 90-percent confidence and prediction intervals 

for the simple and multiple regression equations. These 

equations could be easily modified to calculate confidence 

and prediction intervals at different levels of significance; for 

example, to calculate 95-percent confidence and prediction 

intervals, an alpha value (α) of 0.05 would be used instead 

of the 90-percent confidence interval and prediction interval 

alpha value (α) of 0.10. For the simple and multiple regression 

equations, the lower and upper confidence and prediction 

interval equations are

 ( ( ) ) ' 1

0 0 0 ,

2

 n pLower CI y t s x X X x −

∝ −

  =− × × ′     , (16)

 ( ( ) ) ' 1

0 0 0 ,

2

 n pUpper CI y t s x X X x −

∝ −

  =+ × × ′     , (17)

 ( ( ) ) ' 1

0 0 0 ,

2

 1 n pLower PI y t s x X X x −

∝ −

  = − ×× +     ′ , (18)

 ( ( ) ) ' 1

0 0 0 ,

2

 1 n pUpper PI y t s x X X x −

∝ −

 ′  = + ×× +     , (19)

where

CI = confidence interval;

PI = prediction interval;



0 y = estimated bankfull width, mean depth, 

cross-sectional area, or discharge from 

equations 8–15 (table 6); 

,

2 n p

t ∝ − = the quartile of the student’s t-distribution 

having n-p degrees of freedom with a 

probability of exceedance of 2

∝ ;

n = number of observations, 33 for this study;

p = number of parameters in the regression 

equation, 2 for the simple regression 

equations and 3 for the multiple regression 

equations (includes the intercept);

α = 0.10 for the 90-percent confidence 

and prediction intervals (0.05 for the 

95-percent confidence and prediction 

intervals);

s = root mean square error;

( ) '

0

10

1

x 

log drainage area

  =     for the simple regression equations;

'

0 x = ( )

( ) 10

10

1

 

log drainage area

log meanbasin slope

 

 

 

 for the multiple regression equations;

( ) 1

X X −

′ = covariance matrix = 11 12

21 22

a a

a a

 

    for simple regression equations;
32 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

( ) 1 X X −

′ = covariance matrix = 

11 12 13

21 22 23

31 32 33

aaa

aaa

aaa

 

 

 

   

 for multiple regression equations;

( ) 0 10 x log drainage area =  1    for simple regression equations; and

( ) ( ) 0 10 10 x log drainage area log meanbasin slope =  1    for multiple regression equations.

Parameters of the confidence and prediction interval equations 

16–19 for the simple and multiple regression equations are 

listed in table 7.

Application

Example calculations of the bankfull width are presented 

for the simple and multiple regression equations with the 

90-percent confidence and prediction intervals. The example 

stream site used is USGS streamgage Green River near Great 

Barrington, Mass. (01198000), which has a drainage area of 

51.0 mi2 and a mean basin slope of 8.336 percent (table 5). 

( ) ( ) '

0

10 10

1 1 1

 51.0 1.7076

x

log drainage area log

    = =        

( ) 1 11 12

21 22

 0.208608 0.127177 0.127177 0.090709

a a

X X

a a

−     − = =      − ′ 



x log drainage area log 0 =  1 10 ( 1 51.0 1 1.7076 )= 10 ( ) = [ ]   

( ) ( ) ( )

( ) ( ) ' 1

0

1 0.208608 1.7076 0.127177 0.008559 1 0.127177 1.7076 0.090709 0.027718

x XX −  × + ×−  − × =   =   ×− + ′

  ×  

( ) ( ) ( ) ' 1

0 0 x XX x 0.008559 1 0.027718 1.7076 0.038772 −

× × = − × + × =   ′ .

For the example calculations of bankfull width, equations 

8 (simple regression) and 12 (multiple regression) (table 6) 

are used for the lower and upper 90-percent confidence and 

prediction intervals. Statistical data needed to compute the 

90-percent lower and upper confidence and prediction intervals are in table 7. 

Using the simple regression equation (equation 8, 

table 6), 

Bankfull width = 15.0418 (51.0) 0.4038 = 73.59 ft.

To calculate the associated confidence and prediction 

intervals for the simple regression equation, the following 

matrix is computed: 
Development of Equations for Estimating Bankfull Geometry and Discharge 33

Table 7. Simple and multiple regression equation confidence and prediction interval parameters for estimating the bankfull width, 

mean depth, cross-sectional area, and discharge for streams in and near Massachusetts.

[t-90, the quartile of the student’s t-distribution having either n-2 (simple regression) or n-p (multiple regression, p is the number of explanatory variable 

including the intercept, p = 3 for this study) degrees of freedom with a probability of exceedance of 0.05; t-95, the quartile of the student’s t-distribution having 

either n-2 or n-p degrees of freedom with a probability of exceedance of 0.025; s, root mean square error; n, number of data points; (X'X)-1, covariance matrix]

Bankfull equation t-90 t-95 s n (X'X)-1

Simple regression equations

Width 1.696 2.040 0.0903 33 0.208608 -0.127177

-0.127177 0.090709

Mean depth 1.696 2.040 0.0826 33 0.208608 -0.127177

-0.127177 0.090709

Cross-sectional area 1.696 2.040 0.1308 33 0.208608 -0.127177

-0.127177 0.090709

Discharge 1.696 2.040 0.2608 33 0.208608 -0.127177

-0.127177 0.090709

Multiple regression equations

Width 1.697 2.042 0.0825 33 0.669743 -0.095301 -0.540629

-0.095301 0.092912 -0.037371

-0.540629 -0.037371 0.633828

Mean depth 1.697 2.042 0.0781 33 0.669743 -0.095301 -0.540629

-0.095301 0.092912 -0.037371

-0.540629 -0.037371 0.633828

Cross-sectional area 1.697 2.042 0.1123 33 0.669743 -0.095301 -0.540629

-0.095301 0.092912 -0.037371

-0.540629 -0.037371 0.633828

Discharge 1.697 2.042 0.1986 33 0.669743 -0.095301 -0.540629

-0.095301 0.092912 -0.037371

-0.540629 -0.037371 0.633828
34 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

The associated confidence and prediction intervals are

 ( ( ) ) ' 1

0 0 0 ,

2

 

1.8672 1.696 0.0903 0.038772 1 0 1 0 68.65 n p

y t s x XX x

Lower CI

−

∝ −

 

− ××   ′

  −× × == = ft

 ( ( ) ) ' 1

0 0 0 ,

2

 

1.8672 1.696 0.0903 0.038772 1 0 1 0 78.88 n p

y t s x XX x

Upper CI

−

∝ −

 

+ ××   ′

  +× × == = ft

 ( ( ) ) ' 1

0 0 0 ,

2

 1 

1.8672 1.696 0.0903 1 0.038772 1 0 1 0 51.37 n p

y t s x XX x

Lower PI

−

∝ −

 

− ×× +   ′

  − × ×+ == = ft

 ( ( ) ) ' 1

0 0 0 ,

2

 1 

1.8672 1.696 0.0903 1 0.038772 10 1 0 105.42 ft n p

y t s x XX x

Upper PI

−

∝ −

 

+ ×× +    ′    + × ×+ == = .

Using the multiple regression equation (equation 12, 

table 6),

Bankfull width = 10.6640 (51.0)0.3935 (8.336)0.1751 = 72.63 ft.

To calculate the associated confidence and prediction 

intervals for the multiple regression equation, the following 

matrix is computed: 

( )

( )

( )

( )

'

0 10 10

10 10

1 11

51.0 1.7076

 8.336 0.9210

x log drainage area log

log meanbasin slope log

          = ==               

( ) 11 12 13

21 22 23

31 32 33

 0.669743 0.095301 0.540629

 0.095301 0.092912 0.037371

0.540629 0.037371 0.633828

aaa

XX a a a

aaa

    − −

    = = − −  

    − −

′

 

x log drainage area log meanbasin slope log log 0 =  1 10 ( ) 10 ( 1 51.0 8.336 1 1.7076 0.9210 )= 10 ( ) 10 ( ) = [ ]    

( )

( ) ( ) ( )

( ) ( ) ( )

( ) ( ) ( )

' 1

0

1 0.669743 1.7076 0.095301 0.9210 0.540629 0.009088

 1 0.095301 1.7076 0.092912 0.9210 0.037371 0.028938

1 0.540629 1.7076 0.037371 0.9210 0.633828 0.02068

x XX −

 × + ×− + ×− 

  × = ×− + × + ×− =

×− + ×− + × − 

′

 8

 

 

 

   

( ) ( ) ( ) ( ) ' 1

0 0 x XX x 0.009088 1 0.028938 1.7076 0.020688 0.9210 0.039448 −

× × = × + × + − × =   ′ .
Comparison to Other Studies in the Eastern United States and Southeastern Canada 35

The associated confidence and prediction intervals are 

 ( ( ) ) ' 1

0 0 0 ,

2

 

1.8800 1.697 0.0825 0.039448 1 0 1 0 68.12 n p

y t s x XX x

Lower CI

−

∝ −

 

− ××   ′

  −× × == = ft

 ( ( ) ) ' 1

0 0 0 ,

2

 

1.8800 1.697 0.0825 0.039448 1 0 1 0 77.43 n p

y t s x XX x

Upper CI

−

∝ −

 

+ ××   ′

  +× × == = ft

 ( ( ) ) ' 1

0 0 0 ,

2

 1 

1.8800 1.697 0.0825 1 0.039448 1 0 1 0 52.28 n p

y t s x XX x

Lower PI

−

∝ −

 

− ×× +   ′

  − × ×+ == = ft

 ( ( ) ) ' 1

0 0 0 ,

2

 1 

1.8800 1.697 0.0825 1 0.039448 10 1 0 100.89 n p

y t s x XX x

Upper PI

−

∝ −

 

+ ×× +  

  + × ×+

′

== = ft.

The use of the multiple regression equation not only 

improves the estimated values of the bankfull width, but also 

results in narrower confidence and prediction intervals compared to those that result from the simple regression equations. 

This improvement in confidence intervals and prediction intervals also results when the multiple regression equations are 

used instead of the simple regression equations for bankfull 

cross-sectional area and discharge. 

Comparison to Other Studies in 

the Eastern United States and 

Southeastern Canada

Several studies have been done to develop regional 

curves, simple regression equations, and multiple regression 

equations for areas of the eastern United States and southeastern Canada (table 8). Studies in Indiana, Maryland, Michigan, 

New York, North Carolina, Ohio, Pennsylvania, Vermont, 

Virginia, and southeastern Ontario used field methods consistent with those used in this study to develop regional curves 

and simple regression equations relating bankfull width, mean 

depth, cross-sectional area, and discharge. In most of these 

studies, the intercepts and slopes of the regional equations that 

include bankfull width, mean depth, cross-sectional area, and 

discharge regional equations generally are similar to those of 

this study (table 8). Additionally, median bankfull discharge 

recurrence intervals for all of these studies range from 1 to 

2 years.

Several recent studies have shown that the coefficients 

of simple regression equations, using drainage area as the 

sole explanatory variable to predict bankfull geometry and 

discharge, do not differ substantially within the large areas of 

northeastern United States. Bent (2006) determined that several bankfull studies (table 8) in the Northeast generally could 

be represented with one equation for bankfull width, mean 

depth, cross-sectional area, and discharge. But, two studies 

had at least one bankfull equation that was significantly different from the northeastern United States set of equations—one 

study in the Coastal Plain physiographic province and one 

study in the Piedmont physiographic province. A similar study 

by Johnson and Fecko (2008) for the eastern United States, 

which used a different dataset than Bent (2006) but included 

data from several of the studies in table 8, determined that the 

Appalachian Plateau, New England, and Valley and Ridge 

physiographic provinces could be represented by one equation 

for bankfull width. They also found that bankfull width equations for the the Piedmont and Coastal Plain physiographic 

provinces were significantly different from equations for the 

other physiographic provinces. Faustini and others (2009) 

grouped bankfull width study sites in the northeastern United 

States into three major ecoregions (constructed by aggregating USEPA Level III ecoregions): the northern Appalachians, 

southern Appalachians, and Coastal Plains. The Faustini and 

others (2009) study did not include data from any bankfull 

studies listed in table 8. On the basis of these three regional 

studies, the Coastal Plain physiographic province in the northeastern United States likely is best represented by its own set 

of bankfull equations. 
36 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Table 8. Equation parameters used for estimating bankfull channel geometry and discharge by drainage area for selected hydrologic 

[ft, foot; ft2, square foot; ft3/s, cubic foot per second; No., number; mi2, square mile; R2, coefficient of determination; --, no data; <, less than; ~, approximately; 

settings and 1 site from White (2001) in the carbonate settings. Cinotto (2003) includes 6 sites from White (2001). Chaplin (2005) includes 5 sites from White 

only 37 and 3 sites for Regions A and B, respectively, for the bankfull discharge equations. McCandless (2003b) used 9 sites for the eastern Coastal Plain bankfull 

in Virginia and the 14 sites used by McCandless (2003) for the Coastal Plain of Maryland and Delaware. R2 values for Massachusetts (this study) and Ohio 

State or area of 

United States Hydrologic or physiographic region(s) Reference No. of sites

Drainage 

area range 

(mi2)

Width 

(ft)

Intercept Slope R2 

Indiana Northern Moraine and Lake Region Robinson, 2013 25 0.26–941 13.4 0.318 0.92 

Central Till Plain Region 31 0.04–812 18.2 0.327 0.94 

Southern Hills and Lowlands Region 26 0.06–186 27.2 0.286 0.94 

Maryland1 Allegheny Plateau/Valley and Ridge McCandless, 2003a 14 0.2–73.1 13.87 0.44 0.92 

Maryland Coastal Plain McCandless, 2003b 14 0.3–113 10.3 0.38 0.8 

Maryland1 Piedmont McCandless and Everett, 2002 23 1.47–102 14.78 0.39 0.83 

Maine Coastal and central Dudley, 2004 15 2.92–298 7.67 0.52 0.82 

Massachusetts1 Statewide This study 33 0.60–329 15.0418 0.4038 0.88 

Michigan Southern Lower Michigan Ecoregion Rachol and Boley-Morse, 2009 28 20.9–385 8.19 0.44 0.69 

New Hampshire1 Statewide Shane Csiiki, NH Department of 

Environmental Services, written 

commun., 2013

20 2.94–385 12.335 0.4832 0.79 

New York1 Hydrologic region 4/4a Miller and Davis, 2003 18 3.72–332 12.51 0.51 0.88 

New York1 Hydrologic region 5 Westergard and others, 2005 16 0.7–332 13.2 0.459 0.9 

New York1 Hydrologic region 6 Mulvihill and others, 2005 14 1.02–290 16.9 0.419 0.79 

New York1 Hydrologic region 7 Mulvihill and others, 2006 10 1.07–349 10.8 0.458 0.89 

New York1 Hydrologic region 3 Mulvihill and Baldigo, 2007 12 0.42–329 24 0.292 0.85 

New York1 Hydrologic region 1 and 2 Mulvihill and others, 2007 16 0.52–396 21.5 0.362 0.89 

North Carolina Coastal Plain Sweet and Geratz, 2003 22 0.6–182 9.64 0.38 0.95 

North Carolina Mountains Harman and others, 2000 12 2.0–126 19.9 0.36 0.81 

North Carolina Piedmont-rural Harman and others, 1999 13 0.2–128 11.89 0.43 0.81 

North Carolina Piedmont-urban Doll and others, 2002 17 0.2–42.6 24.39 0.33 0.88 

Ohio Region A Sherwood and Huitger, 2005 45 0.29–685 18 0.356 0.91 

Ohio Region B Sherwood and Huitger, 2005 5 0.55–387 32 0.356 0.91 

Pennsylvania Piedmont White, 2001 6 2.57–102 14.8 0.4613 0.79 
Comparison to Other Studies in the Eastern United States and Southeastern Canada 37

regions or physiographic provinces and states in the eastern United States and southeastern Canada.—Continued

Note: Cinotto (2003) includes 6 sites from White (2001). Chaplin (2005) includes 5 sites from White (2001) and 8 sites from Cinotto (2003) in the non-carbonate 

(2001) and 8 sites from Cinotto (2003) in the non-carbonate settings and 1 site from White (2001) in the carbonate settings. Sherwood and Huitger (2005) used 

discharge equation and 5 sites for the western Coastal Plain bankfull discharge equation. Krstolic and Chaplin (2007) used 6 Coastal Plain sites from their study 

(Sherwood and Huitger, 2005) equations are the adjusted R2. Annable (1996a and b) does not include sites for which bankfull discharge was not determined]

Mean depth 

(ft)

Cross-sectional area 

(ft2)

Discharge 

(ft3/s)

Remarks

Range of recurrence intervals 

for bankfull 

discharge 

(years)

Median 

bankfull 

recurrence 

interval 

Intercept Slope R2 Intercept Slope R2 Intercept Slope R2

1.3 0.176 0.75 17.0 0.495 0.92 -- -- -- -- --

1.6 0.159 0.56 28.8 0.487 0.88 -- -- -- -- --

1.9 0.183 0.58 50.9 0.468 0.87 -- -- -- -- --

0.95 0.31 0.91 13.17 0.75 0.93 34.02 0.94 0.99 1.05–1.8 1.51

1.01 0.32 0.87 10.34 0.7 0.96 14.65 0.76 0.97 Eastern Coastal Plain 1.04–1.37 1.14

31.35 0.73 0.98 Western Coastal Plain

1.18 0.34 0.86 17.42 0.73 0.95 84.56 0.76 0.93 1.26–1.75 1.5

0.594 0.34 0.76 4.55 0.86 0.82 5.19 1.05 0.88 <1.0 <1.0

0.9502 0.296 0.82 14.1156 0.7026 0.91 37.1364 0.7996 0.77 1.03–3.52 1.39

0.67 0.27 0.28 4.38 0.74 0.59 4.05 0.95 0.6 <1.005–10 1.25

1.2277 0.2803 0.8 15.028 0.7649 0.85 41.448 0.9191 0.8 -- --

1.01 0.31 0.85 12.67 0.81 0.9 62.96 0.87 0.81 1.2–2.7 1.42

0.802 0.367 0.91 10.6 0.826 0.98 45.5 0.84 0.94 1.11–6.00 1.39

1.04 0.244 0.64 17.6 0.662 0.89 48 0.842 0.9 1.01–2.35 1.52

1.47 0.199 0.52 15.9 0.656 0.96 37.1 0.765 0.94 1.05–3.60 1.78

1.66 0.21 0.77 39.8 0.503 0.92 83.8 0.679 0.93 1.16–3.35 2

1.06 0.329 0.89 22.3 0.694 0.97 49.6 0.849 0.95 1.01–3.80 1.95

0.98 0.36 0.92 9.43 0.74 0.96 8.79 0.76 0.92 <1.0–1.1 <1.0

1.1 0.31 0.79 22.1 0.67 0.88 115.7 0.73 0.88 1.10–1.90 1.59

1.5 0.32 0.88 21.43 0.68 0.95 89.04 0.72 0.97 1.1–1.8 1.4

2.43 0.33 0.87 60.34 0.65 0.95 306.8 0.63 0.94 1.1–1.5 1.3

1.52 0.265 0.88 27.1 0.621 0.95 93.3 0.637 0.82 1.01–9.65 1.36

2.02 0.265 0.88 64.5 0.621 0.95 230 0.637 0.82 1.26–5.55 1.78

0.7804 0.3919 0.84 11.69 0.8517 0.98 69.6 0.793 0.98 1.2–1.5 1.4
38 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Table 8. Equation parameters used for estimating bankfull channel geometry and discharge by drainage area for selected hydrologic 

[ft, foot; ft2, square foot; ft3/s, cubic foot per second; No., number; mi2, square mile; R2, coefficient of determination; --, no data; <, less than; ~, approximately; 

settings and 1 site from White (2001) in the carbonate settings. Cinotto (2003) includes 6 sites from White (2001). Chaplin (2005) includes 5 sites from White 

only 37 and 3 sites for Regions A and B, respectively, for the bankfull discharge equations. McCandless (2003b) used 9 sites for the eastern Coastal Plain bankfull 

in Virginia and the 14 sites used by McCandless (2003) for the Coastal Plain of Maryland and Delaware. R2 values for Massachusetts (this study) and Ohio 

State or area of 

United States Hydrologic or physiographic region(s) Reference No. of sites

Drainage 

area range 

(mi2)

Width 

(ft)

Intercept Slope R2 

Pennsylvania Piedmont Cinotto, 2003 14 2.57–102 13.6 0.469 0.8 

Pennsylvania1 Non-carbonate areas Chaplin, 2005 55 3.45–214 14.65 0.449 0.81 

Pennsylvania1 Carbonate areas Chaplin, 2005 11 2.57–216 9.83 0.449 0.81 

Vermont1 Statewide Jaquith and Kline, 2001 14 8.9–139 10.18 0.5 0.78 

Virginia, Maryland, 

and West Virginia1

Valley and Ridge Keaton and others, 2005 41 0.1–247 12.445 0.4362 0.89 

Virginia and 

Maryland

Coastal Plain Krstolic and Chaplin, 2007 20 0.28–113 11.9899 0.63803 0.94 

Virginia1 Piedmont Lotspeich, 2009 17 0.29–111 12.964 0.3721 0.913 

West Virginia Eastern region (Valley and Ridge) Messinger and Wiley, 2004 11–18 46.5–1,619 8.76 0.503 0.54 

Western region (Appalachian Plateau) 36–56 2.78–1,354 16 0.423 0.84 

West Virginia1 Appalachian Plateau Messinger, 2009 37 0.76–205 20.4865 0.7133 0.9492 

Ontario, Canada Southern Annable, 1996a and b 47 7.3–456 9.4571 0.442 0.58 

Northeast Appalachian Plateau, Coastal Plain, 

New England, Piedmont, and Valley 

and Ridge

Bent, 2006 204 0.20–332 13.2635 0.4459 0.82 

Eastern Eastern Highlands Faustini and others, 2009 275 ~0.4–730 12.62 0.38 0.75 

Northeast Northern Appalachians Faustini and others, 2009 87 ~1–250 12.13 0.39 0.72 

Eastern Southern Appalachians Faustini and others, 2009 188 ~0.4–730 12.69 0.37 0.77 

Northeast New England Faustini and others, 2009 45 ~1–250 13.02 0.37 0.60 

Northeast Mid-Atlantic Faustini and others, 2009 77 ~1–250 12.11 0.38 0.75 

Eastern Appalachian Plateau, New England, 

and Valley and Ridge

Johnson and Fecko, 2008 154 ~0.2–350 13.34 0.45 -- 

Eastern Piedmont Johnson and Fecko, 2008 36 ~0.3–200 13.98 0.39 -- 

Eastern Coastal Plain Johnson and Fecko, 2008 68 ~0.3–420 10.41 0.38 -- 

Northeast Appalachian Plateau, New England, 

Piedmont, and Valley and Ridge

This study 334 0.1–396 15.1988 0.4190 0.86 

1

Study used in northeastern United States bankfull width regression equation covering the Appalachian Plateau, New England, Piedmont, and Valley and Ridge 
Comparison to Other Studies in the Eastern United States and Southeastern Canada 39

regions or physiographic provinces and states in the eastern United States and southeastern Canada.—Continued

Note: Cinotto (2003) includes 6 sites from White (2001). Chaplin (2005) includes 5 sites from White (2001) and 8 sites from Cinotto (2003) in the non-carbonate 

(2001) and 8 sites from Cinotto (2003) in the non-carbonate settings and 1 site from White (2001) in the carbonate settings. Sherwood and Huitger (2005) used 

discharge equation and 5 sites for the western Coastal Plain bankfull discharge equation. Krstolic and Chaplin (2007) used 6 Coastal Plain sites from their study 

(Sherwood and Huitger, 2005) equations are the adjusted R2. Annable (1996a and b) does not include sites for which bankfull discharge was not determined]

Mean depth 

(ft)

Cross-sectional area 

(ft2)

Discharge 

(ft3/s)

Remarks

Range of recurrence intervals 

for bankfull 

discharge 

(years)

Median 

bankfull 

recurrence 

interval 

Intercept Slope R2 Intercept Slope R2 Intercept Slope R2

0.912 0.339 0.72 12.4 0.81 0.94 53.1 0.842 0.93 1–1.5 1.3

0.875 0.33 0.72 12.04 0.797 0.92 43.21 0.867 0.92 1.0–1.9 1.4

0.894 0.284 0.76 8.62 0.734 0.88 44.29 0.634 0.73 1.2–2.3 1.5

1.22 0.25 0.59 12.21 0.75 0.85 17.69 1.07 0.81 1.12–1.86 1.5

1.001 0.2881 0.87 12.595 0.7221 0.94 43.249 0.7938 0.91 <1.1–2.3 1.3

1.145 0.27345 0.87 10.4459 0.36543 0.89 28.3076 0.59834 0.79 <1–2.1 1.15

0.892 0.3721 0.915 11.636 0.7981 0.95 43.895 0.9472 0.949 1–4.3 1.5

0.59 0.411 0.72 5.48 0.917 0.9 -- -- -- -- --

1.32 0.351 0.71 18.2 0.797 0.93 -- -- -- -- --

1.067 0.3128 0.8783 20.4865 0.7133 0.9767 59.81 0.8538 0.9592 1.1–3 1.4

1.2033 0.2345 0.31 3.4685 0.6765 0.7 41.662 0.7217 0.63 -- --

0.9951 0.3012 0.76 12.8552 0.7537 0.90 40.9545 0.8448 0.80 -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

-- -- -- -- -- -- -- -- -- -- --

1.0377 0.2989 0.80 15.5826 0.7198 0.92 49.4778 0.8206 0.88 -- --

physiographic provinces, and shown in figure 8.
40 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

The equations and data for bankfull width developed for 

Massachusetts in the present study are compared in figure 8 

to the equations and data for bankfull width developed by 

the previous 15 studies listed in table 8 that were located in 

the northeastern United States. The 15 previous studies in 

the northeastern United States studies addressed in figure 8 

include studies in Maryland (two physiographic provinces), 

New Hampshire (statewide), New York (six hydrologic 

regions), Pennsylvania (carbonate and non-carbonate regions), 

Vermont (statewide), Virginia (two physiographic provinces), 

and West Virginia (one physiographic province). The earlier 

Pennsylvania studies by White (2001) and Cinotto (2003) 

were included, although they are listed as not being included 

in table 8) because their data are in the statewide Pennsylvania 

study by Chaplin (2005). The Coastal Plain physiographic 

province studies in Maryland (McCandless, 2003b) and 

Virginia (Krstolic and Chaplin, 2007) were not included 

because their equations did not compare well with those of 

the other 15 studies and the present study for Massachusetts. 

The study in Maine (Dudley, 2004) and the earlier study in 

West Virginia (Messinger and Wiley, 2004) are not included 

in figure 8; the equations from these studies were not 

considered comparable because they were developed using 

office records of data obtained during discharge measurements 

rather than data from field surveys of stream reaches 

specifically conducted for bankfull studies. The studies in 

table 8 from Indiana, Michigan, North Carolina, Ohio, and 

southern Ontario, Canada, were excluded because they were 

not considered part of the Northeast. Thus, the 15 previous 

studies and the present study for Massachusetts included in 

figure 8 represent the Appalachian Plateau, New England, 

Piedmont, and Valley and Ridge physiographic provinces in 

the northeastern United States.

Bankfull width = 15.1988(Drainage area) 0.419

R2 = 0.863

Bankfull width = 15.0418(Drainage area) 0.4038

R2 = 0.877

1

10

100

1,000

0.1 1 10 100 1,000

Bankfull width, in feet

Drainage area, in square miles

Massachusetts study sites

Selected northeastern United States study sites

Northeastern United States study

Massachusetts regression line

Other northeastern United States studies

EXPLANATION

Figure 8. Regression lines for bankfull width in relation to drainage area for selected studies in the northeastern United States.
Limitations of the Regional Curves and Regression Equations and Areas for Further Study 41

For the 16 bankfull width equations (15 previous studies 

and the present study for Massachusetts) shown in figure 8, the 

y-intercepts ranged from 9.83 to 24 with a median of 13.87, 

and the slopes ranged from 0.292 to 0.7133 with a median of 

0.44 (table 8). A regression equation that would represent the 

334 study sites for these 16 bankfull width equations across 

the northeastern United States would have a y-intercept of 

15.1988 and a slope of 0.4190 with a predicted R2 of 0.8607. 

This general equation for bankfull width for the northeastern United States is similar to equations published by Bent 

(2006) for the Northeast, by Johnson and Fecko (2008) for the 

Piedmont and Appalachian-New England-Valley and Ridge 

physiographic provinces, and by Faustini and others (2009) 

for the northern and southern Appalachian and New England 

and Mid-Atlantic water-resources regions (table 8). Bankfull 

equations for mean depth, cross-sectional area, and discharge 

for these 334 study sites (from the 15 previous studies and the 

present study) for the northeastern United States (Appalachian, 

New England, Piedmont, and Valley and Ridge physiographic 

provinces) are also listed in table 8. The regression summary 

statistics and analyses results for these northeastern United 

States bankfull channel geometry and discharge equations are 

in appendix 4.

Several studies in other states determined multiple regression equations to estimate more accurately bankfull characteristics. In Ohio, Sherwood and Huitger (2005) determined that 

bankfull characteristics could be estimated better with multiple 

regression equations than with simple regression equations 

that use drainage area as the sole explanatory variable. They 

found that main-channel slope and mean main-channel elevation (measured using geographic information systems) were 

significant variables, in addition to drainage area, and that 

local channel slope and bed-material size were significant 

variables if they could be field measured at the site of interest. In Virginia, Keaton and others (2005) also determined that 

bankfull characteristics could be estimated better with multiple 

regression equations than with simple regression equations 

using drainage area. They found that the percentage of carbonate bedrock underlying the basin was a significant explanatory 

variable in addition to drainage area in estimating bankfull 

width, cross-sectional area, and discharge.

Limitations of the Regional Curves and 

Regression Equations and Areas for 

Further Study

The bankfull channel geometry and discharge regional 

curves and equations are applicable for stream sites with 

drainage areas of 0.60 to 329 mi2 and mean basin slopes of 

2.2 to 23.9 percent (range of these basin characteristics for the 

stream sites used to develop the regional curves and equations). The equations, which are based on data from streams 

without regulated peak flows, most likely are applicable to all 

streams without flood control structures, such as dams, levees, 

diversions, and so forth. If a stream site has regulated peak 

flows, the regional curves and equations estimate the bankfull 

channel geometry and discharge as if the stream were naturally flowing. 

The bankfull channel geometry and discharge regional 

curves and equations may not be applicable in areas of 

Massachusetts where basin, land use, or climatic conditions 

are appreciably different from those of the sites used to 

develop the curves and equations. For example, the equations 

might not apply to streams with drainage basins in which the 

urban land use (commercial, industrial, transportation, and 

high-density residential) is greater than about 25 percent of 

the total land area. In basins with more urban land, runoff 

peaks can be greatly increased in magnitude. This may affect 

the bankfull channel forming discharges, which may in turn 

affect the bankfull channel geometry characteristics. Basins 

with more urban land also may have stream channels that have 

been altered by development, which may result in unnatural 

bankfull channel geometry characteristics. Additionally, the 

regional curves and equations may not be applicable for 

streams in basins where the surficial geology is almost entirely 

stratified deposits. Stratified deposits are present mainly on 

Cape Cod and the Islands and in southeastern Massachusetts 

close to Cape Cod (area labeled as USEPA Level III 

ecoregion, Atlantic Coastal Pine Barrens in fig. 2). In these 

areas, precipitation mainly percolates into the soil and through 

the unsaturated zone to the groundwater table (reducing 

surface runoff) and later discharges to the stream as base flow. 

Thus, runoff peaks can be greatly diminished in magnitude, 

which may affect the bankfull channel forming discharges. 

The equations also may not be applicable where streams flow 

through extensive wetlands. 

The accuracy of the regional curves and regression 

equations are a function of the quality of the data used in 

their development. These data include identification of 

the bankfull stage indicators, measurement of the bankfull 

channel geometry characteristics, the occurrence of unknown 

regulation that might affect peak flows upstream from a site, 

and the measured basin characteristics. Basin characteristics 

of the stream sites used in the development of the regional 

curves and regression equations are limited by the accuracy 

of the digital data layers used. Digital data layers [such as 

digital elevation models (DEMs) (U.S. Geological Survey, 

2007a), hydrography (U.S. Geological Survey, 2007b), 

wetlands (MassGIS, 2011), surficial geology (MassGIS, 

2007), soils (U.S. Department of Agriculture, Natural 

Resources Conservation Service, Soil Survey Division, 

2004; MassGIS, 2012), and land use (MassGIS, 2009)] in 

the future will likely become available at scales with better 

spatial resolutions than are currently (2013) available. These 

digital data layers likely would improve the accuracy of the 

measured basin characteristics used as explanatory variables 

to predict bankfull channel geometry and discharge, but 

re-examination of the regression equations would be required. 

Digital data layers that might improve the equation include 
42 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

(1) county-level soil-survey maps referred to as Soil Survey 

Geographic (SSURGO) database (U.S. Department of 

Agriculture, Natural Resources Conservation Service, Soil 

Survey Division, 2004; MassGIS, 2012); (2) 1970–2000 

climate data available through the Parameter-elevation 

Regressions on Independent Slopes Model (PRISM) climatemapping system of Spatial Climate Analysis Service at Oregon 

State University (http://www.ocs.oregonstate.edu/prism/); and 

(3) statewide wetlands (1:12,000 scale) interpreted from stereo 

color-infrared photography (MassGIS, 2011).

The regression equations could be incorporated into 

a Web-based application of the USGS STREAMSTATS 

Program (http://water.usgs.gov/osw/programs/streamstats.

html). A map-based interface is used in the Web-based 

application that allows a user to point and click on any 

stream site, and the application will calculate selected 

streamflow statistics for an ungaged site, or the user can view 

available selected streamflow statistics for a gaged site. In 

a similar manner, a user could click on any stream site in 

Massachusetts, and the appropriate equation will estimate 

the bankfull width, mean depth, cross-sectional area, and 

discharge with the 90-percent prediction intervals.

Summary and Conclusions

Regional curves, simple regression equations, and multiple regression equations were developed for estimating bankfull width, mean depth, cross-sectional area, and discharge for 

streams in Massachusetts. The curves and equations provide 

water-resource and conservation managers with methods for 

estimating bankfull characteristics at a specific stream site in 

Massachusetts. This information will assist the environmental 

agencies that administer the Commonwealth of Massachusetts 

Rivers Protection Act of 1996, which establishes a 200-footwide protected riverfront area extending from the mean-annual 

high-water line (bankfull) along each side of a perennial 

stream, with exceptions for some densely developed areas 

(25-foot wide). Additionally, information on bankfull channel geometry and discharge are important to Federal, State, 

and local governments and private organizations involved in 

stream assessment and restoration projects.

The regional curves and equations were developed from 

stream surveys at 33 U.S. Geological Survey streamgages in 

and near Massachusetts. Drainage areas of the 33 sites ranged 

from 0.60 to 329 square miles (mi2). The surveys included 

identification of bankfull stage at 14 to 25 locations about 

a bankfull width apart along the stream reach at each of the 

27 sites. At 2 of these locations at each of the 27 sites, a 

detailed cross section was surveyed to determine the bankfull 

width, mean depth, and cross-sectional area and to characterize the streambed material, using 50-point pebble count of the 

intermediate particle-size diameter. Bankfull discharge and 

the associated recurrence interval were estimated at each of 

the 33 sites. The average and median recurrence intervals of 

bankfull discharge in and near Massachusetts were estimated 

to be 1.53 and 1.34 years, respectively. 

Regional curves and simple regression equations developed for bankfull width, mean depth, cross-sectional area, and 

discharge used drainage area as the sole explanatory variable. 

Drainage area is the most significant explanatory variable in 

estimating these bankfull characteristics, and it is also the 

most commonly used variable for estimation of these bankfull 

characteristics. Additionally, statistical analyses determined 

that estimation of bankfull characteristics could be improved 

with multiple regression equations, which include the explanatory variable mean basin slope in addition to the drainage 

area. Results of simple regression equations using drainage 

area were compared to results from other bankfull studies in 

the northeastern United States. The Massachusetts bankfull 

characteristics curves and equations compared well with similar studies in areas of Maryland, New Hampshire, New York, 

Pennsylvania, Vermont, and Virginia, excluding the Coastal 

Plain physiographic province in Maryland and Virginia. The 

curves and equations also compared well with those developed 

for the northeastern United States (excluding the Coastal Plain 

phyiographic province) using data from the previous studies in 

these states.

Limitations associated with site selection and development of the regression equations result in some constraints 

for the application of equations presented in this report. These 

equations apply only to streams within the study area having 

(1) a basin area that contains less than about 25 percent urban 

area; (2) little to no streamflow regulation, especially by floodcontrol structures; (3) drainage areas greater than 0.60 mi2

and less than 329 mi2, and (4) a mean basin slope greater than 

2.2 percent and less than about 23.9 percent. The equations 

may not be applicable for streams in basins where the surficial 

geology is almost entirely stratified deposits. These stratified 

deposits are present mainly on Cape Cod and the Islands and 

in southeastern Massachusetts close to Cape Cod. The equations also may not be applicable where streams flow through 

extensive wetlands. Regardless of the setting, the regional 

curves presented in this report are not intended for use as the 

sole method for estimating bankfull characteristics; however, 

they may supplement field identification of the bankfull channel when used in conjunction with field-verified bankfull indicators, flood-frequency analysis, or other supporting evidence.
References Cited 43

References Cited

Ahearn, E.A., 2004, Regression equations for estimating flood 

flows for the 2-, 10-, 25, 50-, 100-, and 500-year recurrence 

intervals in Connecticut: U.S. Geological Survey Scientific 

Investigations Report 2004–5160, 68 p., http://pubs.usgs.

gov/sir/2004/5160/pdf/sir2004-5160.pdf.

Annable, W.K., 1996a, Database of morphologic characteristics of watercourses in southern Ontario: Credit Valley 

Conservation Authority and the Ontario Ministry of Natural 

Resources, Watershed Science Centre, Trent University, 

212 p.

Annable, W.K., 1996b, Morphologic relationships of rural 

watercourses in southern Ontario and selected field methods in fluvial geomorphology: Credit Valley Conservation 

Authority and the Ontario Ministry of Natural Resources, 

Watershed Science Centre, Trent University, 92 p.

Armstrong, D.S., Parker, G.W., and Richards, T.A., 2008, 

Characteristics and classification of least altered streamflows in Massachusetts: U.S. Geological Survey Scientific 

Investigations Report 2007–5291, 113 p., plus CD–ROM, 

http://pubs.usgs.gov/sir/2007/5291/.

Bent, G.C., 2006, Equations for estimating bankfull channel geometry and discharge for streams in the northeastern 

United States [abs.]: Proceedings of the Eighth Interagency 

Sedimentation Conference, Reno, Nevada, April 2–6, 

2006, p. 1026, accessed April 16, 2013, http://pubs.usgs.

gov/misc_reports/FISC_1947-2006/pdf/1st-7thFISCsCD/8thFISC/Poster_Bent_AbstractOnly.pdf.

Chaplin, J.J., 2005, Development of regional curves relating 

bankfull channel geometry and discharge to drainage area 

for streams in Pennsylvania and selected areas of Maryland: 

U.S. Geological Survey Scientific Investigations Report 

2005–5147, 34 p., http://pubs.usgs.gov/sir/2005/5147/

SIR2005-5147.pdf.

Cinotto, P.J., 2003, Development of regional curves of 

bankfull channel geometry and discharge for streams in 

non-urban Piedmont Physiographic Province, Pennsylvania 

and Maryland: U.S. Geological Survey Water-Resources 

Investigations Report 03–4014, 27 p., http://pa.water.usgs.

gov/reports/wrir03-4014.pdf.

Denny, C.S., 1982, Geomorphology of New England: U.S. 

Geological Survey Professional Paper 1208, 18 p., 1 pl.

Doll, B.A., Wise-Frederick, D.E., Buckner, C.M., Wilkerson, 

S.D., Harman, W.A., Smith, R.E., and Spooner, Jean, 2002, 

Hydraulic geometry relationships for urban stream throughout the Piedmont of North Carolina: Journal of the American Water Resources Association, v. 38, no. 3, p. 641–651.

Dudley, R.W., 2004, Hydraulic geometry relations for rivers 

in coastal and central Maine: U.S. Geological Survey 

Scientific Investigations Report 2004–5042, 30 p., 

http://water.usgs.gov/pubs/sir/2004/5042/.

Dunne, T., and Leopold, L.B., 1978, Water in environmental 

planning: San Francisco, Calif., W.H. Freeman, 818 p.

Emmett, W.W., 2004, A historical perspective on regional 

channel geometry curves: Stream Notes, January 2004, U.S. 

Department of Agriculture, Forest Service, Rocky Mountain Research Station, Stream Technology Center, p. 5–6, 

accessed April 16, 2013, http://stream.fs.fed.us/news/

streamnt/pdf/jan04.pdf.

Falcone, J.A., 2011, GAGES-II: Geospatial Attributes of 

Gages for Evaluating Streamflow [digital spatial dataset], 

accessed May 28, 2012, at http://water.usgs.gov/GIS/

metadata/usgswrd/XML/gagesII_Sept2011.xml.

Faustini, J.M., Kaufmann, P.R., and Herlihy, A.T., 2009, 

Downstream variation in bankfull width of wadeable 

streams across the conterminous United States: Geomorphology, v. 108, p. 292–311.

Harman, W.A., Wise, D.E., Walker, M.A., Morris, R., Cantrell, 

M.A., Clemmons, M., Jennings, G.D., Clinton, D., and 

Patterson, J.M., 2000, Bankfull regional curves for North 

Carolina mountain streams, in Kane, D.L., ed., American 

Water Resources Association, Water Resources in Extreme 

Environments Symposium, AWRA TPS-00-1, p. 185–190.

Harman, W.H., Jennings, G.D., Patterson, J.M., Clinton, D.R., 

Slate, L.O., Jessup, A.G., Everhart, J.R., and Smith, R.E., 

1999, Bankfull hydraulic geometry relationships for North 

Carolina streams, in Olsen, D.S., and Potyondy, J.P., eds., 

American Water Resources Association, Wildland Hydrology Symposium, Proceedings: Bozeman, Montana, Summer Symposium June 30–July 2, 1999, AWRA TPS-99-3, 

p. 401–408.

Harrelson, C.C., Rawlins C.L., and Potyondy, J.P., 1994, 

Stream channel reference sites: an illustrated guide to field 

technique: U.S. Department of Agriculture, Forest Service, 

Rocky Mountain Forest and Range Experiment Station, 

General Technical Report RM-245, 61 p., accessed April 16, 

2013, http://www.fs.fed.us/rm/pubs_rm/rm_gtr245.pdf.

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

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, Hydrologic analysis and interpretation, chap. A3, 510 p., http://pubs.usgs.

gov/twri/twri4a3/pdf/twri4a3-new.pdf.

Hodgkins, Glenn, 1999, Estimating the magnitude of peak 

flows for streams in Maine for selected recurrence intervals: 

U.S. Geological Survey Water-Resources Investigations 

Report 99–4008, 49 p., http://me.water.usgs.gov/

99-4008.pdf.
44 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Interagency Advisory Committee on Water Data, 1982, 

Guidelines for determining flood-flow frequency: U.S. 

Geological Survey, Bulletin 17B of the Hydrology 

Subcommittee, Office of Water Data Coordination, 183 p., 

http://water.usgs.gov/osw/bulletin17b/dl_flow.pdf.

Jaquith, S., and Kline, M., 2006, Vermont regional hydraulic 

geometry curves: Vermont Department of Environmental 

Conservation, Water Quality Division, River Management 

Program, 12 p., accessed November 18, 2008, at 

http://www.vtwaterquality.org/rivers/docs/rv_hydraulicgeocurves.pdf.

Jarrett, R.D., 1984, Hydraulics of high-gradient streams: 

Journal of Hydraulic Engineering, American Society of 

Civil Engineers, v. 105, no. 11, p. 1519–1539.

Jarrett, R.D., 1986, Evaluation of the slope-area method 

for computing peak discharge: U.S. Geological Survey 

Water-Supply Paper 2310, p. 13–24, http://pubs.usgs.gov/

wsp/2310/report.pdf.

Johnson, P.A., and Fecko, B.J., 2008, Regional channel geometry equations: a statistical comparison for physiographic 

provinces in the eastern U.S.: River Research and Applications, v. 24, p. 823–834.

Keaton, J.N., Messinger, Terence, and Doheny, E.J., 2005, 

Development and analysis of regional curves for streams in 

the non-urban valley and Ridge physiographic provinces, 

Maryland, Virginia, and West Virginia: U.S. Geological 

Survey Scientific Investigations Report 2005–5076, 116 p., 

http://pubs.usgs.gov/sir/2005/5076/sir05_5076.pdf.

Krstolic, J.L., and Chaplin, J.J., 2007, Bankfull regional 

curves for streams in the non-urban, non-tidal Coastal Plain 

Physiographic Province, Virginia and Maryland: U.S. Geological Survey Scientific Investigations Report 2007–5162, 

48 p., http://pubs.usgs.gov/sir/2007/5162/pdf/

SIR2007-5162.pdf.

Leopold, L.B., 1994, A view of the river: Harvard University 

Press, Cambridge, Mass., Harvard University, 298 p.

Limerinos, J.T., 1970, Determination of the Manning coefficient from measured bed roughness in natural channels: 

U.S. Geological Survey Water-Supply Paper 1898–B, 47 p., 

http://pubs.usgs.gov/wsp/1898b/report.pdf.

Lotspeich, R.R., 2009, Regional curves of bankfull channel 

geometry for non-urban streams in the Piedmont 

Physiographic Province, Virginia: U.S. Geological Survey 

Scientific Investigations Report 2009–5206, 51 p., 

http://pubs.usgs.gov/sir/2009/5206/pdf/sir2009-5206.pdf.

Lumia, Richard, Freehafer, D.A., and Smith, M.J., 2006, 

Magnitude and frequency of floods in New York: U.S. 

Geological Survey Scientific Investigations Report 2006–

5112, 152 p., http://pubs.usgs.gov/sir/2006/5112/

SIR2006-5112.pdf.

Massachusetts Department of Transportation, 2010, Design 

of bridges and culverts for wildlife passage at freshwater 

streams: MassDOT, Highway Division, 294 p., accessed 

April 16, 2013, http://www.mhd.state.ma.us/downloads/

projDev/Design_Bridges_Culverts_Wildlife_

Passage_122710.pdf.

Massachusetts Executive Office of Energy and Environmental 

Affairs, Department of Fish and Game, Division of 

Ecological Restoration, 2012, Massachusetts stream 

crossing handbook (2d ed.), 13 p., accessed April 16, 2013, 

http://www.mass.gov/eea/docs/dfg/der/pdf/

stream-crossings-handbook.pdf.

MassGIS, 2007, Surficial geology 1:24,000, accessed October, 

1, 2007, at http://www.mass.gov/anf/research-and-tech/

it-serv-and-support/application-serv/office-of-geographicinformation-massgis/datalayers/sg24k.html.

MassGIS, 2009, Land use (2005)–June 2009, accessed April 3, 

2013, at http://www.mass.gov/anf/research-and-tech/it-servand-support/application-serv/office-of-geographic-information-massgis/datalayers/lus2005.html.

MassGIS, 2011, DEP wetlands (1:12,000) Change–August 

2011, accessed April 3, 2013, at http://www.mass.gov/anf/

research-and-tech/it-serv-and-support/application-serv/

office-of-geographic-information-massgis/datalayers/

wetchange.html.

MassGIS, 2012, NRCS SSURGO–Certified Soils–November 

2012, accessed April 3, 2013, at http://www.mass.gov/anf/

research-and-tech/it-serv-and-support/application-serv/

office-of-geographic-information-massgis/datalayers/soi.

html.

McCandless, T.L., 2003a, Maryland stream survey: bankfull 

discharge and channel characteristics of streams in the 

Allegheny Plateau and the Valley and Ridge hydrologic 

region: U.S. Fish and Wildlife Service, Annapolis, Md., 

CBFO-S03-01, 92 p., accessed April 16, 2013, 

http://www.fws.gov/chesapeakebay/pdf/Plateau.pdf.

McCandless, T.L., 2003b, Maryland stream survey: bankfull 

discharge and channel characteristics of streams in the 

Coastal Plain hydrologic region: Annapolis, Md., U.S. Fish 

and Wildlife Service, CBFO-S03-02, 89 p., accessed April 

16, 2013, http://www.fws.gov/chesapeakebay/pdf/plain.pdf.
References Cited 45

McCandless, T.L., and Everett, R.A., 2002, Maryland stream 

survey: bankfull discharge and channel characteristics of 

streams in the Piedmont hydrologic region: Annapolis, 

Md., U.S. Fish and Wildlife Service, CBFO-S02-01, 163 p., 

accessed April 16, 2013, http://www.fws.gov/chesapeakebay/pdf/Piedmont.pdf.

Messinger, Terence, 2009, Regional curves for bankfull 

channel characteristics in the Appalachian Plateaus, West 

Virginia: U.S. Geological Survey Scientific Investigations Report 2009–5242, 43 p., http://pubs.usgs.gov/

sir/2009/5242/pdf/sir2009-5242.pdf.

Messinger, Terence, and Wiley, J.B., 2004, Regional relations 

in bankfull channel characteristics determined from flow 

measurements at selected stream-gaging stations in West 

Virginia, 1911–2002: U.S. Geological Survey 

Water-Resources Investigations Report 03–4276, 43 p., 

http://pubs.usgs.gov/wri/wri034276/pdf/wri03-4276.pdf.

Miller, Sarah, and Davis, Daniel, 2003, Optimizing Catskill 

Mountain regional bankfull discharge and hydraulic 

geometry relationships: Proceedings of the American Water 

Resources Association, 2003 International Congress, Watershed management for water supply systems, New York City, 

N.Y., June 29–July 2, 2003, 10 p., accessed April 3, 2013, at 

http://www.nyc.gov/html/dep/pdf/resources/smp.pdf.

Minitab, Inc., 2003, Meet Minitab, Release 14 for Windows: 

Minitab, Inc., 138 p.

Mulvihill, C.I., and Baldigo, B.P., 2007, Regionalized equations for bankfull discharge and channel characteristics of 

streams in New York state—hydrologic region 3 east of the 

Hudson River: U.S. Geological Survey Scientific Investigations Report 2007–5227, 15 p., http://pubs.usgs.gov/

sir/2007/5227/pdf/SIR2007-5227.pdf.

Mulvihill, C.I., Ernst, A.G., and Baldigo, B.P., 2005, Regionalized equations for bankfull discharge and channel characteristics of streams in New York state: Hydrologic region 6 

in the southern tier of New York: U.S. Geological Survey 

Scientific Investigations Report 2005–5100, 21 p., 

http://ny.water.usgs.gov/pubs/wri/sir055100/

sir2005-5100.pdf.

Mulvihill, C.I., Ernst, A.G., and Baldigo, B.P., 2006, 

Regionalized equations for bankfull discharge and channel 

characteristics of streams in New York state: Hydrologic 

region 7 in western New York: U.S. Geological Survey 

Scientific Investigations Report 2006–5075, 14 p., 

http://ny.water.usgs.gov/pubs/wri/sir065075/

sir2006-5075.pdf.

Mulvihill, C.I., Filopowicz, Amy, Coleman, Arthur, and 

Baldigo, B.P., 2007, Regionalized equations for bankfull 

discharge and channel characteristics of streams in New 

York state—hydrologic region 1 and 2 in the Adirondack 

Region of northern New York: U.S. Geological Survey 

Scientific Investigations Report 2007–5189, 18 p., at 

http://pubs.usgs.gov/sir/2007/5189/.

Murphy, P.J., 2001, Estimating equation for mixed populations 

of floods in Massachusetts: Journal of Hydrologic Engineering, v. 6, no.1, p. 72–74.

Olson, S.A., 2002, Flow-frequency characteristics of Vermont 

streams: U.S. Geological Survey Water-Resources Investigations Report 02–4238, 47 p., http://pubs.usgs.gov/

wri/wrir02-4238/wrir02-4238.pdf.

Olson, S.A., 2009, Estimation of flood discharges at selected 

recurrence intervals for streams in New Hampshire: U.S. 

Geological Survey Scientific Investigations Report 2008–

5206, 57 p., http://pubs.usgs.gov/sir/2008/5206/pdf/sir2008-

5206.pdf.

Powell, R.O., Miller, S.J., Westergard, B.E., Mulvihill, C.I., 

Baldigo, B.P., Gallagher, A.S., and Starr, R.R., 2004, Guidelines for surveying bankfull channel geometry and developing regional hydraulic-geometry relations for streams in 

New York state: U.S. Geological Survey Open-File Report 

03–92, 20 p., http://ny.water.usgs.gov/pubs/of/of03092/

of03-092.pdf.

Rachol, C.M., and Boley-Morse, Kristine, 2009, Estimated 

bankfull discharge for selected Michigan rivers and regional 

hydraulic geometry curves for estimating bankfull characteristics in southern Michigan rivers: U.S. Geological 

Survey Scientific Investigations Report 2009–5133, 300 p., 

http://pubs.usgs.gov/sir/2009/5133/pdf/sir2009-5133_

web.pdf.

River and Stream Continuity Partnership, 2011, Massachusetts river and stream crossing standards: 26 p., accessed 

April 16, 2013, http://www.streamcontinuity.org/pdf_files/

MA%20Crossing%20Stds%203-1-11%20corrected%203-8-

12.pdf.

Robinson, B.A., 2013, Regional bankfull-channel dimensions 

of non-urban wadeable streams in Indiana: U.S. Geological 

Survey Scientific Investigations Report 2013-5078, 33 p., 

http://pubs.usgs.gov/sir/2013/5078/pdf/sir2013-5078.pdf.

Rosgen, D.L., 1994, A classification of natural rivers: Catena, 

v. 22, p. 169–199.

Rosgen, D.L., 1996, Applied river morphology (2d ed.): 

Pagosa Springs, Colo., Wildland Hydrology, 388 p.
46 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Sherwood, J.M., and Huitger, C.A., 2005, Bankfull characteristics of Ohio streams and their relation to peak 

streamflows: U.S. Geological Survey Scientific Investigations Report 2005–5153, 38 p., http://pubs.usgs.gov/

sir/2005/5153/pdf/Bankfull_book.pdf.

Simcox, A.C., 1992, Water resources of Massachusetts: U.S. 

Geological Survey Water-Resources Investigations Report 

90–4144, 94 p.

Sweet, W.V., and Geratz, J.W., 2003, Bankfull hydraulic 

geometry relationships and recurrence intervals for North 

Carolina’s coastal plain: Journal of the American Water 

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

The Commonwealth of Massachusetts, 2009, Wetlands protection act regulations, 310 CMR10.00, accessed March 23, 

2013, at http://www.mass.gov/eea/agencies/massdep/water/

regulations/310-cmr-10-00-wetlands-protection-actregulations.html.

U.S. Department of Agriculture, Forest Service, 1995, A guide 

for field identification of bankfull stage in the western 

United States: Rocky Mountain Research Station, Stream 

Systems Technology Center, video.

U.S. Department of Agriculture, Forest Service, 2003, Identifying bankfull stage in forested streams in the eastern 

United States: Rocky Mountain Research Station, Stream 

Systems Technology Center, video.

U.S. Department of Agriculture, Forest Service, 2004, Guide 

to identification of bankfull stage in the northeastern United 

States: Rocky Mountain Research Station, Stream Systems 

Technology Center, General Technical Report RMRS-GTR133-CD, 4 CDs.

U.S. Department of Agriculture, Natural Resources Conservation Service, Soil Survey Division, 2004, National 

SSURGO database—data, accessed April 29, 2004, at 

http://www.ftw.nrcs.usda.gov/ssur_data.html.

U.S. Environmental Protection Agency, 2006, Level III ecoregions, accessed February 26, 2006, at http://www.epa.gov/

wed/pages/ecoregions/level_iii.htm.

U.S. Geological Survey, 2007a, National elevation dataset, 

accessed June 8, 2007, at http://ned.usgs.gov/.

U.S. Geological Survey, 2007b, National hydrography dataset, 

accessed June 8, 2007, at http://nhd.usgs.gov/index.html.

Wandle, S.W., Jr., 1983, Estimating peak discharges of small, 

rural streams in Massachusetts: U.S. Geological Survey 

Water-Supply Paper 2214, 26 p. 

Westergard, B.E., Mulvihill, C.I., Ernst, A.G., and Baldigo, 

B.P., 2005, Regional equations for bankfull discharge and 

channel characteristics of stream in New York State–

hydrologic region 5 in central New York: U.S. Geological 

Survey Scientific Investigations Report 2004–5247, 16 p., 

http://ny.water.usgs.gov/pubs/wri/sir045247/.

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

of a references 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., http://pa.water.usgs.gov/

reports/wrir01-4146.pdf.

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

material: Transactions of American Geophysical Union, 

v. 25, p. 951–956.

Zarriello, P.J., Ahearn, E.A., and Levin, S.B., 2012, Magnitude 

of flood flows for selected annual exceedance probabilities 

in Rhode Island through 2010: U.S. Geological Survey 

Scientific Investigations Report 2012–5109, 81 p., 

http://pubs.usgs.gov/sir/2012/5109/.

Zarriello, P.J., and Socolow, R.S., 2003, The U.S. Geological 

Survey streamflow and observation-well network in 

Massachusetts and Rhode Island: U.S. Geological Survey 

Open-File Report 03–277, 114 p., http://pubs.usgs.gov/

of/2003/ofr03277/pdfs/ofr03277all.pdf.
Appendixes 1–4
48 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Appendix 1. Information on the starting and ending locations of surveyed stream reaches and locations of the two surveyed cross sections for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; ft, foot; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island; °, degrees; ʹ, minutes; ′′, seconds; --, no data] USGS station no. Station name Stream- gage latitude Stream- gage longitude Start distance of survey upstream from outside gage (ft) Start- ing and ending location no., where bankfull was iden- tified Distance upstream in survey for starting and ending loca- tion, where bankfull was identified (ft) Starting and ending location where bankfull was identi- fied (latitude) Starting and ending location where bankfull was identi- fied (longitude) Cross- sec- tion no. Distance upstream in survey of cross section (ft) Cross- section latitude Cross- section longitude 01093800 Stony Brook Tributary near Temple, NH 42° 51ʹ 36′′ 71° 50ʹ 0′′ 526 1 62 -- -- 9 326 -- -- 22 742 -- -- 17 595 -- -- 01096000 Squannacook River near West Groton, MA 42° 38ʹ 3′′ 71° 39ʹ 30′′ 936 1 16 42° 38.101ʹ 71° 39.626ʹ 3 197 42° 38.078ʹ 71° 39.608ʹ 18 1,585 42° 37.956ʹ 71° 39.404ʹ 16 1,439 42° 37.97ʹ 71° 39.428ʹ 010965852 Beaver Brook at North Pelham, NH 42° 46ʹ 58′′ 71° 21ʹ 15′′ 776 1 92 42° 47.057ʹ 71° 21.342ʹ 3 230 42° 47.047ʹ 71° 21.317ʹ 21 1,428 42° 46.917ʹ 71° 21.194ʹ 14 1,035 42° 46.983ʹ 71° 21.17ʹ 01100600 Shawsheen River near Wilmington, MA 42° 34ʹ 5′′ 71° 12ʹ 55′′ 124 1 3 42° 34.065ʹ 71° 12.905ʹ 6 516 42° 34.149ʹ 71° 12.926ʹ 20 1,660 42° 34.281ʹ 71° 12.821ʹ 10 746 42° 34.185ʹ 71° 12.908ʹ 01101000 Parker River at Byfield, MA 42° 45ʹ 10′′ 70° 56ʹ 46′′ 1,068 1 7 42° 45.26ʹ 70° 56.752ʹ 1 7 42° 45.26ʹ 70° 56.752ʹ 18 1,065 42° 45.154ʹ 70° 56.734ʹ 2 54 42° 45.256ʹ 70° 56.744ʹ 01103500 Charles River at Dover, MA 42° 15ʹ 22′′ 71° 15ʹ 38′′ 708 1 40 42° 15.446ʹ 71° 15.703ʹ 11 1,301 42° 15.333ʹ 71° 15.478ʹ 20 2,358 42° 15.316ʹ 71° 15.271ʹ 17 2,065 42° 15.318ʹ 71° 15.339ʹ 01105600 Old Swamp River near South Weymouth, MA 42° 11ʹ 25′′ 70° 56ʹ 43′′ 589 1 7 42° 11.408ʹ 70° 56.552ʹ 8 281 42° 11.401ʹ 70° 56.605ʹ 21 779 42° 11.444ʹ 70° 56.706ʹ 14 523 42° 11.425ʹ 70° 56.655ʹ 01105870 Jones River at Kingston, MA 41° 59ʹ 27′′ 70° 44ʹ 3′′ 30 1 41 41° 59.456ʹ 70° 44.043ʹ 6 339 41° 59.449ʹ 70° 43.981ʹ

18 917 41° 59.4ʹ 70° 43.89ʹ 13 680 41° 59.434ʹ 70° 43.943ʹ

01109000 Wading River near Norton, MA 41° 56ʹ 51′′ 71° 10ʹ 38′′ 79 1 3 41° 56.852ʹ 71° 10.594ʹ 5 240 41° 56.889ʹ 71° 10.548ʹ

16 996 41° 56.959ʹ 71° 10.522ʹ 10 554 41° 56.938ʹ 71° 10.539ʹ

01109070 Segreganset River at Dighton, MA 41° 50ʹ 25′′ 71° 8ʹ 36′′ 12 1 23 41° 50.412ʹ 71° 8.569ʹ 8 490 41° 50.351ʹ 71° 8.572ʹ

16 895 41° 50.292ʹ 71° 8.548ʹ 14 784 41° 50.309ʹ 71° 8.55ʹ
Appendixes 1–4 49

Appendix 1. Information on the starting and ending locations of surveyed stream reaches and locations of the two surveyed cross sections for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; ft, foot; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island; °, degrees; ʹ, minutes; ′′, seconds; --, no data]

USGS 

station no. Station name

Streamgage 

latitude

Streamgage 

longitude

Start 

distance 

of survey 

upstream 

from 

outside 

gage 

(ft)

Starting and 

ending 

location 

no., where 

bankfull 

was identified

Distance 

upstream in 

survey for 

starting and 

ending location, where 

bankfull was 

identified 

(ft)

Starting 

and ending 

location 

where 

bankfull 

was identified 

(latitude)

Starting 

and ending 

location 

where 

bankfull 

was identified 

(longitude)

Crosssection 

no.

Distance 

upstream 

in survey 

of cross 

section 

(ft)

Crosssection 

latitude

Crosssection 

longitude

01111300 Nipmuc River near Harrisville, RI 41° 58ʹ 52′′ 71° 41ʹ 11′′ 358 1 5 41° 58.914ʹ 71° 41.185ʹ 9 422 41° 58.897ʹ 71° 41.159ʹ

23 1,167 41° 58.778ʹ 71° 41.22ʹ 13 658 41° 58.846ʹ 71° 41.164ʹ

01111500 Branch River at Forestdale, RI 41° 59ʹ 47′′ 71° 33ʹ 47′′ 113 1 63 41° 59.806ʹ 71° 33.732ʹ 7 510 41° 59.789ʹ 71° 33.663ʹ

15 1,025 41° 59.788ʹ 71° 33.558ʹ 9 658 41° 59.776ʹ 71° 33.624ʹ

01162500 Priest Brook near Winchendon, MA 42° 40ʹ 57′′ 72° 6ʹ 56′′ 113 1 49 42° 40.984ʹ 72° 6.865ʹ 6 371 42° 40.924ʹ 72° 6.862ʹ

22 1,443 42° 40.852ʹ 72° 6.82ʹ 9 554 42° 40.887ʹ 72° 6.859ʹ

01163200 Otter River at Otter River, MA 42° 35ʹ 18′′ 72° 2ʹ 29′′ 89 1 33 42° 35.307ʹ 72° 2.457ʹ 6 562 42° 35.357ʹ 72° 2.52ʹ

14 1,146 42° 35.45ʹ 72° 2.514ʹ 13 1,101 42° 35.445ʹ 72° 2.504ʹ

01169000 North River at Shattuckville, MA 42° 38ʹ 18′′ 72° 43ʹ 32′′ 2,450 1 24 42° 38.547ʹ 72° 43.124ʹ 2 140 42° 38.536ʹ 72° 43.144ʹ

21 2,423 42° 38.311ʹ 72° 43.501ʹ 17 1,937 42° 38.375ʹ 72° 43.45ʹ

01169900 South River near Conway, MA 42° 32ʹ 31′′ 72° 41ʹ 39′′ 520 1 23 42° 32.463ʹ 72° 41.733ʹ 9 524 42° 32.511ʹ 72° 41.644ʹ

20 1,230 42° 32.574ʹ 72° 41.509ʹ 18 1,088 42° 32.578ʹ 72° 41.535ʹ

01170100 Green River near Colrain, MA 42° 42ʹ 12′′ 72° 40ʹ 16′′ 965 1 15 42° 42.344ʹ 72° 40.236ʹ 3 184 42° 42.308ʹ 72° 40.244ʹ

20 1,710 42° 42.124ʹ 72° 40.077ʹ 15 1,237 42° 42.158ʹ 72° 40.176ʹ

01171500 Mill River at Northampton, MA 42° 19ʹ 5′′ 72° 39ʹ 21′′ 926 1 5 42° 19.29ʹ 72° 39.974ʹ 2 62 42° 19.262ʹ 72° 40.014ʹ

21 1,339 42° 19.107ʹ 72° 39.829ʹ 6 346 42° 19.228ʹ 72° 39.966ʹ

01174900 Cadwell Creek near Belchertown, MA 42° 20ʹ 8′′ 72° 22ʹ 12′′ 552 1 33 42° 20.183ʹ 72° 22.167ʹ 6 202 42° 20.16ʹ 72° 22.169ʹ

20 552 42° 20.1ʹ 72° 22.188ʹ 11 344 42° 20.135ʹ 72° 22.173ʹ

01175670 Sevenmile River near Spencer, MA 42° 15ʹ 54′′ 72° 0ʹ 19′′ 664 1 19 42° 15.968ʹ 72° 0.359ʹ 20 19 42° 15.968ʹ 72° 0.359ʹ

19 1,137 42° 15.82ʹ 72° 0.296ʹ 13 518 42° 15.904ʹ 72° 0.311ʹ
50 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Appendix 1. Information on the starting and ending locations of surveyed stream reaches and locations of the two surveyed cross sections for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; ft, foot; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island; °, degrees; ʹ, minutes; ′′, seconds; --, no data] USGS station no. Station name Stream- gage latitude Stream- gage longitude Start distance of survey upstream from outside gage (ft) Start- ing and ending location no., where bankfull was iden- tified Distance upstream in survey for starting and ending loca- tion, where bankfull was identified (ft) Starting and ending location where bankfull was identi- fied (latitude) Starting and ending location where bankfull was identi- fied (longitude) Cross- sec- tion no. Distance upstream in survey of cross section (ft) Cross- section latitude Cross- section longitude 01176000 Quaboag River at West Brimfield, MA 42° 10ʹ 56′′ 72° 15ʹ 51′′ 1,470 1 30 42° 11.119ʹ 72° 15.846ʹ 4 513 42° 11.036ʹ 72° 15.846ʹ 22 2,661 42° 10.719ʹ 72° 15.762ʹ 20 2,380 42° 10.709ʹ 72° 15.721ʹ 01181000 West Branch Westfield River at Huntington, MA 42° 14ʹ 14′′ 72° 53ʹ 46′′ 1,747 1 21 42° 14.277ʹ 72° 54.098ʹ 2 112 42° 14.293ʹ 72° 54.073ʹ 21 2,265 42° 14.159ʹ 72° 53.665ʹ 11 1,040 42° 14.255ʹ 72° 53.874ʹ 01184100 Stony Brook near West Suffield, CT 41° 57ʹ 38′′ 72° 42ʹ 39′′ 373 1 6 41° 57.616ʹ 72° 42.675ʹ 18 560 41° 57.648ʹ 72° 42.587ʹ 25 792 41° 57.627ʹ 72° 42.546ʹ 22 665 41° 57.63ʹ 72° 42.581ʹ 01187300 Hubbard River near West Hartland, CT 42° 2ʹ 14′′ 72° 56ʹ 22′′ 910 1 30 42° 2.323ʹ 72° 56.52ʹ 6 399 42° 2.297ʹ 72° 56.453ʹ 20 1,480 42° 2.155ʹ 72° 56.329ʹ 16 1,195 42° 2.205ʹ 72° 56.334ʹ 01198000 Green River near Great Barrington, MA 42° 11ʹ 31′′ 73° 23ʹ 28′′ 1,165 1 29 42° 11.735ʹ 73° 23.573ʹ 7 613 42° 11.649ʹ 73° 23.513ʹ 20 1,925 42° 11.466ʹ 73° 23.379ʹ 20 1,925 42° 11.466ʹ 73° 23.379ʹ 01199050 Salmon Creek at Lime Rock, CT 41° 56ʹ 32′′ 73° 23ʹ 29′′ 890 1 28 41° 56.67ʹ 73° 23.436ʹ 14 681 41° 56.584ʹ 73° 23.453ʹ 22 1,095 41° 56.516ʹ 73° 23.445ʹ 21 1,033 41° 56.523ʹ 73° 23.454ʹ 01333000 Green River at Williamstown, MA 42° 42ʹ 32′′ 73° 11ʹ 50′′ 1,225 1 17 42° 42.591ʹ 73° 11.986ʹ 8 566 42° 42.527ʹ 73° 11.912ʹ 20 1,560 42° 42.564ʹ 73° 11.726ʹ 15 1,115 42° 42.55ʹ 73° 11.812ʹ
Appendixes 1–4 51

Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name Drainage area (mi2)

Cross-section data

Crosssection no. Entrenchment ratio Width-to- depth ratio Water-surface slope (ft/ft) Wetted perimeter (ft) Hydraulic radius (ft) Cross- sectional area (ft2)

01093800 Stony Brook Tributary near Temple, NH 3.60 9 3.07 14.55 0.0145 25.08 1.58 39.54

17 2.34 16.67 0.0064 24.40 1.53 37.42

01096000 Squannacook River near West Groton, MA 63.7 3 1.82 23.15 0.0067 89.03 3.22 286.89

16 1.74 21.89 0.0214 65.53 3.03 198.36

010965852 Beaver Brook at North Pelham, NH 47.8 3 2.22 14.58 0.0004 58.41 3.82 223.05

14 1.76 15.53 0.0043 43.73 2.82 123.47

01100600 Shawsheen River near Wilmington, MA 36.5 6 5.74 16.10 0.0003 60.76 3.41 207.46

10 5.78 30.08 0.0003 76.02 2.42 183.59

01101000 Parker River at Byfield, MA 21.3 1 3.06 14.12 0.0002 45.67 2.93 133.79

2 2.91 20.00 0.0002 48.23 2.53 121.93

01103500 Charles River at Dover, MA 183 11 3.41 24.87 0.0007 100.65 3.87 390.01

17 5.23 24.89 0.0010 100.89 3.89 392.00

01105600 Old Swamp River near South Weymouth, MA 4.50 8 3.46 31.48 0.0088 41.36 1.24 51.47

14 4.05 22.99 0.0052 31.93 1.29 41.29

01105870 Jones River at Kingston, MA 15.7 6 3.59 21.25 0.0014 44.08 1.93 85.00

13 2.80 16.11 0.0021 36.43 2.06 75.05

01109000 Wading River near Norton, MA 43.3 5 7.15 18.78 0.0033 40.30 2.11 85.06

10 4.49 16.13 0.0014 39.74 2.66 105.60

01109070 Segreganset River at Dighton, MA 10.6 8 5.31 13.73 0.0079 32.67 2.19 71.42

14 3.37 20.86 0.0142 35.76 1.53 54.66

01111300 Nipmuc River near Harrisville, RI 16.0 9 3.78 20.54 0.0053 46.58 2.21 103.07

13 3.46 28.33 0.0007 56.14 2.08 116.63
52 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island] USGS station no. Station name Drainage area (mi2

)

Cross-section data

Crosssection no. Entrenchment ratio Width-to- depth ratio Water-surface slope (ft/ft) Wetted perimeter (ft) Hydraulic radius (ft) Cross- sectional area (ft2

)

01111500 Branch River at Forestdale, RI 91.2 7 2.49 23.71 0.0033 86.23 3.71 319.58

9 2.29 25.09 0.0031 76.46 3.31 253.39

01162500 Priest Brook near Winchendon, MA 19.4 6 2.90 37.48 0.0036 62.26 1.53 94.98

9 3.52 20.77 0.0009 49.81 2.57 127.82

01163200 Otter River at Otter River, MA 34.1 6 2.16 41.30 0.0070 70.11 1.53 107.34

13 1.74 27.39 0.0088 52.55 1.94 102.18

01169000 North River at Shattuckville, MA 89.0 2 7.14 22.16 0.0023 112.39 4.75 534.10

17 1.53 21.63 0.0091 110.80 4.49 497.87

01169900 South River near Conway, MA 24.1 9 1.62 14.94 0.0059 63.53 3.93 249.68

18 1.27 17.59 0.0044 81.94 3.40 278.68

01170100 Green River near Colrain, MA 41.4 3 1.16 38.11 0.0086 107.24 2.91 311.70

15 1.12 28.55 0.0061 106.69 3.31 353.37

01171500 Mill River at Northampton, MA 52.6 2 1.58 24.36 0.0051 88.72 3.42 303.51

6 1.36 23.06 0.0059 97.90 3.05 298.96

01174900 Cadwell Creek near Belchertown, MA 2.55 6 1.42 15.86 0.0240 21.86 1.19 26.05

11 1.46 12.71 0.0256 18.43 1.22 22.48

01175670 Sevenmile River near Spencer, MA 8.81 20 2.66 25.44 0.0056 40.15 1.41 56.43

13 7.09 14.17 0.0018 25.23 1.82 45.99

01176000 Quaboag River at West Brimfield, MA 150 4 1.18 53.90 0.0023 141.04 2.73 384.51

20 1.37 44.65 0.0048 119.55 2.74 327.46

01181000 West Branch Westfield River at Huntington, MA 94.0 2 1.89 35.83 0.0130 115.14 3.07 353.66

11 2.80 42.84 0.0110 165.83 2.59 430.09
Appendixes 1–4 53

Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size 

distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name Drainage area (mi2)

Cross-section data

Crosssection no. Entrenchment ratio Width-to- depth ratio Water-surface slope (ft/ft) Wetted perimeter (ft) Hydraulic radius (ft) Cross- sectional area (ft2)

01184100 Stony Brook near West Suffield, CT 10.4 18 1.30 27.59 0.0133 49.27 1.69 83.40

22 1.32 25.00 0.0124 40.00 1.56 62.26

01187300 Hubbard River near West Hartland, CT 19.9 6 1.87 30.25 0.0364 81.62 2.10 171.40

16 1.15 33.86 0.0202 91.27 1.80 164.03

01198000 Green River near Great Barrington, MA 51.0 7 6.94 27.28 0.0010 81.83 2.54 207.61

20 2.69 19.32 0.0019 67.81 3.01 204.40

01199050 Salmon Creek at Lime Rock, CT 29.4 14 1.22 22.90 0.0092 50.86 2.06 104.75

21 1.31 15.65 0.0066 52.21 2.32 121.03

01333000 Green River at Williamstown, MA 42.6 8 1.17 29.58 0.0120 89.45 2.70 241.38

15 1.49 22.16 0.0049 95.7 2.58 246.86
54 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distri- bution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island] USGS station no. Station name Cross- section no. Limerios (1970) equation Particle size d16 (mm) Particle size d50 (mm) Particle size d84 (mm) Particle size dw (mm) Rough- ness coeffi- cient (based on 

d16)

Roughness 

coefficient 

(based on 

d50)

Roughness 

coefficient 

(based 

on d84)

Roughness 

coefficient 

(based 

on dw)

Discharge 

(ft3/s) 

(based 

on d16)

Discharge 

(ft3/s) 

(based 

on d50)

Discharge 

(ft3/s) 

(based 

on d84)

Discharge 

(ft3/s) 

(based 

on dw)

01093800 Stony Brook Tributary near Temple, NH 9 29.78 71.86 135.63 105.91 0.0301 0.0499 0.0442 0.0451 319 192 217 213

17 18.63 38.07 62.70 50.90 0.0269 0.0393 0.0342 0.0352 221 151 173 169

01096000 Squannacook River near West Groton, MA 3 2.52 141.66 618.54 413.87 0.0185 0.0554 0.0721 0.0682 4,125 1,378 1,059 1,120

16 2.16 140.07 287.44 214.70 0.0181 0.0560 0.0513 0.0514 5,005 1,614 1,765 1,760

010965852 Beaver Brook at North Pelham, NH 3 0.69 9.16 21.25 15.57 0.0157 0.0254 0.0250 0.0249 1,032 639 650 652

14 25.79 58.15 116.30 89.80 0.0279 0.0409 0.0380 0.0385 864 589 634 627

01100600 Shawsheen River near Wilmington, MA 6 0.79 5.61 22.13 15.04 0.0159 0.0233 0.0252 0.0248 763 522 481 489

10 0.74 1.89 6.93 4.80 0.0156 0.0194 0.0206 0.0203 548 440 414 419

01101000 Parker River at Byfield, MA 1 0.67 4.00 29.78 19.14 0.0155 0.0219 0.0269 0.0261 373 263 214 221

2 0.64 3.17 192.00 116.22 0.0153 0.0211 0.0457 0.0425 312 226 104 112

01103500 Charles River at Dover, MA 11 3.17 17.71 89.73 59.47 0.0192 0.0290 0.0341 0.0332 1,975 1,307 1,111 1,143

17 19.60 112.64 186.52 147.66 0.0260 0.0485 0.0420 0.0429 1,754 941 1,087 1,065

01105600 Old Swamp River near South Weymouth, MA 8 6.00 49.76 103.16 77.42 0.0213 0.0454 0.0419 0.0421 390 183 199 198

14 4.00 51.58 83.86 66.19 0.0198 0.0457 0.0386 0.0395 266 115 136 133

01105870 Jones River at Kingston, MA 6 1.74 9.52 26.42 18.88 0.0173 0.0263 0.0268 0.0266 423 279 274 276

13 2.00 12.00 40.81 28.29 0.0177 0.0276 0.0296 0.0291 468 301 281 285

01109000 Wading River near Norton, MA 5 1.78 32.00 70.83 52.28 0.0174 0.0355 0.0341 0.0340 687 338 351 352

10 2.38 28.29 55.43 41.98 0.0183 0.0334 0.0312 0.0314 618 338 362 360

01109070 Segreganset River at Dighton, MA 8 3.03 55.43 422.65 270.52 0.0189 0.0420 0.0678 0.0627 843 379 235 254

14 129.40 196.00 1221.10 1164.40 10.0301 10.0577 10.0550 10.0551 1428 1223 1234 1234
Appendixes 1–4 55

Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name

Crosssection 

no.

Limerios (1970) equation

Particle 

size d16

(mm)

Particle 

size d50

(mm)

Particle 

size d84

(mm)

Particle 

size d

w

(mm)

Roughness 

coefficient 

(based on 

d16)

Roughness 

coefficient 

(based on 

d50)

Roughness 

coefficient 

(based 

on d84)

Roughness 

coefficient 

(based 

on d

w)

Discharge 

(ft3/s) 

(based 

on d16)

Discharge 

(ft3/s) 

(based 

on d50)

Discharge 

(ft3/s) 

(based 

on d84)

Discharge 

(ft3/s) 

(based 

on d

w)

01111300 Nipmuc River near Harrisville, RI 9 4.00 37.25 82.46 61.05 0.0197 0.0369 0.0354 0.0354 962 515 536 536

13 0.69 2.52 14.89 9.76 0.0153 0.0203 0.0237 0.0231 488 369 316 324

01111500 Branch River at Forestdale, RI 7 10.20 53.47 163.25 115.01 0.0231 0.0384 0.0406 0.0399 2,837 1,706 1,615 1,640

9 26.30 215.40 283.60 255.41 20.0213 20.0284 20.0371 20.0330 22,194 21,646 21,261 21,414

01162500 Priest Brook near Winchendon, MA 6 1.08 8.68 32.00 21.91 0.0161 0.0361 0.0385 0.0280 699 312 292 402

9 0.79 13.86 43.37 30.26 0.0157 0.0381 0.0395 0.0291 681 281 271 368

01163200 Otter River at Otter River, MA 6 13.21 73.26 156.77 117.36 0.0249 0.0508 0.0472 0.0474 715 350 377 375

13 0.87 26.93 119.12 79.64 0.0158 0.0341 0.0405 0.0391 1,412 653 549 569

01169000 North River at Shattuckville, MA 2 25.18 44.26 110.85 82.31 0.0272 0.0355 0.0354 0.0354 3,971 3,037 3,048 3,047

17 0.93 73.26 476.47 307.95 0.0164 0.0411 0.0573 0.0542 11,722 4,687 3,365 3,558

01169900 South River near Conway, MA 9 0.83 44.26 146.52 101.27 0.0161 0.0362 0.0390 0.0382 4,416 1,967 1,826 1,863

18 0.71 48.00 138.81 97.76 0.0157 0.0376 0.0391 0.0385 3,965 1,656 1,594 1,619

01170100 Green River near Colrain, MA 3 33.91 76.15 181.19 134.95 0.0296 0.0446 0.0436 0.0436 2,961 1,968 2,013 2,010

15 16.00 71.86 192.00 138.36 0.0251 0.0427 0.0435 0.0430 3,637 2,138 2,103 2,123

01171500 Mill River at Northampton, MA 2 1.15 24.00 88.52 60.43 0.0167 0.0313 0.0344 0.0337 4,396 2,339 2,130 2,176

6 8.00 76.95 156.77 117.95 0.0222 0.0443 0.0412 0.0414 3,249 1,624 1,748 1,740

01174900 Cadwell Creek near Belchertown, MA 6 10.84 50.58 122.01 89.46 0.0241 0.0462 0.0452 0.0450 280 146 149 150

11 6.00 30.50 128.00 86.55 0.0213 0.0380 0.0459 0.0442 287 161 133 138

01175670 Sevenmile River near Spencer, MA 20 8.00 99.12 184.37 141.16 0.0225 0.0604 0.0518 0.0526 351 131 152 150

13 4.00 29.78 105.66 72.73 0.0197 0.0354 0.0393 0.0384 220 123 110 113
56 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distri- bution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island] USGS station no. Station name Cross- section no. Limerios (1970) equation Particle size d16 (mm) Particle size d50 (mm) Particle size d84 (mm) Particle size dw (mm) Rough- ness coeffi- cient (based on 

d16)

Roughness 

coefficient 

(based on 

d50)

Roughness 

coefficient 

(based 

on d84)

Roughness 

coefficient 

(based 

on dw)

Discharge 

(ft3/s) 

(based 

on d16)

Discharge 

(ft3/s) 

(based 

on d50)

Discharge 

(ft3/s) 

(based 

on d84)

Discharge 

(ft3/s) 

(based 

on dw)

01176000 Quaboag River at West Brimfield, MA 4 1.12 48.00 117.90 85.25 0.0165 0.0387 0.0383 0.0380 3,253 1,385 1,399 1,410

20 1.78 64.00 143.72 105.61 0.0175 0.0424 0.0407 0.0406 3,771 1,559 1,624 1,629

01181000 West Branch Westfield River at Huntington, MA 2 32.00 116.30 245.69 185.50 0.0291 0.0516 0.0481 0.0484 4,358 2,458 2,640 2,622

11 76.16 164.28 273.90 221.24 0.0370 0.0633 0.0522 0.0541 3,428 2,004 2,432 2,345

01184100 Stony Brook near West Suffield, CT 18 31.00 3110.90 3301.10 3214.03 30.0160 30.0600 30.0621 30.0607 31,274 3339 3328 3335

22 311.50 364.00 3446.00 3287.95 30.0241 30.0477 30.0821 30.0747 3575 3291 3169 3186

01187300 Hubbard River near West Hartland, CT 6 32.00 156.77 367.08 270.48 0.0299 0.0667 0.0638 0.0636 2,670 1,199 1,253 1,257

16 19.60 146.52 430.83 304.41 0.0269 0.0683 0.0746 0.0724 1,907 752 688 709

01198000 Green River near Great Barrington, MA 7 0.65 4.00 32.00 20.47 0.0153 0.0220 0.0275 0.0267 1,186 828 661 682

20 2.83 12.00 43.37 29.91 0.0188 0.0270 0.0292 0.0287 1,474 1,025 949 964

01199050 Salmon Creek at Lime Rock, CT 14 4.00 96.00 256.00 182.80 0.0197 0.0527 0.0539 0.0530 1,228 460 450 457

21 418.90 4156.80 4855.10 4561.99 40.0263 40.0643 40.10714 40.0969 4974 4399 4240 4265

01333000 Green River at Williamstown, MA 8 2.83 43.37 141.66 98.29 0.0188 0.0380 0.0410 0.0398 4,072 2,031 1,879 1,919

15 0.71 19.60 128.00 82.75 0.0155 0.0305 0.0396 0.0380 3,121 1,588 1,222 1,275
Appendixes 1–4 57

Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name

Crosssection 

no.

Jarrett (1984) equation Channel material Stream-reach data

Watersurface 

slope is 

less than 

0.002 ft/ft

Roughness coefficient 

(based on 

equation)

Discharge 

(ft3/s)

Particle 

size d50

(mm)

Particle-size 

classification 

(based on d50)

Average 

entrenchment 

ratio

Average 

widthto-depth 

ratio

Sinuosity 

(ft/ft)

Watersurface 

slope 

(ft/ft)

Particle 

size d50

(mm)

Particle-size 

classification 

(based on d50)

01093800 Stony Brook Tributary near Temple, NH 9 No 0.0726 133 71.86 Small cobble 2.71 15.61 1.15 0.0096 57.64 Very coarse 

gravel

17 No 0.0534 111 38.07 Very coarse 

gravel

01096000 Squannacook River near West Groton, MA 3 No 0.0483 1,588 141.66 Large cobble 1.78 22.52 1.26 0.0046 118.55 Small cobble

16 No 0.0758 1,198 140.07 Large cobble

010965852 Beaver Brook at North Pelham, NH 3 Yes 0.0161 1,013 9.16 Medium gravel 1.99 15.05 1.30 0.0013 19.6 Coarse gravel

14 No 0.0417 581 58.15 Very coarse 

gravel

01100600 Shawsheen River near Wilmington, MA 6 Yes 0.0147 830 5.61 Fine gravel 5.76 23.09 1.21 0.0011 4.18 Fine gravel

10 Yes 0.0155 551 1.89 Very coarse sand

01101000 Parker River at Byfield, MA 1 Yes 0.0129 449 4.00 Very fine gravel 2.99 17.06 1.64 0.0002 0.9 Coarse sand

2 Yes 0.0132 362 3.17 Very fine gravel

01103500 Charles River at Dover, MA 11 Yes 0.0199 1,918 17.71 Coarse gravel 4.32 24.88 1.08 0.0008 18.13 Coarse gravel

17 Yes 0.0227 2,017 112.64 Small cobble

01105600 Old Swamp River near South Weymouth, 

MA

8 No 0.0623 134 49.76 Very coarse 

gravel

3.76 27.23 1.04 0.0046 50.01 Very coarse 

gravel

14 No 0.0507 104 51.58 Very coarse 

gravel

01105870 Jones River at Kingston, MA 6 Yes 0.0289 255 9.52 Medium gravel 3.20 18.68 1.08 0.0024 13.68 Medium 

gravel

13 No 0.0334 249 12.00 Medium gravel

01109000 Wading River near Norton, MA 5 No 0.0395 304 32.00 Coarse gravel 5.82 17.46 1.40 0.0024 29.64 Coarse gravel

10 Yes 0.0275 413 28.29 Coarse gravel
58 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued [USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island] USGS station no. Station name Cross- section no. Jarrett (1984) equation Channel material Stream-reach data Water- surface slope is less than 0.002 ft/ft Rough- ness coef- ficient (based on equation) Dis- charge (ft3/s) Particle size d50 (mm) Particle-size classification (based on d50) Average en- trench- ment ratio Average width- to-depth ratio Sinu- osity (ft/ft) Water- surface slope (ft/ft) Particle size d50 (mm) Particle-size classification (based on d50) 01109070 Segreganset River at Dighton, MA 8 No 0.0547 292 55.43 Very coarse gravel 4.34 17.30 1.22 0.013 101.69 Small cobble 14 No 0.0724 178 141.66 Large cobble 01111300 Nipmuc River near Harrisville, RI 9 No 0.0469 406 37.25 Very coarse gravel 3.62 24.43 1.14 0.0021 12.44 Medium gravel 13 Yes 0.0219 342 2.52 Very fine gravel 01111500 Branch River at Forestdale, RI 7 No 0.0361 1,824 53.47 Very coarse gravel 2.39 24.40 1.00 0.0022 65.88 Small cobble

9 No 0.0359 1,308 2,155.90 Bedrock

01162500 Priest Brook near Winchendon, MA 6 No 0.0430 262 8.68 Medium gravel 3.21 29.13 1.73 0.002 18.32 Coarse gravel

9 Yes 0.0233 460 13.86 Medium gravel

01163200 Otter River at Otter River, MA 6 No 0.0553 322 73.26 Small cobble 1.95 34.35 1.12 0.0049 48 Very coarse 

gravel

13 No 0.0580 384 26.93 Coarse gravel

01169000 North River at Shattuckville, MA 2 No 0.0302 3,589 44.26 Very coarse 

gravel

4.34 21.89 1.09 0.0052 66.95 Small cobble

17 No 0.0514 3,767 73.26 Small cobble

01169900 South River near Conway, MA 9 No 0.0446 1,605 44.26 Very coarse 

gravel

1.45 16.26 1.00 0.0052 30.21 Coarse gravel

18 No 0.0408 1,533 48.00 Very coarse 

gravel

01170100 Green River near Colrain, MA 3 No 0.0540 1,632 76.15 Small cobble 1.14 33.33 1.09 0.0075 92.81 Small cobble

15 No 0.0464 1,978 71.86 Small cobble

01171500 Mill River at Northampton, MA 2 No 0.0431 1,708 24.00 Coarse gravel 1.47 23.71 1.11 0.0038 16.95 Coarse gravel

6 No 0.0464 1,558 76.95 Small cobble

01174900 Cadwell Creek near Belchertown, MA 6 No 0.0919 74 50.58 Very coarse 

gravel

1.44 14.28 1.19 0.0267 51.17 Very coarse 

gravel

11 No 0.0938 65 30.50 Coarse gravel
Appendixes 1–4 59

Appendix 2. Bankfull data collected at the two surveyed cross sections and stream reach for study sites in and near Massachusetts.—Continued[USGS station no.: Streamgages shown in figure 1 and described in table 1. USGS, U.S. Geological Survey; no., number; mi2, square mile; ft, foot; ft2, square foot; mm, millimeter; dw, weighted particle-size distribution—equation 2 in report (Limerinos, 1970); ft3/sec, cubic feet per second; CT, Connecticut; MA, Massachusetts; NH, New Hampshire; RI, Rhode Island]

USGS 

station no. Station name

Crosssection 

no.

Jarrett (1984) equation Channel material Stream-reach data

Watersurface 

slope is 

less than 

0.002 ft/ft

Roughness coefficient 

(based on 

equation)

Discharge 

(ft3/s)

Particle 

size d50

(mm)

Particle-size 

classification 

(based on d50)

Average 

entrenchment 

ratio

Average 

widthto-depth 

ratio

Sinuosity 

(ft/ft)

Watersurface 

slope 

(ft/ft)

Particle 

size d50

(mm)

Particle-size 

classification 

(based on d50)

01175670 Sevenmile River near Spencer, MA 20 No 0.0515 154 99.12 Small cobble 4.88 19.80 1.20 0.0053 38.07 Very coarse 

gravel

13 Yes 0.0321 135 29.78 Coarse gravel

01176000 Quaboag River at West Brimfield, MA 4 No 0.0330 1,629 48.00 Very coarse gravel 1.28 49.27 1.07 0.0025 76.15 Small cobble

20 No 0.0436 1,521 64.00 Very coarse gravel

01181000 West Branch Westfield River at 

Huntington, MA

2 No 0.0626 2,037 116.30 Small cobble 2.35 39.33 1.10 0.0066 128 Small cobble

11 No 0.0603 2,110 164.28 Large cobble

01184100 Stony Brook near West Suffield, CT 18 No 0.0694 294 2,298.80 Bedrock 1.31 26.29 1.33 0.0064 70.83 Small cobble

22 No 0.0685 203 2,762.61 Bedrock

01187300 Hubbard River near West Hartland, CT 6 No 0.0983 815 156.77 Large cobble 1.51 32.06 1.05 0.0236 179.45 Large cobble

16 No 0.0806 638 146.52 Large cobble

01198000 Green River near Great Barrington, MA 7 Yes 0.0243 750 4.00 Very fine gravel 4.82 23.30 1.05 0.0011 12.39 Medium 

gravel

20 Yes 0.0302 920 12.00 Medium gravel

01199050 Salmon Creek at Lime Rock, CT 14 No 0.0585 415 96.00 Small cobble 1.27 19.27 1.13 0.0034 119.12 Small cobble

21 No 0.0506 509 192.00 Large cobble

01333000 Green River at Williamstown, MA 8 No 0.0620 1,236 43.37 Very coarse gravel 1.33 25.87 1.36 0.0107 59.56 Very coarse 

gravel

15 No 0.0444 1,094 19.60 Coarse gravel

1For cross-section 14 at streamgage 01109070 Segreganset River at Dighton, MA, 12 of 50 Wolman (1954) pebble count samples were classified as bedrock and not used in calculation of the Manning’s roughness coefficient (Limerinos, 1970) using the dw, d16, d50, and d84 (equations 2, 3, 4, 5, and 6 in this report).2For cross-section 9 at streamgage 01111500 Branch River at Forestdale, RI, 27 of 50 Wolman (1954) pebble count samples were classified as bedrock and not used in calculation of the Manning’s roughness 

coefficient (Limerinos, 1970) using the dw, d16, d50, and d84 (equations 2, 3, 4, 5, and 6 in this report).

3For cross-sections 18 and 22 at streamgage 01184100 Stony Brook near West Suffield, CT, 30 of 50 and 44 of 50, respectively, Wolman (1954) pebble count samples were classified as bedrock and not used in 

calculation of the Manning’s roughness coefficient (Limerinos, 1970) using the dw, d16, d50, and d84 (equations 2, 3, 4, 5, and 6 in this report).

4For cross-section 21 at streamgage 01199050 Salmon Creek at Lime Rock, CT, 3 of 50 Wolman (1954) pebble count samples were classified as bedrock and not used in calculation of the Manning’s roughness 

coefficient (Limerinos, 1970) using the dw, d16, d50, and d84 (equations 2, 3, 4, 5, and 6 in this report).
60 Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts

Appendix 3. Results of analyses of simple and multiple regression equations to estimate bankfull 

width, mean depth, cross-sectional area, and discharge for streams in and near Massachusetts.

[DF, degrees of freedom associated with each independent variable; <, less than; log, base-10 logarithm]

Variable DF Parameter estimate Standard error t-value p-value

Simple regression

Log bankfull width

Intercept 1 1.17730 0.04124 28.54 0.000

Log drainage area 1 0.40382 0.02720 14.85 0.000

Log mean depth

Intercept 1 -0.02217 0.03774 -0.59 0.561

Log drainage area 1 0.29598 0.02488 11.89 0.000

Log cross-sectional area

Intercept 1 1.14970 0.05974 19.25 0.000

Log drainage area 1 0.70255 0.03939 17.83 0.000

Log discharge

Intercept 1 1.56980 0.11910 13.18 0.000

Log drainage area 1 0.79964 0.07855 10.18 0.000

Multiple regression

Log bankfull width

Intercept 1 1.02792 0.06755 15.22 0.000

Log drainage area 1 0.39350 0.02516 15.64 0.000

Log mean basin slope 1 0.17514 0.06572 2.67 0.012

Log mean depth

Intercept 1 -0.13700 0.06392 -2.14 0.040

Log drainage area 1 0.28804 0.02381 12.10 0.000

Log mean basin slope 1 0.13463 0.06219 2.16 0.038

Log cross-sectional area

Intercept 1 0.88486 0.09189 9.63 0.000

Log drainage area 1 0.68424 0.03423 19.99 0.000

Log mean basin slope 1 0.31050 0.08939 3.47 0.002

Log discharge

Intercept 1 0.91640 0.16250 5.64 0.00

Log drainage area 1 0.75447 0.06052 12.47 0.00

Log mean basin slope 1 0.76590 0.15810 4.85 0.00
Appendixes 1–4 61

Appendix 4. Summary statistics, confidence and prediction interval parameters, and results of analyses of simple regression equations for estimating the bankfull width, mean depth, cross-sectional area, and discharge for streams in the northeastern United States.[R2, coefficient of determination; Se, standard error of the estimate; Sp, standard error of the prediction; t-90, the quartile of the student’s t-distribution having n-2 (simple regression) degrees of freedom with a probability of exceedance of 0.05; t-95, the quartile of the student’s t-distribution having n-2 degrees of freedom with a probability of exceedance of 0.025; n, number of data points; s, root mean square error; (X’X)-1, covariance matrix; DF, degrees of freedom associated with each independent variable; log, base-10 logarithm]

Bankfull equation

Summary statistics Confidence and prediction interval parameters

R2

Adjusted 

R2

Predicted 

R2

S

e

(log)

S

e

(%)

S

p

(log)

S

p

(%) t-90 t-95 s n (X’X)-1

Bankfull Width (ft)= 15.1988 [Drainage Area (mi2)]0.4190 0.863 0.862 0.8607 0.1198 28.12 0.1206 28.31 1.650 1.968 0.1198 334 0.014888427 -0.008356732

-0.008356732 0.005871240

Bankfull Mean Depth (ft) = 1.0377 [Drainage Area (mi2)]0.2989 0.804 0.803 0.8013 0.1057 24.70 0.1064 24.88 1.650 1.968 0.1057 334 0.014888427 -0.008356732

-0.008356732 0.005871240

Bankfull Cross-Sectional Area (ft2) = 15.5826 [Drainage 

Area (mi2)]0.7198

0.915 0.914 0.9134 0.1547 36.78 0.1586 37.77 1.650 1.968 0.1547 334 0.014888427 -0.008356732

-0.008356732 0.005871240

Bankfull Discharge (ft3/s) = 49.4778 [Drainage Area (mi2)]0.8208 0.878 0.877 0.8762 0.2195 53.95 0.2208 54.31 1.650 1.968 0.2195 334 0.014888427 -0.008356732

-0.008356732 0.005871240

Results of analyses

Variable DF Parameter estimate Standard error t-value p-value

Log bankfull widthIntercept 1 1.18181 0.01462 80.86 0.000Log drainage area 1 0.41901 0.00918 45.65 0.000Log mean depthIntercept 1 0.01607 0.01290 1.25 0.214Log drainage area 1 0.29886 0.00810 36.88 0.000Log cross-sectional areaIntercept 1 1.19264 0.01921 62.07 0.000Log drainage area 1 0.71983 0.01207 59.66 0.000Log dischargeIntercept 1 1.69441 0.02678 63.26 0.000Log drainage area 1 0.82085 0.01682 48.81 0.000
THIS PAGE INTENTIONALLY LEFT BLANK
Prepared by the Pembroke and West Trenton 

Publishing Service Centers.

For more information concerning this report, contact:

Office Chief

U.S. Geological Survey

New England Water Science Center 

Massachusetts-Rhode Island Office

10 Bearfoot Road

Northborough, MA 01532

dc_ma@usgs.gov

or visit our Web site at:

http://ma.water.usgs.gov
Bent and Waite—Equations for Estimating Bankfull Channel Geometry and Discharge for Streams in Massachusetts—Scientific Investigations Report 2013–5155

Printed on recycled paper

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20135155