Prepared in cooperation with the Rhode Island Water Resources Board

Equations for Estimating Selected Streamflow 

Statistics in Rhode Island

Scientific Investigations Report 2014–5010

U.S. Department of the Interior

U.S. Geological Survey
Front cover. Photograph of Wood River at Escoheag, Rhode Island (USGS partial-record station 01117720), also known as Stepstone Falls in 

the Arcadia Management Area in Rhode Island.
Equations for Estimating Selected 

Streamflow Statistics in Rhode Island

By Gardner C. Bent, Peter A. Steeves, and Andrew M. Waite

Prepared in cooperation with the Rhode Island Water Resources Board

Scientific Investigations Report 2014–5010

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: 2014

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Suggested citation:

Bent, G.C., Steeves, P.A., and Waite, A.M., 2014, Equations for estimating selected streamflow statistics in Rhode 

Island: U.S. Geological Survey Scientific Investigations Report 2014–5010, 65 p., http://dx.doi.org/10.3133/

sir20145010.

ISSN 2328-031X (print)

ISSN 2328-0328 (online)

ISBN 978-1-4113-3770-1
iii

Acknowledgments

The authors thank private landowners, towns, and the State of Rhode Island for allowing access 

to their land to collect streamflow data needed to develop equations for estimating selected 

streamflow statistics. The authors also thank the Rhode Island Water Resources Board and 

Rhode Island Department of Environmental Management for providing input on the selected 

streamflow statistics.

Thanks are extended to Stacey Archfield, Ken Eng, Gregory Granato, Julie Kiang, and David 

Lorenz of the U.S. Geological Survey (USGS) for their input on development of the equations and 

to Domenic Murino, Mark Nimiroski, Lance Ramsbey, and the many other USGS employees who 

measured the streamflows in Rhode Island, Connecticut, and Massachusetts for this study.

v

Contents

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

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

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

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

Previous Studies ...................................................................................................................................2

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

Development of the Streamflow Statistics and Basin Characteristics Datasets ...............................6

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

Flow Duration.........................................................................................................................................9

Low-Flow Frequency............................................................................................................................9

Annual and Monthly Statistics .........................................................................................................14

Flow Statistics for Long-Term Streamgages ..................................................................................16

Flow Statistics for Short-Term Streamgages and Partial-Record Stations ..............................17

Basin Characteristics for Streamgages and Partial-Record Stations.......................................19

Equations for Estimating Selected Streamflow Statistics ....................................................................21

Drainage-Area Ratio Methods .........................................................................................................21

Regional Regression Analyses.........................................................................................................23

Development of Regression Equations ..................................................................................24

Weighting Procedures ..............................................................................................................25

Final Regression Equations......................................................................................................26

Prediction Intervals ...................................................................................................................40

Example Computations .............................................................................................................40

Limitations of Regression Equations ......................................................................................42

StreamStats Application and Considerations for Additional Study ..................................46

Summary and Conclusions.........................................................................................................................46

References Cited..........................................................................................................................................47

Figures

1. Map showing locations of the drainage basins in the study area in and near 

Rhode Island..................................................................................................................................3

2. Map showing locations of the index, long-term, and short-term streamgages in and 

near Rhode Island.........................................................................................................................4

3. Graph showing annual mean streamflows at the streamgages Branch River at 

Forestdale, R.I. (01111500), and Pawcatuck River at Wood River Junction, R.I. 

(01117500), for water years 1942–2009 ......................................................................................5

4. Map showing surficial geology in Rhode Island .....................................................................7

5. Map showing general land use in Rhode Island.....................................................................8

6. Flow-duration curves at the streamgages Adamsville Brook at Adamsville, R.I. 

(01106000), and Beaver River near Usquepaug, R.I. (01117468)..........................................14

7. Graph showing example of the fit of the log-Pearson Type III distribution to the 

annual 7-day low flow at the streamgage Branch River at Forestdale, R.I. (01111500), 

for water years 1941–2006.........................................................................................................16
vi

8. Map showing locations of the partial-record stations in and near Rhode Island...........18

9. Graph showing example of Maintenance of Variance Extension, type 1 (MOVE.1), 

relation between concurrent daily mean streamflows at the short-term streamgage 

Chickasheen Brook at West Kingston, R.I. (01117424), and the index streamgage 

Beaver River near Usquepaug, R.I. (01117468)......................................................................19

10. Graph showing example of Maintenance of Variance Extension, type 1 (MOVE.1), 

relation between concurrent miscellaneous streamflow measurements at the 

partial-record station Burnt Swamp Brook near Grant Mills, R.I. (01113670), and 

daily mean streamflows at the index streamgage Wading River near Norton, Mass. 

(01109000).....................................................................................................................................20

11. Maps showing the residuals between measured streamflows and streamflows 

calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, 

C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term 

streamgages in and near Rhode Island ..................................................................................28

12. Graphs showing comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, 

D, 50-, E, 25-, and F, 5-percent flow durations estimated from measured streamflow 

and regression equations for long-term and short-term streamgages in and near 

Rhode Island................................................................................................................................34

Tables

1. Description of long- and short-term streamgages in and near Rhode Island..................10

2. List of selected streamflow statistics computed for long- and short-term 

streamgages and partial-record stations in and near Rhode Island.................................15

3. Estimated streamflow statistics for long- and short-term streamgages in and near 

Rhode Island..................................................................................................................................9

4. Description of partial-record stations in and near Rhode Island.......................................54

5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), 

record-extension technique to estimate long-term streamflow statistics for shortterm streamgages and partial-record stations in and near Rhode Island........................60

6. Estimated streamflow statistics for partial-record stations in and near Rhode 

Island ............................................................................................................................................19

7. List of basin characteristics determined for long- and short-term streamgages and 

partial-record stations in and near Rhode Island .................................................................22

8. Basin characteristics for long- and short-term streamgages in and near Rhode 

Island ............................................................................................................................................21

9. Basin characteristics for partial-record stations in and near Rhode Island....................21

10. Pearson’s correlation coefficients for basin characteristics evaluated as potential 

explanatory variables for regression equations for estimating selected streamflow 

statistics for long- and short-term streamgages in Rhode Island......................................24

11. Summary of regression equations and measures of model accuracy for estimating 

selected streamflow statistics in Rhode Island.....................................................................27

12. Information needed for calculating the 90-percent prediction intervals for estimates 

of selected statistics calculated by regression equations for streamflows in 

Rhode Island................................................................................................................................43

13. Range of basin characteristics used as explanatory variables in the regression 

equations for estimating selected streamflow statistics in Rhode Island........................46
vii

Conversion Factors, Datum, and Abbreviations

Multiply By To obtain

Length

inch (in.) 25.4 millimeter (mm)

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

square mile (mi2) 2.590 square kilometer (km2)

Flow rate

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

cubic foot per second per square mile 

[(ft3/s)/mi2]

0.01093 cubic meter per second per square 

kilometer [(m3/s)/km2]

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).

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

Abbreviations

Agencies

CLEAR University of Connecticut—Center for Land Use Education and Research

MAGIC University of Connecticut—Map and Geographic Information Center

MassGIS		 Massachusetts Office of Geographic Information

NRCS Natural Resources Conservation Service

RIDEM Rhode Island Department of Environmental Management

RIGIS Rhode Island Geographic Information System

RIWRB Rhode Island Water Resources Board

USGS U.S. Geological Survey
viii

Basin Characteristics

DRNAREA Drainage area, in square miles

STRDENED Stream density, in miles per square mile

Miscellaneous

7Q2	 	 	 7-day, 2-year low-flow frequency

7Q10	 	 	 7-day, 10-year low-flow frequency

BCF bias correction factor

GIS geographic information system

GNWISQ		 Get National Water Information System Streamflow

LTG long-term streamgage

MOVE.1 Maintenance of Variance Extension, type 1

MSE mean square error

NWIS National Water Information System—USGS

NED National Elevation Dataset—USGS

NHD National Hydrography Dataset—USGS

PRISM Parameter-Elevation Regressions on Independent Slopes Model—Climate Group, 

 Oregon State University

r	 	 	 Pearson’s correlation coefficient

R2	 	 	 coefficient of determination

RI–ABF Rhode Island Aquatic Base-Flow Methodology

RMSE root mean square error

SSURGO Soil Survey Geographic Database—Natural Resources Conservation Service

STG short-term streamgage

WLS weighted least-squares regression analysis

WREG weighted-multiple-linear regression program
Equations for Estimating Selected Streamflow Statistics 

in Rhode Island

By Gardner C. Bent, Peter A. Steeves, and Andrew M. Waite

Abstract

Regional regression equations were developed for 

estimating selected natural—unaffected by alteration—

streamflows of specific flow durations and low-flow frequency 

statistics for ungaged stream sites in Rhode Island. Selected 

at-site streamflow statistics are provided for 41 long-term 

streamgages, 21 short-term streamgages, and 135 partialrecord stations in Rhode Island, eastern Connecticut, and 

southeastern and south-central Massachusetts. The regression 

equations for estimating selected streamflow statistics and 

the at-site statistics estimated for each of the 197 sites may be 

used by Federal, State, and local water managers in addressing 

water issues in and near Rhode Island. 

Multiple and simple linear regression equations were 

developed to estimate the 99-, 98-, 95-, 90-, 85-, 80-, 75-, 

70-, 60-, 50-, 40-, 30-, 25-, 20-, 15-, 10-, 5-, 2-, and 1-percent 

flow durations and the 7Q2 (7-day, 2-year) and 7Q10 

(7-day, 10-year) low-flow-frequency statistics. An additional 

49 selected statistics, for which regression equations were not 

developed, also were estimated for the long- and short-term 

streamgages and partial-record stations for flow durations 

between the 99.99 and 0.01 percent and for the mean annual, 

mean monthly, and median monthly streamflows. A total 

of 70 selected streamflow statistics were estimated for 

41 long-term streamgages, 21 short-term streamgages, and 

135 partial-record stations in and near Rhode Island. Estimates 

of the long-term streamflow statistics for the 21 short-term 

streamgages and 135 partial-record stations were developed 

by the Maintenance of Variance Extension, type 1 (MOVE.1), 

record-extension technique. 

The equations used to estimate selected streamflow 

statistics were developed by relating the 19 flow-duration 

and 2 low-flow-frequency statistics to 31 different basin 

characteristics (physical, land-cover, and climatic) at the 

41 long-term and 19 of 21 short-term streamgages (a total of 

60 streamgages) in and near Rhode Island. The 135 partialrecord stations were not used in the regression analyses. The 

regression analyses were done by using a user-weighted leastsquares technique in the weighted-multiple-linear regression 

program for the 90- to 1-percent flow-duration statistics. For 

the 99-, 98-, and 95-percent flow durations and the 7Q2 and 

7Q10 statistics, left-censored regression analyses were used to 

account for zero flows at a few streamgages. The regression 

analyses determined that two basin characteristics—

drainage area and stream density—were the only significant 

explanatory variables for 16 of the 19 flow-duration and 

the 2 low-flow regression equations. For the 10-, 15-, and 

20-percent flow-duration regression equations, drainage area 

was the only significant explanatory variable. The standard 

error of the estimate for the 21 regression equations ranged 

from 17.58 to 141.83 percent. The 99- to 85-percent flow 

durations and the low-flow statistics 7Q2 and 7Q10 had the 

highest standard errors of the estimate, ranging from 48.68 

to 141.83 percent. The standard error of the estimate for the 

medium- to high-flow statistics—the 80- to 1-percent flow 

durations—ranged from 17.58 to 37.65 percent, with the 

standard errors for the 60- to 1-percent flow durations all being 

less than about 21 percent. Data also are provided to allow 

the user to calculate the 90-percent prediction intervals for the 

21 streamflow statistics. 

The equations, which are based on data from streams 

with little to no flow alterations, will provide an estimate of 

the natural flows for a selected site. They will not estimate 

flows for altered sites with dams, surface-water withdrawals, 

groundwater withdrawals (pumping wells), diversions, and 

wastewater discharges. If the equations are used to estimate 

streamflow statistics for altered sites, the user should adjust 

the flow estimates for the alterations. The regression equations should be used only for ungaged sites with drainage 

areas between 0.52 and 294 square miles and stream densities 

between 0.94 and 3.49 miles per square mile; these are the 

ranges of the explanatory variables in the equations.

Introduction

Flow statistics for streams are crucial for waterresources planning, management, and permitting to ensure 

adequate water for consumptive use, water-quality standards, 

recreation, and aquatic habitat. For example, the minimum 

7-day-average flow that has a probability of occurring once 

every 10 years (7Q10) is a streamflow statistic frequently 

referenced by regulatory agencies as a threshold criterion 

for waste-load assimilation of point discharges and other 

water-resource-protection issues. Information on streamflow 
2 Equations for Estimating Selected Streamflow Statistics in Rhode Island

statistics is critical for water-resource managers who make 

decisions, especially during drought periods. For example, 

in Rhode Island (fig. 1), drought periods occurred during 

1930–31, 1941–45, 1949–50, 1963–67, 1980–81, and 

1987–88 (Walker and Lautzenheiser, 1991). Most of these 

drought periods correspond to intervals when the annual 

mean streamflow was well below the long-term mean annual 

streamflow records for Branch River at Forestdale, R.I. 

(01111500), and Pawcatuck River at Wood River Junction, 

R.I. (01117500) (figs. 2 and 3), in northern and southern 

Rhode Island, respectively. Other shorter periods of low flow 

similar to those during the drought period noted previously 

can be seen in 1957, 1985, 1995, 2002, and 2008 (fig. 3).

In Rhode Island, instream flow standards have become 

more of a critical topic since the early 2000s with reports 

on how to develop these standards by the Rhode Island 

Water Resources Board (RIWRB) Water Allocation Program 

Advisory Committee (2004). The State developed a modified 

Aquatic Baseflow (RI–ABF) Methodology (Rhode Island 

Department of Environmental Management, Office of Water 

Resources, 2005) to assist in developing these instream 

streamflow standards. The RI–ABF methodology includes a 

site-specific standard that allows for maximum sustainable use 

of the State’s waters but that is also protective of the biological, chemical, and physical integrity of those waters. A draft 

describing a streamflow-depletion methodology (Rhode Island 

Department of Environmental Management, Office of Water 

Resources, 2010) was developed to determine the maximum 

volume of water that can be extracted from a stream (whether 

as direct stream withdrawals or indirect groundwater withdrawals) yet leave sufficient streamflow to maintain habitat 

conditions essential to a healthy aquatic ecosystem.

Additionally, the Rhode Island Department of 

Environmental Management (RIDEM) and Rhode Island 

Water Resources Board Streamflow Committee (2004) made 

recommendations for a streamgage network to allow proper 

management of the State’s water resources. The streamgage 

network is intended to provide streamflow data for the 

development of regression equations for estimated streamflow 

statistics at ungaged sites in Rhode Island.

This study was done from 2007–11 by the U.S. 

Geological Survey (USGS) in cooperation with the RIWRB. 

This study provides the RIWRB; RIDEM; Providence Water 

Supply Board; other federal, state, county, city, and town 

agencies; nongovernmental and private organizations; and 

the public with regression equations for estimating selected 

streamflow statistics for ungaged stream sites and at-site 

streamflow statistics for long- and short-term streamgages and 

partial-record stations in and near Rhode Island. Streamflow 

statistics can inform planning, management, and permitting 

decisions related to ensuring adequate water for consumptive 

use, water-quality standards, recreation, and aquatic habitat 

in Rhode Island. In addition, the streamflow statistics can be 

used by the RIWRB in identifying water sources where uses 

might exceed the safe yield under the Rhode Island General 

Laws 46–15.7–3.

Purpose and Scope

This report describes regression equations developed for 

estimating selected statistics for streamflows in Rhode Island 

from basin, land-use, and climatological characteristics. The 

selected streamflow statistics estimated with the regression 

equations are for natural flow conditions (unaltered streamflows). The report provides estimates of selected streamflow 

statistics for long- and short-term streamgages and partialrecord stations in and near Rhode Island. Streamflow statistics 

for which regression equations were developed include the 

99-, 98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, 50-, 40-, 30-, 25-, 

20-, 15-, 10-, 5-, 2-, and 1-percent flow durations and the 7Q2 

(7-day, 2-year) and 7Q10 (7-day, 10-year) low-flow frequencies. An evaluation of the accuracies of the equations and the 

limitations for their use are provided with example applications. Additionally, estimated statistics are provided for longand short-term streamgages and partial-record stations for 

other selected flow durations between the 99.99- and 0.01-

percentiles and for the mean annual, mean monthly, and 

median monthly streamflows; however, regression equations 

were not developed for these statistics.

Previous Studies

Kliever (1996) estimated the 99-, 98-, 97-, 95-, 90-, 

85-, 80-, 70-, 60-, 50-percent flow durations, 7Q10, and 

mean monthly streamflows for August, February, April, 

and May for 16 partial-record stations in northern Rhode 

Island. Cervione and others (1993) calculated the 80-, 90-, 

95-, 98-, and 99-percent flow durations for 25 partial-record 

stations in southern Rhode Island. Cervione and others 

(1993) also presented a regression equation to estimate the 

7Q10 for selected streams in Rhode Island. The equation 

does not provide an estimate of the potential error of the 

7Q10 and is based on only 4 continuous-record streamgages 

in southwestern Rhode Island, 5 streamgages in eastern 

Connecticut, 8 streamgages in western Connecticut, 

2 streamgages in western Massachusetts, and 2 streamgages 

in eastern New York with data through water year 1991. 

Currently (2014) selected streamflow statistics may be 

estimated for about 25 continuous-record streamgages, 

10 discontinued streamgages, and about 90 partial-record 

stations throughout Rhode Island. Wandle and Randall (1994) 

developed regression equations for estimating the 7Q2 and 

7Q10 for central New England, which includes Rhode Island. 

Seven of the 51 streamgages used in the regression analyses 

were in Rhode Island. Ries (1990) estimated mean annual 

runoff from major drainage areas in Rhode Island and 

Massachusetts to Narragansett Bay. Additionally, Haecker 

(2000) provided estimates of base flow at selected streams in 

Rhode Island. 

In the adjacent States of Connecticut and Massachusetts, 

several additional studies have published regression equations 

for estimating selected low-flow statistics over the last 
Introduction 

3

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

71°00’ 71°30' 72°00’

42°00’

41°30'

93

95

495

495

95

95

95

395

295

295

195

146

84

90

90

146

95

Block Island

71°37'30" 71°32'30"

41°12'30"

41°10'

Providence

Blackstone Charles

Sudbury

Quinebaug

Pawcatuck

South Coastal

Pawtuxet

Taunton

Woonasquatucket Moshas- suck

Tenmile

Chicopee

Connecticut

Connecticut

Thames

and

Long Island Sound

Buzzards Bay

Narragansett Bay and 

Mt. Hope Bay Shore

South Coastal

Shetucket

French

BostonHarbor

Connecticut

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

EXPLANATION

State boundaryMajor drainage-basin boundary and basin nameHydrographic featuresInterstate highway markersState highway markers

Pawcatuck

195

146

Figure 1. Locations of the drainage basins in the study area in and near Rhode Island.
4 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320

01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100

01115098

01114500 01114000

01113695

01112700 01111500

01111400

01111300

01111050

01111225

01109220

01109200

01109090

01109000

01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

01117471

01111410

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320

01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100

01115098

01114500 01114000

01113695

01112700 01111500

01111400

01111300

01111050

01111225

01109220

01109200

01109090

01109000

01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

01117471

01111410

71°00’ 71°30' 72°00’

42°00’

41°30'

Blackstone Charles

Sudbury

Quinebaug

Pawcatuck

South Coastal

Pawtuxet

Taunton

Woonasquatucket Moshassuck

Tenmile

Chicopee

Connecticut

Connecticut

Thames

and

Long Island Sound

Buzzards Bay

South Coastal

Shetucket

French

BostonHarbor

Connecticut

Narragansett Bay and 

Mt. Hope Bay Shore

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

EXPLANATION

Major drainage-basin boundarySurface-water sites—With identifier

Index streamgage and long-term

streamgage

Long-term streamgageShort-term streamgageShort-term streamgage not used in

regression analyses

01117500011176000111801001117471

Figure 2. Locations of the index, long-term, and short-term streamgages in and near Rhode Island.
Introduction 5

0

50

100

150

200

250

300

350

1942194419461948195019521954195619581960196219641966196819701972197419761978198019821984198619881990199219941996199820002002200420062008

Streamflow, in cubic feet per second

Water year

Annual mean (01111500)

Annual mean (01117500)

EXPLANATION

Mean annual (01117500)

Mean annual (01111500)

Figure 3. Annual mean streamflows at the streamgages Branch River at Forestdale, R.I. (01111500), and Pawcatuck River at Wood 

River Junction, R.I. (01117500), for water years 1942–2009.

20 years. Ahearn (2008 and 2010) and Ahearn and others 

(2006) provided estimated streamflow statistics and regression 

equations for various flow durations, 7Q2, 7Q10, and 

seasonal flows based on aquatic habitat needs in Connecticut. 

Fennessey and Vogel (1990), Vogel and Kroll (1990), Ries 

(1990), Risley (1994), Ries (1994a, 1994b, 1997, and 1999), 

Ries and Friesz (2000), Ries and others (2000), and Archfield 

and others (2010) provided estimated streamflow statistics 

and regression equations for various flow durations, 7Q2, 

and 7Q10 in Massachusetts. Armstrong and others (2008) 

provided regression equations for estimating median monthly 

streamflows in Massachusetts. Bent and Archfield (2002) 

and Bent and Steeves (2006) provided logistic regression 

equations for estimating the probability of a stream flowing 

perennially in Massachusetts.

Description of Study Area

Rhode Island encompasses 1,045 square miles (mi2) in 

the northeastern United States (fig. 1). Altitudes range from 

sea level (defined as the North American Vertical Datum of 

1988) in coastal areas to 812 feet (ft) above sea level in the 

northwest. Altitudes generally increase from southeast to 

northwest in Rhode Island. The climate is humid and temperate. Average annual precipitation ranged from 40 to 53 inches 

(in.) during 1971–2000 and is fairly evenly distributed 

throughout the months (National Oceanic and Atmospheric 

Administration, 2002). Average annual temperature ranged 

from 48 to 52 oF; the minimum ranged from 26 to 33 oF in 

January, and the maximum ranged from 71 to 73 o

F in July 

(National Oceanic and Atmospheric Administration, 2002). 
6 Equations for Estimating Selected Streamflow Statistics in Rhode Island

About half of the annual precipitation is returned to the atmosphere through evaporation and plant transpiration, with the 

remainder becoming groundwater recharge or stream runoff. 

Surficial deposits that overlie bedrock in most of 

Rhode Island were deposited mainly during the last glacial 

period but can include areas of recent flood-plain alluvium 

deposits. In this report, these surficial deposits are classified 

as either till (which includes till or bedrock, sandy till over 

sand, and end-moraine deposits) or outwash (stratified) 

deposits (which includes sand and gravel, coarse sand, finegrained sand, and flood-plain alluvium deposits) (fig. 4). Till 

(also known as ground moraine) is an unsorted, unstratified 

mixture of clay, silt, sand, gravel, cobbles, and boulders that 

were deposited by glaciers, commonly on top of bedrock 

throughout much of the State. Surficial till is primarily found 

in upland areas but can also be found at depth in river valleys. 

Outwash 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. Outwash deposits are 

more widespread in central and southern Rhode Island than in 

eastern, northern, and western Rhode Island (fig. 4) (Trench, 

1991; DeSimone and Ostiguy, 1999, p. 4). The outwash 

deposits are mainly along the major river valleys, and the till 

deposits and exposed bedrock are in the upland areas. In the 

southern coastal area of the State is a large mixed deposit 

(fig. 4), often referred to as the Charlestown moraine, that acts 

as a physical barrier to surface-water flow heading south and 

sends it toward the southwest to a point of discharge into the 

Atlantic Ocean (Masterson and others, 2007; Friesz, 2010; and 

Bent and others, 2011).

Land in Rhode Island is primarily forested outside of the 

Providence metropolitan area (fig. 5). The Providence metropolitan area is generally bound by Interstates I–95, I–295, 

and I–195 and the State border with Massachusetts (fig. 1) 

and consists primarily of moderate- to high-density housing 

and commercial and industrial facilities (fig. 5). From 1970 

to 1995 there was a 47-percent increase in the developed land 

area in Rhode Island, with the greatest increases in the areas 

of residential, commercial, and industrial land (Rhode Island 

Statewide Planning Program, 2000). 

Rhode Island is within the central highlands, coastal 

lowlands, and coastal plain physiographic provinces (Denny, 

1982). The central highlands physiographic province is limited to west central and northwestern areas of the State. The 

remainder of the State is within the coastal lowlands physiographic province, excluding Block Island, which is within 

the coastal plain province. Rhode Island is entirely within the 

Northeastern Coastal Zone of the U.S. Environmental 

Protection Agency (EPA) (2006) level III ecoregions, excluding Block Island, which is within the Atlantic Coastal Pine 

Barrens ecoregion. The level III ecoregions are delineated on 

the basis of geology, physiography, vegetation, climate, soils, 

land use, wildlife, and hydrology.

Block Island (fig. 1—inset map), which is about 10 miles 

(mi) south of the mainland coast of Rhode Island, was not 

included in the study area because the topographic map of 

Block Island for the 12-mi2 island shows no streams. Veeger 

and Johnston (1996) reported that streams are absent throughout most of the island, except for a few springs along the base 

of the sea cliffs on the southern part of the island.

Development of the Streamflow 

Statistics and Basin Characteristics 

Datasets

Historical streamflow data for USGS streamgages are 

available in the USGS National Water Information System 

(NWIS) database at the Web site http://waterdata.usgs.gov/

nwis. These streamflow data can be analyzed to determine 

particular statistics—such as flow durations, flow frequencies, 

and monthly and annual statistics—which are used by water 

managers throughout the country. Basin characteristics for 

physical, land-use, and climatological data are developed 

with geographic information system (GIS) data layers from 

Federal, State, and local government agencies and nongovernmental agencies.

Site Selection

All active and discontinued long- and short-term 

streamgages and partial-record stations in Rhode Island, 

eastern Connecticut, and southeastern and south-central 

Massachusetts were evaluated for possible use in the regional 

regression analyses. Long-term streamgages were defined 

as those having 8 or more years of record (both water years1

and climatic years2) through water year 2006. Short-term 

streamgages were defined as those having fewer than 8 years 

of record through water year 2009. Partial-record stations were 

considered if they had at least 10 streamflow measurements 

through water year 2006. Sites in eastern Connecticut and 

southeastern and south-central Massachusetts were limited 

to those within about 25 mi of the Rhode Island border. 

All of the sites in the three States considered are within the 

Northeast Coastal Zone of the U.S. Environmental Protection 

Agency Ecoregion level III (2006) and are based on geology, 

physiography, vegetation, climate, soils, land use, wildlife, 

and hydrology. 

All potential sites were evaluated for flow alteration 

processes such as water withdrawals, diversions, flood 

1

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

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

2

A climatic year is the 12-month period beginning April 1 and ending 

March 31. It is numbered by the calendar year in which it ends.
Development of the Streamflow Statistics and Basin Characteristics Datasets 7 Rhode Island Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320 01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01116905

01117370

01116300

01115900

01115770

01115670

01115630

01115187

01115100 01115098

01114500

01114000

01113695

01112700 01111500

01111400

01111300

01111225

01111050

01109220

01109200

01109090

01109000

01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

01111410

01117471

71°00' 71°30' 72°00'

42°00’

41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

EXPLANATION

Surficial geology—From Rhode Island

Geographic Information System (2007)

TillMixedSand / tillBedrock

Surface-water sites—With identifier

Index streamgage and long-term

streamgage

Long-term streamgageShort-term streamgageShort-term streamgage not used in

regression analyses

011175000111760001118010

01117471

Outwash

Figure 4. Surficial geology in Rhode Island.
8 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320

01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100

01115098 01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111050

01111225

01109220

01109200

01109090

01109000 01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

01111410

01117471

71°00’ 71°30' 72°00’

42°00’

41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

EXPLANATION

Land use 2003–04—From Rhode Island Geographic Information System (2008b)

Open water and riverDevelopedNondeveloped

Surface water sites—With identifier

Index streamgage and long-termstreamgageLong-term streamgageShort-term streamgageShort-term streamgage not used inregression analyses

01117500011176000111801001117471

Figure 5. General land use in Rhode Island.
Development of the Streamflow Statistics and Basin Characteristics Datasets 9

control, and wastewater discharge. Those sites with known 

flow-altered processes within their drainage basins that were 

significant enough to clearly change the recorded daily mean 

streamflows for more than several days during each water 

year were excluded from the dataset. The final list of sites 

included 41 long-term streamgages (22 in Rhode Island, 

10 in Connecticut, and 9 in Massachusetts), 21 short-term 

streamgages (11 in Rhode Island, 6 in Connecticut, and 4 

in Massachusetts), and 135 partial-record stations (95 in 

Rhode Island, 25 in Connecticut, and 15 in Massachusetts).

Flow Duration

Flow durations represent the percentage of time that 

a given flow is equaled or exceeded without regard to the 

sequence of recorded flows (Searcy, 1959). Typically, 

flow durations characterize the range of flow rates for the 

period over which data were collected. Flow durations were 

computed for complete water years for the entire period of 

record for 41 long-term streamgages (table 1 and fig. 2) with 

8 or more complete water years of record. Flow durations 

are computed by sorting the daily mean streamflows for the 

period of record from largest to smallest and assigning each 

streamflow value a rank, starting with 1 for the largest value. 

The frequencies of exceedance are then computed by using the 

Weibull plotting-position formula (Weibull, 1939): 

P = 100 * [M / (n + 1)] (1)

where

P is the probability that a given streamflow will 

be equaled or exceeded (percent of time),

M is the ranked position (dimensionless), and

n is the number of events (daily mean 

streamflow values) for the period of record 

(dimensionless).

Examples of flow-duration curves are provided for the 

Adamsville Brook at Adamsville, R.I. (01106000), and for the 

Beaver River near Usquepaug, R.I. (01117468), streamgages 

(fig. 6). The drainage areas to these streamgages are similar 

in size, about 9 mi2, and their record lengths are fairly similar—38 and 36 years, respectively—but both show distinctly 

different flows over much of the flow-duration curve. These 

differences are the results of their different periods of record, 

physical basin characteristics, land-use characteristics, and (or) 

climatic factors.

The program Make Plotting Position (MkPP) (Granato, 

2009) computed the selected flow durations by using the 

Weibull plotting-position formula. The selected flow durations 

range from 99.99 to 0.01 percent, with the number of selected 

durations increasing in the extreme percentile ranges (99.99 

to 90 and 10 to 0.01) (table 2). These selected flow durations 

were considered to most accurately define the flow-duration 

curve for a streamgage or for estimating streamflows at an 

ungaged site. The streamflow data to be used in the MkPP 

program were downloaded for complete water years during 

the streamgages’ periods of record through water year 2006 

by using the computer program Get National Water Information System Streamflow (GNWISQ) (Granato, 2009). For the 

streamgages Miscoe Brook near Franklin, Mass. (01103220), 

Catamint Brook at Cumberland, R.I. (01113695), and Queen 

River at Liberty Road, at Liberty, R.I. (01117370), data 

through water year 2009 were used, so that these streamgages 

could be used in this study as long-term streamgages (8 or 

more complete water years of record) instead of being used 

as short-term streamgages with estimated statistics. Estimated 

streamflows for the selected flow durations at the long-term 

streamgages are presented in table 3.

Table 3. Estimated streamflow statistics for long- and short-term 

streamgages in and near Rhode Island.

[Available separately at http://pubs.usgs.gov/sir/2014/5010/

tables/sir2014-5010_bent_table03.xlsx]

Low-Flow Frequency

Low-flow frequencies typically are computed for 

streamgages by use of annual series of selected low flows 

based on the lowest mean streamflow for a specified number of consecutive days (Riggs, 1972). Any combination of 

number of days of mean minimum flow and years of recurrence may be used to determine the low-flow frequencies. The 

annual series for the determination of low-flow frequencies for 

this study was based on a climatic year. Use of a climatic year 

rather than a water year allows for an analysis of an uninterrupted low-flow period; in Rhode Island, this low-flow period 

typically occurs from early August through mid-October.

Low-flow frequencies were computed for selected days 

and frequencies for 41 long-term streamgages (table 1 and 

fig. 2) with 8 or more complete climatic years. Low-flow 

frequencies are based on the D-day, Y-year frequency statistic 

of daily mean streamflow. This statistic is the minimum 

consecutive D-day mean streamflow that is expected to occur 

once in any Y-year period, or that has a probability of 1/Y of 

not being exceeded in any given year. The two commonly 

used indexes of low-flow frequencies were determined for 

this report: the 7-day, 2-year low-flow frequency (7Q2) and 

the 7-day, 10-year low-flow frequency (7Q10). The 7Q2 is 

the annual minimum average streamflow for 7 consecutive 

days that has a probability of 0.50 (1/recurrence interval) of 

not being exceeded in a given year. The 7Q10 is the annual 

minimum average streamflow for 7 consecutive days that has 

a probability of 0.10 of not being exceeded in a given year. 

The 7Q10 is commonly used in regulating waste disposal 

to streams by many States (U.S. Environmental Protection 

Agency, 1986).
10 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 1. Description of long- and short-term streamgages in and near Rhode Island. [Locations of USGS stations shown in figure 2. River basins shown in figure 1. Numbers and names of index streamgages in bold and highlighted in light gray. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; p, present; Ave., Avenue; Rd., Road; Rt., Route; ft, feet; LTG, long-term streamgage; Index, index streamgage; STG, short-term streamgage; GIS, geographic information system; NWIS, National Water Information System] USGS station no. Station name River basin Latitude (decimal degree) Longitude (decimal degree) Drain- age area (mi2

)

1

Period of 

record

Number 

of complete 

water 

years 

used in 

analyses

Number 

of complete 

climatic 

years 

used in 

analyses

Streamgage type Remarks

01103220 Miscoe Brook near Franklin, MA Charles 42.04093 -71.42673 1.17 2000–09 9 8 LTG --

01105600 Old Swamp River near South Weymouth, 

MA

Boston Harbor 42.19038 -70.94477 4.39 1966–p 40 39 Index and 

LTG

--

01105730 Indian Head River at Hanover, MA South Coastal 42.10066 -70.82254 30.10 1966–p 40 39 Index and 

LTG

Some flow alteration by mills and 

ponds upstream

01106000 Adamsville Brook at Adamsville, RI Buzzards Bay 41.55844 -71.12921 8.09 1940–78 and 

1987

38 37 Index and 

LTG

--

01107000 Dorchester Brook near Brockton, MA Taunton 42.06149 -71.06588 4.88 1963–74 11 11 LTG --

01108000 Taunton River near Bridgewater, MA Taunton 41.93399 -70.95643 261.52 1929–76, 

1985–88, and 1996–p

58 57 LTG Some flow alteration by reservoirs 

and powerplants upstream and diversions for municipal supplies

01109000 Wading River near Norton, MA Taunton 41.94760 -71.17672 43.66 1925–p 81 80 Index and 

LTG

Some flow alteration by reservoirs 

and powerplants upstream and diversions for municipal supplies

01109090 Rattlesnake Brook near Assonet, MA Taunton 41.77677 -71.08921 4.28 2007–09 3 3 STG --

01109200 West Branch Palmer River near Rehoboth, 

MA

Narragansett Bay 

and Mt. Hope Bay Shore

41.87955 -71.25449 4.64 1962–74 11 10 LTG --

01109220 Palmer River at South Rehoboth, MA Narragansett Bay 

and Mt. Hope Bay Shore

41.80927 -71.27783 31.23 2006–09 4 4 STG Occasional flow alteration by fish 

ladder upstream

01111050 Mumford River at Uxbridge, MA Blackstone 42.07510 -71.62590 56.16 2004–06 2 2 STG --

01111225 Emerson Brook near Uxbridge, MA Blackstone 42.04454 -71.62201 7.47 2007–09 2 2 STG --

01111300 Nimpuc River near Harrisville, RI Blackstone 41.98121 -71.68590 15.83 1964–91, 94–p 40 39 Index and 

LTG

--

01111400 Chepachet River at Chepachet, RI Blackstone 41.92288 -71.65757 17.46 1965–73 8 8 LTG --

201111410 Chepachet River west of Gazza Road at 

Gazzaville, RI

Blackstone 41.94093 -71.64812 19.10 1973–75 and 

2004–05

2 1 STG --
Development of the Streamflow Statistics and Basin Characteristics Datasets 11

Table 1. Description of long- and short-term streamgages in and near Rhode Island.—Continued[Locations of USGS stations shown in figure 2. River basins shown in figure 1. Numbers and names of index streamgages in bold and highlighted in light gray. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; p, present; Ave., Avenue; Rd., Road; Rt., Route; ft, feet; LTG, long-term streamgage; Index, index streamgage; STG, short-term 

streamgage; GIS, geographic information system; NWIS, National Water Information System]

USGS 

station no. Station name River basin

Latitude 

(decimal 

degree)

Longitude 

(decimal 

degree)

Drainage 

area 

(mi2

)

1

Period of 

record

Number 

of complete 

water 

years 

used in 

analyses

Number 

of complete 

climatic 

years 

used in 

analyses

Streamgage type Remarks

01111500 Branch River at Forestdale, RI Blackstone 41.99649 -71.56256 91.22 1940–p 66 66 Index and 

LTG

Some flow alteration by ponds 

upstream

01112700 Blackstone River Tributary at Woonsocket, 

RI

Blackstone 42.00510 -71.48923 2.22 1965–74 9 6 LTG --

01113695 Catamint Brook at Cumberland, RI Blackstone 41.98510 -71.41367 3.51 1999–2009 10 5 LTG --

01114000 Moshassuck River at Providence, RI Moshassuck 41.83399 -71.41061 23.36 1963–p 43 42 LTG Some flow alteration

01114500 Woonasquatucket River at Centerdale, RI Woonasquatucket 41.85899 -71.48728 37.70 1941–p 65 64 LTG Some flow alteration by reservoirs upstream

01115098 Peeptoad Brook at Elmdale Rd. near 

North Scituate, RI

Pawtuxet 41.85260 -71.60618 4.96 1994–p 12 10 Index and 

LTG

--

01115100 Mosquitohawk Brook near North Scituate, RI Pawtuxet 41.85149 -71.62284 3.05 1965–74 9 4 LTG --

01115187 Ponaganset River at South Foster, RI Pawtuxet 41.81871 -71.70507 14.02 1994–p 12 12 Index and 

LTG

--

01115630 Nooseneck River at Nooseneck, RI Pawtuxet 41.62677 -71.63256 8.20 1964–81 and 

2007–p

17 17 LTG --

01115670 Congdon River near Nooseneck, RI Pawtuxet 41.61232 -71.62284 4.46 2007–p 3 3 STG --

01115770 Carr River near Nooseneck, RI Pawtuxet 41.64316 -71.60784 6.74 1964–80 and 

2007–12

15 15 LTG Some flow diversions for municipal 

supply upstream

01115900 Flat River near Coventry, RI Pawtuxet 41.71454 -71.65257 9.09 1961–64 2 2 STG --

01116300 Furnace Hill Brook at Cranston, RI Pawtuxet 41.75649 -71.49728 3.91 1964–74 9 7 LTG --

01116905 Hunt River 250 ft downstream of Fry Brook 

at Frenchtown, RI

Hunt 41.63000 -71.47889 16.25 2007–p 2 2 STG Some flow alteration by municipal 

supplies upstream

01117370 Queen River at Liberty Rd. at Liberty, RI Pawcatuck 41.53899 -71.56867 19.30 1999–p 11 10 LTG Occasional flow withdrawals for 

irrigation upstream

01117410 Usquepaug River at Rt. 138 at Usquepaug, RI Pawcatuck 41.50260 -71.60784 33.05 1999–2004 4 4 STG Occasional flow withdrawals for 

irrigation upstream

01117424 Chickasheen Brook at West Kingston, RI Pawcatuck 41.48038 -71.57340 4.82 2002–04 2 2 STG Occasional flow withdrawals for 

irrigation upstream
12 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 1. Description of long- and short-term streamgages in and near Rhode Island.—Continued [Locations of USGS stations shown in figure 2. River basins shown in figure 1. Numbers and names of index streamgages in bold and highlighted in light gray. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; p, present; Ave., Avenue; Rd., Road; Rt., Route; ft, feet; LTG, long-term streamgage; Index, index streamgage; STG, short-term streamgage; GIS, geographic information system; NWIS, National Water Information System] USGS station no. Station name River basin Latitude (decimal degree) Longitude (decimal degree) Drain- age area (mi2

)

1

Period of 

record

Number 

of complete 

water 

years 

used in 

analyses

Number 

of complete 

climatic 

years 

used in 

analyses

Streamgage type Remarks

01117430 Pawcatuck River at Rt. 2 at Kenyon, RI Pawcatuck 41.44621 -71.62117 72.41 1958–60, 

2002–04, and 2007–p

3 3 STG Some flow alteration by municipal 

supplies and withdrawals for irrigation upstream

01117468 Beaver River near Usquepaug, RI Pawcatuck 41.49260 -71.62812 9.18 1974–p 31 31 Index and 

LTG

--

201117471 Beaver River at Shannock Hill Road near 

Shannock, RI

Pawcatuck 41.46427 -71.62784 11.90 2002–04 2 2 STG Occasional flow withdrawals for 

irrigation upstream

01117472 Beaver River at Kenyon, RI Pawcatuck 41.45232 -71.62812 12.36 1975–79 3 3 STG Occasional flow withdrawals for 

irrigation upstream

01117500 Pawcatuck River at Wood River 

Junction, RI

Pawcatuck 41.44510 -71.68090 99.33 1940–p 65 65 Index and 

LTG

Occasional flow alteration by ponds 

and mills upstream and withdrawals for irrigation upstream

01117600 Meadow Brook near Carolina, RI Pawcatuck 41.46649 -71.69007 5.09 1965–74 and 

2002–04

11 9 LTG Occasional flow withdrawals for 

irrigation upstream

01117800 Wood River near Arcadia, RI Pawcatuck 41.57399 -71.72062 35.17 1964–81, 

83–p

41 40 Index and 

LTG

--

01118000 Wood River at Hope Valley, RI Pawcatuck 41.49816 -71.71646 73.47 1941–p 65 65 Index and 

LTG

Some flow alteration by ponds 

upstream

01118010 Pawcatuck River at Burdickville, RI Pawcatuck 41.41621 -71.72896 204.33 2002–04 2 2 STG Occasional flow alteration by ponds 

and mills upstream and withdrawals for irrigation upstream

01118300 Pendleton Hill Brook near Clarks Falls, 

CT

Pawcatuck 41.47482 -71.83424 3.99 1959–p 48 47 Index and 

LTG

--

01118360 Ashaway River at Ashaway, RI Pawcatuck 41.42343 -71.79174 28.27 2002–04 2 2 STG --01118400 Shunock River at North Stonington, CT Pawcatuck 41.41010 -71.84479 16.31 2002–04 2 2 STG --01118500 Pawcatuck River at Westerly, RI Pawcatuck 41.38371 -71.83312 293.88 1940–p 65 65 LTG Some flow alteration by municipal 

supplies, ponds, mills, and withdrawals for irrigation upstream
Development of the Streamflow Statistics and Basin Characteristics Datasets 13

Table 1. Description of long- and short-term streamgages in and near Rhode Island.—Continued[Locations of USGS stations shown in figure 2. River basins shown in figure 1. Numbers and names of index streamgages in bold and highlighted in light gray. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; p, present; Ave., Avenue; Rd., Road; Rt., Route; ft, feet; LTG, long-term streamgage; Index, index streamgage; STG, short-term 

streamgage; GIS, geographic information system; NWIS, National Water Information System]

USGS 

station 

no.

Station name River basin

Latitude 

(decimal 

degree)

Longitude 

(decimal 

degree)

Drainage 

area 

(mi2

)

1

Period of 

record

Number 

of complete 

water 

years 

used in 

analyses

Number 

of complete 

climatic 

years 

used in 

analyses

Streamgage type Remarks

01118668 Whitford Brook below Williams Brook near 

Old Mystic, CT

Long Island 

Sound

41.40788 -71.96396 13.29 2000–02 3 3 STG --

01119280 Willimantic River at Stafford Springs, CT Shetucket 41.94537 -72.30452 52.83 1963–67 5 5 STG --

01119320 Roaring Brook near Stafford Springs, CT Shetucket 41.93426 -72.26091 15.15 1961–66 5 5 STG --

01120000 Hop River near Columbia, CT Shetucket 41.72760 -72.30230 74.54 1932–71 39 38 LTG --

01120500 Safford Brook near Woodstock Valley, CT Shetucket 41.92649 -72.05702 4.17 1951–81 31 28 LTG --

01121000 Mount Hope River near Warrenville, CT Shetucket 41.84371 -72.16897 29.00 1941–p 66 65 Index and 

LTG

Occasional flow alteration by ponds 

upstream

01123000 Little River near Hanover, CT Shetucket 41.67177 -72.05230 29.99 1952–p 55 54 Index and 

LTG

--

01124750 Browns Brook near Webster, MA French 42.05676 -71.83035 0.52 1963–77 15 7 LTG --

01125415 Muddy Brook at Childs Hill Rd. near 

Woodstock, CT

Quinebaug 41.96565 -71.96202 19.94 1979–83 4 4 STG --

01125490 Little River at Harrisville, CT Quinebaug 41.92760 -71.93007 35.73 1962–71 10 9 LTG --

01125600 Mashamoquet Brook at Abington, CT Quinebaug 41.87426 -72.00924 11.02 1962–63 1 1 STG --

01126000 Fivemile River at Killingly, CT Quinebaug 41.83732 -71.88535 57.91 1937–71 33 33 LTG Some flow alteration01126200 Bucks Horn Brook at Greene, RI Quinebaug 41.69316 -71.74340 5.49 1965–74 9 8 LTG --

01126500 Moosup River at Moosup, CT Quinebaug 41.71038 -71.88591 83.32 1933–71 39 38 LTG Some flow alteration01126600 Blackwell Brook near Brooklyn, CT Quinebaug 41.76538 -71.95646 16.97 1964–76 13 12 LTG --

01126950 Pachaug River at Pachaug, CT Quinebaug 41.58482 -71.93341 53.26 1962–73 12 10 LTG Some flow alteration01175670 Sevenmile River near Spencer, MA Chicopee 42.26509 -72.00480 8.81 1960–p 45 45 Index and 

LTG

Occasional flow alteration by ponds 

upstream

1Drainage areas (in mi2) were determined with a GIS and do not supersede areas listed in the USGS NWIS database.2Short-term streamgage not used in regression analyses.
14 Equations for Estimating Selected Streamflow Statistics in Rhode Island

0.01 0.1 0.5 1 2 5 10 20 30 40 50 60 70 80 90 95 98 99 99.5 99.9 99.99

Percentage of time mean daily streamflow is equaled or exceeded

0.01

0.1

1

10

100

1,000

Streamflow, in cubic feet per second

EXPLANATION

 Adamsville Brook at Adamsville, Rhode Island (01106000) water years 1941−1978

 Beaver River near Usquepaug, Rhode Island (01117468) water years 1971−2006

Figure 6. Flow-duration curves at the streamgages Adamsville Brook at Adamsville, R.I. (01106000), and Beaver River near 

Usquepaug, R.I. (01117468).

Daily streamflow data were downloaded by using the 

USGS database software ADAPS (Automatic Data Processing 

System). The streamflow data were downloaded for complete climatic years during the period of record through water 

year 2006. The input streamflow data were formatted, managed, and displayed by using the USGS computer software 

programs Input and Output for a Watershed Data Management (IOWDM) file (Lumb and others, 1990) and ANNIE 

(Flynn and others, 1995). The computer program Surface 

Water Statistics (SWSTAT) (http://water.usgs.gov/software/

SWSTAT/) (A.M. Lumb, W.O. Thomas, Jr., and K.M. Flynn, 

U.S. Geological Survey, written commun., 1997) was used 

to determine the annual low-flow frequency statistics for the 

USGS streamgages. SWSTAT ranks the seasonal and annual 

series of minimum mean n-day streamflows and then fits them 

to a log-Pearson Type III distribution. A resulting line of fit is 

then plotted through the values. The annual series were then 

checked for trends, but no trends were evident in the annual 

7-day low flows at the long-term streamgages with more 

than 50 years of record. Some long-term streamgages with 

less than 50 years of record showed no clear trend, a slight 

upward trend over time, or a slight downward trend over time. 

The results were highly variable, and no clear trend could be 

identified for the annual 7-day low flows in Rhode Island. The 

estimated 7Q2 and 7Q10 flows for the long-term streamgages 

are presented in table 3. An example of the fit of the logPearson Type III distribution to the annual 7-day low flow is 

provided for the Branch River at Forestdale, R.I. (01111500), 

streamgage (fig. 7). 

Annual and Monthly Statistics

The streamflow statistics mean annual, mean monthly, 

and median monthly streamflows also were computed by 

using The Nature Conservancy (2007) computer program 
Development of the Streamflow Statistics and Basin Characteristics Datasets 15

Table 2. List of selected streamflow statistics computed for long- and short-term streamgages and partial-record stations in and near 

Rhode Island.

[Streamflow statistics for which regression equations are presented in this study are in bold and highlighted in light gray.]

Streamflow statistic

Flow duration

1

99.99

1

99.95

99.9

99.5

99

98

97

96

95

94

93

92

91

90

85

80

75

70

65

60

55

50

45

40

35

30

25

20

15

10

9

8

7

6

5

4

3

2

1

0.5

0.1

1

0.05

1

0.01

Streamflow statistic

Low-flow frequency

7Q2

7Q10

Mean annual

Mean monthly

October

November

December

January

February

March

April

May

June

July

August

September

Median monthly

October

November

December

January

February

March

April

May

June

July

August

September

1

Could not be calculated for long- and short-term streamgages where 

there were less than 10,000 daily mean streamflow values available.
16 Equations for Estimating Selected Streamflow Statistics in Rhode Island

7−day low flow

Log−Pearson Type III

1

10

100

98 95 90 80 70 50 30 20 10 5

Annual nonexceedance probability, in percent

Streamflow, in cubic feet per second

2

EXPLANATION

Figure 7. Example of the fit of the log-Pearson Type III distribution to the annual 7-day low flow at the streamgage Branch River at 

Forestdale, R.I. (01111500), for water years 1941–2006.

Indicators of Hydrologic Alteration (IHA). Data for 41 longterm streamgages (table 1 and fig. 2) were downloaded from 

NWISweb by using GNWISQ (Granato, 2009). Streamflow 

statistics were computed for 41 long-term streamgages with 

at least 8 or more complete water years of record (table 3). 

Eight years is the minimum length of record needed for 

obtaining this information. The longer a period of record for 

a streamgage, the more information that data can provide to 

the users, and the more any influence of extended wet or dry 

periods on the streamflow data tends to be minimized. Thus, 

for this study, the term “long-term streamgages” refers to those 

affected by little to no upstream flow alterations and with at 

least 8 years of record. The August median flow is an important statistical measure for fisheries and often is used for summer maintenance of aquatic habitat in New England streams 

(U.S. Fish and Wildlife Service, 1981).

Flow Statistics for Long-Term Streamgages

Flow statistics for long-term streamgages are critical 

for understanding water resources in an area, especially for 

those streamgages whose upstream basins included few or 

no flow alterations. The records from these streamgages can 

provide information on the variability of annual, seasonal, 

and daily streamflows, potential trends, low flows, and peak 

flows. Those long-term streamgages affected the least by 

upstream flow alterations and with at least 10 years of record 

are referred to as index streamgages. The records from index 

streamgages were those records determined to be acceptable 

for use in extending the records for short-term streamgages 

and partial-record stations. 
Development of the Streamflow Statistics and Basin Characteristics Datasets 17

Flow Statistics for Short-Term Streamgages and 

Partial-Record Stations

Estimates of streamflow often are needed for short-term 

streamgages, whose periods of record may not represent longterm hydrologic conditions, and for partial-record stations 

with only a limited number of streamflow measurements. 

Through correlation and streamflow-record extension techniques, streamflow statistics for the short-term streamgages 

and partial-record stations can be estimated. Estimates can be 

made on the basis of the relation between daily mean streamflows at the short-term streamgages and the concurrent daily 

mean streamflows at nearby index streamgages. For this study, 

only short-term streamgages (table 1 and fig. 2) and partialrecord stations (table 4, in back of report and fig. 8) with little 

to no flow alteration and, respectively, at least 1 year of record 

and 10 streamflow measurements, in and near Rhode Island 

were used. For short-term streamgages and partial-record stations, daily mean streamflows and miscellaneous streamflow 

measurements, respectively, are related to the concurrent daily 

mean streamflows at nearby index streamgages. The index 

streamgage selected for the relation to a short-term streamgage 

or partial-record station is based on proximity, similarity of the 

physical, land-cover, land-use, surficial-deposits, and climatological characteristics between the two sites, and the linearity and Pearson’s correlation coefficient (r) of the relation 

between streamflows. For this study, the relation is defined 

by use of a streamflow-record extension technique known as 

the Maintenance of Variance Extension, type 1 (MOVE.1) 

(Hirsch, 1982). 

The selection of index streamgages used for estimating 

streamflows at short-term streamgages and partial-record 

stations must satisfy several criteria: (1) the flow is 

essentially natural (very little to no alteration), (2) most 

or all of the period of record coincides with that for shortterm streamgages and partial-record stations, and (3) the 

period of record is greater than 10 years. For this study, 

16 long-term streamgages were identified as possible index 

streamgages (table 1 and fig. 2). Of the 16 index streamgages, 

9 were located in Rhode Island, 3 in Connecticut, and 4 in 

Massachusetts. Only the Adamsville Brook at Adamsville, R.I. 

(01106000), streamgage is not currently (2014) operated. After 

this streamgage was discontinued in 1978, it was operated 

continuously for part of the 1987 water year, and concurrent 

streamflow measurements were made (on the same day) 

during water years 1992–93 and 2003–04 with streamflow 

measurements at nearby partial-record stations.

Scatterplots of log-transformed streamflow at each 

short-term streamgage and partial-record station in relation 

to concurrent log-transformed daily mean streamflow at each 

of the 16 index streamgages were made by using Microsoft 

Excel and the computer program SREF (Granato, 2009) to 

determine the nature and quality of the relations between 

the streamflows. For partial-record stations with zero-flow 

measurements, a value of 0.01 cubic feet per second (ft3/s) for 

the zero-flow measurement was used for computation of the 

logarithms. Graphical plots of the relations of the data were 

evaluated to make sure they were linear. Generally, the relation 

with the highest correlation coefficient between the streamflows at the short-term streamgage or partial-record station and 

the index streamgage was used. For this study, the MOVE.1 

technique (Hirsch, 1982) was then used to provide an equation that related streamflow at the short-term streamgage or 

partial-record station to the concurrent streamflow at the index 

streamgage. The MOVE.1 equation is

i i – ( ) Sy YY X X

Sx

= + (1)

where

Yi is the streamflow or streamflow statistic at the 

short-term streamgage or partial-record 

station, 

Xi is the streamflow or streamflow statistic at the 

index streamgage,

Y is the mean of the daily mean streamflows or 

streamflow measurements at the shortterm streamgage or partial-record station, 

respectively,

X is the mean of the concurrent daily mean 

streamflows at the index streamgage,

Sy is the standard deviation of the daily mean 

streamflows or streamflow measurements 

at the short-term streamgage or partialrecord station, respectively, and

Sx is the standard deviation of the concurrent 

daily mean streamflows at the index 

streamgage.

The streamflow data used in the MOVE.1 equation is base-10 

log transformed, and the resulting streamflow (Yi

) must then be 

re-transformed back to arithmetic units.

Examples of the MOVE.1 relation for the short-term 

streamgage Chickasheen Brook at West Kingston, R.I. 

(01117424), to the index streamgage Beaver River near 

Usquepaug, R.I. (01117468), and for the partial-record station Burnt Swamp Brook near Grant Mills, R.I. (01113670), 

to the index streamgage Wading River near Norton, Mass. 

(01109000), are shown in figures 9 and 10, respectively. 

Streamflow statistics were estimated by using the 

MOVE.1 record-extension technique for 21 short-term 

streamgages (table 1 and fig. 2) and 135 partial-record stations in and near Rhode Island (table 4, in back of report and 

fig. 8). The index streamgage selected for estimating selected 

streamflow statistics at the short-term streamgage or partialrecord station, the correlation coefficient describing that 

relation, and the number of data points used in the analyses 

are listed in table 5 (in back of report). Additionally, information about the relation between the sites, such as the minimum, 

maximum, and range of the flow duration(s) for which a daily 

mean streamflow at a short-term or streamflow measurement at a partial-record station were used in the analysis, also 
18 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01123000

01121000

01118300

01118000

01117800

01117500

01117468

01115187

01115098

01111500 01111300

01109000

01106000

01105730

01105600

9

8 7

6

5

4

3

2

1

99

98

96

97 95

93

92

91

90

89

88

85

84

83

82

81

80

79

78

77 76

74

75

73

72

71

70

69

68

67

66

63

62

61

60

59

58

57

56 55 54

53 52

51

50

49

48

47

46 45

44

43

42 41

40

39

38

37

33

34

35

36

32

31

30

28

29 26

25

24

23

22

21

20 19

18

17

15

16

14

13

12

11

10

135

134

133

132

131

130

129

128

127

126

125

124

123

122

121 120

118117

116

115

113

111

112

110

109

107

106

105

103

102

100

119

108

104 114

94

87 86

64 65

27

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

EXPLANATION

Surface-water sites

—With identifier

Index streamgagePartial-record station

01117500

1

Figure 8. Locations of the partial-record stations in and near Rhode Island. Partial-record station numbers are listed in table 4 (in back of report).
Development of the Streamflow Statistics and Basin Characteristics Datasets 19

0.1

1

10

100

1 10 100 1,000

Daily mean streamflow at the short-term streamgage Chickasheen Brook at 

West Kingston, Rhode Island (01117424), in cubic feet per second 

Daily mean streamflow at index streamgage Beaver River near Usquepaug, Rhode Island (01117468), in cubic feet per second

Concurrent daily mean streamflow

MOVE.1 line

EXPLANATION

Figure 9. Example of Maintenance of Variance Extension, type 1 (MOVE.1), relation between concurrent daily mean 

streamflows at the short-term streamgage Chickasheen Brook at West Kingston, R.I. (01117424), and the index streamgage 

Beaver River near Usquepaug, R.I. (01117468).

is presented in the table 5 (in back of report). Analyses for 

several partial-record stations in and near Rhode Island are 

not presented in the report because (1) the best correlation 

coefficients were less than 0.80; (2) the record had fewer than 

10 streamflow measurements; (3) the streamflow measurements covered less than 50 percent of the range of the flowduration curve; or (4) known alterations in the drainage basin 

could have affected streamflows. Results of the estimated 

streamflow statistics for 21 short-term streamgages and for 

135 partial-record stations are in tables 3 and 6, respectively.

Table 6. Estimated streamflow statistics for partial-record 

stations in and near Rhode Island.

[Available separately at http://pubs.usgs.gov/sir/2014/5010/

tables/sir2014-5010_bent_table06.xlsx]

Basin Characteristics for Streamgages and 

Partial-Record Stations

The characteristics of streamflow are directly related to a 

drainage basin’s physical, land-cover, land-use, geologic, and 

climatic characteristics. Characteristics of the drainage basin 

were selected for use as potential explanatory variables in the 

regression analysis on the basis of their theoretical relations 

to streamflows, the results of previous streamflow studies in 

similar hydrologic regions, and the feasibility of determining 

the basin characteristics with digital datasets and GIS technology. Measuring the basin characteristics with GIS technology 

facilitates automation of the process and the process of solving 

the regional regression equations by using the USGS StreamStats Web-based application.
20 Equations for Estimating Selected Streamflow Statistics in Rhode Island

0.01

0.1

1

10

100

1 10 100 1,000

Miscellaneous streamflow measurements at partial-record station Burnt Swamp Brook 

near Grant Mills, Rhode Island (01113670), in cubic feet per second 

Daily mean streamflow at index streamgage Wading River near Norton, Massachusetts (01109000), in cubic feet per second

Concurrent streamflow

MOVE.1 line

EXPLANATION

Figure 10. Example of Maintenance of Variance Extension, type 1 (MOVE.1), relation between concurrent miscellaneous streamflow 

measurements at the partial-record station Burnt Swamp Brook near Grant Mills, R.I. (01113670), and daily mean streamflows at the 

index streamgage Wading River near Norton, Mass. (01109000).

The geospatial data layers for calculation of basin 

characteristics are as follows: (1) total length of streams data 

are from the National Hydrography Dataset (NHD) (U.S. 

Geological Survey, 2007a); (2) elevation data, also used for 

slope calculations, are from the National Elevation Dataset 

(NED) (U.S. Geological Survey, 2007b); (3) land-cover and 

land-use data are from Rhode Island Geographic Information 

System (RIGIS) (Rhode Island Geographic Information 

System, 2008a), the Massachusetts Office of Geographic 

Information (MassGIS) (Massachusetts Office of Geographic 

Information, 2009), and the University of Connecticut—

Center for Land Use Education and Research (CLEAR) 

(University of Connecticut—Center for Land Use Education 

and Research, 2007a); (4) impervious-cover data are from 

RIGIS (Rhode Island Geographic Information System, 2008b), 

MassGIS (Massachusetts Office of Geographic Information, 

2007a), and CLEAR (University of Connecticut—Center for 

Land Use Education and Research, 2007b); (5) surficialgeology data (1:24,000 scale) are from RIGIS (Rhode 

Island Geographic Information System, 2007), MassGIS 

(Massachusetts Office of Geographic Information, 2007b), 

and the University of Connecticut—Map and Geographic 

Information Center (MAGIC) (University of Connecticut—

Map and Geographic Information Center, 2007); (6) soil 

hydrologic group data are from the Natural Resources 

Conservation Service (NRCS) Soil Survey Geographic 

database (SSURGO) (Natural Resources Conservation 

Service, 2007); and (7) climatic (precipitation and temperature 

1971–2000) are from the Parameter-Elevation Relationships 

on Independent Slopes Model (PRISM) Climate Group, 

Oregon State University (2007). The basin boundaries for the 

41 long-term and 21 short-term streamgages and 135 partialrecord stations were overlaid on areal coverages of the basin 
Equations for Estimating Selected Streamflow Statistics 21

characteristics of interest to determine the characteristics’ 

values for the upstream basin to each site. 

A GIS database was set up to store the characteristics of 

the drainage basins for the streamgages used in the regression analysis. The data layer from the NHD for total length of 

streams (U.S. Geological Survey, 2007a) was edited. Where a 

stream had more than one flow path (for example, around an 

island or in outlets from wetland areas), coverage was limited 

to only one flow path. Also, any stream segment shown crossing a basin boundary other than at the basin outlet was deleted 

so that all stream segments were within the basin boundary. 

This data layer for edited total length of streams was used with 

the basin characteristic data for drainage area (represented 

by the variable DRNAREA3) to determine the basin characteristic data for stream density (represented by the variable 

STRDENED3), which is the edited total length of streams 

divided by the drainage area. The names, units of measure, 

and sources of data for each measured basin characteristic are 

listed in table 7. The basin characteristics for long- and shortterm streamgages and partial-record stations are in tables 8 

and 9, respectively. 

Table 8. Basin characteristics for long- and short-term 

streamgages in and near Rhode Island.

[Available separately at http://pubs.usgs.gov/sir/2014/5010/

tables/sir2014-5010_bent_table08.xlsx]

Table 9. Basin characteristics for partial-record stations in and 

near Rhode Island.

[Available separately at http://pubs.usgs.gov/sir/2014/5010/

tables/sir2014-5010_bent_table09.xlsx]

Equations for Estimating Selected 

Streamflow Statistics

Streamflow information for ungaged sites is critical 

for Federal, state, county, city, and town agencies; 

nongovernmental and private organizations; and individuals 

and public groups dealing with water-resources issues. Flowfrequency and duration-streamflow statistics for streams at 

ungaged sites can be estimated by using several methods. 

These methods include (1) a drainage-area ratio and (2) a 

regression equation relating streamflow statistics to basin 

characteristics. Additionally, streamflow statistics may be 

estimated for an ungaged site with at least 10 miscellaneous 

streamflow measurements by the correlation of measured 

streamflows with concurrent daily mean streamflows at nearby 

continuous-record streamgages (index streamgages) followed 

by the streamflow-record-extension technique known as 

the Maintenance of Variance Extension, type 1 (MOVE.1) 

(Hirsch, 1982).

3

USGS StreamStats basin-characteristics label (http://streamstatsags.cr.usgs.

gov/ss_defs/basin_char_defs.aspx).

Drainage-Area Ratio Methods

The drainage-area ratio method is based on the assumption that the streamflow at an ungaged site is the same per unit 

drainage-basin area as that at a nearby hydrologically similar 

streamgage with little to no flow alteration of the upstream 

basin. Drainage areas to the ungaged site and the streamgage 

are determined from topographic maps or the USGS StreamStats web application (http://streamstats.usgs.gov/index.

html). Streamflow statistics are computed for the streamgage, 

and then the statistics (streamflow values) are divided by the 

drainage area to determine the streamflow for each statistic per 

unit area in cubic feet per second per square mile (ft3/s/mi2) 

at the streamgage. These values are multiplied by the drainage area to the ungaged site to obtain estimated statistics for 

that site. This method is most commonly applied if the index 

streamgage is on the same stream as the ungaged site because 

the accuracy of the method depends on the proximity of the 

two sites, on similarities in drainage area, and on other physical and climatic characteristics of their drainage basins. 

Several studies have provided estimates of the maximum 

difference in drainage areas for which the use of the drainagearea ratio method would generate more accurate estimates 

of streamflow statistics than the use of regression equations. 

Guidelines have been provided for estimating peak-flow 

statistics, and usually the recommendation has been that the 

drainage area to the ungaged site should be 0.5 to 1.5 times 

the drainage area to the index streamgage (Choquette, 1988, 

p. 41; Koltun and Roberts, 1990, p. 6; Lumia, 1991, p. 34; 

Bisese, 1995, p. 13; Koltun and Whitehead, 2002, p. 22; and 

Martin and Arihood, 2010, p. 28). One report (Koltun and 

Schwartz, 1987, p. 32) recommended a narrower range of 

0.85 to 1.15 times the drainage area of the index streamgage 

for estimating low flows at ungaged sites in Ohio. Ries and 

Friesz (2000), however, determined that the drainage-area 

ratio method could be used to estimate low-flow statistics for 

ungaged sites in Massachusetts if the drainage area for an 

ungaged site was between 0.3 and 1.5 times the drainage area 

of the index streamgage site. They found that this method 

was generally as accurate as or more accurate than regression 

equations for this range of drainage areas.

In the drainage-area ratio method, the streamflow values 

are transferred from a streamgage to the ungaged site by the 

following formula:

 u

u g

g

DRNAREA Q Q DRgNAREA

 

= ×    

(2)

where

Qu is the estimated streamflow at the ungaged 

site,

Qg is the streamflow at the streamgage,

DRNAREAu is the drainage area at the ungaged site, and

DRNAREAg is the drainage area at the streamgage.
22 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Table 7. List of basin characteristics determined for long- and short-term streamgages and partial-record stations in and near 

Rhode Island.

[The geospatial datalayers for calculation of basin characteristics are as follows: total length of streams data are from an edited version of the National Hydrography Dataset (U.S. Geological Survey, 2007a); elevation data, also used for slope calculations, are from the National Elevation Dataset (NED) (U.S. Geological 

Survey, 2007b); land-cover and land-use data (2003/2004) are from the Rhode Island Geographic Information System (RIGIS) (Rhode Island Geographic Information System, 2008a), the Massachusetts Office of Geographic Information (MassGIS) (Massachusetts Office of Geographic Information, 2009), and the University of Connecticut Center for Land Use Education and Research (CLEAR) (University of Connecticut Center for Land Use Education and Research, 2007a); 

impervious-cover data are from RIGIS (Rhode Island Geographic Information Systems, 2008b), MassGIS (Massachusetts Geographic Information System, 

2007a), and CLEAR (University of Connecticut Center for Land Use Education and Research, 2007b); surficial-geology data (1:24,000 scale) are from RIGIS 

(Rhode Island Geographic Information System, 2007), MassGIS (Massachusetts Office of Geographic Information, 2007b), and the University of Connecticut 

Map and Geographic Information Center (MAGIC) (University of Connecticut Map and Geographic Information Center, 2007); soil hydrologic group data are 

from the Natural Resources Conservation Service (NRCS) Soil Survey Geographic database (SSURGO) (Natural Resources Conservation Service, 2007); and 

climatic data (precipitation and temperature 1971–2000) are from the Parameter-Elevation Relationships on Independent Slopes Model (PRISM) Climate Group, 

Oregon State University (2007). NAVD 88, North American Vertical Datum of 1988; NAD 83, North American Datum of 1983]

Physical characteristics

Drainage area (DRNAREA1), in square miles

Basin perimeter, in miles

Total length of streams, in miles

Stream density (STRDENED1) (total length of streams divided by drainage area), in miles per square mile

Stream slope between 10 and 85 percent of the main channel river length, in percent

Mean basin slope, in percent

Maximum basin elevation, in feet relative to NAVD 88

Minimum basin elevation, in feet relative to NAVD 88

Mean basin elevation, in feet relative to NAVD 88

Basin relief (maximum minus minimum basin elevation), in feet

Basin outlet elevation, in feet relative to NAVD 88

Basin centroid location—easting, state plane feet, relative to NAD 83

Basin centroid location—northing, state plane feet, relative to NAD 83

Basin outlet location—easting, state plane feet, relative to NAD 83

Basin outlet location—northing, state plane feet, relative to NAD 83

Areal proportions of land-cover, land-use, and surficial-deposits characteristics

Forested land, in percent

Agricultural land, in percent

Water bodies, in percent

Forested wetlands, in percent

Nonforested wetlands, in percent

Total wetlands (forested and nonforested), in percent

Impervious land, in percent

Urban land (high-density residential, commercial, industrial, and transportation land use), in percent

Sand and gravel deposits, in percent

NRCS SSURGO soil hydrologic groups A, B, C, and D, in percent

Climatological characteristics

PRISM Precipitation 1971–2000, drainage-basin average for mean annual, in inches

PRISM Temperature 1971–2000, drainage-basin average for mean annual maximum, in degrees Celsius

1

USGS Streamstats basin characteristics label (http://streamstatsags.cr.usgs.gov/ss_defs/basin_char_defs.aspx).
Equations for Estimating Selected Streamflow Statistics 23

Eash and Barnes (2012) did a comparison of estimates 

of the 7-day 10-year low flow by using regional regression 

equations, the drainage-area ratio method, and the weighted 

drainage-area ratio method to estimates from streamflow 

records for 48 streamgages (31 pairs of streamgages) on the 

same rivers in Iowa. They found that the weighted drainagearea ratio provided the best estimate if the drainage area to the 

ungaged site was between 0.4 and 1.5 times the drainage area 

to the streamgage. 

In the weighted drainage-area ratio method, the streamflow values are transferred from a streamgage to the ungaged 

site by using the following formula:

 

2 1 gs

gr gs

uw ur

gr g

Q DRNAREA

Q Q

Q Q Q DRNAREA

            × ×−               =× −    

   

 (3)

where

Quw is the weighted estimated streamflow at the 

ungaged site,

Qur is the streamflow at the ungaged site estimated 

from the regression equation,

Qgs is the streamflow at the streamgage estimated 

from measured data,

Qgr is the streamflow at the streamgage estimated 

from the regression equation,

|DRNAREA| is the absolute value of the difference between 

the drainage areas to the streamgage 

(DRNAREAg) and the ungaged site 

(DRNAREAu), 

DRNAREAg is the drainage area to the streamgage, and 

DRNAREAu is the drainage area to the ungaged site.

As gs

gr

Q

Q approaches 1, or the difference in drainage areas 

approaches 50 percent, the weighting factor approaches 1 and 

no longer has an effect on the regression equation estimate 

for the ungaged site. Additionally, both the drainage-area and 

weighted drainage-area ratio methods may not be applicable 

for ungaged sites where changes in the physical, land-cover, 

land-use, surficial-deposits, or climatological characteristics 

or alterations to streamflows between the ungaged site and the 

streamgage are substantial. The error associated with estimates 

based on the drainage-area and weighted drainage-area ratio 

methods can not be calculated.

Regional Regression Analyses

Studies to develop regional regression equations for 

estimating streamflow statistics at ungaged sites have been 

done in many states throughout the U.S. and specifically in 

the states adjacent to Massachusetts. Multiple regression 

analyses provide a mathematical equation for estimating a 

response (dependent) variable—streamflow statistic—from 

one or more explanatory (independent) variable(s), such as 

basin characteristics. Ideally, the development of regression 

equations involves the use of streamflow data from a large 

number of long-term streamgages on unaltered streams 

evenly distributed across the region of interest and with a 

range of basin characteristics. But in many cases, the number 

of streamgages representing unaltered flow is limited, the 

streamgage network is often biased toward representing 

larger streams or rivers, the network is unevenly distributed 

geographically, and the range of basin characteristics upstream 

of streamgages does not cover the complete range found 

in the region. In Rhode Island, the number of streamgages 

on streams with little to no flow alteration is limited; for 

this reason, nearby streamgages in eastern Connecticut and 

southeastern and south-central Massachusetts were also 

included. The records for these streamgages were used to 

develop regional regression equations for estimating selected 

streamflow statistics at ungaged sites in Rhode Island.

Multiple regression is used to create equations that relate 

streamflow statistics for streamgages to the physical, landcover, land-use, surficial-deposit, and climatological characteristics of their upstream drainage areas. Once an optimal equation has been determined, a streamflow statistic at a nearby 

ungaged site in a basin with similar characteristics can then be 

estimated by applying the equation to the ungaged site.

The basic equation describing a linear multiple regression 

analysis is

Y b bX bX bX e i = + + +...+ + 0 11 2 2 nn i (4)

where

Yi is the response (dependent) variable 

(estimated streamflow statistic) for the 

ungaged site i,

b0 to bn are the coefficients determined in the analysis, 

Xi to Xn are the explanatory (independent) variables 

(basin characteristics) for the ungaged site 

i, and

ei is the residual error or difference between the 

observed and estimated response variables 

for ungaged site i.

Linear regression analysis is based on the following 

assumptions: (1) the mean of the residuals (ei) is zero, (2) the 

variance of the residuals is constant, (3) the residuals are normally distributed, and (4) the residuals are independent of each 

other. In addition to these assumptions, the selected explanatory variables (X) should have a physical basis as predictors 

of the streamflow statistic, the explanatory variables (basin 

characteristics) in the equation should not be highly correlated 

with each other, and the signs of the terms of the equation 

should make hydrological sense. For example, the variable 

drainage area should have a positive coefficient because an 
24 Equations for Estimating Selected Streamflow Statistics in Rhode Island

increase in drainage area should result in an increase in the 

value of the streamflow statistic. 

In almost all regionalization studies to determine lowflow and peak-flow statistics, the response and explanatory 

variable datasets are skewed. As a consequence, the data need 

to be transformed to ensure that the mean of the residuals 

equals zero. In many studies, a logarithmic transformation is 

used. A base10 log-transformed multiple regression equation 

has the form

i 01 12 2 n ni logY b b logX b logX b logX e = + + +...+ + . (5)

After the coefficients have been determined through 

regression analysis, the equation is transformed back to its 

original units in a form that can be used to estimate a specific 

streamflow statistic at an ungaged site. The retransformed 

equation has the following form:

0 1 2 

 12 = 10 ... 10 n i b b b b e Y XX X i n + + ++ + . (6)

A linear regression equation provides an unbiased estimate of the mean response of the response variable. Although 

estimates provided by equation 5 are unbiased, these estimates are in log units, whereas estimates in the original units 

are needed to calculate specific streamflow statistics at an 

ungaged site. Estimates from equation 6 are in the original 

units. However, this equation predicts the median, instead 

of the mean, value of the response variable. A streamflow 

statistic based on a median creates an estimate that is biased 

and tends to be lower than the mean (Ries and Friesz, 2000). 

Bias correction factors (BCFs) were used in some studies in 

Massachusetts and New Hampshire to remove the bias from 

the estimate (Ries, 1994a and b; Ries and Friesz, 2000; Flynn, 

2003a and b, and Archfield and others, 2010). In other studies 

(Risley, 1994; Stuckey, 2006; Armstrong and others, 2008; 

and Ahearn, 2010), BCFs were not used, likely because they 

were generally very small. In this study, BCFs were also not 

used, because if they were, then the streamflows estimated 

from the regression equations would not have an equal chance 

of being higher or lower than their actual values (Julie Kiang, 

U.S. Geological Survey, oral commun., 2011). 

Development of Regression Equations

In regional regression studies, explanatory and response 

variables often need to be transformed before the regression 

equation is created to ensure a linear relation. Scatterplots, 

correlation tables, and linear regression analyses were done 

by applying the statistical software Minitab (2003) to the 

selected streamflow statistics at long-term and short-term 

streamgages (table 3) and the basin characteristics (table 8) 

to determine if variable transformations were needed. The 

scatterplots indicated that a log transformation was needed to 

meet the assumptions of linear regression. Thus, the logarithmic (base-10) transformation was selected and applied to 

streamflow statistics (response variables) and basin characteristics (explanatory variables) to linearize the relation between 

the explanatory variables and the response variables, to ensure 

equal variance about the regression line, and to decrease the 

spread of the data.

Several potential explanatory variables (basin characteristics) for the drainage basin upstream of a few streamgages had 

one or a few values of zero. The variables were generally limited to land-cover, land-use or surficial deposits characteristics 

of the drainage basin, such as forested land, water bodies, 

wetlands, impervious land, and sand and gravel deposits. To 

logarithmically (base-10) transform all the values of that basin 

characteristic, a constant value of 0.01, 0.10, or 1.00 (depending on the lowest values other than the zero values) was added 

to all values of that basin characteristic. 

Scatterplots of logarithmic (base-10) transformed basin 

characteristics were then examined to determine if particular 

characteristics were correlated with other characteristics (r) 

(table 10). If two basin characteristics were found to have a 

moderate or strong correlation (an absolute value of Pearson’s 

r greater than or equal to 0.50), then those basin characteristics 

were tested separately in the variable-selection process of the 

regression analyses. This separate testing was done to eliminate redundant basin characteristics in the variable-selection 

process. For example, the basin characteristics denoted as 

“drainage area” and “total length of streams” had very strong 

correlations of r=0.98 and higher (table 10). For this reason, these basin characteristics were tested separately in the 

variable-selection process.

Table 10. Pearson’s correlation coefficients for basin 

characteristics evaluated as potential explanatory variables for 

regression equations for estimating selected streamflow statistics 

for long- and short-term streamgages in Rhode Island.

[Available separately at http://pubs.usgs.gov/sir/2014/5010/

tables/sir2014-5010_bent_table10.xlsx]

For the initial regression analyses of the selected potential explanatory variables, the automated statistical procedures 

called “best subsets” and “stepwise” were used in Minitab 

(2003). Both selection procedures determined the statistical 

contribution that was entered in the equation for each of the 

explanatory variables (basin characteristics), and variables 

were retained or deleted based on their statistical importance. 

In the procedure “best subsets” (Minitab, 2003), the 

two equations with the highest coefficients of determination 

(R2), the Mallow’s Cp closest to the number of explanatory 

variables plus the constant 1, and the lowest root mean square 

errors were evaluated for each of the possible combinations of 

selected explanatory variables to determine the best possible 

combinations of the explanatory variables. The procedure 

identified the best two combinations of explanatory variables 

for models with a specified number of explanatory variables. 

With this procedure, each explanatory variable can be included 

or excluded independently of the other explanatory variables. 
Equations for Estimating Selected Streamflow Statistics 25

Efroymson’s stepwise selection procedure (Efroymson, 

1960), is similar to forward selection, which involves testing explanatory variables one by one and including them in 

the equation if they are statistically significant; however, as 

each new variable is added to the subset, partial correlations 

are considered to determine whether any of the variables in 

the subset should be dropped. In the procedure “stepwise” 

(Minitab, 2003), the procedure essentially outputs the best 

potential combination of explanatory variables (which have 

T-statistic values whose absolute values are greater than or 

equal to 2.00 and p-values less than or equal to 0.05) for 

models with increasing numbers of explanatory variables until 

no additional variables meet the criteria for T-statistic values 

and p-values. Additionally for each model, R2, Mallow’s Cp, 

and s (root mean square error) are presented to assist in evaluation of the models. In these analyses, basin characteristics 

that were found to be highly correlated (absolute value of r

greater than or equal to 0.50) were entered only one at a time 

during the “best subsets” and “stepwise” procedures to prevent 

regression problems. 

If the two “best subsets” and “stepwise” procedures identified the same set of basin characteristics, then the top few 

potential explanatory variables were further evaluated with 

the ordinary-least-squares (OLS) regression procedure. For 

the explanatory variables, the p-value, T-statistic value, and 

VIF (variance inflation factor) statistics were evaluated. For 

the model output parameters R2, s, PRESS statistic, unusual 

observations (large standard residuals and (or) X values with 

large influence), and the Durbin-Watson statistic were evaluated. The histogram, normal probability, and graphs of the 

residuals as functions of the fitted values and the order of the 

data also were evaluated. Additionally, the statistic named 

“high influence,” the Cook’s Distance statistic, and the DFITS 

statistic were evaluated.

After the evaluation of selected streamflow statistics 

estimated for the short-term streamgages (table 3) and partialrecord stations (table 6), only the short-term streamgages were 

selected for inclusion with the 41 long-term streamgages for 

the regression analysis. Two of the 21 short-term streamgages 

were not included in the regression analyses because the 

record for another streamgage nearby on the same river 

was longer, and the drainage areas and basin characteristics 

of the two streamgages were similar. Exclusion of these 

two streamgages removed redundancy of those streamflow 

statistics and basin characteristics in the regression analyses. 

The two short-term streamgages excluded were Chepachet 

River near Gazzaville, R.I. (01111410), and Beaver River at 

Shannock Hill Road near Shannock, R.I. (01117471) (fig. 2). 

The partial-record stations were not included in the 

regression analyses because of several factors: 

1. The 135 partial-record stations had from 11 to 87 streamflow measurements for use in the MOVE.1 relation with 

an index streamgage for estimating long-term streamflow 

statistics, whereas a 1-year of continuous record at a 

streamgage would provide 365 daily mean streamflow 

values for use in the MOVE.1 relation with an index 

streamgage for estimating long-term statistics.

2. Weighting procedures for partial-record stations have 

differed among previous studies. For example, Stuckey 

(2006) assigned 1 year of record to partial-record stations for every year when a streamflow measurement was 

made, whereas Ahearn (2010) assigned 5 years of record 

to partial-record stations for every year when a measurement was made. Either of these weighting procedures 

could result in more years of record for a partial-record 

station than for a short-term streamgage which was operated for 1 or more years. If the number of streamflow 

measurements for a partial-record station were divided by 

365 days, the partial-record station would have so little 

weight that its effect in the regression analyses would be 

negligible.

3. Boxplots of selected basin characteristics for partialrecord stations were compared with boxplots for the longterm and short-term streamgages, and the comparison 

showed that the partial records did not expand the range 

of the basin characteristics.

4. The computer program entitled “Displaying Redundant 

Partial Record Sites—drprs” (Charles Berenbrock and 

Ken Eng, U.S. Geological Survey, written commun., 

2009) was used to evaluate the data from the partialrecord stations for possible use in the regional regression 

analyses. Results showed that the range between the minimum and maximum values for the basin characteristics 

were adequately covered by data from the long- and shortterm streamgages. Additionally, the program showed that 

there were no areal gaps within the study area that could 

have been covered by the partial-record stations. 

5. The regression equations might be overly influenced by 

estimated streamflow statistics from a large number of 

partial-record stations with small drainage areas. 

6. The streamflow statistics for the index streamgages are 

already included in the regression analyses, and they also 

were used to estimate the long-term streamflow statistics 

for the short-term streamgages that are also included in 

the analyses.

Weighting Procedures

For flow-duration statistics, a weighted procedure similar 

to that used by Ahearn (2010) in Connecticut and Stuckey 

(2006) in Pennsylvania was used. The weight factor for the 

record of each streamgage used in the regression analyses was 

increased in proportion to the length of the record. The weight 

was assigned by multiplying the number of years in the period 

of record by the total number of streamgages in the study and 

dividing the product by the total number of years of record 

for all streamgages in the study. For example, the weight for 
26 Equations for Estimating Selected Streamflow Statistics in Rhode Island

the short-term streamgage Ashaway River at Ashaway, R.I. 

(01118360), with the equivalent of 2 years of record would 

be 0.0882 [(2 years × 60 streamgages) ÷ (1,361 total years)], 

whereas the weight for Adamsville Brook at Adamsville, R.I. 

(01106000), with the equivalent of 38 years of record would 

be 1.6752 [(38 years × 60 streamgages) ÷ (1,361 total years)].

Final Regression Equations

The response variables (flow duration and low-flowfrequency statistics) included some zero flows for the lower 

flow statistics at some streamgages. Of the 60 streamgages’ 

statistics used in the regression analyses, 4 had zero flow 

at the 7Q10, and 99- and 98-percent flow durations. Two 

streamgages also had zero flow at the 7Q2 and 95-percent flow 

duration (table 3). The value of zero cannot be logarithmically 

transformed, but logarithmic transformation of streamflow statistics (that are not normally distributed) is needed to develop 

regression equations. 

The method of handling the zero values in a regression 

analysis depends on the number of streamgages in the 

dataset with response variables equal to zero. If the number 

is sufficient, logistic regression or a Tobit model can be used 

(Tasker, 1989; Ludwig and Tasker, 1993; Kroll and Stedinger, 

1999; Hortness, 2006). If the number is small, left-censored 

regression analysis, which uses an adjusted maximumlikelihood estimation (Cohn, 1988, and Helsel, 2005) or a 

method that adds a small constant value (0.01, 0.10, and 

1.00) to all response variables in a dataset, is used (Kroll and 

Stedinger, 1999). 

Given the small number of streamgage in this study with 

zero-flow statistics for the 7Q10 and 7Q2 and 99-, 98-, and 

95-percent flow durations, left-censored regression analyses were used to develop the regression equations for these 

streamflow statistics. The left-censored regression analyses were done by using USGS library S–Plus for Windows 

(Lorenz and others, 2011) in the program TIBCO Spotfire S–

Plus (TIBCO Software, Inc., 2008). This procedure in S–Plus 

uses the adjusted maximum-likelihood estimation, which is 

recommended for data that is log-normally distributed. The 

adjusted maximum-likelihood estimation is described by Cohn 

(1988) and Helsel (2005). 

For the flow-duration statistics 90-, 85-, 80-, 75-, 70-, 

60-, 50-, 40-, 30-, 25-, 20-, 15-, 10-, 5-, 2-, and 1-percent, 

the final regression equations were developed by using the 

user-weighted least-squares (WLS) regression technique in the 

weighted-multiple-linear regression (WREG) program (Eng 

and others, 2009). 

The regression analyses determined that drainage area 

(represented by the variable DRNAREA) (mi2) was a significant explanatory variable in all 21 of the regression equations. 

Drainage area generally is the most significant explanatory 

variable in all regional streamflow regression equations, 

whether for low flows, peak flows, mean annual, mean 

monthly, or median monthly statistics. The final regression 

equations for the 21 streamflow statistics are listed in table 11.

Stream density (STRDENED) (mi/mi2), which is the 

total length of streams (mi) divided by the drainage area (mi2), 

also was a significant explanatory variable in all but 3 of the 

21 regression equations. The three streamflow statistics for 

which STRDENED was not significant were the 20-, 15-, and 

10-percent flow durations. Stream density is less commonly 

a significant explanatory variable than drainage area but has 

been used in low-flow regression equations for a region of 

Pennsylvania (Stuckey, 2006), logistic regression equations 

for estimating the probability of a stream flowing perennially 

in Massachusetts (Bent and Archfield, 2002), and peak-flow 

equations for Rhode Island (Zarriello and others, 2012). 

Stream density had a negative coefficient in several 

regression equations for estimating low flows in Pennsylvania 

(Stuckey, 2006) and in the logistic regression equation for 

estimating the probability of streams flowing perennially in 

Massachusetts (Bent and Archfield, 2002). Zarriello and others 

(2012) found stream density to have a positive coefficient in 

the regression equations for estimating peak flows in Rhode 

Island. The coefficient for STRDENED in this study changed 

from negative in the low-flow regression equations to positive in the high-flow equations. For example, the coefficient 

for STRDENED decreased from -2.29 in the equation for 

the 99-percent flow duration to -0.18 in the equation for the 

25-percent flow duration, and then increased from +0.18 at the 

5-percent flow duration to +0.49 at the 1-percent flow duration 

(table 11). At high-flow durations, a greater stream density 

allows runoff to be quickly routed out of the basin (less water 

being available during lower flows) through its larger network 

of flow paths; the increasing streamflow is represented by the 

positive coefficient. STRDENED is not a significant explanatory variable between the 20- and 10-percent flow durations 

because the coefficient is changing from positive to negative; 

as a result, its effect on streamflow is minimal. At low-flow 

durations, a greater stream density in a basin allows base flow 

to be routed out of the basin earlier in the runoff recession 

(less base flow being available during lower flows) through 

its larger network of flow paths intercepting the water table; 

the decreasing streamflow is represented by the negative 

coefficient. 

The standard error of the estimate for the 21 regression 

equations ranged from 17.58 to 141.83 percent (table 11). The 

low-flow statistics—the 99- to 85-percent flow durations and 

7Q2 and 7Q10—had higher standard errors of the estimate, 

ranging from 48.68 to 141.83 percent. The standard error 

of the estimate for the medium- to high-flow statistics—the 

80- to 1-percent flow durations—ranged from 17.58 to 

37.65 percent, with the standard errors for the 60- to 1-percent 

flow durations all being less than about 21 percent. Although 

the standard errors of the estimate are high for the low-flow 

statistics, they are similar to those calculated for regional 

regression equations developed to estimate low-flow statistics 

in Connecticut (Ahearn, 2010) and Massachusetts (Ries 

and Friesz, 2000). Additionally, high standard errors of the 

estimate for low-flow equations are common in statewide 

studies throughout the U.S. The user-WLS regression 
Equations for Estimating Selected Streamflow Statistics 27

Table 11. Summary of regression equations and measures of model accuracy for estimating selected streamflow statistics in 

Rhode Island.

[DRNAREA, drainage area in square miles; STRDENED, drainage density in miles per square mile; WLS, weighted-least-squares regression; WREG, 

weighted-multiple-linear regression (Eng and others, 2009); S+, statistical software program in S programming language (TIBCO Software, Inc., 2008); --, no 

data available]

Streamflow 

statistic

Regression equation

Number 

of 

stations

Standard 

error of the 

estimate 

(base-10 

logarithm)

Standard 

error of the 

estimate 

(percent)

Standard 

error of 

prediction 

(base-10 

logarithm)

Standard 

error of 

prediction 

(percent)

Regression method

Flow duration

1 9.3325(DRNAREA)0.94(STRDENED)0.49 60 0.0909 21.15 0.0915 21.31 User WLS–WREG

2 7.4131(DRNAREA)0.96(STRDENED)0.36 60 0.0820 19.06 0.0827 19.21 User WLS–WREG

5 5.4954(DRNAREA)0.98(STRDENED)0.18 60 0.0840 19.52 0.0846 19.67 User WLS–WREG

10 4.3652(DRNAREA)1.00 60 0.0758 17.58 0.0762 17.67 User WLS–WREG

15 3.4674(DRNAREA)1.01 60 0.0766 17.78 0.0770 17.87 User WLS–WREG

20 2.7542(DRNAREA)1.02 60 0.0785 18.22 0.0789 18.32 User WLS–WREG

25 2.6915(DRNAREA)1.03(STRDENED)-0.18 60 0.0768 17.83 0.0774 17.96 User WLS–WREG

30 2.3442(DRNAREA)1.04(STRDENED)-0.23 60 0.0789 18.31 0.0795 18.45 User WLS–WREG

40 1.8621(DRNAREA)1.05(STRDENED)-0.29 60 0.0778 18.07 0.0784 18.20 User WLS–WREG

50 1.4791(DRNAREA)1.05(STRDENED)-0.39 60 0.0803 18.65 0.0809 18.79 User WLS–WREG

60 1.0715(DRNAREA)1.07(STRDENED)-0.50 60 0.0887 20.65 0.0894 20.80 User WLS–WREG

70 0.6761(DRNAREA)1.13(STRDENED)-0.68 60 0.1080 25.25 0.1088 25.44 User WLS–WREG

75 0.5248(DRNAREA)1.17(STRDENED)-0.84 60 0.1304 30.72 0.1314 30.96 User WLS–WREG

80 0.4074(DRNAREA)1.21(STRDENED)-1.01 60 0.1581 37.65 0.1593 37.95 User WLS–WREG

85 0.2951(DRNAREA)1.26(STRDENED)-1.18 60 0.2003 48.68 0.2025 49.27 User WLS–WREG

90 0.1995(DRNAREA)1.35(STRDENED)-1.48 60 0.2894 74.76 0.2915 75.45 User WLS–WREG

95 0.1006(DRNAREA)1.48(STRDENED)-1.80 60 0.3659 101.67 -- -- Left censored–S+

98 0.0591(DRNAREA)1.58(STRDENED)-2.08 60 0.4018 116.35 -- -- Left censored–S+

99 0.0441(DRNAREA)1.64(STRDENED)-2.29 60 0.4560 141.83 -- -- Left censored–S+

Low-flow frequency

7Q2 0.1104(DRNAREA)1.48(STRDENED)-1.91 60 0.3918 112.10 -- -- Left censored–S+

7Q10 0.0311(DRNAREA)1.71(STRDENED)-2.53 60 0.4537 140.65 -- -- Left censored–S+

technique in the WREG program or in the left-censored 

regression analyses do not calculate the R2

.

A review of areal plots of the residuals (differences 

between streamflow statistics estimated from measured 

streamflow and those estimated from the regression equations) 

for the 7Q10 low-flow frequency and the 95-, 75-, 50-, 25-, 

and 5-percent flow-duration statistics at the 60 streamgages 

did not indicate any strong regional biases (clear groups of 

negative or positive residuals) (figs. 11A–F). Additionally, 

plots of the streamflow statistics estimated from measured 

streamflow (observed data) as functions of the same statistics 

estimated from the regression equations (predicted data) are 

presented in figures 12A–F. For the lower flows (7Q10 and 

95-percent flow duration), the range of the data is clearly 

wider than that for medium and higher flows—for example, 

at the 50-percent flow duration (at which the flow is equal or 

exceeded 50 percent of the time). Again, a wide range between 

observed and predicted data is generally found in all studies to develop regional regression equations for estimating 

low flows; the higher standard errors of the estimate—48.68 

to 141.83 percent—for the 99- to 85-percent flow durations 

and 7Q2 and 7Q10 regression equations also reflect this wide 

range (table 11). In figures 12A and B (7Q10 and 95-percent 

flow durations, respectively), the data for streamflows less 

than 0.10 ft3/s clearly show a wide range. For streamflows 

less than 0.10 ft3

/s there is possibly a small bias towards the 

regression equations, which generated values higher than the 

measured streamflows. In addition, the values for streamflows 

greater than about 50 ft3/s indicate a small amount of bias 

towards the regression equations. In the other plots for the 
28 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320 01119280

01118668

01118500

01118300

01118400

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100

01115098 01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111050

01111225

01109220

01109200

01109090

01109000 01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

1.000 to > 0.3500.350 to > 0.0000.000 to > -0.250-0.250 to -1.100

EXPLANATION

Regression residuals for 7-day,  10-year (7Q10) low-flow frequency,  in base-10 logarithms

Figure 11. The residuals between measured streamflows and streamflows calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term streamgages in and near Rhode Island.

A
Equations for Estimating Selected Streamflow Statistics 29 Rhode Island Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320 01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117370

01117424

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100 01115098

01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111225

01111050

01109220

01109200

01109090

01109000 01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

0.650 to > 0.2500.250 to > 0.0000.000 to > -0.200-0.200 to -1.200

EXPLANATION

Regression residuals for 

95-percent flow duration,in base-10 logarithms

Figure 11. The residuals between measured streamflows and streamflows calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term streamgages in and near Rhode Island.—Continued

B
30 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320

01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117370

01117424

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100 01115098 01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111050

01111225

01109220

01109200

01109090

01109000 01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

0.250 to > 0.1000.100 to > 0.0000.000 to > -0.100-0.100 to -0.350

EXPLANATION

Regression residuals for

75-percent flow duration in base-10 logarithms

Figure 11. The residuals between measured streamflows and streamflows calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term streamgages in and near Rhode Island.—Continued

C
Equations for Estimating Selected Streamflow Statistics 31 Rhode Island Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320 01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100

01115098

01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111225

01111050

01109220

01109200

01109090

01109000

01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

0.200 to > 0.0500.050 to > 0.0000.000 to > -0.050-0.050 to -0.350

EXPLANATION

Regression residuals for 50-percent flow duration, in base-10 logarithms

Figure 11. The residuals between measured streamflows and streamflows calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term streamgages in and near Rhode Island.—Continued

D
32 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Rhode Island

Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320 01119280

01118668

01118500

01118400

01118300

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100

01115098 01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111225

01111050

01109220

01109200

01109090

01109000 01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

EXPLANATION

0.150 to > 0.0500.050 to > 0.0000.000 to > -0.050-0.050 to -0.400

Regression residuals for

25-percent flow duration,in base-10 logarithms

Figure 11. The residuals between measured streamflows and streamflows calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term streamgages in and near Rhode Island.—Continued

E
Equations for Estimating Selected Streamflow Statistics 33 Rhode Island Sound

Cape Cod

Bay 

Buzzards

Bay

00 10

20 MILES

20 KILOMETERS

10 Base from U.S. Geological Survey digital data, 1:25,000

Rhode Island State Plane Coordinate System. 1983 North American Datum

01175670

01126950

01126600

01126500

01126200

01126000

01125600

01125490

01125415

01124750

01123000

01121000

01120500

01120000

01119320 01119280

01118668

01118500

01118300

01118400

01118010

01118000

01117800

01117600

01117500 01117472

01117468

01117430

01117424

01117370

01116905

01116300

01115900

01115770

01115670

01115630

01115187

01115100 01115098 01114500

01114000

01113695

01112700

01111500

01111400

01111300

01111225

01111050

01109220

01109200

01109090

01109000 01108000

01107000

01106000

01105730

01105600

01103220

01118360

01117410

71°00' 71°30' 72°00'

42°00'41°30'

M A S S A C H U S E T T S

RHODEISLAND

CONNECTICUT

0.300 to > 0.0500.050 to > 0.0000.000 to > -0.050-0.050 to -0.400

EXPLANATION

Regression residuals for 5-percent flow duration, in base-10 logarithms 

Figure 11. The residuals between measured streamflows and streamflows calculated by regression equations for the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations for long-term and short-term streamgages in and near Rhode Island.—Continued

F
34 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Figure 12. Comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations estimated 

from measured streamflow and regression equations for long-term and short-term streamgages in and near Rhode Island.

A

0.001

0.01

0.1

1

10

100

1,000

0.001 0.01 0.1 1 10 100 1,000

Streamflow estimated from regression equation, in cubic feet per second

Streamflow estimated from measured streamflow, in cubic feet per second

7-day 10-year low flow (7Q10)

EXPLANATION
Equations for Estimating Selected Streamflow Statistics 35

0.001

0.01

0.1

1

10

100

1,000

0.001 0.01 0.1 1 10 100 1,000

Streamflow estimated from regression equation, in cubic feet per second

Streamflow estimated from measured streamflow, in cubic feet per second 

EXPLANATION

95-percent flow duration

B

Figure 12. Comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations estimated 

from measured streamflow and regression equations for long-term and short-term streamgages in and near Rhode Island.—Continued
36 Equations for Estimating Selected Streamflow Statistics in Rhode Island

0.1

1

10

100

1,000

0.1 1 10 100 1,000

Streamflow estimated from regression equation, in cubic feet per second

Streamflow estimated from measured streamflow, in cubic feet per second 

EXPLANATION

75-percent flow duration

C

Figure 12. Comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations estimated 

from measured streamflow and regression equations for long-term and short-term streamgages in and near Rhode Island.—Continued
Equations for Estimating Selected Streamflow Statistics 37

0.1

1

10

100

1,000

0.1 1 10 100 1,000

Streamflow estimated from regression equation, in cubic feet per second

Streamflow estimated from measured streamflow, in cubic feet per second

EXPLANATION

50-percent flow duration

D

Figure 12. Comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations estimated 

from measured streamflow and regression equations for long-term and short-term streamgages in and near Rhode Island.—Continued
38 Equations for Estimating Selected Streamflow Statistics in Rhode Island

1

10

100

1,000

10,000

1 10 100 1,000 10,000

Streamflow estimated from regression equations, in cubic feet per second

Streamflow estimated from measured streamflow, in cubic feet per second

EXPLANATION

25-percent flow duration

E

Figure 12. Comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations estimated 

from measured streamflow and regression equations for long-term and short-term streamgages in and near Rhode Island.—Continued
Equations for Estimating Selected Streamflow Statistics 39

1

10

100

1,000

10,000

1 10 100 1,000 10,000

Streamflow estimated from regression equation, in cubic feet per second

Streamflow estimated from measured streamflow, in cubic feet per second

EXPLANATION

5-percent flow duration

F

Figure 12. Comparisons of the A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, E, 25-, and F, 5-percent flow durations estimated 

from measured streamflow and regression equations for long-term and short-term streamgages in and near Rhode Island.—Continued
40 Equations for Estimating Selected Streamflow Statistics in Rhode Island

75-, 50-, 25-, and 5-percent flow durations (figs. 12C–F), no 

clear bias of the streamflow values generated by regression 

equations with respect to measured streamflows is evident. 

Maps showing the residuals between measured streamflows 

and streamflows calculated by regression equations for the 

A, 7Q10 low-flow frequency, and B, 95-, C, 75-, D, 50-, 

E, 25-, and F, 5-percent flow durations for long-term and 

short-term streamgages in and near Rhode Island.

Prediction Intervals

Prediction intervals indicate the uncertainty inherent 

in use of the equations. At the 90-percent confidence level, 

prediction intervals can be calculated for estimates obtained 

from the regression equations. The assurance is 90 percent 

that the true value of the streamflow statistic for an ungaged 

site will be within the prediction interval. The lower and 

upper boundaries of the 90-percent prediction intervals can be 

computed by 

( ) LPI UPI

Q Q Q QT Q T

  = ≤≤ × =     , (7)

where

Q is the estimated streamflow statistic for the 

site,

QLPI is the estimated lower boundary of the 

90-percent prediction interval,

QUPI is the estimated boundary of the upper 

90-percent prediction interval, and

T is the 90-percent prediction interval 

determined from equation 8 below.

( /2, ) 10 n p i t S

T  −   ×   = (8)

where

t

(α/2,n–p) is the critical value from the student’s t

distribution,

α is the alpha level (α = 0.10 for 90-percent 

prediction intervals),

	 n–p is the number of degrees of freedom with n

data values (for 60 streamgages) used in 

the regression analysis,

p is the number of parameters in the equation 

(equal to the number of explanatory 

variables or basin characteristics plus one), 

and

Si is computed from equation 9 below.

Critical values from the student’s t distribution are listed 

in many introductory statistics textbooks.

The value of Si is computed using the equation

( ) 0.5 2 '

i ii S xUx = + ××   

  (9)

where

γ2 is the model-error variance (equal to the root 

mean square error (RMSE) squared),

xi is a row vector of the logarithms of the basin 

characteristics for site i which has been 

augmented by a 1 as the first element,

U is the covariance matrix for the regression 

coefficients, and

xi' is the transpose of xi (Ludwig and Tasker, 

1993).

The values of t

(α/2,n–p) and U needed for equations 8 and 9 

for the 21 regression equations are presented in table 12. The 

values of γ2 needed in equation 9 can be calculated by squaring the value of the user-weighted WLS–RMSE or the leftcensored regression-RMSE (base-10 logarithm) in table 12. 

Example Computations

Two example computations of selected regression 

equations and the 90-percent prediction intervals of the 

estimates are provided. The first computation is provided for 

Dunderry Brook at Meetinghouse Lane at Little Compton, 

R.I. (01106110) (fig. 8 and table 4, in back of report). The 

values of the explanatory variables used in the regression 

equation for the 90-percent flow duration (table 11) were a 

drainage area (DRNAREA) of 1.26 mi2 (x1) and a stream 

density (STRDENED) of 2.96 mi/mi2 (x2) (table 9). Substituting the values in the equation for the 95-percent flow duration 

produces

Q90 = 0.1995 × (1.26 mi2)1.35 × (2.96 mi/mi2)-1.48 = 0.055 ft3/s.

Calculation of the 90-percent prediction intervals use 

equations 7–9. The calculation starts with equation 9, then 

goes to equation 8, and then equation 7. Data needed for equations 8 and 9 are in table 12. 

For equation 9 the model error variance, γ2, equals the 

user-weighted WLS–RMSE (base-10 logarithm) (table 12) 

squared, γ2 = (0.2894)2 = 0.0838, and U also comes from 

table 12.
Equations for Estimating Selected Streamflow Statistics 41

' 22

2

 = (((1 × 0.225593836) + ((log10 (1.26 mi )) × -0.070349579) + ((log10 (2.96 mi/mi ))

 × -0.395675480)) × 1) + (((1 × -0.070349579) + ((log10 (1.26 mi )) × 0.0531

i i x Ux × ×

2 2

2

12461)

 + ((log10 (2.96 mi/mi )) × 0.021187091)) × (log10 (1.26 mi ))) + (((1 × -0.395675480)

 + ((log10 (1.26 mi )) × 0.021187091) + ((log10 (2.96 2

2

mi/mi )) × 1.175994738)) 

 × ((log10 (2.96 mi/mi ))

' = (((0.2256) + (-0.0071) + (-0.1865)) × 1) + (((-0.0703) + (0.0053) + (0.0010)) × 0.1004) 

 + (((-0.3957) + (0.0021) + (0.5542)) × 0.4713))

i i x Ux × ×

( ) ( ) ( ) ' 0.0320 1 0.0640 0.1004 0.1606 0.4713 i i xUx × × = × +− × + ×

( ) ( ) ( ) ' 0.0320 0.0064 0.0757 0.1013 i i xUx × × = +− + =

( ) 0.5 2 ' i ii S xUx = + ×× =   

  [0.0838 + 0.1013]0.5 = [0.1851]0.5 = 0.4302

 0.225593836 0.070349579 0.395675480

0.070349579 0.053112461 0.021187091

0.395675480 0.021187091 1 .175994738

U

  − −

  = −

  −

For equation 8, the value of t from the student’s t distribution 

= t

(0.10/2, 60-3) = 1.672 (table 12).

( /2, ) [ × ] 10 np i t S T ∝ − = = 10[1.672 × 0.4302] = 10[0.7193] = 5.2396

For equation 7,

QLPI = Q90/T = 0.055/5.2396 = 0.010 ft3/s

QUPI = Q90 × T = 0.055 × 5.2396 = 0.288 ft3/s

QLPI ≤ Q90 ≤ QUPI = 0.010 ft3/s ≤ 0.055 ft3/s ≤ 0.288 ft3/s.

The second example computation is provided for 

Fisherville Brook at Liberty Church Rd. near Exeter, R.I. 

(01117360) (fig. 8 and table 4, in back of report). The values 

of the explanatory variables used in the regression equation 

for the 7Q10 low-flow frequency (table 11) were a drainage area (DRNAREA) of 8.09 mi2

 (x1) and a stream density 

(STRDENED) of 1.51 mi/mi2 (x2) (table 9). Substituting 

the values in the equation for the 7Q10 low-flow frequency 

produces

Q7Q10 = 0.0311 × (8.09 mi2)1.71 × (1.51 mi/mi2)-2.53 = 0.391 ft3/s

The calculation starts with equation 9, then goes to equation 8, and then equation 7. Data needed for equations 8 and 9 

are in table 12. 

For equation 9 the model error variance, γ2, equals the 

left-censored regression-RMSE (base-10 logarithm) (table 12) 

squared, γ2 = (0.4853)2 = 0.2355, and U also comes from 

table 12. 
42 Equations for Estimating Selected Streamflow Statistics in Rhode Island

'22

2

 = (((1 × 0.225593836) + ((log10 (8.09 mi )) × -0.070349579) + ((log10 (1.51 mi/ mi ))

 × -0.395675480)) × 1) + (((1 × -0.070349579) + ((log10 (8.09 mi )) × 0.05

i i x Ux × ×

2 2

2

3112461)

 + ((log10 (1.51 mi/mi )) × 0.021187091)) × (log10 (8.09 mi ))) + (((1 × -0.395675480)

 + ((log10 (8.09 mi )) × 0.021187091) + ((log10 (1.5 2

2

1 mi/mi )) × 1.175994738)) 

 × ((log10 (1.51 mi/mi ))

'

 = (((0.2256) + (-0.0639) + (-0.0708)) × 1) + (((-0.0703) + (0.0482) + (0.0038)) × 0.9079)

 + (((-0.3957) + (0.0192) + (0.2105)) × 0.1790))

i i xUx × ×

( ) ( ) ( ) ' 0.0909 1 0.0183 0.9079 0.1660 0.1790 i i xUx × × = × +− × +− ×

( ) ( ) ( ) ' 0.0909 0.0166 0.0297 0.0446 i i xUx × × = +− +− =

( ) 0.5 2 ' i ii S xUx = + ×× =   

  [0.2355 + 0.0446]0.5 = [0.2801]0.5 = 0.5292

 0.225593836 0.070349579 0.395675480

0.070349579 0.053112461 0.021187091

0.395675480 0.021187091 1 .175994738

U

  − −

  = −

  −

The value of t from the student’s t distribution = t

(0.10/2, 60-3) = 

1.672 (table 12).

( /2, ) [ × ] 10 np i t S T ∝ − = = 10[1.672 × 0.5292] = 10[0.8848] = 7.6701

For equation 7,

QLPI = Q90/T = 0.391/7.6701= 0.051 ft3

/s

QUPI = Q90 × T = 0.391 × 7.6701 = 3.00 ft3

/s

QLPI ≤ Q7Q10 ≤ QUPI = 0.051 ft3

/s ≤ 0.391 ft3/s ≤ 3.00 ft3/s.

Limitations of Regression Equations

Use of the regression equations presented in this report 

in determining selected streamflow statistics is limited by the 

range of the basin-characteristics data used to develop the 

equations and by the accuracy of the estimates. These equations should not be used for the determination of streamflow 

statistics at ungaged sites for which the basin characteristics 

are outside the range of those used to develop the regression 

equations. The ranges of the basin-characteristics data used 

as explanatory variables to develop the flow-duration and 

low-flow-frequency regression equations are listed in table 13, 

and the corresponding accuracies of the estimates calculated 

by these equations are in table 11. The use of these regression 

equations requires that the physical and climatic basin characteristics be determined in a GIS based on the same datasets 

(table 13) that were used to develop the equations outlined in 

this report.

The equations, which are based on data from streams 

with little to no flow alteration, will give estimates only 

of the natural flows for a selected site. They will not give 

estimates of altered flow for sites where the flow is affected 

by structures and artificial processes such as dams, surfacewater withdrawals, groundwater withdrawals (pumping wells), 

diversions, and wastewater discharges. To apply the equations 

to streamflow data for such sites, the user should adjust the 

estimates for the alterations accordingly. The equations are 

not applicable in areas of Rhode Island where groundwater 

contributing areas and surface-water drainage areas to stream 

sites differ appreciably. In these areas, groundwater can flow 

from one surface-water drainage area into another; therefore, 

for basins whose groundwater contributing areas are larger 

than their surface-water drainage areas, the equations would 

likely underestimate streamflows. Conversely, for areas 

whose groundwater-contributing areas are smaller than their 

surface-water drainage areas, the equation would likely 

overestimate streamflows. Several areas in Rhode Island 

where groundwater contributing areas and surface-water 

drainage areas to stream sites differ appreciably include 

Queens Fort Brook in the Usquepaug-Queen River Basin 

(Allen and others, 1966; Dickerman and others, 1997; Barlow 

and Dickerman, 2001; Granato and others, 2003; Zarriello 

and Bent, 2004; and Bent and others, 2011), Mishnock River 

and Old Hickory Brook in the Big River Basin (Granato and 

others, 2003; and Granato and Barlow, 2005), several coastal 

rivers in the Hunt-Annaquatuck-Pettaquamscutt River Basin 

(Rosenshein and others, 1968; Barlow and Dickerman, 2001; 
Equations for Estimating Selected Streamflow Statistics 43

Table 12. Information needed for calculating the 90-percent prediction intervals for estimates of selected statistics calculated by regression equations for streamflows in 

Rhode Island.

[Flow duration is percentage of time that streamflow was equaled or exceeded. p, number of parameters is equal to the number of explanatory variables plus one; t, student’s t distribution; WLS, weighted-leastsquares regression; RMSE, root mean square error; MSE, mean square error; U, covariance matrix for the regression coefficients. DRNAREA, drainage area in square miles; STRDENED, drainage density in miles per square mile; --, none; 7Q2, the annual minimum average streamflow for 7 consecutive days that has a 0.50 probability of not being exceeded in a given year; 7Q10, the annual minimum average streamflow for 7 consecutive days that has a 0.10 probability of not being exceeded in a given year]

Streamflow 

statistic type

Streamflow 

statistic

Regression equation

Number of 

stations

Number of 

explanatory 

variables

p alpha t

Userweighted WLS–

MSE 

(percent)

Userweighted 

WLS–

RMSE

(base-10 

logarithm)

Leftcensored 

regression–

MSE 

(percent)

Leftcensored 

regression–

RMSE

(base-10 

logarithm)

U

Flow duration 1 9.3325(DRNAREA)0.94(STRDENED)0.49 60 2 3 0.10 1.672 21.15 0.0909 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 2 7.4131(DRNAREA)0.96(STRDENED)0.36 60 2 3 0.10 1.672 19.06 0.0820 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 5 5.4954(DRNAREA)0.98(STRDENED)0.18 60 2 3 0.10 1.672 19.52 0.0840 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 10 4.3652(DRNAREA)1.00 60 1 2 0.10 1.6715 17.58 0.0758 -- -- 0.092464766 -0.063220965

-0.063220965 0.052730748

Flow duration 15 3.4674(DRNAREA)1.01 60 1 2 0.10 1.6715 17.78 0.0766 -- -- 0.092464766 -0.063220965

-0.063220965 0.052730748

Flow duration 20 2.7542(DRNAREA)1.02 60 1 2 0.10 1.6715 18.22 0.0785 -- -- 0.092464766 -0.063220965

-0.063220965 0.052730748

Flow duration 25 2.6915(DRNAREA)1.03(STRDENED)-0.18 60 2 3 0.10 1.672 17.83 0.0768 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 30 2.3442(DRNAREA)1.04(STRDENED)-0.23 60 2 3 0.10 1.672 18.31 0.0789 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738
44 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 12. Information needed for calculating the 90-percent prediction intervals for estimates of selected statistics calculated by regression equations for streamflows in Rhode Island.—Continued [Flow duration is percentage of time that streamflow was equaled or exceeded. p, number of parameters is equal to the number of explanatory variables plus one; t, student’s t distribution; WLS, weighted-least- squares regression; RMSE, root mean square error; MSE, mean square error; U, covariance matrix for the regression coefficients. DRNAREA, drainage area in square miles; STRDENED, drainage density in miles per square mile; --, none; 7Q2, the annual minimum average streamflow for 7 consecutive days that has a 0.50 probability of not being exceeded in a given year; 7Q10, the annual minimum average stream- flow for 7 consecutive days that has a 0.10 probability of not being exceeded in a given year] Streamflow statistic type Stream- flow statistic Regression equation Num- ber of sta- tions Num- ber of explan- atory vari- ables p alpha t User- weight- ed WLS– MSE (percent) User- weighted WLS– RMSE (base-10 loga- rithm) Left- censored regres- sion– MSE (percent) Left- censored regres- sion– RMSE (base-10 logarithm) U Flow duration 40 1.8621(DRNAREA)1.05(STRDENED)-0.29 60 2 3 0.10 1.672 18.07 0.0778 -- -- 0.225593836 -0.070349579 -0.395675480 -0.070349579 0.053112461 0.021187091 -0.395675480 0.021187091 1.175994738 Flow duration 50 1.4791(DRNAREA)1.05(STRDENED)-0.39 60 2 3 0.10 1.672 18.65 0.0803 -- -- 0.225593836 -0.070349579 -0.395675480 -0.070349579 0.053112461 0.021187091 -0.395675480 0.021187091 1.175994738 Flow duration 60 1.0715(DRNAREA)1.07(STRDENED)-0.50 60 2 3 0.10 1.672 20.65 0.0887 -- -- 0.225593836 -0.070349579 -0.395675480 -0.070349579 0.053112461 0.021187091 -0.395675480 0.021187091 1.175994738 Flow duration 70 0.6761(DRNAREA)1.13(STRDENED)-0.68 60 2 3 0.10 1.672 25.25 0.1080 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 75 0.5248(DRNAREA)1.17(STRDENED)-0.84 60 2 3 0.10 1.672 30.72 0.1304 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 80 0.4074(DRNAREA)1.21(STRDENED)-1.01 60 2 3 0.10 1.672 37.65 0.1581 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 85 0.2951(DRNAREA)1.26(STRDENED)-1.18 60 2 3 0.10 1.672 48.86 0.2009 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738
Equations for Estimating Selected Streamflow Statistics 45

Table 12. Information needed for calculating the 90-percent prediction intervals for estimates of selected statistics calculated by regression equations for streamflows in 

Rhode Island.—Continued

[Flow duration is percentage of time that streamflow was equaled or exceeded. p, number of parameters is equal to the number of explanatory variables plus one; t, student’s t distribution; WLS, weighted-leastsquares regression; RMSE, root mean square error; MSE, mean square error; U, covariance matrix for the regression coefficients. DRNAREA, drainage area in square miles; STRDENED, drainage density in miles per square mile; --, none; 7Q2, the annual minimum average streamflow for 7 consecutive days that has a 0.50 probability of not being exceeded in a given year; 7Q10, the annual minimum average streamflow for 7 consecutive days that has a 0.10 probability of not being exceeded in a given year]

Streamflow 

statistic type

Streamflow 

statistic

Regression equation

Number of 

stations

Number of 

explanatory 

variables

p alpha t

Userweighted WLS–

MSE 

(percent)

Userweighted 

WLS–

RMSE

(base-10 

logarithm)

Leftcensored 

regression–

MSE 

(percent)

Leftcensored 

regression–

RMSE

(base-10 

logarithm)

U

Flow duration 90 0.1995(DRNAREA)1.35(STRDENED)-1.48 60 2 3 0.10 1.672 74.76 0.2894 -- -- 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 95 0.1006(DRNAREA)1.48(STRDENED)-1.80 60 2 3 0.10 1.672 -- -- 101.67 0.3659 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 98 0.0591(DRNAREA)1.58(STRDENED)-2.08 60 2 3 0.10 1.672 -- -- 116.35 0.4018 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Flow duration 99 0.0441(DRNAREA)1.64(STRDENED)-2.29 60 2 3 0.10 1.672 -- -- 141.83 0.4560 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Low-flow 

frequency

7Q2 0.1104(DRNAREA)1.48(STRDENED)-1.91 60 2 3 0.10 1.672 -- -- 88.75 0.3310 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738

Low-flow 

frequency

7Q10 0.0311(DRNAREA)1.71(STRDENED)-2.53 60 2 3 0.10 1.672 -- -- 157.66 0.4853 0.225593836 -0.070349579 -0.395675480

-0.070349579 0.053112461 0.021187091-0.395675480 0.021187091 1.175994738
46 Equations for Estimating Selected Streamflow Statistics in Rhode Island

Table 13. Range of basin characteristics used as explanatory 

variables in the regression equations for estimating selected 

streamflow statistics in Rhode Island.

[DRNAREA, drainage area; STRDENED, drainage density; mi2, square 

miles; mi/mi2, miles per square mile]

Explanatory variable Minimum 

value

Maximum 

value

Drainage area (DRNAREA) (mi2

) 0.52 294

Drainage density (STRDENED) (mi/mi2

) 0.94 3.49

and Barlow and Ostiguy, 2007), and the South Coastal Basin 

(Friesz, 2004; Masterson and others, 2007; and Friesz, 2010). 

The regression equations are not applicable to other areas of 

Rhode Island having known appreciable differences between 

surface-water drainage areas and groundwater contributing 

areas. Additionally, the equation is not applicable to streams 

with losing reaches. Losing streams are defined as streams 

or stream reaches that lose water to the groundwater system 

(Winter and others, 1998, p. 9–10 and 16–17). Generally, 

a stream reach is losing where the groundwater table does 

not intersect the streambed in the channel (the water table is 

below the streambed) during low-flow periods. Losing stream 

reaches commonly begin where the stream flows from an area 

of the basin underlain by till or bedrock onto an area underlain 

by stratified deposits (where hillsides meet river valleys). 

At such junctures, a stream can lose a substantial amount of 

water through its streambed. The accuracies of the regression 

equations are functions of the quality of the data used in to 

develop the equations. These data include the streamflow 

data used to estimate the statistics, information about possible 

unknown flow alterations to the stream above a site, and the 

measured basin characteristics. Basin characteristics used in 

the development of the regression equations are limited by 

the accuracy of the digital data layers available and used at 

the time (2014) of this study. In the future, geospatial data 

layers of basin characteristics (table 7) likely will be more 

detailed and accurate and at higher resolution, for stream 

networks from the USGS NHD (http://nhd.usgs.gov/); 

elevation from USGS NED (http://ned.usgs.gov/); land cover, 

land use, and surficial geology from RIGIS (http://www.edc.

uri.edu/rigis/default.html), MassGIS (http://www.mass.gov/

anf/research-and-tech/it-serv-and-support/application-serv/

office-of-geographic-information-massgis/), MAGIC (http://

magic.lib.uconn.edu/), and University of Connecticut CLEAR 

(http://clear.uconn.edu/projects/landscape/); soils from NRCS 

SSURGO (http://soils.usda.gov/survey/geography/ssurgo/); 

and climate from the PRISM Climate Group, Oregon State 

University (http://www.prism.oregonstate.edu/).

StreamStats Application and Considerations for 

Additional Study

The USGS National StreamStats Web-based application 

(at http://water.usgs.gov/osw/streamstats/; Ries, 2007, and 

Turnipseed and Ries, 2007) includes a map-based interface 

that allows a user to click on the centerline for any stream site, 

which causes the application to calculate selected streamflow 

statistics and the 90-percent prediction intervals from the 

equations for that ungaged stream site. The application also 

provides the user with the basin-characteristic values that 

were used to calculate the regression equations. The regression equations’ basin-characteristic values for a user-selected 

stream site are determined by the use of digital map data from 

ArcGIS (geographic information system software from the 

Environmental Systems Research Institute, Inc. (Esri) 

(http://www.esri.com/)). The output includes a map of the 

drainage-basin boundary determined for the stream site, the 

values of the GIS-measured basin characteristics, the estimated streamflow statistics, and prediction intervals for the 

estimates. The user can also click on streamgage and partialrecord station symbols and be provided selected streamflow 

statistics and basin characteristics from a database for that site.

As considerations for additional study, the 21 selected 

regression equations for streamflow statistics (table 11), 

as well as the 90-percent prediction intervals, could be 

incorporated into the USGS National StreamStats Web-based 

application. The at-site estimates of the selected streamflow 

statistics at the long- and short-term streamgages and 

partial-record stations could also be put into the StreamStats 

database for retrieval. Another consideration is that new basin 

characteristics that were not available for this study could be 

tested as potential explanatory variables. These digital data 

layers likely would improve the accuracy of the measured 

basin characteristics used as explanatory variables to estimate 

selected streamflow statistics in Rhode Island but only after 

re-examination of the regression equations.

Summary and Conclusions

The equations for estimating selected streamflow statistics may be used by Federal, State, and local water managers 

in addressing numerous water issues. This report documents 

the development of regression equations by the U.S. Geological Survey (USGS), in cooperation with the Rhode Island 

Water Resources Board, that can be used statewide for determining selected statistics for streamflows unaffected by alterations at ungaged sites in Rhode Island. Multiple and simple 

linear regression equations were developed to estimate the 99-, 

98-, 95-, 90-, 85-, 80-, 75-, 70-, 60-, 50-, 40-, 30-, 25-, 20-, 

15-, 10-, 5-, 2-, and 1-percent flow durations and the frequency 

statistics 7Q2 (7-day, 2-year) and 7Q10 (7-day, 10-year). An 

additional 49 selected statistics also were estimated for longand short-term streamgages and partial-record stations for flow 
References Cited 47

durations between the 99.99 and 0.01 percent, and the mean 

annual, mean monthly, and median monthly streamflows. Data 

also are provided to allow the user to calculate the 90-percent 

prediction intervals for the 21 streamflow statistics.

A total of 70 selected streamflow statistics were determined for 41 long-term streamgages (with 8 or more water 

and climatic years of record), 21 short-term streamgages (with 

1 to 7 water and climatic years of record), and 135 partialrecord stations (with more than 11 miscellaneous streamflow 

measurements) in Rhode Island, eastern Connecticut, and 

southeastern and south-central Massachusetts. Estimates of the 

long-term streamflow statistics for 21 short-term streamgages 

and 135 partial-record stations were developed by using 

the Maintenance of Variance Extension, type 1 (MOVE.1), 

technique. This technique involved fitting the MOVE.1 equation for daily mean streamflows at short-term streamgages 

and miscellaneous streamflow measurements at partial-record 

stations to concurrent daily mean streamflows at the 16 index 

streamgages. In general, the index streamgage which provided 

the relation with the highest Pearson’s correlation coefficient 

(r) and the most linear plot of the data was selected.

The regression analyses for developing equations to 

estimate selected streamflow statistics related the 19 flowduration and 2 low-flow frequency statistics to 31 different 

drainage-basin characteristics (physical, land-cover, and 

climatic characteristics) for 41 long-term and 19 of 21 shortterm streamgages (60 total streamgages) in Rhode Island 

and nearby in Connecticut and Massachusetts. Two of the 

21 short-term streamgages were excluded from the regression 

analyses because the period of record for another streamgage 

nearby on the same river was longer; this longer record was 

used in the analyses. In addition, the drainage areas and basin 

characteristics of the two streamgages were similar. Use of the 

streamflow records, drainage areas, and basin characteristics 

for both sites would have produced redundant data points in 

the regression analyses. The 135 partial-record stations were 

not used in the regression analyses. 

A user-weighted least-squares (WLS) regression technique in the weighted-multiple-linear regression (WREG) 

program was used in the regression analyses for the 90- to 

1-percent flow durations. Left-censored regression analyses 

were used to account for zero flows at the 99- and 98-percent 

and 7Q10 flow durations (for four streamgages) and at the 

95-percent and 7Q2 flow durations (for two streamgages). 

Coefficients of determination (R2) are not determined when 

the user-WLS regression technique is used in WREG or in the 

left-censored regression analyses. 

The regression analyses determined that the basin characteristics drainage area (DRNAREA) and stream density (total 

length of streams divided by the drainage area) (STRDENED) 

were the only significant explanatory variables for 16 of the 

19 flow-duration and the 2 low-flow-frequency regression 

equations. For the other three flow-duration (10-, 15-, and 

20-percent) equations, drainage area was the only significant 

explanatory variable. 

The standard error of the estimate for the 21 regression 

equations ranged from 17.58 to 141.83 percent. The low-flow 

statistics for the 99- to 85-percent flow durations and 7Q2 and 

7Q10 had the highest standard errors of the estimate, ranging from 48.68 to 141.83 percent. The standard error of the 

estimate for the medium- to high-flow statistics—the 80- to 

1-percent flow durations—ranged from 17.58 to 37.65 percent, 

with the standard errors for the 60- to 1-percent flow durations 

all being less than about 21 percent. 

The equations, which are based on data from streams 

with little to no flow alteration, will give an estimate of only 

the natural flows at a selected site. They will not give an estimate of altered flows at a site where the streamflow is affected 

by structures and artificial processes such as dams, surfacewater withdrawals, groundwater withdrawals (pumping wells), 

diversions, and wastewater discharges. If the equations are 

used to estimate statistics for sites where streamflow has been 

altered, the user should adjust the estimates accordingly. The 

regression equations should be used only for ungaged sites 

with drainage areas between 0.52 and 294 square miles (mi2)

and stream densities between 0.94 and 3.49 miles per square 

miles (mi/mi2). The equations are not applicable (1) for Block 

Island because there are no streams on the island, (2) in areas 

where groundwater-contributing areas and surface-water 

drainage areas to stream sites differ appreciably, and (3) for 

losing stream reaches where the stream may flow from of a till 

and bedrock hillside into a sand and gravel river valley.

As considerations for additional study, the 21 regression 

equations developed for this study, as well as the 90-percent 

prediction intervals of the estimate, could be added to the 

USGS National StreamStats Web-based application 

(http://water.usgs.gov/osw/streamstats/). The 21 selected 

streamflow statistics, plus the additional statistics: 24 flow 

durations between the 99.99 and 0.01 percent, mean annual 

flow, and 12 mean and median monthly flows estimated for the 

long- and short-term streamgages and partial-record stations 

also could be incorporated into the StreamStats database.

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Tables 4, 5
54 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 4. Description of partial-record stations in and near Rhode Island. [Station no.: locations of partial-record stations shown by number in figure 8. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; p, present; --, none; NWIS, National Water Information System] Sta- tion no. USGS station no. Station name Latitude (decimal degrees) Longitude (decimal degrees) Drain- age area (mi2

)

1

Water years with 

streamflow measurements

Number of 

streamflow 

measurements 

through water 

year 2006

Remarks

1 01105928 Buttonwood Brook near South Dartmouth, MA 41.60427 -70.95559 3.00 1972–74, 1992, and 

2003

15 --

2 01105930 Paskamanset River at Turner Pond near New Bedford, MA 41.67871 -70.97726 8.14 1991–93 and 2003 26 --3 01105935 Destruction Brook near South Dartmouth, MA 41.57233 -71.01254 2.70 1972–74, 1991–93, 

and 2003

30 --

4 01105937 Shingle Island River near North Dartmouth, MA 41.68205 -71.01754 8.55 1957, 1972–74, 

1991–93, 1995–96, and 2003

34 --

5 01105950 Kirby Brook near Head of Westport, MA 41.60066 -71.07310 3.71 1965, 1972–74, 1992, 

and 2003

16 --

6 01106005 Angeline Brook near Head of Westport, MA 41.55149 -71.10504 3.27 1972–74, 1992, and 

2003

16 --

7 01106110 Dundery Brook, Meetinghouse Lane at Little Compton, RI 41.50733 -71.17949 1.26 2004 14 --8 01106130 Little Creek, Green End Avenue, near Whitehall, RI 41.50927 -71.24505 1.42 2004 14 --9 01106150 Bailey Brook, Forest Avenue, near Middletown, RI 41.52982 -71.29116 1.28 2004 14 --

10 01107400 Fall Brook near Middleborough, MA 41.86538 -70.90837 9.21 1966–68, 1978–81, 

and 1983

36 --

11 01109087 Assonet River at Assonet, MA 41.79927 -71.05977 20.7 1986–88 and 1990–91 22 --

12 01109135 Cole River near Swansea, MA 41.77510 -71.19866 7.74 1986–88, 1996, and 

2003

22 --

13 01109185 East Branch Palmer River near Rehoboth, MA 41.86010 -71.22922 5.17 1992–94 and 2003 13 --14 01109225 Rocky Run near Rehoboth, MA 41.78121 -71.25033 7.24 1972–74, 1979–81, 

1983, 1986–88, and 1994–96

42 --

15 01109270 Runnings River at Seekonk, MA 41.82371 -71.33283 4.12 1972–74, 1982–83, 

1992, and 2003

20 --

16 01109280 Runnings River, Fall River Avenue, at Seekonk, MA 41.81649 -71.33561 5.88 1986–88 17 --17 01109290 Annawamscutt Brook, Rt. 103, at Peck Corner, RI 41.75955 -71.34311 1.14 2004 14 --18 01109381 Speedway Brook at Attleboro, MA 41.92704 -71.28505 2.86 1992–94, and 2003 13 --19 01111261 Clear River at North Road at Laurel Hill, RI 41.96704 -71.70868 12.5 1993–95, and 2003 16 --20 01111330 Clear River at Oakland, RI 41.95677 -71.64923 45.4 1993–94, and 2003 16 --21 01111470 Tarklin Brook at Oak Valley, RI 41.96871 -71.60034 9.25 1993–94 and 2002–03 18 --22 01112190 Muddy Brook at South Milford, MA 42.09315 -71.51923 6.23 1978, 1985–86, 

1994–97, and 2003

21 --

23 01113670 Burnt Swamp Brook near Grants Mills, RI 42.01399 -71.38978 4.67 1986, 1993–94, and 

2003

17 --

24 01113710 Ash Swamp Brook at Nate Whipple Highway at Diamond Hill, RI 41.98260 -71.41200 4.27 1993–97 26 --25 01114400 Stillwater River at Pleasant View Road at Spragueville, RI 41.88510 -71.53312 12.8 1993–94 and 2003 16 Occasional flow alteration by 

upstream reservoir
Table 4 55

Table 4. Description of partial-record stations in and near Rhode Island.—Continued[Station no.: locations of partial-record stations shown by number in figure 8. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; 

p, present; --, none; NWIS, National Water Information System]

Station 

no.

USGS 

station 

no.

Station name

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Drainage area 

(mi2)1

Water years with 

streamflow measurements

Number of 

streamflow 

measurements 

through water 

year 2006

Remarks

26 01115010 Woonasquatucket River at Providence, RI 41.82232 -71.43978 48.0 1986–88 18 Occasional flow alteration by 

upstream reservoir

27 01115110 Huntinghouse Brook at Elmdale Road at North Scituate, RI 41.84677 -71.61173 6.23 1993–2007 and 

2009–p

83 Operated as a continuous 

streamgage since water year 2009–p

28 01115114 Rush Brook near Elmdale Road near North Scituate, RI 41.83760 -71.61201 4.70 1998–2006 and 

2009–p

55 Operated as a continuous 

streamgage since water year 2009–p

29 01115120 Unnamed Tributary to Regulating Reservoir near North Scituate, RI 41.83149 -71.60895 0.28 1994–2006 and 

2009–p

79 Operated as a continuous 

streamgage since water year 2009–p

30 01115160 Blanchard Brook near North Scituate, RI 41.85427 -71.57534 1.18 1995 and 2000 11 --31 01115165 Unnamed Tributary to Moswansicut Pond near North Scituate, RI 41.83816 -71.56840 0.30 1994–95, 2003, and 

2009–11

17 --

32 01115170 Moswansicut Stream near North Scituate, RI 41.84093 -71.58451 3.25 1994–95 and 2000–p 57 Operated as a continuous 

streamgage since water year 2009–p

33 01115178 Pine Swamp Brook at Rt. 116 at North Scituate, RI 41.82871 -71.58701 0.45 1993–95, 2003, and 

2009–p

16 --

34 01115180 Brandy Brook at Rt. 116 at Saundersville, RI 41.81954 -71.58590 1.57 1993–2006 and 

2009–p

83 --

35 01115182 Halls Estate Brook at Rt. 116 near North Scituate, RI 41.80760 -71.58534 0.28 1993–95, 2003, and 

2009–p

20 --

36 01115183 Quonapaug Brook at Rt. 116 near North Scituate, RI 41.79760 -71.58479 1.96 1993–p 84 Operated as a continuous 

streamgage since water year 2009–p

37 01115184 Spruce Brook near North Scituate, RI 41.78871 -71.62006 1.22 1994–2007 and 

2009–p

80 Operated as a continuous 

streamgage since water year 2009–p

38 01115185 Winsor Brook at Winsor Road near South Foster, RI 41.83621 -71.72257 4.33 1993–95, 1998–2007, 

and 2009–11

73 --

39 01115190 Dolly Cole Brook at Old Danielson Pike at South Foster, RI 41.82232 -71.70035 4.90 1993–p 87 Operated as a continuous 

streamgage since water year 2009–p

40 01115200 Shippee Brook Tributary at North Foster, RI 41.83149 -71.75229 2.37 1994–95, 2003, and 

2009–11

18 --
56 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 4. Description of partial-record stations in and near Rhode Island.—Continued [Station no.: locations of partial-record stations shown by number in figure 8. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; p, present; --, none; NWIS, National Water Information System] Sta- tion no. USGS station no. Station name Latitude (decimal degrees) Longitude (decimal degrees) Drain- age area (mi2

)

1

Water years with 

streamflow measurements

Number of 

streamflow 

measurements 

through water 

year 2006

Remarks

41 01115265 Hemlock Brook at King Road near Foster, RI 41.79065 -71.69868 8.72 1996–p 66 Operated as a continuous 

streamgage since water year 2009–p

42 01115270 Hemlock Brook at Hemlock Road near Clayville, RI 41.79149 -71.68229 10.6 1993–94 and 2003 14 --43 01115273 Unnamed Tributary to Westconnaug Reservoir near Clayville, RI 41.75038 -71.68312 0.72 1994–95, 2003, and 

2009–10

20 --

44 01115274 Westconnaug Brook at Isthmus Road near Clayville, RI 41.76149 -71.68812 1.48 1994–95, 2003, and 

2009–11

20 --

45 01115275 Bear Tree Brook near Clayville, RI 41.78260 -71.67479 0.62 1994–95, 2000–07, 

and 2009–p

60 Operated as a continuous 

streamgage since water year 2009–p

46 01115276 Westconnaug Stream at Plainfield Pike, RI 41.78538 -71.66729 5.18 1994–95, 2003, and 

2008–p

19 Operated as a continuous 

streamgage since water year 2009–p

47 01115280 Cork Brook at Rockland Scituate Road near Clayville, RI 41.80399 -71.64979 1.79 1993–p 86 Operated as a continuous 

streamgage since water year 2009–p

48 01115297 Wilbur Hollow Brook at Old Plainfield Pike near Clayville, RI 41.76482 -71.63562 4.33 1993–p 86 Operated as a continuous 

streamgage since water year 2009–p

49 01115350 Coventry Brook at Rt. 12 near Clayville, RI 41.74621 -71.60979 0.78 1993–95 15 --50 01115400 Kent Brook at Rt. 116 at Waterman Four Corners, RI 41.77954 -71.56951 0.85 1986, 1993–95, and 

2009–11

19 --

51 01115700 Congdon River Tributary near Nooseneck, RI 41.61288 -71.61784 0.48 1995–99 31 --52 01115730 Carr River near Washington, RI 41.63371 -71.58062 2.30 1995 and 1997–99 24 --53 01115800 Big River near Nooseneck, RI 41.64482 -71.61284 22.5 1993–99 and 2007–12 50 Operated as a continuous 

streamgage during water years 2007–12

54 01115830 Bear Brook near Coventry, RI 41.66038 -71.62784 3.98 1961–63 and 1996–99 38 --55 01115963 Old Hickory Brook near Washington, RI 41.65649 -71.59951 0.28 1996–99 30 --56 01115965 Lake Mishnock outflow near Washington, RI 41.65566 -71.59062 0.29 1996–99 30 --57 01115970 Mishnock River near Washington, RI 41.67899 -71.58062 3.02 1961–63 and 1996–99 39 --58 01116602 Pocasset River, Memorial Avenue, at Johnston, RI 41.82760 -71.50784 2.99 2004 14 --59 01116609 Pocasset River at Cranston, RI 41.75982 -71.44339 19.9 2004 14 --60 01116635 Old Mill Creek at Warwick, RI 41.71205 -71.37533 5.38 1986–88 and 2003 22 --
Table 4 57

Table 4. Description of partial-record stations in and near Rhode Island.—Continued[Station no.: locations of partial-record stations shown by number in figure 8. USGS, U.S. Geological Survey; no., number; mip, present; --, none; NWIS, National Water Information System]

2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; 

Station 

no.

USGS 

station 

no.

Station name

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Drainage area 

(mi2)1

Water years with 

streamflow measurements

Number of 

streamflow 

measurements 

through water 

year 2006

Remarks

61 01116750 Maskerchugg River, Boston Post Road, East Greenwich, RI 41.65010 -71.45784 5.73 1986–88 and 2003 22 --62 01116800 Scabbletown Brook near Davisville, RI 41.59427 -71.49839 1.33 1961–63 and 1995–97 29 --63 01116820 Hunt River Tributary near Davisville, RI 41.60427 -71.49506 1.31 1961–63 and 1995–97 26 --64 01116850 Hunt River at Davisville, RI 41.62371 -71.48200 5.80 1961–63, 1991, and 

1995–97

16 --

65 01116875 Frenchtown Brook at Rt. 2 near Davisville, RI 41.62482 -71.49228 6.56 1995–97 17 --66 01116880 Frenchtown Brook at Davisville, RI 41.62593 -71.48367 6.98 1961–63, 1991, and 

1995–97

16 --

67 01116895 Fry Brook near East Greenwich, RI 41.63232 -71.48673 3.09 1995–97 18 --68 01116950 Sandhill Brook at Davisville, RI 41.60955 -71.47034 1.77 1961–63, 1995–97, 

and 2003

18 --

69 01116980 Sandhill Brook near East Greenwich, RI 41.62927 -71.44700 3.64 1961–64, 1995–97, 

and 2003

17 --

70 01117050 Cocumcussoc Brook near Wickford, RI 41.58371 -71.45895 1.41 1995–97 18 --71 01117070 Annaquatucket River at Wickford Junction, RI 41.57343 -71.48784 2.87 1961–63, 1996–97, 

and 2003

16 --

72 01117170 Mattatuxet River at Allenton, RI 41.53788 -71.46867 1.62 1961–64, 1995–97, 

and 2003

18 --

73 01117200 Mattatuxet River near Saunderstown, RI 41.51955 -71.44506 4.76 1961–64 and 1995–97 24 --74 01117230 Saugatucket River at Peacedale, RI 41.46482 -71.49089 9.20 2004 14 --75 01117237 Saugatucket River, Church Street, at Peacedale, RI 41.44760 -71.49700 15.1 2004 14 --76 01117260 Unnamed Tributary to Card Ponds near Perryville, RI 41.38260 -71.57145 2.08 2004 14 --77 01117285 King Tom Pond Inlet near Charlestown, RI 41.38455 -71.65562 2.54 1966 and 2004 16 --78 01117336 Chipuxet River near West Kingston, RI 41.51760 -71.52534 6.35 1959–60, 1972, 1980, 

and 2002–2004

19 --

79 01117354 Queen River, Rt. 102, at Exeter, RI 41.57871 -71.54312 2.77 1993 and 2000–04 29 --80 01117355 Queen River at William Reynolds Road near Exeter, RI 41.56260 -71.54784 3.74 1959–60, 1988–93, 

and 1999–02

63 Occasional flow alterations by 

upstream withdrawals for 

irrigation

81 01117360 Fisherville Brook at Liberty Church Road near Exeter, RI 41.56427 -71.56451 8.09 1959–60, 1988–93, 

and 2000–04

65 --

82 01117367 Queens Fort Brook near intersection of Dawley and 

School Lands Roads near Exeter, RI

41.54649 -71.55256 3.90 2000–03 29 --

83 01117368 Queen River at Dawley Road near Exeter, RI 41.54871 -71.56034 18.1 1993 and 2000–02 23 --84 01117375 Unnamed Tributary to Queen River at Mail Road at Liberty, RI 41.53899 -71.57951 0.77 1988–91 and 

1999–2004

48 --

85 01117380 Locke Brook at Mail Road at Liberty, RI 41.53732 -71.58756 4.20 1959–60, 1989–91, 

1993, and 2000–04

61 --
58 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 4. Description of partial-record stations in and near Rhode Island.—Continued [Station no.: locations of partial-record stations shown by number in figure 8. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; p, present; --, none; NWIS, National Water Information System] Sta- tion no. USGS station no. Station name Latitude (decimal degrees) Longitude (decimal degrees) Drain- age area (mi2

)

1

Water years with 

streamflow measurements

Number of 

streamflow 

measurements 

through water 

year 2006

Remarks

86 01117385 Rake Factory Brook at Glen Rock Road at Glen Rock, RI 41.51899 -71.59895 0.28 1988–91 and 

1999–2004

51 --

87 01117390 Glen Rock Brook at Glen Rock Road at Glen Rock, RI 41.51649 -71.60590 2.82 1989–91, 1993, and 

2000–04

59 --

88 01117400 Sherman Brook at Glen Rock Road at Glen Rock, RI 41.51788 -71.60451 1.03 1989–91, 1993, and 

2000–04

58 --

89 01117421 Chickasheen Brook at Rt. 2 at West Kingston, RI 41.49843 -71.56478 3.28 2002–04 14 --90 01117450 Pasquiset Brook at Rt. 2 at Kenyon, RI 41.44399 -71.62701 6.02 1966–67, 1974, 1976, 

1980, and 2002–04

20 --

91 01117465 Beaver River near Wyoming, RI 41.52566 -71.63923 5.25 1966–67, 1974, 1976, 

1991, and 2002–04

22 --

92 01117480 Taney Brook at Carolina, RI 41.46066 -71.64784 1.61 1966–67 and 2002–04 18 --93 01117700 Cedar Swamp Brook at Wood River Junction, RI 41.42704 -71.69507 4.81 1966–67 and 2002–04 18 --94 01117720 Wood River at Escoheag, RI 41.61260 -71.76035 11.3 1966–67, 1991, and 

2002–04

20 --

95 01117740 Kelley Brook at Escoheag, RI 41.61232 -71.75312 4.40 1966–67, 1991, and 

2002–04

20 --

96 01117750 Factory Brook near Summit, RI 41.63316 -71.72229 1.16 1966 and 2002–04 15 --97 01117760 Flat River at Plain Road near Arcadia, RI 41.59566 -71.72007 8.22 1979, 1982, and 

2002–04

15 --

98 01117780 Breakheart Brook, Frosty Hollow Road, near Arcadia, RI 41.58788 -71.70951 6.56 1966–67, 1979, 1982, 

1991–92, and 2002–04

22 --

99 01117840 Parris Brook at Blitzkrieg Trail near Arcadia, RI 41.56510 -71.72590 6.61 1966–67, 1979, 1991, 

and 2002–04

22 --

100 01117860 Roaring Brook at Arcadia, RI 41.55843 -71.68507 5.04 1966–67, 1991, and 

2002–04

21 --

101 01117900 Brushy Brook near Hope Valley, RI 41.52871 -71.73646 3.64 1966–67, 1977, 1979, 

1991, and 2002–04

21 --

102 01117950 Moscow Brook near Hope Valley, RI 41.52732 -71.73618 6.21 1966–67, 1977, 1979, 

1991, and 2002–04

22 --

103 01118006 Canonchet Brook, Rockville-Alton Road, Hope Valley, RI 41.47760 -71.72923 6.61 1977, 1979, 1980, 

1991, and 2002–04

19 --

104 01118008 Wood River Tributary at Alton, RI 41.43760 -71.72312 2.05 1977 and 2002–04 15 --105 01118009 Wood River near Alton, RI 41.43621 -71.72090 88.3 1977, 1979–81, 1991, 

and 2002–04

18 --
Table 4 59

Table 4. Description of partial-record stations in and near Rhode Island.—Continued[Station no.: locations of partial-record stations shown by number in figure 8. USGS, U.S. Geological Survey; no., number; mi2, square miles; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; 

p, present; --, none; NWIS, National Water Information System]

Station 

no.

USGS 

station 

no.

Station name

Latitude 

(decimal 

degrees)

Longitude 

(decimal 

degrees)

Drainage area 

(mi2)1

Water years with 

streamflow measurements

Number of 

streamflow 

measurements 

through water 

year 2006

Remarks

106 01118022 Perry-Healy Brook at Klondike Road near Bradford, RI 41.37454 -71.71590 2.36 2002–04 13 --107 01118055 Tomaquag Brook at Rt. 216 at Bradford, RI 41.41111 -71.76417 6.71 1991 and 2002–04 16 --108 01118255 Green Fall River at Laurel Glen, CT 41.47232 -71.81618 7.58 1963–67 and 2002–04 24 --109 01118340 Wyassup Brook at Rt. 216 at Clarks Falls, CT 41.45472 -71.82667 11.5 2002–04 14 --

110 01118350 Green Fall River at Clarks Falls, CT 41.45482 -71.81396 20.0 1961–73 25 --

111 01118352 Glade Brook near Laurel Glen, CT 41.46815 -71.80813 1.83 1965–67 and 2002–04 18 --

112 01118355 Paramenter Brook near Hopkinton, RI 41.44760 -71.79035 2.45 1966–67 and 2002–04 17 --

113 01118365 Lewis Pond Outlet near Potter Hill, RI 41.42038 -71.82174 1.60 1966–67 and 2002–04 18 --

114 01118373 Shunock River at North Stonington, RI 41.44093 -71.88229 7.77 1965 and 2002–04 15 --

115 01118375 Assekonk Brook near North Stonington, CT 41.43871 -71.91035 1.70 1963–65 and 2002–04 26 --

116 01118380 Assekonk Brook at North Stonington, CT 41.43871 -71.88424 3.88 1963–65 and 2002–04 22 --

117 01118700 Whitford Brook at Old Mystic, CT 41.39482 -71.96063 15.0 1961–73 23 --

118 01118750 Haleys Brook near Old Mystic, CT 41.38899 -71.98591 4.41 1962–65, 1967, 

1969–75, 1977–78, and 1984

33 --

119 01125260 Muddy Brook at Rt. 197 at North Woodstock, CT 41.99565 -71.99063 7.47 1962 and 1979–81 21 --

120 01125300 English Neighborhood Brook at North Woodstock, CT 41.99093 -71.99702 4.47 1961–75, 1977–78, 

and 1984

39 --

121 01125400 Muddy Brook at East Woodstock, CT 41.98426 -71.98063 12.9 1961–63 and 1979–81 30 --122 01125404 Muddy Brook near East Woodstock, CT 41.97649 -71.96896 16.2 1979–81 18 --123 01125411 Muddy Brook near Woodstock, CT 41.96732 -71.96396 18.0 1979–81 19 --124 01125440 Mill Brook at South Woodstock, CT 41.94038 -71.95730 6.73 1961–63 and 1982–83 22 --125 01125650 Wappoquia Brook near Pomfret, CT 41.86593 -71.95785 4.27 1961–75, 1977–78, 

and 1984

39 --

126 01125800 Fivemile River near East Thompson, CT 41.98649 -71.81535 10.5 1961–73 19 --127 01125900 Cady Brook at East Putnam, CT 41.90899 -71.81924 8.33 1961–75, 1977–79, 

and 1984

32 --

128 01126100 Whetstone Brook at Elmville, CT 41.83621 -71.86674 13.7 1961–63 12 --129 01126111 Fivemile River at Danielson, CT 41.80204 -71.88702 74.8 1962, 1991–95, 

1997–99, and 2001

30 --

130 01126300 Quaduck Brook at North Sterling, CT 41.77177 -71.79618 8.21 1960–64 15 --

131 01126510 Moosup River near Central Village, CT 41.72065 -71.91618 87.8 1962 and 2000–01 12 --132 01126700 Kitt Brook near Canterbury, CT 41.68065 -71.97785 9.99 1961–75 27 --133 01126800 Cory Brook near Canterbury, CT 41.65260 -71.99563 5.73 1961–63 13 --134 01126920 Mount Misery Brook near Voluntown, CT 41.59343 -71.86591 7.95 1961–63 13 --135 01127100 Broad Brook near Preston City, CT 41.55399 -71.97035 12.3 1961–65 and 1967–75 27 --

1Drainage areas (in mi2) were determined with a GIS and do not supersede areas listed in the USGS NWIS database.
60 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique to estimate long-term streamflow statistics for short- term streamgages and partial-record stations in and near Rhode Island. [USGS station no.: locations of short-term streamgages shown in figure 2 and described in table 1. Locations of partial-record stations shown in figure 8 and described in table 4 (in back of report). USGS, U.S. Geological Survey; no., number; MOVE.1, Maintenance of Variance Extension, type 1; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; ft, foot; --, none] Sta- tion no. USGS station no. Station name and location Number of wa- ter years with daily mean streamflow or streamflow measure- ments used in relation Number of daily mean stream- flows or streamflow measure- ments used in relation Num- ber of zero-flow measure- ments used in relation MOVE.1 index stream- gage Correlation coefficient between streamflow data at site and index stream- gage Approximate minimum- flow duration covered by streamflow data, in percent Approximate maximum- flow duration covered by streamflow data, in percent Approximate total flow- duration range covered by streamflow data, in percent Short-term streamgages -- 01109090 Rattlesnake Brook near Assonet, MA 2 639 -- 01115098 0.92 99.5 0.1 99.4 -- 01109220 Palmer River at South Rehoboth, MA 3 950 -- 01115098 0.94 99.5 0.1 99.4 -- 01111050 Mumford River at Uxbridge, MA 2 731 -- 01117800 0.91 99.0 0.1 98.9 -- 01111225 Emerson Brook near Uxbridge, MA 2 758 -- 01111500 0.94 99.5 0.5 99.0 -- 01111410 Chepachet River west of Gazza Road at Gazzaville, RI 5 1,496 -- 01123000 0.89 99.0 0.1 99.0 -- 01115670 Congdon River near Nooseneck, RI 2 731 -- 01117468 0.94 98.0 0.5 97.5 -- 01115900 Flat River near Coventry, RI 3 914 -- 01109000 0.92 99.5 0.5 99.0 -- 01116905 Hunt River, 250 ft downstream of Fry Brook, at Frenchtown, RI 2 548 -- 01117468 0.95 99.5 0.5 99.0 -- 01117410 Usquepaug River at Rt. 138 at Usquepaug, RI 5 1,761 -- 01117468 0.98 99.5 0.1 99.4 -- 01117424 Chickasheen Brook at West Kingston, RI 4 811 -- 01117468 0.94 96.0 1.0 95.0 -- 01117430 Pawcatuck River at Rt. 2 at Kenyon, RI 5 1,828 -- 01117500 0.99 99.9 1.0 98.9 -- 01117471 Beaver River at Shannock Hill Road near Shannock, RI 3 800 -- 01117468 0.98 96.0 1.0 95.0 -- 01117472 Beaver River at Kenyon, RI 4 1,188 -- 01117468 0.97 98.0 0.1 97.9 -- 01118010 Pawcatuck River at Burdickville, RI 4 863 -- 01117500 0.99 99.9 1.0 98.9

-- 01118360 Ashaway River at Ashaway, RI 4 853 -- 01117800 0.96 99.0 0.1 98.9

-- 01118400 Shunock River at North Stonington, RI 3 807 -- 01117800 0.97 94.0 0.1 93.9

-- 01118668 Whitford Brook below Williams Brook near Old Mystic, CT 5 1,158 -- 01118300 0.95 99.5 0.5 99.0

-- 01119280 Willimantic River at Stafford Springs, CT 5 1,826 -- 01123000 0.92 100.0 0.5 99.5

-- 01119320 Roaring Brook near Stafford Springs, CT 6 1,887 -- 01121000 0.94 99.5 0.5 99.0

-- 01125415 Muddy Brook at Childs Hill Road near Woodstock, CT 5 1,801 -- 01121000 0.93 99.0 0.1 99.0

-- 01125600 Mashamoquet Brook at Abington, CT 2 548 -- 01175670 0.92 99.5 0.5 99.0

Partial-record stations

1 01105928 Buttonwood Brook near South Dartmouth, MA 5 15 1 01106000 0.89 100.0 20.0 80.02 01105930 Paskamanset River at Turner Pond near New Bedford, MA 4 26 -- 01109000 0.90 99.5 20.0 79.5

3 01105935 Destruction Brook near South Dartmouth, MA 7 27 -- 01105600 0.93 98.0 45.0 53.0

4 01105937 Shingle Island River near North Dartmouth, MA 10 32 -- 01109000 0.85 98.0 20.0 78.0

5 01105950 Kirby Brook near Head of Westport, MA 6 16 1 01106000 0.90 95.0 20.0 75.0
Table 5 61

Table 5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique to estimate long-term streamflow statistics for shortterm streamgages and partial-record stations in and near Rhode Island.—Continued[USGS station no.: locations of short-term streamgages shown in figure 2 and described in table 1. Locations of partial-record stations shown in figure 8 and described in table 4 (in back of report). USGS, U.S. Geological Survey; no., number; MOVE.1, Maintenance of Variance Extension, type 1; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; ft, foot; --, none]

Station 

no.

USGS 

station 

no.

Station name and location

Number of water years with 

daily mean 

streamflow or 

streamflow 

measurements used 

in relation

Number of 

daily mean 

streamflows or 

streamflow 

measurements used 

in relation

Number of 

zero-flow 

measurements 

used in 

relation

MOVE.1 

index 

streamgage

Correlation 

coefficient 

between 

streamflow 

data at site 

and index 

streamgage

Approximate 

minimumflow duration 

covered by 

streamflow 

data, 

in percent

Approximate 

maximumflow duration 

covered by 

streamflow 

data, 

in percent

Approximate 

total flowduration 

range 

covered by 

streamflow 

data, 

in percent

Partial-record stations—Continued

6 01106005 Angeline Brook near Head of Westport, MA 5 16 1 01106000 0.94 100.0 20.0 80.0

7 01106110 Dundery Brook, Meetinghouse Lane at Little Compton, RI 1 13 -- 01106000 0.97 80.0 15.0 65.0

8 01106130 Little Creek, Green End Avenue, near Whitehall, RI 1 14 -- 01106000 0.95 85.0 15.0 70.0

9 01106150 Bailey Brook, Forest Avenue, near Middletown, RI 1 13 -- 01109000 0.96 91.0 8.0 83.0

10 01107400 Fall Brook near Middleborough, MA 8 36 -- 01109000 0.96 99.5 0.0 99.5

11 01109087 Assonet River at Assonet, MA 5 22 -- 01109000 0.93 98.0 0.1 97.9

12 01109135 Cole River near Swansea, MA 4 15 -- 01106000 0.92 80.0 1.0 79.0

13 01109185 East Branch Palmer River near Rehoboth, MA 4 13 1 01109000 0.92 99.5 9.0 90.5

14 01109225 Rocky Run near Rehoboth, MA 13 38 -- 01109000 0.93 99.5 9.0 90.5

15 01109270 Runnings River at Seekonk, MA 7 20 -- 01109000 0.96 85.0 0.5 84.5

16 01109280 Runnings River, Fall River Avenue, at Seekonk, MA 3 17 -- 01109000 0.94 93.0 0.1 92.9

17 01109290 Annawamscutt Brook, Rt. 103, at Peck Corner, RI 1 14 -- 01109000 0.94 91.0 8.0 83.0

18 01109381 Speedway Brook at Attleboro, MA 4 13 -- 01109000 0.94 99.5 15.0 84.5

19 01111261 Clear River at North Road at Laurel Hill, RI 4 15 -- 01111500 0.84 96.0 20.0 76.0

20 01111330 Clear River at Oakland, RI 3 15 -- 01111500 0.95 96.0 20.0 76.0

21 01111470 Tarklin Brook at Oak Valley, RI 3 12 -- 01111300 0.95 92.0 35.0 57.0

22 01112190 Muddy Brook at South Milford, MA 8 21 -- 01111300 0.92 99.0 30.0 69.0

23 01113670 Burnt Swamp Brook near Grants Mills, RI 4 16 -- 01109000 0.94 99.0 15.0 84.0

24 01113710 Ash Swamp Brook at Nate Whipple Highway at Diamond Hill, RI 5 26 -- 01105730 0.96 99.5 2.0 97.5

25 01114400 Stillwater River at Pleasant View Road at Spragueville, RI 3 16 -- 01109000 0.94 99.5 15.0 84.5

26 01115010 Woonasquatucket River at Providence, RI 3 18 -- 01111500 0.97 90.0 0.1 90.0

27 01115110 Huntinghouse Brook at Elmdale Road at North Scituate, RI 12 73 7 01115187 0.97 98.0 0.1 97.9

28 01115114 Rush Brook near Elmdale Road near North Scituate, RI 9 54 2 01115187 0.95 98.0 2.0 96.0

29 01115120 Unnamed Tributary to Regulating Reservoir near 

North Scituate, RI

13 69 21 01117468 0.90 98.0 2.0 96.0

30 01115160 Blanchard Brook near North Scituate, RI 2 11 2 01115187 0.99 96.0 20.0 76.0
62 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique to estimate long-term streamflow statistics for short- term streamgages and partial-record stations in and near Rhode Island.—Continued [USGS station no.: locations of short-term streamgages shown in figure 2 and described in table 1. Locations of partial-record stations shown in figure 8 and described in table 4 (in back of report). USGS, U.S. Geological Survey; no., number; MOVE.1, Maintenance of Variance Extension, type 1; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; ft, foot; --, none] Sta- tion no. USGS station no. Station name and location Number of wa- ter years with daily mean streamflow or streamflow measure- ments used in relation Number of daily mean stream- flows or streamflow measure- ments used in relation Num- ber of zero-flow measure- ments used in relation MOVE.1 index stream- gage Correlation coefficient between streamflow data at site and index stream- gage Approximate minimum- flow duration covered by streamflow data, in percent Approximate maximum- flow duration covered by streamflow data, in percent Approximate total flow- duration range covered by streamflow data, in percent Partial-record stations—Continued 31 01115165 Unnamed Tributary to Moswansicut Pond near North Scituate, RI 3 16 -- 01117800 0.94 100.0 30.0 70.0 32 01115170 Moswansicut Stream near North Scituate, RI 8 48 -- 01115187 0.88 98.0 1.0 97.0 33 01115178 Pine Swamp Brook at Rt. 116 at North Scituate, RI 3 13 3 01111300 0.94 99.0 15.0 84.0 34 01115180 Brandy Brook at Rt. 116 at Saundersville, RI 12 71 -- 01115187 0.95 98.0 1.0 97.0 35 01115182 Halls Estate Brook at Rt. 116 near North Scituate, RI 3 15 5 01111300 0.91 99.0 30.0 69.0 36 01115183 Quonapaug Brook at Rt. 116 near North Scituate, RI 12 70 8 01115187 0.94 98.0 4.0 94.0 37 01115184 Spruce Brook near North Scituate, RI 12 73 -- 01115187 0.94 98.0 0.1 97.9 38 01115185 Winsor Brook at Winsor Road near South Foster, RI 11 61 9 01115187 0.96 98.0 2.0 96.0 39 01115190 Dolly Cole Brook at Old Danielson Pike at South Foster, RI 13 82 -- 01111300 0.91 99.0 0.5 98.5 40 01115200 Shippee Brook Tributary at North Foster, RI 2 11 -- 01115187 0.96 96.0 30.0 66.0 41 01115265 Hemlock Brook at King Road near Foster, RI 11 66 -- 01115187 0.96 98.0 2.0 96.0 42 01115270 Hemlock Brook at Hemlock Road near Clayville, RI 3 14 -- 01123000 0.93 99.5 35.0 64.5 43 01115273 Unnamed Tributary to Westconnaug Reservoir near Clayville, RI 2 11 1 01115187 0.98 98.0 20.0 78.0 44 01115274 Westconnaug Brook at Isthmus Road near Clayville, RI 2 11 4 01115187 0.92 98.0 20.0 78.0

45 01115275 Bear Tree Brook near Clayville, RI 8 52 -- 01115187 0.87 98.0 2.0 96.0

46 01115276 Westconnaug Stream at Plainfield Pike, RI 3 17 -- 01117800 0.92 100.0 30.0 70.0

47 01115280 Cork Brook at Rockland Scituate Road near Clayville, RI 12 77 6 01115187 0.97 98.0 0.1 97.9

48 01115297 Wilbur Hollow at Old Plainfield Pike near Clayville, RI 14 86 1 01117800 0.92 100.0 4.0 96.0

49 01115350 Coventry Brook at Rt. 12 near Clayville, RI 3 15 -- 01117800 0.89 100.0 45.0 55.0

50 01115400 Kent Brook at Rt. 116 at Waterman Four Corners, RI 2 12 2 01117468 0.94 99.5 45.0 54.5

51 01115700 Congdon River Tributary near Nooseneck, RI 5 30 -- 01117468 0.95 97.0 5.0 92.0

52 01115730 Carr River near Washington, RI 4 23 -- 01117800 0.94 98.0 4.0 94.0

53 01115800 Big River near Nooseneck, RI 7 50 -- 01117800 0.97 98.0 1.0 97.0

54 01115830 Bear Brook near Coventry, RI 4 30 -- 01117800 0.87 94.0 7.0 87.0

55 01115963 Old Hickory Brook near Washington, RI 4 30 -- 01117800 0.85 94.0 7.0 87.0

56 01115965 Lake Mishnock outflow near Washington, RI 4 29 -- 01117468 0.86 97.0 8.0 89.0

57 01115970 Mishnock River near Washington, RI 4 30 -- 01117800 0.83 94.0 7.0 87.0

58 01116602 Pocasset River, Memorial Avenue, at Johnston, RI 1 14 -- 01115187 0.95 85.0 25.0 60.0

59 01116609 Pocasset River at Cranston, RI 1 14 -- 01115187 0.92 85.0 25.0 60.0

60 01116635 Old Mill Creek at Warwick, RI 4 22 -- 01111300 0.87 85.0 0.5 84.5
Table 5 63

Table 5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique to estimate long-term streamflow statistics for shortterm streamgages and partial-record stations in and near Rhode Island.—Continued[USGS station no.: locations of short-term streamgages shown in figure 2 and described in table 1. Locations of partial-record stations shown in figure 8 and described in table 4 (in back of report). USGS, U.S. Geological Survey; no., number; MOVE.1, Maintenance of Variance Extension, type 1; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; ft, foot; --, none]

Station 

no.

USGS 

station 

no.

Station name and location

Number of water years with 

daily mean 

streamflow or 

streamflow 

measurements used 

in relation

Number of 

daily mean 

streamflows or 

streamflow 

measurements used 

in relation

Number of 

zero-flow 

measurements 

used in 

relation

MOVE.1 

index 

streamgage

Correlation 

coefficient 

between 

streamflow 

data at site 

and index 

streamgage

Approximate 

minimumflow duration 

covered by 

streamflow 

data, 

in percent

Approximate 

maximumflow duration 

covered by 

streamflow 

data, 

in percent

Approximate 

total flowduration 

range 

covered by 

streamflow 

data, 

in percent

Partial-record stations—Continued

61 01116750 Maskerchugg River, Boston Post Road, East Greenwich, RI 3 20 -- 01117468 0.95 98.0 0.5 97.5

62 01116800 Scabbletown Brook near Davisville, RI 3 18 -- 01115098 0.98 95.0 5.0 90.0

63 01116820 Hunt River Tributary near Davisville, RI 3 17 -- 01117800 0.95 99.0 4.0 95.0

64 01116850 Hunt River at Davisville, RI 7 15 -- 01118300 0.81 99.0 20.0 79.0

65 01116875 Frenchtown Brook at Rt. 2 near Davisville, RI 3 17 -- 01117800 0.98 99.0 4.0 95.0

66 01116880 Frenchtown Brook at Davisville, RI 7 15 -- 01109000 0.92 98.0 15.0 83.0

67 01116895 Fry Brook near East Greenwich, RI 3 16 -- 01118300 0.95 95.0 6.0 89.0

68 01116950 Sandhill Brook at Davisville, RI 7 18 -- 01118300 0.89 97.0 20.0 77.0

69 01116980 Sandhill Brook near East Greenwich, RI 8 17 -- 01118300 0.89 95.0 20.0 75.0

70 01117050 Cocumcussoc Brook near Wickford, RI 3 18 -- 01118300 0.96 95.0 6.0 89.0

71 01117070 Annaquatucket River at Wickford Junction, RI 5 14 -- 01118300 0.87 97.0 20.0 77.0

72 01117170 Mattatuxet River at Allenton, RI 8 17 -- 01123000 0.87 99.5 25.0 74.5

73 01117200 Mattatuxet River near Saunderstown, RI 3 17 -- 01117468 0.84 93.0 5.0 88.0

74 01117230 Saugatucket River at Peacedale, RI 1 14 -- 01117468 0.98 91.0 15.0 76.0

75 01117237 Saugatucket River, Church Street, at Peacedale, RI 1 14 -- 01117468 0.98 91.0 15.0 76.0

76 01117260 Unnamed Tributary to Card Ponds near Perryville, RI 1 14 -- 01117468 0.82 91.0 15.0 76.0

77 01117285 King Tom Pond Inlet near Charlestown, RI 2 14 -- 01123000 0.88 92.0 25.0 67.0

78 01117336 Chipuxet River near West Kingston, RI 4 15 -- 01117468 0.90 99.5 10.0 89.5

79 01117354 Queen River, Rt. 102, at Exeter, RI 5 26 -- 01117468 0.96 98.0 2.0 96.0

80 01117355 Queen River at William Reynolds Road near Exeter, RI 10 60 -- 01117468 0.96 97.0 7.0 90.0

81 01117360 Fisherville Brook at Liberty Church Road near Exeter, RI 11 62 -- 01117468 0.97 98.0 4.0 94.0

82 01117367 Queens Fort Brook near intersection of Dawley and School Lands 

Roads near Exeter, RI

4 28 1 01117468 0.92 98.0 2.0 96.0

83 01117368 Queen River at Dawley Road near Exeter, RI 4 23 -- 01117468 0.99 98.0 5.0 93.0

84 01117375 Unnamed Tributary to Queen River at Mail Road at Liberty, RI 10 46 11 01117468 0.93 99.5 8.0 91.5

85 01117380 Locke Brook at Mail Road at Liberty, RI 9 56 -- 01117468 0.97 98.0 4.0 94.0
64 Equations for Estimating Selected Streamflow Statistics in Rhode Island Table 5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique to estimate long-term streamflow statistics for short- term streamgages and partial-record stations in and near Rhode Island.—Continued [USGS station no.: locations of short-term streamgages shown in figure 2 and described in table 1. Locations of partial-record stations shown in figure 8 and described in table 4 (in back of report). USGS, U.S. Geological Survey; no., number; MOVE.1, Maintenance of Variance Extension, type 1; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; ft, foot; --, none] Sta- tion no. USGS station no. Station name and location Number of wa- ter years with daily mean streamflow or streamflow measure- ments used in relation Number of daily mean stream- flows or streamflow measure- ments used in relation Num- ber of zero-flow measure- ments used in relation MOVE.1 index stream- gage Correlation coefficient between streamflow data at site and index stream- gage Approximate minimum- flow duration covered by streamflow data, in percent Approximate maximum- flow duration covered by streamflow data, in percent Approximate total flow- duration range covered by streamflow data, in percent Partial-record stations—Continued 86 01117385 Rake Factory Brook at Glen Rock Road at Glen Rock, RI 10 41 17 01117800 0.92 99.5 6.0 93.5 87 01117390 Glen Rock Brook at Glen Rock Road at Glen Rock, RI 9 59 -- 01117468 0.96 98.0 2.0 96.0 88 01117400 Sherman Brook at Glen Rock Road at Glen Rock, RI 9 55 -- 01118300 0.94 98.0 3.0 95.0 89 01117421 Chickasheen Brook at Rt. 2 at West Kingston, RI 2 12 -- 01117468 0.91 92.0 10.0 82.0 90 01117450 Pasquiset Brook at Rt. 2 at Kenyon, RI 7 18 -- 01118300 0.95 99.9 15.0 84.9 91 01117465 Beaver River near Wyoming, RI 8 22 -- 01118300 0.95 99.5 15.0 84.5 92 01117480 Taney Brook at Carolina, RI 5 18 -- 01118300 0.91 99.5 15.0 84.5 93 01117700 Cedar Swamp Brook at Wood River Junction, RI 5 17 -- 01118300 0.94 99.5 15.0 84.5 94 01117720 Wood River at Escoheag, RI 6 20 -- 01118300 0.97 99.5 20.0 79.5 95 01117740 Kelley Brook at Escoheag, RI 5 18 -- 01117800 0.96 95.0 20.0 75.0 96 01117750 Factory Brook near Summit, RI 2 13 -- 01117800 0.96 91.0 20.0 71.0 97 01117760 Flat River at Plain Road near Arcadia, RI 4 14 -- 01117800 0.98 98.0 20.0 78.0 98 01117780 Breakheart Brook, Frosty Hollow Road, near Arcadia, RI 8 21 -- 01117800 0.96 98.0 20.0 78.0 99 01117840 Parris Brook at Blitzkrieg Trail near Arcadia, RI 7 22 -- 01118300 0.96 99.5 20.0 79.5

100 01117860 Roaring Brook at Arcadia, RI 6 21 -- 01117800 0.92 98.0 20.0 78.0

101 01117900 Brushy Brook near Hope Valley, RI 8 21 -- 01118300 0.97 99.5 15.0 84.5

102 01117950 Moscow Brook near Hope Valley, RI 8 22 -- 01117800 0.96 98.0 15.0 83.0

103 01118006 Canonchet Brook, Rockville-Alton Road, Hope Valley, RI 7 19 -- 01117468 0.99 99.5 10.0 89.5

104 01118008 Wood River Tributary at Alton, RI 3 14 -- 01117468 0.99 98.0 10.0 88.0

105 01118009 Wood River near Alton, RI 8 18 -- 01118000 0.99 99.5 40.0 59.5

106 01118022 Perry-Healy Brook at Klondike Road near Bradford, RI 3 12 -- 01117468 0.98 98.0 10.0 88.0

107 01118055 Tomaquag Brook at Rt. 216 at Bradford, RI 4 16 -- 01117468 0.97 98.0 10.0 88.0

108 01118255 Green Fall River at Laurel Glen, CT 8 23 -- 01118300 0.95 99.5 20.0 79.5

109 01118340 Wyassup Brook at Rt. 216 at Clarks Falls, CT 3 14 -- 01118300 0.96 99.5 20.0 79.5

110 01118350 Green Fall River at Clarks Falls, CT 13 25 -- 01118300 0.94 99.0 0.5 98.5
Table 5 65

Table 5. Summary of data used by the Maintenance of Variance Extension, type 1 (MOVE.1), record-extension technique to estimate long-term streamflow statistics for shortterm streamgages and partial-record stations in and near Rhode Island.—Continued[USGS station no.: locations of short-term streamgages shown in figure 2 and described in table 1. Locations of partial-record stations shown in figure 8 and described in table 4 (in back of report). USGS, U.S. Geological Survey; no., number; MOVE.1, Maintenance of Variance Extension, type 1; CT, Connecticut; MA, Massachusetts; RI, Rhode Island; Rt., Route; ft, foot; --, none]

Station 

no.

USGS 

station 

no.

Station name and location

Number of water years with 

daily mean 

streamflow or 

streamflow 

measurements used 

in relation

Number of 

daily mean 

streamflows or 

streamflow 

measurements used 

in relation

Number of 

zero-flow 

measurements 

used in 

relation

MOVE.1 

index 

streamgage

Correlation 

coefficient 

between 

streamflow 

data at site 

and index 

streamgage

Approximate 

minimumflow duration 

covered by 

streamflow 

data, 

in percent

Approximate 

maximumflow duration 

covered by 

streamflow 

data, 

in percent

Approximate 

total flowduration 

range 

covered by 

streamflow 

data, 

in percent

Partial-record stations—Continued

111 01118352 Glade Brook near Laurel Glen, CT 5 17 1 01118300 0.97 99.5 20.0 79.5

112 01118355 Paramenter Brook near Hopkinton, RI 5 17 -- 01118300 0.98 99.0 15.0 84.0

113 01118365 Lewis Pond Outlet near Potter Hill, RI 4 17 -- 01117800 0.95 99.0 15.0 84.0

114 01118373 Shunock River at North Stonington, RI 3 14 -- 01117800 0.98 98.0 15.0 83.0

115 01118375 Assekonk Brook near North Stonington, CT 6 26 1 01118300 0.89 99.9 20.0 79.9

116 01118380 Assekonk Brook at North Stonington, CT 5 20 -- 01118300 0.96 95.0 20.0 75.0

117 01118700 Whitford Brook at Old Mystic, CT 13 23 -- 01118300 0.96 99.0 0.5 98.5

118 01118750 Haleys Brook near Old Mystic, CT 15 33 -- 01118300 0.98 98.0 2.0 96.0

119 01125260 Muddy Brook at Rt. 197 at North Woodstock, CT 4 21 -- 01121000 0.97 99.0 0.5 98.5

120 01125300 English Neighborhood Brook at North Woodstock, CT 18 39 -- 01121000 0.96 99.0 0.1 99.0

121 01125400 Muddy Brook at East Woodstock, CT 6 30 -- 01121000 0.97 99.0 0.5 98.5

122 01125404 Muddy Brook near East Woodstock, CT 4 18 -- 01121000 0.94 91.0 2.0 89.0

123 01125411 Muddy Brook near Woodstock, CT 3 19 -- 01121000 0.97 91.0 0.5 90.5

124 01125440 Mill Brook at South Woodstock, CT 5 22 -- 01123000 0.92 98.0 0.5 97.5

125 01125650 Wappoquia Brook near Pomfret, CT 18 39 -- 01121000 0.97 98.0 0.1 98.0

126 01125800 Fivemile River near East Thompson, CT 13 19 -- 01121000 0.97 99.0 8.0 91.0

127 01125900 Cady Brook at East Putnam, CT 19 32 -- 01123000 0.95 98.0 0.1 97.9

128 01126100 Whetstone Brook at Elmville, CT 3 11 -- 01123000 0.96 98.0 9.0 89.0

129 01126111 Fivemile River at Danielson, CT 10 30 -- 01123000 0.89 99.5 2.0 97.5

130 01126300 Quaduck Brook at North Sterling, CT 5 14 -- 01121000 0.99 99.0 2.0 97.0

131 01126510 Moosup River near Central Village, CT 2 8 -- 01115187 0.99 94.0 15.0 79.0

132 01126700 Kitt Brook near Canterbury, CT 15 27 -- 01121000 0.98 99.0 2.0 97.0

133 01126800 Cory Brook near Canterbury, CT 3 13 -- 01118300 0.95 97.0 15.0 82.0

134 01126920 Mount Misery Brook near Voluntown, CT 3 13 -- 01123000 0.96 98.0 5.0 93.0

135 01127100 Broad Brook near Preston City, CT 14 25 -- 01118300 0.97 97.0 1.0 96.0

Prepared by the Pembroke Publishing Service Center.

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
ISSN 2328-031X (print)

ISSN 2328-0328 (online)

http://dx.doi.org/10.3133/sir20145010

Bent and others—Equations for Estimating Selected Streamflow Statistics in Rhode Island—Scientific Investigations Report 2014–5010

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