U.S. Department of the Interior

U.S. Geological Survey

Scientific Investigations Report 2012–5109

Prepared in cooperation with the Department of Homeland Security

Federal Emergency Management Agency

Magnitude of Flood Flows for Selected 

Annual Exceedance Probabilities in 

Rhode Island Through 2010
Front cover. March–April 2010 flooding along the Woonasquatucket River at Valley Street in Providence, Rhode Island, looking northward 

toward Atwells Avenue (traffic light) from Helme Street.

Back cover. Historical marker found along Simmons Brook at Simmonsville east of Providence, Rhode Island.
Magnitude of Flood Flows for Selected 

Annual Exceedance Probabilities in 

Rhode Island Through 2010

By Phillip J. Zarriello, Elizabeth A. Ahearn, and Sara B. Levin

Prepared in cooperation with the Department of Homeland Security 

Federal Emergency Management Agency

Scientific Investigations Report 2012–5109

U.S. Department of the Interior

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

KEN SALAZAR, Secretary

U.S. Geological Survey

Marcia K. McNutt, Director

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

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reproduce any copyrighted materials contained within this report.

Suggested citation:

Zarriello, P.J., Ahearn, E.A., and Levin, S.B., 2012, Magnitude of flood flows for selected annual exceedance 

probabilities in Rhode Island through 2010: U.S. Geological Survey Scientific Investigations Report 2012–5109, 81 p. 

(Also available at http://pubs.usgs.gov/sir/2012/5109.)
iii

Contents

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

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

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

Study Area..............................................................................................................................................2

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

Data Compilation............................................................................................................................................6

Record Extension..................................................................................................................................6

Historic Data..........................................................................................................................................9

Magnitude of Flood Flows at Streamgages.............................................................................................10

Skew Coefficient.................................................................................................................................11

Low Outlier Adjustment ............................................................................................................11

High Outlier Adjustment............................................................................................................13

Generalized Regional Skew .....................................................................................................13

Quantifying Uncertainty in Annual Peak Records.........................................................................15

Annual Exceedance Probability Flood Estimates..........................................................................18

Uncertainty of Estimates ...................................................................................................................18

Magnitude of Flood Flows at Ungaged Streams ....................................................................................19

Basin Characteristics.........................................................................................................................19

Exploratory Analysis...........................................................................................................................19

Regional Regression Equations........................................................................................................19

Accuracy and Limitations..................................................................................................................22

Uncertainty Estimates of Regionalized Equations.........................................................................25

Factors Affecting Flood Flow Estimates...................................................................................................27

Urban Influence...................................................................................................................................27

Trends in Annual Peak Flows............................................................................................................30

Application of Methods and Significance of Results ............................................................................35

Weighted Estimates of Flood Flows at Streamgages ...................................................................35

Flood Flows at Streamgages with Limited Record........................................................................36

Flood Flows at an Ungaged Site on a Gaged Stream ...................................................................38

Comparison with a Previous Rhode Island Flood Study...............................................................40

Annual Exceedance Probability of the 2010 Flood in Rhode Island ...........................................41

Summary and Conclusions.........................................................................................................................43

Acknowledgments.......................................................................................................................................44

Selected References...................................................................................................................................44

Glossary.........................................................................................................................................................49

Tables 7, 13, and 15 ......................................................................................................................................51

Appendix 1. Basin Characteristics Considered for Use in the Regional Regression Analysis ...78

Appendix 2. Measurement of Regression Error..................................................................................80

Appendix 3. Link to Spreadsheet RI_Flood-Flow-Equations.xls .......................................................81
iv

Figures

1. Map showing general area and selected streamgages used in the Rhode Island 

flood frequency study ..................................................................................................................3

2. Map showing land cover in the study area in Rhode Island, Connecticut, and 

Massachusetts from the 2006 National Land Cover Database.............................................4

3. Map showing hurricane and hurricane related storm tracks from 1851 through 2008 

in and near Rhode Island.............................................................................................................5

4. Map showing streamgage skews used to develop the regional skew at selected 

streamgages in Rhode Island, eastern Connecticut, and south-central and eastern 

Massachusetts............................................................................................................................14

5. Graph showing upper stage-discharge rating and range of uncertainty of higher 

annual peak flows used in flood frequency analysis at Mount Hope River near 

Warrenville, CT (01121000) ........................................................................................................16

6. Graphs showing uncertainty of A, annual peak and historic flows used to compute 

B, flood frequency curve at Mount Hope River near Warrenville, CT (01121000)............17

7. Boxplots showing selected streamgage basin characteristics in Rhode Island, 

Connecticut, and Massachusetts used in flood frequency analysis .................................20

8. Boxplot showing residuals of generalized least squares (GLS) regional regression of floods for 20- to 0.2-percent annual exceedance probabilities at 41 selected 

streamgages in Rhode Island, Connecticut, and Massachusetts......................................22

9. Map showing residuals of generalized least squares (GLS) regional regression and 

at-site 1-percent annual exceedance probability flood flows at 41 selected 

streamgages in Rhode Island, Connecticut, and Massachusetts......................................23

10. Graphs showing flood magnitudes for selected annual exceedance probabilities determined from at-site analyses and from regional flood flow equations at 

A, 41 streamgages in Rhode Island, Connecticut, and Massachusetts, and B, 18 

streamgages in Rhode Island ...................................................................................................24

11. Graph showing regional regression estimates of the flood flows and confidence 

intervals for a hypothetical basin.............................................................................................26

12. Graphs showing relation of the magnitude of the 20-percent annual exceedance 

probability flood determined by regionalized equation to impervious area for A, all 

basins and B, basins grouped by ranges of the basin underlain by sand and gravel.....28

13. Graph showing ratio of flood magnitudes for select annual exceedance probabilities 

normalized by drainage area between streamgages with different extents of basin 

urbanization .................................................................................................................................29

14. Boxplot showing ratio of urban to rural peak discharges for 20- and 1-percent annual 

exceedance probability flood in five states with separate flood flow equations ............30

15. Graphs showing trends in A, annual peak flows and detrended annual peaks, 

B, annual peak flows by quartile group, and C, decadal count of annual peak flows 

by quartile group for Branch River at Forestdale, RI (01111500).........................................32

16. Graph showing average number of annual peak flows by decade by quartile range 

among 15 streamgages with statistically significant trends above about the 

90-percent confidence level .....................................................................................................33

17. Boxplot showing projected influence of trends in annual peak flows at 15 longterm streamgages by the A, flood magnification factor and B, recurrence reduction 

factor.............................................................................................................................................34

18. Boxplot showing range of differences between flood flows calculated from at-site 

analysis of annual peak flows and weighted independent estimate for selected 

annual exceedance probabilities.............................................................................................36
v

19. Boxplot showing differences from at-site analyses and regional regression 

equations in this study and regression equations from previous study by Johnson 

and Laraway (1977) for 18 streamgages in Rhode Island (table 7) for 10-, 1-, and 

0.2-percent annual exceedance probability floods ..............................................................41

Tables

1. Streamgages compiled from the U.S. Geological Survey National Water Information 

System (NWIS) peak-flow database and pertinent characteristics used in regional 

flood flow analysis for Rhode Island .........................................................................................7

2. Streamgages used in the flood frequency analysis with extended record made with 

the maintenance of variance extension (MOVE).....................................................................9

3. Streamgages with historic records used in the study .........................................................10

4. Outliers detected in peak-flow database for streamgages used in the floodfrequency analysis .....................................................................................................................12

5. Summary of generalized skew values determined for Rhode Island and nearby 

surrounding areas ......................................................................................................................14

6. Annual exceedance probability, flood quantiles, and confidence limits for Mount 

Hope River near Warrenville, CT (01121000) ..........................................................................18

7. Estimated magnitude of flood flows and confidence limits for selected annual 

exceedance probabilities at selected streamgages in Rhode Island, Connecticut, 

and Massachusetts for the period of record through 2010 .................................................52

8. Ranges of the basin characteristic values used to develop regional flood flow 

regression equations .................................................................................................................21

9. Pseudo-coefficient of determination (pseudo-R2), average variance of prediction, 

and standard error of prediction for the regional flood flow regression equations........25

10. Model error variance and covariance values needed to determine the uncertainty 

of the regional regression equations ......................................................................................26

11. Characteristics of three basins used to compare effects of urbanization .......................28

12. Trends in annual peak flows at streamgages with 70 or more years of unregulated 

systematic recorded identified by the Kendall trend test....................................................31

13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual 

exceedance probability floods determined from at-site analyses, regional regression 

equations, and weighted independent estimates .................................................................61

14. Streamgages with short-term records in Rhode Island that were not used in the 

regional flood frequency analysis............................................................................................37

15. Estimated magnitude of flood flows and confidence limits for annual exceedance 

probabilities at short-term streamgages in Rhode Island ...................................................70

16. Regional exponent for drainage area adjustment of a flood flows at an ungaged site 

on gaged stream determined from the regional regression of drainage area.................39

17. March–April 2010 flood peak and annual exceedance probability at active 

streamgages in Rhode Island ...................................................................................................42
vi

Conversion Factors, Datum, and Abbreviations

Inch/Pound to SI

Multiply By To obtain

Length

foot (ft) 0.3048 meter (m)

mile (mi) 1.609 kilometer (km)

Area

acre 0.4047 hectare (ha)

square mile (mi2) 259.0 hectare (ha)

Volume

cubic foot (ft3) 0.02832 cubic meter (m3)

Flow rate

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

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

 °C= (°F–32)/1.8

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

(NAVD 88).

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

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

Abbreviations

AEP annual exceedance probability

AVP average variance of prediction

BDF basin development factor

B17B Bulletin 17B

DA drainage area

EMA expected moments algorithm

FEMA Federal Emergency Management Agency

GLS generalized least square

IACWD Interagency Committee on Water Data

IMPERV impervious area

LPIII log-Pearson type III

MGB multiple Grubbs-Beck test

MOVE maintenance of variance extension

NFF National Flood Frequency
vii

NHD National Hydrography Dataset

NOAA National Oceanic and Atmospheric Administration

NWIS National Water Information System

OLS ordinary least squares

PILP potentially influential low peaks

RMSE root mean square error

StorNHD basin storage

STRDEN stream density

USACE U.S. Army Corps of Engineers

USGS U.S. Geological Survey

VIF variance inflation factor

WIE Weighted Independent Estimator

WLS weighted least squares
THIS PAGE INTENTIONALLY LEFT BLANK
Magnitude of Flood Flows for Selected Annual 

Exceedance Probabilities in Rhode Island Through 2010

By Phillip J. Zarriello, Elizabeth A. Ahearn, and Sara B. Levin

Abstract

Heavy persistent rains from late February through March 

2010 caused severe widespread flooding in Rhode Island 

that set or nearly set record flows and water levels at many 

long-term streamgages in the State. In response, the U.S. 

Geological Survey, in partnership with the Federal Emergency 

Management Agency, conducted a study to update estimates 

of flood magnitudes at streamgages and regional equations 

for estimating flood flows at ungaged locations. This report 

provides information needed for flood plain management, 

transportation infrastructure design, flood insurance studies, 

and other purposes that can help minimize future flood damages and risks.

The magnitudes of floods were determined from 

the annual peak flows at 43 streamgages in Rhode Island 

(20 sites), Connecticut (14 sites), and Massachusetts 

(9 sites) using the standard Bulletin 17B log-Pearson type 

III method and a modification of this method called the 

expected moments algorithm (EMA) for 20-, 10-, 4-, 2-, 1-, 

0.5-, and 0.2-percent annual exceedance probability (AEP) 

floods. Annual-peak flows were analyzed for the period of 

record through the 2010 water year; however, records were 

extended at 23 streamgages using the maintenance of variance extension (MOVE) procedure to best represent the 

longest period possible for determining the generalized skew 

and flood magnitudes. Generalized least square regression 

equations were developed from the flood quantiles computed at 41 streamgages (2 streamgages in Rhode Island 

with reported flood quantiles were not used in the regional 

regression because of regulation or redundancy) and their 

respective basin characteristics to estimate magnitude of 

floods at ungaged sites. Of 55 basin characteristics evaluated as potential explanatory variables, 3 were statistically 

significant—drainage area, stream density, and basin storage. 

The pseudo-coefficient of determination (pseudo-R2) indicates 

these three explanatory variables explain 95 to 96 percent of 

the variance in the flood magnitudes from 20- to 0.2-percent 

AEPs. Estimates of uncertainty of the at-site and regression 

flood magnitudes are provided and were combined with their 

respective estimated flood quantiles to improve estimates of 

flood flows at streamgages.

This region has a long history of urban development, 

which is considered to have an important effect on flood flows. 

This study includes basins that have an impervious area ranging from 0.5 to 37 percent. Although imperviousness provided 

some explanatory power in the regression, it was not statistically significant at the 95-percent confidence level for any of 

the AEPs examined. Influence of urbanization on flood flows 

indicates a complex interaction with other characteristics that 

confounds a statistical explanation of its effects.

Standard methods for calculating magnitude of floods for 

given AEP are based on the assumption of stationarity, that is, 

the annual peak flows exhibit no significant trend over time. A 

subset of 16 streamgages with 70 or more years of unregulated 

systematic record indicates all but 4 streamgages have a statistically significant positive trend at the 95-percent confidence 

level; three of these are statistically significant at about the 

90-percent confidence level or above. If the trend continues 

linearly in time, the estimated magnitude of floods for any 

AEP, on average, will increase by 6, 13, and 21 percent in 10, 

20, and 30 years’ time, respectively.

In 2010, new peaks of record were set at 18 of the 

21 active streamgages in Rhode Island. The updated flood 

frequency analysis indicates the peaks at these streamgages 

ranged from 2- to 0.2-percent AEP. Many streamgages in 

the State peaked at a 0.5- and 0.2-percent AEP, except for 

streamgages in the Blackstone River Basin, which peaked 

from a 4- to 2-percent AEP.

Introduction

Following heavy persistent rains from late February 

through March 2010, severe flooding set or nearly set record 

streamflows and water levels, causing a state of emergency to 

be declared in many communities in Rhode Island, and a statewide presidential disaster declaration (EM–3311) on March 

30, 2010. The President’s action affected the emergency recovery operations in Bristol, Kent, Newport, Providence, and 

Washington Counties. The flood has been characterized as the 

worst in 200 years and is estimated to have caused damages 

in the hundreds of millions of dollars. As part of the recovery operations, the U.S. Department of Homeland Security’s 

Federal Emergency Management Agency (FEMA) required 

analysis of the flood to assess damages and to prepare for and 

minimize future flood damages.
2 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Flood flows in Rhode Island have not been comprehensively examined since the mid-1970s (Johnson and Laraway, 

1977) and then only for a limited range of basin sizes and 

recurrence probabilities. Flood magnitudes for a range of 

annual exceedance probabilities (AEPs) are an important part 

of determining flood prone areas and risk assessment. Floods 

for a given AEP magnitude are routed through hydraulic 

models that convert the flow into a water level on the basis of 

the river’s capacity or conveyance. The best possible estimates 

of flood magnitudes for given AEP at gaged and ungaged sites 

is crucial for delineating flood zones, flood plain management, 

and designing infrastructure such as bridges and culverts so 

the conveyance capacity of a river is not unduly impaired.

Evaluation of the March–April 2010 peak discharge 

relative to the magnitude of floods over a range of AEPs is an 

important part of the post flood analysis and future flood management needs. The U.S. Geological Survey (USGS) entered 

into an agreement with FEMA in August 2010 to document 

and characterize the March–April 2010 flood. This report 

addresses the magnitude of floods at gaged and ungaged sites 

as part of that effort.

Purpose and Scope

The purpose of this report is to document the magnitude 

of flood flows over a range of AEPs at streamgages in 

Rhode Island and to document statewide regional equations 

for estimating flood flows at ungaged locations. The data 

used in this report were compiled from annual peak flows 

from 43 streamgages in Rhode Island, Connecticut, and 

Massachusetts through the 2010 water year. The report 

presents estimates of flood flows at streamgages at 20-, 10-, 

4-, 2-, 1-, 0.5-, and 0.2-percent AEPs, which also have been 

referred to as 5-, 10-, 25-, 50-, 100-, 200-, and 500-year 

return interval floods, respectively. Regression equations for 

calculating flood flows from selected basin characteristics 

for the same exceedance probabilities at ungaged streams 

and improving the estimated flood flows at gaged sites are 

presented. This report describes trends in the annual peak flow 

data and the implications for future floods. Also discussed are 

the influences of urbanization and the limitations of the study.

Study Area

The study area includes selected streamgages across 

Rhode Island and from eastern Connecticut and south-central 

and southeastern Massachusetts (fig. 1). Streamgages outside 

of the Rhode Island provide additional information that is 

representative of the hydrologic region, which can improve the 

analysis of flood magnitudes in Rhode Island.

Southern and eastern Rhode Island, southern Connecticut, 

and eastern Massachusetts are in the Coastal Lowland 

physiographic province of New England (Denny, 1982), 

which is characterized by low topography ranging in elevation 

from sea level to several hundred feet (fig. 1). Central and 

northwestern Rhode Island, northeastern Connecticut, 

and central Massachusetts are in the Central Uplands 

physiographic province of New England. This region is 

characterized by gently rolling hills with more incised valleys. 

The maximum elevation in the region is about 610 feet (ft).

Climate in the basin is classified as moist continental 

(National Oceanic and Atmospheric Administration, 2002) 

with a mean annual precipitation of about 46 inches that is 

normally evenly distributed throughout the year. Mean annual 

temperature is about 50°F in the region. Surficial geology consists of mainly glacial stratified deposits along the major river 

valleys and glacial till or exposed bedrock in the upland areas.

Land cover in the region ranges from highly developed in 

and near major metropolitan centers such as Providence, RI, 

to predominantly forested (fig. 2). Most developed areas are 

in eastern Rhode Island and Massachusetts, the Connecticut 

Valley (to the west), and coastal areas. Land cover and other 

characteristics vary by basin and are discussed in greater detail 

in the section describing basin characteristics used to develop 

region flood flow equations.

Hurricanes, remnants of hurricanes, and storms that 

never developed to hurricane strength are major causes of 

floods in southern New England. The National Oceanic and 

Atmospheric Administration (NOAA; undated) online tool for 

historical hurricane tracks indicates that 50 hurricanes, tropical 

storms, tropical depressions, and extratropical storms have 

passed within a 75 mile radius of central Rhode Island from 

1851 through 2008 (fig. 3). These storms typically originate in 

the central Atlantic and follow a track along the eastern United 

States up through New England. The hurricane tracking 

program lists 24 storms that passed through the region since 

1904 when streamflow data were first collected in the area; 20 

of these occurred since 1944 when streamgages have been in 

more widespread operation.

Previous Studies

Major storms of New England from 1635 through the 

late 1800s have been summarized by Perley (1891); however, 

most accounts of these historical events focused on damages 

to sailing ships and harbors that were the main livelihood of 

communities at that time. From these accounts, the types of 

storms and frequency can be inferred but little information 

is given on the physical dimensions of storms, such as the 

magnitude of the peak flow or depth of flooding. More specific 

accounts of the magnitude of large floods in Rhode Island and 

other affected areas have been described by Kinnison (1930) 

for the 1927 flood and limited information on major floods 

prior to the 1927, Grover (1937) for the flood of 1936, Paulsen 

and others (1940) for the 1938 flood, Bogart (1960) for 1955 

flood, Wood and others (1970) for the March 1968 flood, 

and Parker and others (1998) for the June 1998 flood. These 

accounts summarize streamflow information that was available 

at the time and indirect measurements of peak flows made 

following the floods. This usually entailed a hydraulic analysis 

made from high water marks surrounding a channel structure, 

such as a low-head dam, or a channel constriction, such as a 

bridge opening.
Introduction 3

Figure 1. General area and selected streamgages used in the Rhode Island flood frequency study.

01193500

01176000

01175670

01126600

01126500

01126000

01124500

01124000

01123000

01122500

01122000

01121000

01120500

01120000

01119500

01118500

01118300

01117800

01117500

01117468

01117350

01117000

01116000

01115630

01115187

01114500

01114000

01112500

01111500

01111400

01111300

01111000

1109500

01109403

01109060

01109000 01108000

01106000

01105000

01116500

01118000

01117420

01127500

Elevation

High: 610

Low: 0

01116000 Streamgage and number

EXPLANATION

Physiographic divide

(Denney, 1982)

Base from U.S. Geological Survey National Elevation Dataset 1-Arc Second, North American Vertical Datum 1988

Geographic projection, North American Datum 1983

Other data from various sources and projections

COASTAL LOWLANDS

CENTRAL UPLANDS

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

0 10 20 MILES

0 10 20 KILOMETERS

42°20'

42°

41°40'

41°20'

72°40' 72°20' 72° 71°40' 71°20' 71°
4 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Figure 2. Land cover in the study area in Rhode Island, Connecticut, and Massachusetts from the 2006 National Land Cover Database.

0 5 10 20 MILES

0 10 20 KILOMETERS

EXPLANATION

Water

Developed, open space

Developed, low intensity

Developed, medium intensity

Developed, high intensity

Barren

Decodious forest

Evergreen forest

Mixed forest

Shrub

Grassland

Pasture and hay

Cultivated crops

Forested wetland

Nonforested wetland

Boston

Providence

Worcester

Hartford

Springfield

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

72°40' 72°20' 72°0' 71°40' 71°20' 71°0'

42°20'

42°0'

41°40'

41°20'

41°0'

Base from National Land Cover Database 2006

USA Contiguous Alberts Equal Area projection 
Introduction 5

Major floods of New England by Thomson and others 

(1964) summarized major events up to the early 1960s from 

actual records, including those previously mentioned, and 

from other sources, such as newspaper stories and accounts 

by local residents. The earliest flood reported in Rhode 

Island was from the Providence Gazette of January 13, 1770, 

for Pawtuxet River and other rivers— “* * * a great flood 

* * * many Mills, Bridges, etc. carried away. * * * Rivers 

higher than they have been known these 30 years, some say 

50.” (Thomson and others, 1964, p. M10). Similar to the 

description of storms of New England by Perley (1891), 

Thomson and others (1964) accounts of flooding often 

lack sufficient detail to provide information on the physical 

dimensions of the storm that could be used in flood 

frequency analysis.

The first regionalized flood flow estimates for New 

England were published by the U.S. Army Corps of Engineers 

(USACE) in 1958. The USACE study provided different 

frequency curves for hurricane and nonhurricane floods and 

emphasized the difficulty of estimating the true frequency 

of large floods. The study concluded that the floods of 1927, 

1936, and 1955 in New England were rare events. Mixed 

population distributions for nonhurricane and hurricane related 

events at selected streamgages in Massachusetts were also 

found by Murphy (2001a,b). One limitation of a mixed population distribution analysis is the number of floods of hurricane 

origin. Moreover, the record 2010 flood, the largest flood in 

most parts of Rhode Island, was not of hurricane origin and, 

therefore, not associated with the largest flood events.

Benson (1962) evaluated floods and methods for computing the magnitude of floods in the United States for frequencies ranging from 1.2 to 300 years. Green (1964) developed 

regional flood frequency curves for the United States, of which 

Rhode Island would be included in the North Atlantic Slope 

basins that covered Maine to Connecticut. The report by Green 

contains a compilation of peak flow data through the 1960 

water year and frequency curves for floods for a given exceedance probability to drainage area by subregions.

In 1977, Johnson and Laraway published flood flow 

equations for Rhode Island for small rural basins less than 

10 square miles (mi2) in area. The equations were developed 

for estimating the magnitude of 50- and 20-percent AEPs 

Figure 3. Hurricane and hurricane related storm tracks from 1851 through 2008 in and near Rhode Island.

Extratropical storm

Category 3 hurricane

Category 2 hurricane

Category 1 hurricane

Tropical storm

Tropical depression

EXPLANATION

Image from National Oceanic and Atmospheric Administration Historical Hurricane Tracks at http://www.csc.noaa.gov/hurricanes 
6 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

floods (2- and 5-year floods) from 38 streamgages using 

annual peak flow records for the 1966–71 water years. 

Regression equations for estimating flood flows at ungaged 

sites were developed that use basin area, mean basin elevation, 

and forest cover as explanatory variables. When the National 

Flood Frequency (NFF) software program was introduced 

in 1994 (Jennings and others, 1994) the Rhode Island flood 

flow equations developed by Johnson and Laraway (1977) 

were incorporated into the database along with 10-, 4-, and 

2-percent AEP flood flows that were estimated from the 

50-percent AEP using factors presented by Green (1964). 

Comparison of flood records for the long term (1941–67) and 

the short term (1966–71) suggest that the extrapolated values 

should include an additional adjustment coefficient of 0.79 to 

correct for the short-term record. Estimates for extreme floods 

(0.2-percent AEP) were also incorporated into NFF by linear 

interpolation as described by Thomas and Kirby (2002).

Data Compilation

Data from the USGS National Water Information System 

(NWIS) peak-flow database (U.S. Geological Survey, 2012) 

were initially compiled for 84 streamgages. This initially 

included all streamgages in Rhode Island with a record for 9 or 

more years (42 total) and selected streamgages in Connecticut 

(28 streamgages) and Massachusetts (14 streamgages) that 

were screened for their proximity to Rhode Island as well 

as for regulation, record length, and quality. Many of the 

streamgages were removed from further analysis because 

of short record length, regulation, or suspect data quality. 

Of the initial 84 streamgages, 40 were used in the regional 

skew analysis—17 in Rhode Island, 14 in Connecticut, and 

9 in Massachusetts (fig. 1; table 1). The development of the 

regional regression equations included Adamsville Brook 

at Adamsville, RI (01106000), which was not used in the 

regional skew analysis because the record is from a relatively 

dry period, which caused an uncharacteristic large 

negative skew.

Magnitudes of floods for select AEPs were determined 

at the 41 streamgages used in the regional regression analysis 

and at long-term streamgages at Pawtuxet River at Cranston, 

RI (01116500), and Wood River near Arcadia, RI (01117800); 

these two streamgages were not used in the regional skew 

or regression analysis, however. Pawtuxet River at Cranston 

is regulated by the Scituate Reservoir and is not suitable 

for use in a regional analysis. Wood River near Arcadia is 

highly correlated with the downstream streamgage at Hope 

Valley (01118000) and is considered redundant. In statistical 

analyses, redundant sites incorrectly represent information in a 

regional context because they are not considered independent 

observations due to the fact that they share similar basin 

characteristics and hydrologic responses (Gruber and 

Stedinger, 2008).

Some streamgages are affected by flood control structures designed to decrease peak flows—Little River near 

Oxford, MA (01124500), Quinebaug River at Quinebaug, CT 

(01124000), Natchaug River at Willimantic, CT (01122000), 

and Shetucket River near Willimantic, CT (01122500). Flood 

control structures were built after these streamgages were in 

operation between 19 and 28 years; thus, these sites still have 

a sufficient period of unregulated flow that can be used in the 

flood frequency analysis. Unregulated annual peak flows at 

these streamgages were estimated after flood control structures 

were built using record extension methods. Annual peak flows 

also were estimated at relatively short-term streamgages and 

at long-term streamgages that were discontinued for short periods. The record extension provides the longest period possible 

for the flood frequency analysis.

Record Extension

Annual peak flow records were extended using a mathematical procedure developed by Hirsch (1982) known as 

maintenance of variance extension (MOVE). The method 

maintains the mean and variance of two streamgage records 

to extend the short-term record with the long-term streamgage 

(index station). MOVE is applied to the logarithms of the concurrent annual peaks of the two streamgage records.

Although the extended record analysis can potentially 

improve the regional skew estimate to better reflect long term 

conditions, it can also introduce increased inter-streamgage 

correlation by repeated use of an index station. Records were 

extended at 34 of the 84 streamgages initially selected. However, because the number of suitable index stations is limited, 

record extension was limited to 22 streamgages used in the 

skew and regression analyses (table 2) so that an index station 

was used no more than four times. Typically, an index station 

was used no more than twice to minimize inter-streamgage 

correlation in subsequent statistical analysis. Streamgages 

with extended record were selected on the basis of the length 

of record extended, the quality of the record extension, the 

number of times an index station was used, and the value of 

the streamgage in the analysis. Selection of extended record 

streamgages was generally made on the basis of the least 

amount of extended record and the greatest number of concurrent peaks as well as the best MOVE fit determined from the 

correlation coefficient and the root mean square error (RMSE). 

Several index streamgages were tested to determine the best 

streamgage to use for the record extension.

The index station record generally overlaps the shortterm record and most concurrent peaks were related to the 

same event. Correspondingly, the number of concurrent peaks 

is generally equal to the length of the short-term record, but 

if the records do not overlap or if the annual peaks are not 

related to the same event, then the number of concurrent 

peaks was less. Concurrent records ranged from 11 to 65 years 

and averaged 34 years. Scatterplots indicate that the relation between the base 10 logarithms (log10) transformed peak 
Data Compilation 

7

Table 1. Streamgages compiled from the U.S. Geological Survey National Water Information System (NWIS) peak-flow database and pertinent characteristics used in regional flood flow analysis for Rhode Island.—Continued[Years, number of years of systematic record or if regulated, number of years of unregulated record; DA, drainage area; mi2, square miles; STRDEN, stream density; mi/mi2, miles per square mile; StorNHD, storage; MBslp, mean basin slope; IMPERV, impervious area; SG, basin underlain by sand and gravel; R, River, nr, near; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

U.S. Geological Survey streamgage Record DA

(mi2)

STRDEN

(mi/mi2)

Percent

Number Name Begin End Years StorNHD MBslp IMPERV SG

Rhode Island streamgages

01106000a Adamsville Brook at Adamsville, RI 1941 1978 39 8.01 2.94 12.38 3.14 2.62 1.1001109403 Ten Mile R at Pawtucket Ave at East Providence, RI 1986 2010 24 53.75 2.34 7.55 3.60 23.97 57.9601111300 Nipmuc River nr Harrisville, RI 1964 2010 44 15.84 2.51 4.14 6.38 1.11 27.6501111400 Chepachet River at Chepachet, RI 1965 1975 11 17.46 2.03 10.03 9.55 2.42 35.1701111500 Branch River at Forestdale, RI 1940 2010 71 91.22 2.31 7.71 8.76 3.26 30.1901112500 Blackstone River at Woonsocket, RI 1929 2010 82 403.97 2.46 6.82 7.84 10.52 27.9701114000 Moshassuck River at Providence, RI 1963 2010 48 23.28 1.75 3.94 6.21 37.25 28.3601114500 Woonasquatucket River at Centerdale, RI 1941 2010 69 38.19 2.46 10.73 10.25 11.63 22.2901115187 Ponaganset River nr South Foster, RI 1994 2010 16 14.36 2.53 6.69 6.00 1.21 14.5601115630 Nooseneck River at Nooseneck, RI 1964 1981 22 8.20 1.25 3.38 6.45 2.26 35.0501116000 South Branch Pawtuxet River at Washington, RI 1940 2010 71 62.80 1.70 7.83 5.89 4.57 40.3301116500b Pawtuxet River at Cranston, RI 1939 2010 72 22.89 1.99 7.92 5.73 14.72 50.8901117000 Hunt River nr East Greenwich, RI 1940 2010 71 9.59 1.64 8.43 4.89 3.15 41.1201117350 Chipuxet River at West Kingston, RI 1973 2010 37 19.75 1.73 4.42 5.26 2.62 31.8101117420 Usquepaug River nr Usquepaug, RI 1976 2010 35 36.12 1.65 6.68 5.01 1.92 34.0401117468 Beaver River nr Usquepaug, RI 1977 2010 34 9.22 1.51 5.75 6.56 1.60 25.1001117500 Pawcatuck River at Wood River Junction, RI 1940 2010 70 100.13 1.43 14.88 4.67 2.64 43.7801117800b Wood River nr Arcadia, RI 1964 2010 47 35.14 1.35 7.84 6.92 0.83 27.0601118000 Wood River at Hope Valley, RI 1941 2010 69 74.53 1.45 7.85 6.52 1.95 25.2701118500 Pawcatuck River at Westerly, RI 1940 2010 70 294.88 1.62 11.77 5.73 2.89 35.27
8 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010 Table 1. Streamgages compiled from the U.S. Geological Survey National Water Information System (NWIS) peak-flow database and pertinent characteristics used in regional flood flow analysis for Rhode Island.—Continued [Years, number of years of systematic record or if regulated, number of years of unregulated record; DA, drainage area; mi2, square miles; STRDEN, stream density; mi/mi2, miles per square mile; StorNHD, storage; MBslp, mean basin slope; IMPERV, impervious area; SG, basin underlain by sand and gravel; R, River, nr, near; RI, Rhode Island; MA, Massachusetts; CT, Connecticut] U.S. Geological Survey streamgage Record DA (mi2

)

STRDEN

(mi/mi2

)

Percent

Number Name Begin End Years StorNHD MBslp IMPERV SG

Massachusetts streamgages

01105000 Neponset River at Norwood, MA 1939 2010 71 34.80 2.02 10.57 5.54 16.70 56.7301108000 Taunton River nr Bridgewater, MA 1929 2010 65 261.36 2.37 18.96 3.11 10.94 51.7601109000 Wading River nr Norton, MA 1925 2010 86 43.41 2.18 11.91 3.86 10.52 58.3001109060 Threemile River at North Dighton, MA 1966 2010 44 84.34 2.43 12.18 3.31 12.38 64.3801109500 Kettle Brook at Worcester, MA 1923 1978 56 31.29 3.16 8.93 7.99 9.80 17.1601111000 Mumford River at East Douglas, MA 1939 1951 13 29.12 2.62 10.85 7.26 1.45 13.1701124500 Little River nr Oxford, MA 1939 2010 19 27.41 3.26 11.37 8.03 1.73 9.2101175670 Sevenmile River nr Spencer, MA 1960 2010 50 8.81 3.01 6.09 8.65 0.77 12.7601176000 Quaboag River at West Brimfield, MA 1912 2010 98 149.47 3.01 8.55 8.78 1.83 21.31

Connecticut streamgages

01118300 Pendleton Hill Brook nr Clarks Falls, CT 1959 2010 52 4.00 1.57 5.86 7.76 0.50 9.9901119500 Willimantic River nr Coventry, CT 1932 2010 79 122.27 2.83 4.69 9.12 1.90 12.2201120000 Hop River nr Columbia, CT 1933 1984 52 74.54 2.31 5.28 7.71 1.70 9.9701120500 Safford Brook nr Woodstock, CT 1951 1981 31 4.17 2.60 3.39 8.73 0.60 1.1601121000 Mount Hope River nr Warrenville, CT 1941 2010 70 29.00 3.45 5.08 8.33 0.71 5.1101122000 Natchaug River at Willimantic, CT 1931 2010 21 170.28 3.24 6.04 8.65 1.35 14.2601122500 Shetucket River nr Willimantic, CT 1905 2010 28 401.43 2.86 5.36 8.52 1.88 13.7901123000 Little River nr Hanover, CT 1952 2010 61 29.99 3.53 6.77 8.18 0.57 18.3001124000 Quinebaug River at Quinebaug, CT 1932 2010 28 151.08 3.20 7.91 9.95 2.43 15.1201126000 Fivemile River at Killingly, CT 1938 1984 48 57.99 2.70 10.94 7.06 1.72 22.4001126500 Moosup River at Moosup, CT 1933 1984 52 83.35 2.07 5.81 6.62 1.72 23.9501126600 Blackwell Brook nr Brooklyn, CT 1962 1976 15 16.96 2.69 7.64 8.17 0.78 8.7201127500 Yantic River at Yantic, CT 1931 2010 80 89.20 2.84 7.07 7.29 1.44 15.7001193500 Salmon River at East Hampton, CT 1929 2010 82 100.61 2.31 5.73 8.12 1.92 11.68

aNot used in regional skew analysis.bNot used in regional skew or regression analysis.
Data Compilation 9

discharges is linear. Correlation coefficients between the shortand long-term streamgage records ranged from 0.84 to 0.98 

with an average of 0.91.

The systematic peak flow records used in the statistical analysis ranged from 11 to 98 years with average length 

of 51 years prior to record extension. After records were 

extended at 22 of the 40 streamgages used in the regional 

skew analysis, record length ranged from 56 to 98 years 

with an average length of 76 years. In effect, this represents 

the annual peak flows and the corresponding conditions that 

produced those peaks from about 1934 to 2010 for developing a regional skew. Streamgages with extended records, on 

average, had about 44 years of systematic record and about 

34 years of extended record.

Historic Data

Historic data are peak flows or stages, or both, that 

are outside the period of continuous record, also referred to 

as the systematic record. Historic peaks in the USGS peakflow database are typically large infrequent events where an 

effort was made to quantify the flood prior to an established 

streamgage. Sometimes this information is also collected 

after a streamgage is discontinued for later use in flood frequency studies.

Seven of the selected streamgages used in this study have 

one or more historic peaks from the 1927, 1936, and 1938 

water years (table 3). Historic data used in this study were 

at long-term streamgages that began operation following the 

Table 2. Streamgages used in the flood frequency analysis with extended record made with the maintenance of 

variance extension (MOVE).

[RI, Rhode Island; MA, Massachusetts; CT, Connecticut; R, River; Ave., Avenue; nr, near]

U.S. Geological Survey streamgage Number of

concurrent

peaks

Index

streamgage

Extended record

Number Name Correlation

coefficient

Total

years

Rhode Island streamgages

01111300 Nipmuc River near Harrisville, RI 44 01111500 0.95 71

01111400 Chepachet River at Chepachet, RI 11 01111500 0.86 71

01114000 Moshassuck River at Providence, RI 13 01114500 0.85 69

01115187 Ponaganset River near South Foster, RI 16 01111500 0.95 71

01115630 Nooseneck River at Nooseneck, RI 22 01111500 0.84 70

01117350 Chipuxet River at West Kingston, RI 37 01111500 0.92 71

01117420 Usquepaug River near Usquepaug, RI 35 01117500 0.96 70

01117468 Beaver River near Usquepaug, RI 35 01117500 0.94 69

1117800a Wood River near Arcadia, RI 47 01118000 0.95 69

Massachusetts streamgages

01108000 Taunton River near Bridgewater, MA 65 01109000 0.85 85

01109060 Threemile River at North Dighton, MA 44 01109000 0.98 85

01109403 Ten Mile R at Pawtucket Ave. at East Providence, RI 24 01109000 0.97 85

01111000 Mumford River at East Douglas, MA 13 01109000 0.92 71

01175670 Sevenmile River nr Spencer, MA 50 01176000 0.89 97

Connecticut streamgages

01118300 Pendleton Hill Brook near Clarks Falls, CT 52 01118000 0.88 69

01120000 Hop River near Columbia, CT 52 01193500 0.91 78

01120500 Safford Brook near Woodstock, CT 30 01121000 0.87 70

01122000 Natchaug River at Willimantic, CT 20 01119500 0.94 80

01122500 Shetucket River near Willimantic, CT 20 01119500 0.95 87

01124000 Quinebaug River at Quinebaug, CT 28 01119500 0.92 92

01126000 Fivemile River at Killingly, CT 33 01123000 0.84 74

01126500 Moosup River at Moosup, CT 52 01127500 0.86 78

01126600 Blackwell Brook near Brooklyn, CT 15 01123000 0.97 59

a

Streamgage not used in regional skew or regression analyses, but flood quantiles report for site. 
10 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

major flood of 1938; most historic data were obtained after the 

1936 flood. These data were determined by indirect measurements, such as flow over a dam, slope area, or contracted 

opening methods, using high water marks obtained following 

the flood. Indirect discharge measurements are subject to large 

uncertainties with a ±20 percent error generally considered a 

good measurement. Although the historic peaks are large in 

magnitude, they are generally well below the largest systematic record peak (table 3). The historic peak discharges 

ranked from second to the 20th highest peak of record and are 

generally appreciably smaller than the largest peak of record. 

Historic stage only records are believed to be caused by a tidal 

surge or are otherwise unrelated to the stage discharge relation 

at the streamgage and could not be used.

As previously described, larger historic peaks likely 

occurred but information on these events is qualitative and 

predates most efforts to quantify the magnitude of the event. 

One exception was found in the flood insurance study for the 

City of Warwick (Federal Emergency Management Agency, 

1981), which states:

“On February 11–14, 1886, a flood known as the 

greatest ever on the main stem Pawtuxet River 

resulted in 7 to 8 inches of rainfall over the basin 

augmented by snowmelt with an estimated water 

equivalent of 2 inches (Green, 1964). Experienced 

flood levels were 6 to 7 feet higher than any other 

known flood before or since this event. There was 

no record of flows on the main stem, but previous 

studies by the COE [U.S. Army Corps of Engineers] 

estimated the discharge of the river was about 

14,000 ft3/s in the vicinity of the present U.S. Geological Survey (USGS) gage site in Cranston.”

No other information about how the 1886 flood peak was 

determined or reference to this event for design purposes in 

other areas in the region could be found.

The 1886 peak discharge is about equal to the measured 

2010 flood peak at Pawtuxet River at Cranston, RI (01116500) 

streamgage, which is the largest recorded peak. Other supporting information on the magnitude of the 1886 flood was qualitative (Kinnison, 1930; Green, 1964; Thomson and others, 

1964). Kinnison (1930) described the 1886 flood as being of 

such magnitude that “Records of this storm served as a basis 

for waterway design in this district since that time.” The 1886 

peak was treated as an historic peak in the flood analysis at 

Pawtuxet River at Cranston, RI (01116500) streamgage in this 

study, but it should also be noted this streamgage was not used 

in the regional analysis because of upstream regulation from 

a supply reservoir. Updated at-site flood statistics are reported 

for the streamgage because of flooding issues along this river. 

It should also be noted that the river was unregulated at the 

time of the 1886 flood, but the available storage in the supply 

reservoir was exhausted at the time of the 2010 peak (flow was 

going over the spillway), which indicates that the 2010 peak 

was minimally affected by regulation.

Magnitude of Flood Flows at 

Streamgages

The magnitude of floods at streamgages is typically 

determined from the statistical properties of the annual 

peak flows using guidelines developed by the Interagency 

Committee on Water Data (IACWD) last published in 1981 

and revised in 1982, known and herein referred to as Bulletin 

17B. Bulletin 17B generally recommends fitting annual 

peak flows at a streamgage to a log-Pearson type III (LPIII) 

distribution to describe the likelihood of occurrence, or the 

annual exceedance probability (AEP) of a flood, the procedure 

herein is referred to as B17B. The magnitude of the flood for 

a given AEP using B17B is computed from three properties 

Table 3. Streamgages with historic records used in the study. 

[--, no data in peak-flow file; stage, stage only; discharge, in cubic feet per second; years are water years; RI, Rhode Island; CT, Connecticut]

U.S. Geological Survey streamgage Systematic 

record Historic record peak discharge Systematic record peak

Number Name Begin End 1927 1936 1938 Rank Discharge Year

01111500 Branch River at Forestdale, RI 1940 2010 -- 5,800 -- 2 6,290 2006

01118000 Wood River at Hope Valley, RI 1941 2010 -- 1,540 -- 8 5,470 2010

01118500 Pawcatuck River at Westerly, RI 1940 2010 6,300 3,150 Stage 3, 20 10,800 2010

01114500 Woonasquatucket River at Centerdale, RI 1941 2010 -- 1,000 -- 13 1,750 2010

01116000 South Branch Pawtuxet River at Washington, RI 1940 2010 -- 1,810 -- 4 5,480 2010

01117000 Hunt River near East Greenwich, RI 1940 2010 -- -- Stage -- 2,420 2010

01123000 Little River near Hanover, CT 1952 2010 -- 1,450 2,100 18, 4 2,964 1978
Magnitude of Flood Flows at Streamgages 11

of the logs of the annual peak data—the mean, the standard 

deviation, and the skew using the following equation:

logQ X K S P P = + , (1)

where

QP is the P-percent AEP flow, in cubic feet 

per second;

X is the mean of the logarithms of the annual 

peak flows;

KP is a factor based on the skew coefficient and 

the given percent AEP and obtained from 

appendix 3 in Bulletin 17B; and

S is the standard deviation of the logarithms of 

the annual peak flows, which is a measure 

of the degree of variation of the annual 

values about the mean value.

A relatively new procedure for calculating the magnitude 

of flood flows from annual peak flow records, known as the 

expected moments algorithm (EMA), also was used in this 

study. The EMA also uses a LPIII distribution, but unlike the 

LPIII procedures outlined in B17B, which are constrained 

to the moments of point values, the EMA can accommodate 

interval data to better define the distribution characteristics 

of annual peak flows (Cohn and others, 1997). Interval data 

can represent conditions such as the potential range of annual 

peak flows outside of the systematic and historic record and 

the uncertainties around recorded peaks used in the analysis. 

The EMA then uses an iterative procedure to recompute the 

moments from the interval data starting from the systematic 

record moments; the algorithm converges when the newly 

computed moments no longer appreciably differ from the last 

iteration of the computed moments. If only a systematic record 

is used in the analysis (that is, no interval data is used) and 

low outliers are not present, B17B and EMA analyses produce 

the same result. However, the confidence intervals around the 

flood quantiles differ because of different methods used by 

each procedure (Cohn and others, 2001). The EMA is expected 

to replace the standard LPIII procedure in Bulletin 17B in the 

next update of the guidelines and was applied in this study by 

use of the FORTRAN program PeakfqSA (Tim Cohn, U.S. 

Geological Survey, written commun., March 9, 2011) and the 

USGS PeakFQ program version 6.0.14667.

Often peak flow records do not follow a normal distribution, which affects the shape of the frequency distribution 

curve and, thus, the magnitude of floods for a given exceedance probability. The asymmetry of the frequency distribution 

curve is measured by the station skew. A single station, especially one with a short record, typically does not provide an 

accurate estimate of the “true” skew. To compensate, Bulletin 

17B recommends weighting the station skew with a generalized skew computed regionally from many streamgages to 

better utilize available information.

Skew Coefficient

Skews are highly influenced by the leverage of 

observations in the upper and lower tails of the annual peak 

flow record. Negative skews indicate that the left side of the 

probability distribution function is longer than the right side 

and that the bulk of the values lie to the right of the mean. 

In other words, smaller annual peaks outweigh the larger 

annual peaks, resulting in smaller computed flood flow for 

a given exceedance probability than records that are skewed 

to the right. The extent of this effect becomes more evident 

as the exceedance probability decreases. Bulletin 17B gives 

specific procedures for testing and handling high and low 

outliers because of their effect on the statistical properties of 

the data. It should be noted that skews are computed from the 

average cubed deviations from the mean of the logarithms of 

annual peak flows; thus, the shorter the record, the greater the 

likelihood that the skew will be leveraged by values at the tails 

of the distribution.

Low Outlier Adjustment

When streamgage records are skewed to the left by low 

outliers, the magnitude of flood flows are leveraged downward. Because the primary interest of a flood frequency 

analysis is the magnitude of floods that occur infrequently 

(AEP of 20 percent or less) Bulletin 17B outlines a conditional 

probability adjustment for low outliers before further analysis 

is made. Low outliers were initially detected and conditioned 

using the PeakFQ software (Flynn and others, 2006), which 

uses procedures described in Bulletin 17B; however, the test 

detects and conditions only the lowest outlier in the dataset. 

Single low outliers were detected in 5 of 40 streamgages used 

in the regional skew analysis (table 4).

Cohn and others developed a test to detect multiple low 

outliers (Tim Cohn, U.S. Geological Survey, written commun., 

March 3, 2011) using a modified version of the Grubbs-Beck 

test (Grubbs and Beck, 1972), referred to as the multiple 

Grubbs-Beck (MGB) test. The MGB test was used to check 

all streamgage records used in the analysis. Low outliers were 

detected at the same streamgages as previously detected by 

PeakFQ, but multiple low outliers were detected at Taunton 

River near Bridgewater, MA (01108000), at Moshassuck 

River in Providence, RI (01114000), and at Adamsville Brook 

in Adamsville, RI (01106000) at the 95-percent confidence 

level. Inspection of the Taunton River annual peak distribution 

indicates only a single low outlier was warranted, and only a 

single low outlier adjustment was used in subsequent analysis. 

Six low outliers were detected in the Adamsville Brook record 

that was conditioned in the at-site analysis using procedures 

in the EMA, which treats low outliers differently than the 

procedure outlined in Bulletin 17B. The EMA uses the MGB 

test to detect potentially influential low peaks (PILPs) and uses 

an iterative process to find the cutoff threshold along the LPIII 

distribution where PILPs no longer significantly affect the 

probability distribution. Annual peaks below that threshold are 
12 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 4. Outliers detected in peak-flow database for streamgages used in the flood-frequency analysis.

[Years of record applies to the systematic record; Thres-H, discharge threshold determined by Bulletin 17B test for high outliers; Thres-I, smallest retained 

observation determined by the modified Grubbs-Beck test; WY, water year in which outlier was detected; Q, magnitude of the outlier, in cubic feet per second 

(ft3/s); --, no outliers detected; streamgages with no detected outliers are not listed; RI, Rhode Island; CT, Connecticut; MA, Massachusetts]

U.S. Geological Survey streamgage Years of

record

High outliers Low outliers

Number Name Thres-H WY Q Thres-I WY Q

Rhode Island streamgages

01106000 Adamsville Brook at Adamsville, RI 39 436 -- -- 117 a --

01112500 Blackstone River at Woonsocket, RI 82 27,010 1955 32,900 1,970 -- --

01114000 Moshassuck River at Providence, RI 47 2,110 -- -- 667 b --

(extended record) 69 2,290 -- -- 469 1981 294

(extended record) 1949 403

01116000 South Branch Pawtuxet River, RI 70 3,570 2010 5,480 245 -- --

01116500 Pawtuxet River at Cranston, RI 71 7,700 2010 14,200 695 -- --

01117000 Hunt River near East Greenwich, RI 70 1,750 2010 2,380 114 -- --

01117350 Chipuxet River at West Kingston, RI 37 595 2010 748 50 1981 20

(extended record) 70 457 2010 748 38 1981 20

01117420 Usquepaug River near Usquepaug, RI 35 1,700 2010 2,070 140 -- --

(extended record) 70 1,460 2010 2,070 140 -- --

01117468 Beaver River near Usquepaug, RI 34 655 2010 901 46 -- --

(extended record) 69 554 2010 901 33 -- --

01117500 Pawcatuck River at Wood River Junction, RI 70 2,400 2010 3,490 350 -- --

01118000 Wood River at Hope Valley, RI 69 3,200 2010 5,470 460 -- --

01118500 Pawcatuck River at Westerly, RI 70 7,620 2010 10,800 1,270 -- --

Connecticut streamgages

01119500 Willimantic River near Coventry, CT 79 15,920 1955 24,200 728 -- --

01122000 Natchaug River at Willimantic, CT 21 17,410 1938 26,000 1,610 -- --

(extended record) 80 24,520 1955 36,600 1,370 -- --

(extended record) 1938 26,000

01122500 Shetucket River near Willimantic, CT 28 30,960 1938 52,200 3,030 -- --

(extended record) 87 45,530 1955 67,700 2,940 -- --

(extended record) 1938 52,200

01124000 Quinebaug River at Quinebaug, CT 28 22,840 1955 49,300 1,020 -- --

(extended record) 92 21,550 1955 49,300 589 -- --

01193500 Salmon River at East Hampton, CT 82 18,290 1982 18,500 940 -- --

Massachusetts streamgages

01108000 Taunton River near Bridgewater, MA 65 6,080 -- -- 1,250 1985 795

(extended record) 85 6,577 -- -- 1,736c 1985 795

01109500 Kettle Brook at Worcester, MA 56 3,330 1955 3,970 93 -- --

01124500 Little River near Oxford, MA 19 3,220 1955 8,340 66 -- --

(extended record) 98 2,890 1955 8,340 138 -- --

01175670 Sevenmile River near Spencer, MA 50 767 – – 64 1965 33

(extended record) 98 1,180 1955 3,270 33 -- --

(extended record) 1938 1,950

01176000 Quaboag River at West Brimfield, MA 98 5,480 1955 12,800 540 -- --

(extended record) 1938 8,470

a

Water years 1965, 1966, 1949, 1955, 1951, and 1950 with discharges of 66, 74, 85, 87, 90, and 103 ft3/s, respectively. 

b

Water years 1981, 1970, and 1971 with discharges of 294, 503, and 507 ft3/s, respectively.

c

Fifteen low outliers detected, but only the 1985 peak plotted below the probability distribution curve.
Magnitude of Flood Flows at Streamgages 13

treated as interval data that are less than the cutoff threshold 

value during the iterative process the EMA uses to converge 

on a new probability distribution. Despite the censoring of 

multiple PILPs at the Adamsville Brook streamgage, the EMA 

analysis still resulted in a large negative skew (-0.47) at this 

site that is atypical of the region. For this reason, the skew at 

the Adamsville Brook streamgage was not used to develop the 

regional skew.

High Outlier Adjustment

High outliers were detected in most of the streamgage 

annual peak records by PeakFQ (Flynn and others, 2006), 

which uses procedures described in Bulletin 17B. Historic 

peak flow data for the streamgages used in this study, as previously discussed, are often appreciably less than the highest 

peak in the systematic record. Other historical information is 

qualitative and does not provide the quantitative magnitude of 

the flood needed to treat high outliers.

High outliers detected in the streamgage records were 

retained as part of the systematic record without adjustment 

other than adjustments made for historic peaks in the peakflow database. In some cases, when the historic peak is appreciably less than the highest peaks in the systematic record, 

a high outlier threshold was specified in the B17B analysis 

that was set equal to the computed high outlier threshold for 

the period of systematic record. This prevents the computed 

high outlier threshold with historic data being set lower than 

warranted by the distribution of the peak flow values when 

relatively small historic peaks are present in the data. However, because of the short time span between the historic data 

and the start of the systematic data, the high outlier threshold 

has little effect on the flood frequency analysis.

High outliers were detected in 20 of 40 streamgages 

used in the regional skew analysis (table 4). At most of these 

streamgages only a single high outlier was detected. Spatially 

plotted station skews indicate two areas with high skews 

(fig. 4) corresponding to high outliers that originate from the 

1938, 1955, 1982, and 2010 floods (table 4). The recent 2010 

flood accounted for all the high outliers in central Rhode 

Island. This flood resulted from a succession of low pressure 

systems from late February through late March that collectively produced as much as 25 inches of rain, which is more 

than half the total average annual rainfall. The resulting peak 

flows often exceeded the previously recorded peak by two to 

three times in the central Rhode Island area and appreciably 

affected 9 of the 14 streamgages used flood flow analysis in 

the state.

In early June 1982, a large low pressure system moved 

slowly into the northeast and stalled, resulting in up to 

16 inches of rain during a 4-day period. The heaviest rain was 

in south-central Connecticut that resulted in a high outlier at 

Salmon River at East Hampton, CT (01193500). The event 

also produced high outliers at several other streamgages in 

this area that were not used in the final analysis in this study 

because of data concerns. In August 1955, back-to-back 

hurricanes, Connie and Diane, resulted about 20 inches of rain 

in a 2 week period in south-central Massachusetts, resulting 

in outliers at streamgages in south-central Massachusetts and 

north-central Connecticut. In September 1938, a large rainfall followed by a hurricane related rainfall event centered in 

northern Connecticut and central Massachusetts produced high 

outliers at three streamgages in that region. The 1938 flood 

was considered a major event; however, the 1938 peak has 

subsequently been exceeded by other peaks and is no longer 

detected as a high outlier at most streamgages that were in 

operation at the time or had an historic peak of the 1938 flood.

Generalized Regional Skew

The primary purpose of the generalized skew is to adjust 

the at-site skew to best reflect regional and long term conditions. Bulletin 17B recommends that generalized skews be 

developed from a minimum of 40 streamgages that are within 

a 100 mile radius of each other and have a record of at least 

25 years. Skews were determined from the annual peak flow 

records at the 40 streamgages listed in table 1 and from subsets of these streamgages. Skews were examined to determine 

if geographic patterns exist, but none were found except for 

patterns related to high outliers previously described.

After conditioning for low outliers and historic adjustments, skews were determined from the at-site analysis of 

annual peak flows (table 5) following B17B methods as 

implemented in PeakFQ. The skew computed from records 

for all 40 streamgages averaged 0.567 with a standard error of 

estimate, also known as the root mean square error (RMSE), 

of 0.626. Skews and RMSEs were determined from subsets 

of streamgages with successively longer records greater 

than or equal to 25, 50, and 60 years. As the period of record 

increased, the number of streamgages available progressively 

decreased; the average skew generally increases and RMSE 

decreases with the increasing period of record (table 5).

The average skew and RMSE also was determined 

from the same 40 streamgages using the extended record at 

23 streamgages as previously described after conditioning 

for low outliers and historic adjustments. Skews at some 

streamgages also were determined using the EMA to account 

for uncertainties in the annual peaks, better define the 

range of possible flows in the interval between historic and 

systematic data, and to censor multiple low outlier values. The 

accounting of data uncertainties used by the EMA is described 

in more detail in the section on “Quantifying Uncertainty 

of Annual Peaks.” At several streamgages with one or more 

low outliers or historic values, the standalone version of the 

EMA (PeakfqSA; Tim Cohn, U.S. Geological Survey, written 

commun., March 9, 2011) differed from the skew produced by 

the EMA implemented in PeakFQ version 6.0.14667. At these 

streamgages, the skew produced by B17B as implemented 

in PeakFQ was used to compute the regional skew; however, 

the differences were small and resulted in little change in the 

outcome of a regional skew.
14 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Figure 4. Streamgage skews used to develop the regional skew at selected streamgages in Rhode Island, eastern Connecticut, and 

south-central and eastern Massachusetts.

Table 5. Summary of generalized skew values determined for Rhode Island and nearby surrounding areas.

[RMSE, root mean square error; ≥, greater than or equal in reference to the length of the systematic record]

Selection criterion Number of 

streamgages

Record length (years) Skew RMSE

Average Minimum

All streamgages (no record extension) 40 51 11 0.567 0.624

≥ 25 years 29 60 28 0.576 0.555

≥ 50 years 21 69 50 0.512 0.438

≥ 60 years 16 75 61 0.603 0.427

All streamgages (23 with extended record) 40 77 56 0.522 0.463

42°20'

42°

41°40'

41°20'

72°40' 72°20' 72° 71°40' 71°20' 71°

EXPLANATION

Base from various sources and projections

Skew image interpolated from basin centroid point values by radial constant trending

Skew values

High: 1.65

Low: -0.12

Streamgage basin centroid

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

0 10 20 MILES

0 10 20 KILOMETERS

01193500

01127500

01126600

01126500

01126000

01124000

01123000

01122500

01121000

01120500

01120000

01119500

01118300

01109500

01176000

01175670

01105000 01124500

01109403

01109060

01109000

01108000

01115630

01111400

01111000

01117000

01116000

01114500

01114000

01118500

01118000

01117500

01117468

01115187

01111300

01117420

01122000
Magnitude of Flood Flows at Streamgages 15

The average skew of 0.52 and RMSE of 0.46 determined 

from 40 streamgages, 22 of which had extended record, were 

used to weigh the skews in the final at-site analysis of flood 

flows. These values are believed to best represent the generalized skew and error for the region by incorporating the largest 

number of streamgages and longest period possible. If the 

analysis were limited to streamgages with 25 or more years, 

as recommended in Bulletin 17B, about 24 percent of the 

streamgages would drop from the analysis.

The RMSE is a measure of the accuracy of the at-site 

skew, which is computed by the square root of the sum of 

the square differences between the at-site skew and the mean 

skew, divided by the number of sites minus one. The RMSE is 

used in the computation of the weighted skew and the confidence bounds of the flood magnitude in the at-site analyses. As 

currently implemented, the RMSE reflects sample and model 

error that has been separated in recent advances for computing generalized skews using Bayesian generalized least square 

(GLS) methods (Reis and others, 2005; Gruber and others, 

2007). The Bayesian GLS methods could not be applied in 

this study because of time constraints; however, the robustness 

of the method should be considered in future flood frequency 

studies. It should be noted that the RMSE within the range of 

computed RMSE values (table 5) had only a minor effect on 

the flood magnitude and confidence intervals.

A larger regional skew could be warranted on the basis of 

the streamgages with high skews (fig. 4) associated with the 

four independent floods previously described. Areas minimally 

affected by these events and correspondingly areas of lower 

skews have an equal likelihood of an event of similar severity, 

which could justify a regional skew based on the average of 

the high skew values. The skew determined from the actual 

and extended records for the 18 streamgages with one or 

more high outliers averaged 0.93 (RMSE 0.37), or about 

79 percent larger than the skew determined from the average 

skew (0.52) of the 40 streamgages. Sensitivity of the AEP 

flood magnitudes to the higher regional skew was evaluated 

for each of the 18 streamgages, which averaged 79 years in 

length and ranged from 56 to 98 years. Results indicate that, 

when the generalized skew increases from 0.52 to 0.93, the 

magnitudes of 1- and 0.2-percent AEP floods increase on 

average by about 7 and 13 percent, respectively. Conversely, 

floods with a 20-percent AEP decreased on average by 

0.7 percent. Magnitudes increased by less than 5 percent for 

10- to 2-percent AEP floods when the regional skew increased. 

However, a larger regional skew will have a greater effect on 

the flood magnitudes at a site as the streamgage record length 

at the site decreases.

Quantifying Uncertainty in Annual Peak Records

At a number of streamgages used in this study, the upper 

end of the stage-discharge rating is defined by one or more 

indirect measurements of streamflow. These measurements 

are based on hydraulic principles of contracted openings, flow 

over a dam, or slope area, and field information collected 

following a flood on high water levels and geometry of 

the channel and other structures. Even the best indirect 

measurements are subject to large uncertainties because of 

the accuracy of high water marks, debris confounding the 

hydraulic characteristics of structures, coefficients required by 

the hydraulic model, and other factors. Discharge determined 

by indirect methods sometimes far exceeds the highest direct 

streamflow measurements, which are generally made with 

greater accuracy. When this happens, the magnitude of annual 

peak flows above the direct streamflow measurement is 

affected by the accuracy of the indirect measurement. This in 

turn influences the magnitude of low probability floods, which 

are determined in large part by the largest peaks in the record 

that are defined by the upper part of the stage-discharge rating 

and its inaccuracies.

The uncertainty of annual peak flows associated with an 

indirect measurement or other causes can be incorporated into 

the at-site analysis by uncertainty estimates around the suspect 

peaks using the EMA. As an example, the high flow rating at 

Mount Hope River near Warrenville, CT (01121000) is defined 

by an indirect measurement following the 1955 flood using 

the contracted opening method. The indirect measurement of 

5,590 cubic feet per second (ft3/s) is the highest flow of record 

at this streamgage and is 2.6 times larger than the highest 

direct flow measurement of 2,150 ft3/s. During the 70-year 

streamflow record (1941–2010), 11 systematic annual peaks 

were 5 to 260 percent greater than the highest measured 

streamflow, with a median of 27 percent larger. Examination 

of the high flow rating (fig. 5) indicates a bend to the right 

above the measured flows to draw the rating through the 

indirect measurement. Without the indirect measurement, the 

hydrologic characteristics of the site indicate that the rating 

would likely have been extended as a straight line on a loglog scale as indicated by the red line on figure 5. Assuming 

the gage height for the 1955 peak is correct, the discharge 

estimated from the straight line rating is about 36 percent less 

than the indirect measurement. It should also be noted that the 

rating changes over time below about 1,200 ft3/s because of 

shifts in the channel control; the rating in effect at the time of 

the peak below 1,200 ft3/s best represents the stage-discharge 

relation at that time.

Uncertainty estimates of annual peak flows above 

2,000 ft3/s were estimated on the basis of the difference 

between the current high flow rating (blue line) and the 

extrapolated straight line rating (red line) in figure 5 that 

were incorporated in the EMA analysis as a lower uncertainty 

interval (fig. 6A). The uncertainty of specified annual peak 

flows was only bounded by a lower threshold to reflect the 

difference between the ratings of the blue and red lines. Also 

included in the analysis was an estimated peak flow from 

the 1938 flood, which was listed only as a peak stage in the 

peak-flow database that does not appear to be relevant to the 

gage datum. It was assumed that stage was entered only in the 

peak-flow database because an indirect measurement for this 

flood was made far upstream of the current streamgage; the 
16 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

drainage area at the streamgage is 28.6 mi2, whereas the 1938 

indirect measurement was made at a drainage area of 6.5 mi2. 

The 1938 indirect measurement adjusted for drainage area 

was estimated to be 3,780 ft3/s and was considered reasonable 

given the magnitudes of the 1938 and 1955 flood discharges 

at a nearby long-term streamgage (Hop River near Columbia, 

CT–0112000). Nevertheless, a ±25 percent lower and upper 

confidence interval was assigned to the 1938 peak discharge 

at Mount Hope River at Warrenville (2,840 and 4,720 ft3/s, 

respectively) to reflect the normal error of an indirect measurement and the drainage area difference. In addition, the period 

between the historic peak (1938) and the start of the systematic record (1941) was assigned a perception threshold of 

2,000 ft3/s (blue vertical bar; fig. 6A), which informs the 

EMA analysis that peak flows during this period did not 

exceed that threshold.

The resulting probability distribution curves (fig. 6B) 

indicate that the EMA begins to deviate from the B17B curve 

at about the 20-percent exceedance probability, and the difference increases as the exceedance probability decreases. 

The EMA fitted curve is about equal to the lower 95-percent 

confidence B17B curve at the lower exceedance probabilities. Flood magnitudes calculated by the EMA that incorporate some of the data uncertainties at the Mount Hope River 

streamgage decreased relative to the flow computed by B17B 

from about 4 to 18 percent for the 10- to 0.2-percent exceedance probability, respectively (table 6). However, it should be 

noted that, despite the decrease in the fitted distribution curves 

from the B17B to the EMA, the magnitude of floods at the 

upper confidence level for lower probability floods was appreciably larger for the EMA than for the B17B distribution. The 

magnitudes of the upper confidence level EMA flows were 

about 6 to 60 percent larger for the 10- to 0.2-percent exceedance probability, respectively, relative to the B17B upper 

confidence level (fig. 6B; table 6).

Similar hydrologic judgment was used to determine 

uncertainties at other streamgages used in the analysis. Of 

the 43 streamgages used, uncertainty limits were specified at 20 streamgages for similar reasons described in the 

Mount Hope River example. The uncertainties of extended 

record peak flows were sometimes assigned on the basis of 

the quality of fit between the short-term streamgage and the 

index station, which in some cases were compounded by the 

uncertainties of both streamgage records. On average, the 

skew decreased by about 16 percent at streamgages where 

uncertainties were applied in the EMA analysis compared with 

the skew determined from B17B analysis.

Figure 5. Upper stage-discharge rating and range of uncertainty of higher annual peak flows used in flood frequency 

analysis at Mount Hope River near Warrenville, CT (01121000).

Ratings in this range

varied over time and

are not shown

Stage, in feet

Discharge, in cubic feet per second

1,000 10,000

4.6

6.6

8.6

10.6

400 5,000

Estimate of annual peak uncertainty used in flood frequency 

analysis determined from the difference between the existing 

stage-discharge rating (blue line) drawn through the indirect 

discharge measurement and the rating extended from direct 

discharge measurements (red line)

Uncertainty interval

of annual peak

Direct discharge measurement 

EXPLANATION

Current rating (no. 37)

Rating estimated from direct discharge measurements

Indirect discharge measurement 

Annual peaks above 2,000 cubic feet per second 
Magnitude of Flood Flows at Streamgages 17

Figure 6. Uncertainty of A, annual peak and historic flows used to compute B, flood frequency 

curve at Mount Hope River near Warrenville, CT (01121000). The perception threshold, assigned to 

the period between the historic peak (1938) and the start of the systematic record (1941), informs 

the EMA analysis that peak flows during this period did not exceed that threshold. Bulletin 17B is 

Interagency Committee on Water Data (1981).

1930 1940 1950 1960 1970 1980 1990 2000 2010

Water year

100

1,000

10,000

Historic peak

Systematic peak

Uncertainty interval

Perception threshold (1938–41)

Discharge, in cubic feet per second

EXPLANATION

98 90 60 30 10 2 0.2

Annual exceedance probability, in percent

100

1,000

10,000

100,000

Peak discharge, in cubic feet per second

Fitted frequency

Systematic peak

Historic peak

95-percent confidence interval

Uncertainty interval of annual flood peak

Perception threshold (1938–41)

Expected Moments Algorithm (EMA)

EXPLANATION

Fitted frequency

95-percent confidence interval

Bulletin 17B Log Pearson-Type III (LPIII)

A. Annual peak flow and historical flows

B. Flood-frequency estimates and uncertainty
18 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Annual Exceedance Probability Flood Estimates

The magnitudes of flood flows were computed at 43 

streamgages in Rhode Island (20 sites), Connecticut (14 sites), 

and Massachusetts (9 sites) using B17B as implemented in 

PeakFQ (Flynn and others, 2006). At-site flood magnitudes 

also were computed by the EMA analysis (Cohn and others, 1997, 2001; Griffs and others, 2004) as implemented in 

PeakFQ version 6.0.14667 and in PeakfqSA (Tim Cohn, U.S. 

Geological Survey, written commun., March 9, 2011). All 

at-site analyses were determined using a weighted regional 

skew of 0.52 and RMSE of 0.46, except for Pawtuxet River 

at Cranston, RI (01116500), where only the at-site skew was 

used because of upstream regulation from a supply reservoir.

Results (table 7, in back of report) are presented for 20-, 

10-, 4-, 2-, 1-, 0.5-, and 0.2-percent AEPs, which are also 

referred to as 5-, 10-, 25-, 50-, 100-, 200-, and 500-year floods. 

The results include a B17B analysis for the streamgage period 

of record and for extended record were applicable, except for 

Chepachet River at Chepachet, RI (01111400), which only has 

11 years of record and, therefore, only the extended record 

analysis is presented. For comparison purposes, the table also 

provides the flood flows computed from the systematic record, 

which are based on the station skew and do not account for 

low outlier or historic data adjustments.

Values listed in bold in table 7 (in back of report) are the 

values used to develop the regionalized flood flow regression 

equations. In general, values used in the regional regression 

were computed by B17B for the period of record if the record 

was not extended. If the record was extended, then the B17B 

extended record analysis values were used in the regional 

regression. If the uncertainties incorporated into the EMA 

were appreciable, then the EMA computed values were used; 

if the uncertainties are not appreciable or no uncertainties were 

incorporated into the analysis, then the EMA values are the 

same (or nearly so given rounding differences) to the B17B 

analysis for the same period of record. The EMA uncertainty 

estimates are summarized in the footnote for each streamgage 

where applicable.

Flood magnitude results are provided for Wood River 

near Arcadia, RI (01117800), but the streamgage was not 

used in the development of the regional flood flow equations. This long-term streamgage has 47 years of record, but 

the annual peak flows are highly correlated to the annual 

peaks at the downstream gage at Hope Valley (01118000) and 

therefore considered redundant. Pawtuxet River at Cranston, 

RI (01116500) also was not used in the regional regression 

because of upstream regulation.

Uncertainty of Estimates

Many factors affect the confidence interval surrounding 

estimates of the flood magnitude for a given AEP. Foremost is 

the extent to which the sample population (annual peak flows) 

represents the true population of flood magnitudes. Bulletin 

17B incorporates this uncertainty by the length of the record, 

and the mean and variability of the peak flows used in the 

analysis; the confidence level decreases, particularly at the 

tails of the distribution, as the record length decreases and the 

variability increases.

In addition to the improvements the EMA makes for 

quantifying uncertainty for the period of nonsystematic record 

and for specific peaks used in the analysis, the EMA also 

provides a more robust estimate of the overall uncertainty 

of the flood magnitude by a derived approximation of the 

variance of the EMA moments and flood quantile estimators 

(Cohn and others, 2001). In practice, annual peaks, 

particularly high outliers, are generally within the 95-percent 

confidence level determined by the EMA but often are well 

outside the 95-percent confidence level determined by B17B. 

Hence, the confidence intervals for a given AEP are much 

broader for the EMA than for B17B, but are more realistic of 

the range of potential flows for a given AEP.

Table 6. Annual exceedance probability, flood quantiles, and confidence limits for Mount Hope River near Warrenville, CT (01121000).

[Values are in cubic feet per second except for percent difference. CT, Connecticut; AEP, annual exceedance probability; B17B, Bulletin 17B (Interagency 

Committee on Water Data, 1981); EMA, expected moments algorithm; %, percent]

AEP

(percent)

B17B EMA

Percent difference

Estimate

95% confidence

Estimate

95% confidence

Lower Upper Lower Upper Estimate Lower Upper

10 2,370 2,060 2,810 2,280 1,910 2,970 -3.8 -7.3 5.7

4 3,360 2,830 4,170 3,120 2,500 4,670 -7.1 -12 12

2 4,270 3,510 5,480 3,860 2,970 6,550 -9.6 -15 20

1 5,350 4,300 7,100 4,700 3,470 9,160 -12 -19 29

0.5 6,640 5,210 9,100 5,670 4,000 12,800 -15 -23 41

0.2 8,720 6,640 12,400 7,160 4,750 19,700 -18 -28 59
Magnitude of Flood Flows at Ungaged Streams 19

Magnitude of Flood Flows at Ungaged 

Streams

Equations to estimate magnitude of floods at selected 

AEPs at ungaged sites were developed from flood magnitudes 

at selected streamgages described above and their respective 

basin characteristics. Basin characteristics are used to explain 

the variability of flow for a given AEP through regional 

regression techniques. Similar to the at site analysis, regression equations were developed for 20-, 10-, 4-, 2-, 1-, 0.5-, and 

0.2-percent AEP floods. The development of regional flood 

flow equations consist of three basic parts—(1) compilation of 

basin characteristics, (2) exploratory analysis of the characteristics and flood flows to evaluate the best explanatory variables and their transformations, and (3) use of robust regression methods to develop the final equations and uncertainty of 

the estimates.

Basin Characteristics

Basin characteristics are used to relate the magnitude of 

floods determined from the streamgage analyses to develop 

equations for estimating flood magnitudes at ungaged streams. 

A total of 55 basin and climate characteristics were compiled 

for the initial exploratory analysis of potential explanatory variables (appendix 1). These variables can be broadly 

characterized by land use type, terrain, infiltration, basin and 

stream morphology, and climate. The distribution of selected 

basin characteristics (fig. 7) for the 41 streamgages used in the 

analysis varied by state; generally, the characteristics overlap 

among states with differences reflecting the region characteristics shown in figures 1 and 2.

Exploratory Analysis

From the potential explanatory variables compiled, 

variables were evaluated for cross correlation and linearity. Variables that required transformation to achieve better 

linear relation are those that have a large range in values and 

are typically direct measures of a basin characteristic such as 

the drainage area (independent variable) and for flood flows 

(dependent variable). Most independent variables examined did not require transformation because they represent a 

characteristic that is normalized by the basin size or expressed 

in terms of a percentage, such as the percentage of basin that 

is impervious. Regardless of whether a transformation was 

needed, transformations were tested because of potential gains 

in the normality of the regression residuals. Exploratory statistics were made using TIBCO Spotfire S+ (version 8.1).

The ordinary least squares (OLS) method was used to 

identify explanatory variables that best describe the flood 

magnitudes for the selected AEPs using an automated subset 

selection from possible subsets of selected variables. Subsets 

of variables were made so that well correlated variables were 

not used simultaneously to avoid covariance that can adversely 

affect a regression. Variables within a subset are automatically 

tested individually and in various combinations to determine 

which variables or combinations of variables best explain the 

variability of the flood magnitudes for a given AEP among 

streamgages used in the analysis.

The explanatory variables that best describe the flood 

flows were selected on the basis of several factors, including 

the standard error (SE) of the estimate, Mallow’s Cp statistic, 

(3) adjusted R2, residual sum of squares (PRESS) statistic, 

and the statistical significance of the explanatory variables. 

The OLS models with a smaller SE, Mallow’s Cp, and PRESS 

values and higher adjusted R2 values were identified. In addition, the explanatory variables were selected based on normality of the distributed error or residuals and for multicolinearity 

by the variance inflation factor (VIF). From this analysis, six 

variables were chosen for further analysis—drainage area 

(DA), stream density (STRDEN), storage (StorNHD), mean 

basin slope (MBSLP), impervious area (IMPERV), and area 

underlain by sand and gravel (SG). The ranges of values used 

in the analysis are listed in table 8; the values by streamgage 

are listed in appendix 1.

The variables in table 8 were further tested using 

weighted least squares (WLS) regression, which indicated 

that transforming all variable values to base 10 logarithms 

produced slightly better models than only transforming flow 

and drainage area needed to satisfy requirements for linearity. 

WLS also was used to test different weighting schemes based 

on the period of record that was adjusted on the basis the overall quality of the record, and the amount of extended record 

and its quality. In all cases, the period of actual record produced a slightly better model fit than the other weights tested.

Regional Regression Equations

The final regression equations were developed by the 

generalized least squares (GLS) method as implemented in the 

Weighted Multiple Linear Regression program (WREG) version 1.03 (Eng and others, 2009). GLS in WREG incorporates 

the evolution of the technique as developed and described 

over time by Stedinger and Tasker (1985, 1986), Tasker and 

Stedinger (1989), Martins and Stedinger (2002), and Griffis 

and Stedinger (2007, 2009). The advantage of GLS compared 

with OLS and WLS is that GLS accounts for differences in 

available record length (as does WLS), but also accounts for 

the spatial correlation of concurrent annual peak flows among 

streamgages used in the regression. The GLS procedure 

separates the total variance of the residuals by model error and 

sample error by an estimator of the sampling error covariance 

matrix for each flood quantile and the error associated with the 

weighted skew. Collectively, the enhanced features of a GLS 

regression provide the most robust model for regionalization 

of flood flows (Griffis and Stedinger, 2007).

The best explanatory variables determined from the OLS 

and WLS analyses (table 8) were tested in GLS using the 
20 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Figure 7. Selected streamgage basin characteristics in Rhode Island (RI), Connecticut (CT), and Massachusetts (MA) used in flood 

frequency analysis.

EXPLANATION

Outlier

90th percentile

75th percentile

Median

Outlier

10th percentile

25th percentile

Miles per square mile

Percent

Mean Basin Slope

CT MA RI

Relief, in feet

Relief

Mean 

Elevation

Elevation, in feet NAVD 88

Stream Density

0

100

200

300

400

500

600

700

800

900

1.0

1.5

2.0

2.5

3.0

3.5

4.0

2

4

6

8

10

12

100

300

500

700

900

1100

1300

14 11 16 14 11 16

14 11 16

Number of Observations

All

41 41

41

Impervious Area

CT MA RI

Forest

Percent Percent Percent

0

10

20

30

40

50

60

70

20

30

40

50

60

70

80

90

0

10

20

30

40

Sand & Gravel

All

Water

Wetlands

CT MA RI

Area, in miles squared Percent Percent Percent

Storage Water & Wetlands

Drainage Area

0

1

2

3

4

5

6

0

100

200

300

400

500

0

5

10

15

20

25

0

5

10

15

20

25

All
Magnitude of Flood Flows at Ungaged Streams 21

period of actual systematic record to develop the covariance 

matrix and weights. The final analysis used log10 transformations for all variables. For all the AEPs flood quantiles DA, 

STRDEN, and StorNHD were statistically significant at the 

95-percent confidence level. The MBslp was not significant at 

the 95-percent confidence level for flood flows at and below 

the 4-percent AEP but was increasingly statistically significant 

for floods at and above the 2-percent AEP. However, including the MBslp in the regional equation was determined to be 

marginally beneficial at the lower exceedance probabilities 

and was dropped from the final equations. IMPERV, which 

is a surrogate measure of urbanization, was not statistically 

significant at the 95-percent confidence level at any AEP, but 

its influence on flood flows is discussed in more detail in the 

section on “Urban Influence.”

The final regional regression equations for the 20- 

through 0.2-percent AEPs (5- to 500-year floods) are:

. . Q log DA log STRDEN lo

20

2 124 0 870 0 770 0 856 10 10 10

% = ( . + × ( )+ × ( )− × . g S 10 ( torNHD))

(2)

. . Q log DA log STRDEN lo

10

2 264 0 870 0 790 0 893 10 10 10

% = ( . + × ( )+ × ( )− . × g S 10 ( torNHD)) (3)

. . Q log DA log STRDEN log

4

2 428 0 862 0 802 0 919 10 10 10

% = ( . + × ( )+ × ( )− . × 10 (StorNHD)) (4)

. . Q log DA log STRDEN log

2

2 537 0 857 0 801 0 940 10 10 10

% = ( . + × ( )+ × ( )− . × 10 (StorNHD)) (5)

. . Q log DA log STRDEN log

1

2 623 0 852 0 792 0 941 10 10 10

% = ( . + × ( )+ × ( )− . × 10 (StorNHD)) (6)

Q log DA log STRDEN l

0 5

2 713 0 851 0 816 0 975 10 10 10

.

( . . . .

% = + × ( )+ × ( )− × og10 (StorNHD)) (7)

Q log DA log STRDEN l

0 2

2 815 0 850 0 829 1 002 10 10 10

.

( . . . .

% = + × ( )+ × ( )− × og10 (StorNHD)) (8)

where

Q20% .... Q0.2% are flow magnitudes for 20- to 0.2-percent 

AEP floods, in cubic feet per second;

DA is the drainage area of the basin, in square 

miles;

STRDEN is the basin stream density, in miles per square 

mile; and

StorNHD is the basin storage, in percent.

Note that DA and STRDEN are positive coefficients, 

which means that, as DA and STRDEN increase, so does the 

magnitude of flow. StorNHD has a negative coefficient, which 

means that, as StorNHD increases, flow decreases. This is a 

reflection of the effects of storage in mitigating flood flows.

Equal distribution of residuals, the difference between the 

simulated and observed, is an important consideration in the 

validity of a linear regression model. Boxplots show residuals are nearly equally distributed around zero for each of the 

AEP flood quantiles (fig. 8), indicating the regression models 

are unbiased. Furthermore, the residuals show no spatial pattern (fig. 9), but appear to be inversely related to the station 

skew (fig. 4). Streamgages with high skews tend to have low 

residuals, and streamgages with low skews tend to have high 

residuals. One possible explanation is that streamgages with 

high at-site skews will have a lower weighted skew, causing 

the flow magnitudes to decrease and the residual to increase. 

Conversely, streamgages with low at-site skews will have a 

higher weighted skew, causing the flow magnitudes to increase 

and the residual to decrease.

No streamgage appears to have undue leverage or influence in the regression. However, Pendleton Hill Brook near 

Clark Falls, CT (01118300) is among the streamgages with 

the greatest leverage and influence because it has the smallest drainage area (4.0 mi2

) used in the analysis, and drainage 

area is the strongest explanatory variable. This underscores the 

importance of the inclusion of small basins in future regional 

regression equations if the equations are going to be applied to 

small drainage basins.

Table 8. Ranges of the basin characteristic values used to develop regional flood flow regression equations.

Basin characteristic Name Minimum Mean Maximum

Drainage area, in square miles DA 4.00 80.2 404

Stream density, in miles per square mile STRDEN 1.25 2.38 3.53

Storage, in percentage of basin in open water and wetlandsa StorNHD 3.37 8.08 19.0

Mean basin slope, in percent MBSlp 3.11 6.92 10.2

Impervious area, in percentage of basin area IMPERV 0.50 5.24 37.2

Sand and gravel, in percentage of basin underlain SG 1.10 25.9 64.4

a

As defined in the National Hydrography Dataset (NHD).
22 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Accuracy and Limitations

Regression equations are statistical models developed 

from explanatory variables that best explain the variability 

of flood flows and are subject to the limitations of the data. 

These include the range of explanatory variables used in the 

analysis and the scatter or variance between the predicted and 

observed values. How well the predicted values represent the 

true values, or the accuracy of a regression, is an important 

consideration in the application of the model and the interpretation of the results.

The three parameter regionalized flood flow equations 

(2–8) best fit the computed at-site AEP flood flows (fig. 10A) 

without overfitting the data. At higher flows, the regionalized 

equations tend to undersimulate flood flows, but these values 

are from basins larger than 100 mi2 outside of Rhode Island 

(fig. 10B). In addition, the Rhode Island regionalized flood 

flow equations are primarily needed for basins smaller than 

100 mi2 because the large basins in the state have long-term 

streamgages to can be used for flood analysis.

Several metrics of model fit are generated for the GLS 

analysis in WREG; these include the pseudo coefficient of 

determination (pseudo-R2), the average standard error of prediction, and the standard model error. The pseudo-R2

 (Griffis 

and Stedinger, 2007) value is based on the variability in the 

dependent variable (flood flow) explained by the regression 

after removing the effect of time sampling error. The pseudoR2

 is similar to the standard regression coefficient of determination (R2

) in that, the closer the value is to 1.0, the better the 

model fit and the greater the amount of variance explained by 

the regression. Pseudo-R2 ranged from 94 to 96 percent and 

was slightly lower at the higher and lower AEPs flood quantiles (table 9). The percent average standard error of prediction 

(table 9) is the percentage form of the mean of the variances of 

prediction calculated at each of the streamgages used in constructing the regression model (Tasker and Stedinger, 1986). 

The square root of the variance of prediction is the standard 

error of prediction. Both are measures in the spread or dispersion of the predicted value from the observed value; hence, the 

lower the values, the less the expected spread of predictions 

around the true (unknown) value. Details of how the average 

variance of prediction and average standard error of prediction 

are determined are given in appendix 2.

The equations produce estimates of flood flows for the 

select exceedance probabilities where human influences have 

little or no effect on the magnitude of floods. Rivers with large 

regulated impoundments for water supply or flood control, for 

example, would not be an appropriate use of these equations. 

Applicability of flood flow estimates determined from basin 

characteristics outside the range characteristics from which the 

equations were derived (table 8) is unknown.

Figure 8. Residuals of generalized least squares (GLS) regional regression of floods for 20- to 0.2-percent annual 

exceedance probabilities at 41 selected streamgages in Rhode Island, Connecticut, and Massachusetts.

EXPLANATION

Outlier

90th percentile

Outlier

10th percentile

Median

75th percentile

25th percentile

20 10 4 2 1 0.5 0.2

Annual percent exceedance probability

0

0.2

0.4

-0.2

-0.4

Residuals, in log10 cubic feet per second
Magnitude of Flood Flows at Ungaged Streams 23

Figure 9. Residuals of generalized least squares (GLS) regional regression and at-site 1-percent annual exceedance probability flood 

flows at 41 selected streamgages in Rhode Island, Connecticut, and Massachusetts.

CONNECTICUT

MASSACHUSETTS

RHODE

ISLAND

01193500

01127500

01126600

01126500

01126000

01124000

01123000

01122500

01121000

01120500

01120000

01119500

01118300

01109500

01176000

01175670

01124500 01105000

01109403

01109060

01109000

01108000

01115630

01111400

01111000

01117000

01116000

01114500

01114000

01118500

01118000

01117500

01117468

01115187

01111300

01117420

01122000

01106000

42°20'

42°

41°40'

41°20'

72°40' 72°20' 72° 71°40' 71°20' 71°

EXPLANATION

High: 0.25

Low: -0.25

Base from various sources and projections

Residuals interpolated from basin centroid point residual values by radial constant trending

Residual values

Streamgage basin centroid

0 10 20 MILES

0 10 20 KILOMETERS
24 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

100

1,000

10,000

100,000

100 1,000 10,000 100,000

At-site flood magnitude, in cubic feet per second

Regional model flood magnitude, in cubic feet per second 

Q

Q

Q

Q

Q

Q

Q

Percent annual exceedance probability

A. Rhode Island, Connecticut, and Massachusetts streamgages 

20%

10%

4%

2%

1%

0.5%

0.2%

EXPLANATION

EXPLANATION

100

1,000

10,000

100,000

100 1,000 10,000 100,000

At-site flood magnitude, in cubic feet per second

Regional model of flood magnitude, in cubic feet per second 

B. Rhode Island streamgages 

Percent annual exceedance probability

Q

Q

Q

20%

10%

4%

Q

Q

Q

Q

2%

1%

0.5%

0.2%

Figure 10. Flood magnitudes for selected annual exceedance probabilities determined from at-site 

analyses and from regional flood flow equations at A, 41 streamgages in Rhode Island, Connecticut, and 

Massachusetts, and B, 18 streamgages in Rhode Island.
Magnitude of Flood Flows at Ungaged Streams 25

Uncertainty Estimates of Regionalized Equations

The uncertainty of a regression equation is indicated 

by the confidence interval. A confidence interval is the 

spread between the minimum and maximum values within 

which there is a stated probability that the true value of the 

response variable can exist. As an example, the minimum 

and maximum values at the 95-percent confidence level for 

the 1-percent AEP flood for an ungaged site means there is 

95-percent confidence that the true value of the 1-percent AEP 

flood is within the stated intervals.

Tasker and Driver (1988) have shown that a 100(1–α) 

confidence interval for the true value of a streamflow statistic 

obtained for an ungaged site from a regression equation can be 

computed by:

Q

C

< < Q Q ×C, (9)

where

Q is the flood magnitude for the ungaged site, in 

cubic feet per second; and

C is the confidence interval computed as:

C = 1 Z Sp i 0 2

α ,

, (10)

where

Z α

2 is the normal critical value at a particular 

alpha level (α) divided by 2 (α of 0.05 is 

for a 95-percent confidence level and is 

equal to 1.96), and

Sp,i is standard error of prediction for site i.

The value of Sp,i is computed using the equation:

Sp,i = [γ2 + xiUxi′]0.5 (11)

where

	 γ2 model error variance,

xi a row vector of the logarithms of the 

explanatory variables (DA, STRDEN, and 

StorNHD) for site i, augmented by a 1 as 

the first element;

U covariance matrix for the regression 

coefficients; and

xi′ transpose of xi (Ludwig and Tasker, 1993).

An example calculation of the 95-percent confidence 

interval is given for a hypothetical ungaged stream site with 

the following characteristics—DA of 30 mi2, STRDEN of 

3.53 (mi/mi2), and StorNHD of 6.77 percent. The xi vector 

computed from the explanatory basin characteristics is

xi = {1, log10(30.0), log10(3.53), log10(6.77)}.

The model error variance (γ2) and the covariance matrix 

(U) were determined from the WREG GLS analysis and are 

reported in table 10. For a 1-percent AEP flood (100-year 

flood) the procedure for computing the 95-percent confidence 

interval is as follows:

• compute Sp,i using equation 11:

 Sp,I =(0.00908+0.00361)0.5 = 0.11264;

converted from log10 units, this equals a range of -22.8 

to 29.6 percent

• compute C using equation 10:

C=10(1.96×0.11264) = 1.66255

• compute the 1-percent AEP flood from equation 6:

Q1% = 3,590 ft3/s

• compute the 95-percent confidence interval from 

equation 9:

3 590

1 66255

3 950 1 66255 1

,

. , . < < Q % × ,

• or

2,160 ft3/s < 3,590 ft3/s < 5,960 ft3/s.

A spreadsheet for solving the regional regression equations at ungaged sites from user specified explanatory values 

for flood magnitudes with a 20-, 10-, 4-, 2-, 1-, 0.5-, and 

0.2-percent AEPs and the 95-percent confidence interval can 

be accessed through a hyperlink in appendix 3. The graphical results from the hypothetical test basin computed from the 

spreadsheet are shown in figure 11.

Table 9. Pseudo-coefficient of determination (pseudo-R2), 

average variance of prediction, and standard error of prediction 

for the regional flood flow regression equations.

Annual 

exceedance 

probability 

(percent)

Pseudo-R2 

(percent)

Average 

variance 

of prediction 

(percent)

Average 

standard error of 

prediction

 (percent)

20 96 27.2 25.1

10 95 25.9 23.4

4 96 24.0 20.9

2 96 24.5 21.1

1 96 24.2 20.6

0.5 96 26.6 22.3

0.2 95 29.6 24.8
26 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 10. Model error variance and covariance values needed to determine the uncertainty of the regional regression equations.

[γ2, the regression model error variance in equation 11; U, the covariance matrix in equation 11; The matrix horizontal and vertical variables are defined by the 

constant and the independent variables in equations 2–8 in the order they are given]

Annual exceedance 

probability 

(percent)

Model error

(γ2)

Covariance matrix 

(U)

20 0.0115 0.01494 -0.00113 -0.00998 -0.00962

-0.00113 0.00153 -0.00046 -0.00143

-0.00998 -0.00046 0.03065 -0.00023

-0.00962 -0.00143 -0.00023 0.01350

10 0.0101 0.01508 -0.00117 -0.01026 -0.00911

-0.00117 0.00146 -0.00021 -0.00139

-0.01026 -0.00021 0.03025 -0.00024

-0.00911 -0.00139 -0.00024 0.01273

4 0.0081 0.01522 -0.00113 -0.01083 -0.00857

-0.00113 0.00136 0.00009 -0.00139

-0.01083 0.00009 0.03150 -0.00075

-0.00857 -0.00139 -0.00075 0.01215

2 0.0082 0.01710 -0.00123 -0.01244 -0.00938

-0.00123 0.00147 0.00022 -0.00156

-0.01244 0.00022 0.03611 -0.00113

-0.00938 -0.00156 -0.00113 0.01338

1 0.0078 0.01847 -0.00122 -0.01446 -0.00998

-0.00122 0.00154 0.00042 -0.00177

-0.01446 0.00042 0.04305 -0.00227

-0.00998 -0.00177 -0.00227 0.01479

0.5 0.0092 0.02183 -0.00150 -0.01640 -0.01158

-0.00150 0.00180 0.00046 -0.00199

-0.01640 0.00046 0.04755 -0.00195

-0.01158 -0.00199 -0.00195 0.01672

0.2 0.0113 0.02696 -0.00184 -0.02055 -0.01427

-0.00184 0.00223 0.00059 -0.00247

-0.02055 0.00059 0.05946 -0.00252

-0.01427 -0.00247 -0.00252 0.02067

Figure 11. Regional regression estimates of 

the flood flows and confidence intervals for a 

hypothetical basin. The hypothetical basin has a 

drainage area (DA) of 30 square miles, a stream 

density (STRDEN) of 3.53 miles per square mile, and 

storage (StorHDN) of 6.77 percent.

100

1,000

10,000

100 10 1.0 0.1

Annual exceedance probability, in percent

Discharge, in cubic feet per second

Regional regression flood magnitude

95-percent confidence interval

EXPLANATION
Factors Affecting Flood Flow Estimates 27

Factors Affecting Flood Flow Estimates

Many factors affect the magnitude of flood flows, some 

of which are incorporated into the regional regression equations by the most significant explanatory variables. Two 

important factors not included in the regional regression that 

can affect estimates of the magnitude of floods are the extent 

of urbanization and trends in the annual peak flows. Urbanization can restrict infiltration of precipitation and alter drainage 

patterns to move water away from developed areas. To the 

extent that the streamgages used in the analysis reflect different degrees of urbanization, and if the effects of urbanization 

are reasonably stable over the streamgage record, the at-site 

analysis includes these effects in the computed flood magnitudes. Hence, regional regression equations developed reflect 

the effects of urbanization over the range of urban gradients of 

the streamgages used. The basic question is how representative the streamgages used in the analysis are to other urbanized basins where flood flow regression equations are applied. 

Trends in annual peak flows affect the fundamental statistical 

basis for flood frequency analysis as currently performed, 

which is based on the assumption of stationarity. Trends can 

affect both the at-site analyses of flood flows and the regression equations on which they are based.

Urban Influence

Urban drainage basins contain appreciable amounts of 

impervious surface, such as roads and rooftops, which restrict 

infiltration of precipitation into the soil and alter drainage 

systems to move water away from developed areas through 

storm water drainage systems and channelized streams. These 

changes can result in increased storm runoff and can alter 

the timing of runoff in a way that increases the magnitude 

of the peak streamflow for a given amount of precipitation. 

The effects of imperviousness have been found to be more 

pronounced for small, more frequent storms than large 

infrequent storms (Hollis, 1975; Konrad, 2003). The reason 

for this is that, during large storms, soils become saturated, 

preventing further infiltration; this causes surface runoff to 

increase similar to the effect an impervious surface has for any 

size storm. Nevertheless, urban adjustments to regionalized 

flood flow equations for rural basins have been made to 

include some measure of urbanization, such as impervious 

surface (Southard, 2010), population density (Watson and 

Schopp, 2009), or composite urban indices, such as the basin 

development factor, which accounts for impervious surface as 

well as storm sewers, culverts, and stream channel alterations 

(Sauer and others, 1983; Sherwood, 1994).

The suite of basin characteristics tested in the development of regional flood flow equations for Rhode Island 

includes the percentage of the basin that is covered by impervious area (IMPERV). IMPERV was considered an important 

factor because of the long history of development in this 

region and the recognition that most basins of interest with 

respect to flooding are urbanized to some extent. IMPERV in 

the basins used in the regionalization analysis ranged from 

0.5 to 37 percent with a mean of 5.2 percent (table 8), but the 

inter-quartile range among all basins was between 1.4 and 

4.6 percent, which limits the extent that to which urbanization 

can be addressed from the available data.

As previously mentioned, IMPERV was not a statistically 

significant explanatory variable at the 95-percent confidence 

level for any of the exceedance probabilities examined. 

Despite this lack of significance in this analysis, other studies (Robbins and Pope, 1996; Southard, 2010; Gotvald and 

Knaak, 2011) found that imperviousness is an important 

predictor of the magnitude of flood flows. The exploratory 

statistical analysis done in this study indicated that IMPERV 

provided some explanatory power, generally ranking fifth or 

sixth among the variables examined.

The relation of IMPERV to the magnitude of the AEP 

flood quantile was further examined and was found to be 

complicated by other basin characteristics that can offset the 

effects of urbanization. Most notable was no relation was 

found between the magnitude of the 20-percent AEP flow and 

imperviousness for all basins (fig. 12A) but when the basins 

are stratified by surficial geology type, basins underlain by 

more than 40 percent sand and gravel show an increasing 

relation between the magnitude of the 20-percent AEP flow 

and imperviousness (fig. 12B). Areas with higher percentages 

of sand and gravel generally allow for greater storm water 

infiltration; thus, when the infiltration capacity is reduced 

by imperviousness, the effects on peak flows become more 

apparent than in areas with naturally lower infiltration. Sand 

and gravel deposits also tend to be in valley fill areas in the 

lower parts of the basin where urban areas tend to be more 

concentrated. Where urban areas are concentrated in the lower 

basin the effects on peak runoff are less pronounced because 

the enhanced drainage from the urban areas accelerates the 

peak relative to the peak from the upper parts of the basin that 

can reduce overall peak flow from the basin. This interplay 

between variables complicates the effects of urbanization and 

its significance in regional analyses.

The relative increase in the annual maximum discharge 

in urbanized basins has been shown to be more substantial 

for small frequent floods than for large infrequent floods 

(Hollis, 1975; Konrad and Booth, 2002; Konrad, 2003). A 

similar relation can be seen at three long-term streamgages 

in Moshassuck River at Providence, RI (01114000), 

Woonasquatucket River at Centerdale, RI (01114500), 

and Wood River near Arcadia, RI (01117800). All three 

sites generally have similar dominant explanatory basin 

characteristics (table 11) except for the percentage of 

impervious area (about 37, 12, and 0.8 percent, respectively). 

The dominant explanatory basin characteristics at these sites 

ranged between 23.1 to 38.3 mi2 for DA, 1.35 to 2.46 mi/mi2

for STRDEN, and 4 to 11 percent for StorNHD. The mean 

basin slope (6 to 10 percent) and percentage of area underlain 

by sand and gravel (22 to 28 percent) are also similar among 

basins. The basins are also in close proximity to each other; 
28 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

the Moshassuck River and the Woonasquatucket River Basins 

share a common divide, and the Wood River Basin is about 

24 miles to the southwest of the other basins. Recent urban 

development in these basins has been mostly redevelopment 

of old development that dates back to the early industrial 

revolution (1800s) in the United States. Thus, the period of 

common streamflow record from these basins that starts in 

1964 is largely unaffected by new urban growth.

The 47-year common streamflow record and similar 

basin characteristics among these basins, other than the extent 

of imperviousness, provides an opportunity to compare the 

effects of urbanization. The at-site analysis as described previously was performed for each of these streamgages using a 

common period of record (1964–2010). The AEP flood quantiles were normalized for drainage area for comparison. Flood 

magnitudes increased as the percent impervious area increased 

for high AEP flows (smaller more frequent floods). However, 

when expressed as a ratio of the flood magnitude of the more 

urbanized basin to the less urbanized basin, the differences 

between basins becomes less clear (fig. 13). In all cases, the 

ratio decreases as the AEP decreases; that is, the effects of 

urbanization decrease for larger less frequent floods. The ratio 

of the Woonasquatucket River to the Wood River is near one 

at the 1-percent AEP flood flow and becomes less than one 

for less frequent floods. Further, the relative difference in the 

normalized flood magnitude between the two most urbanized 

basins (Moshassuck and the Woonasquatucket River) and the 

least urbanized basin (Wood River) decrease more as the AEP 

decreases relative to the differences between the two more 

urbanized basins. The most prominent decrease in the ratio 

Table 11. Characteristics of three basins used to compare effects of urbanization.

[DA, drainage area; mi2, square mile; Elev, elevation in North American Vertical Datum of 1988; STRDEN, stream density; mi2, square miles; mi/mi2, miles 

per square mile; IMPERV, imperviousness; StorNHD, storage; S&G, sand and gravel]

Number River DA 

(mi2)

Elev 

(feet)

STRDEN

(mi/mi2)

Percent

Slope Forest IMPERV StorNHD S&G

01114000 Moshassuck 23.1 202 1.75 6.2 53 37.2 3.9 28.4

01114500 Woonasquatucket 38.3 360 2.46 10.2 73 11.6 10.7 22.3

01117800 Wood 35.2 390 1.35 6.9 71 0.83 7.8 27.1

0 10 20 30 40

Percent impervious

Discharge, in cubic feet per second per square mile

0

20

40

60

80

100

0 10 20 30 40

High>40 percent

Medium 20 to 40 percent

Low <20 percent

Percent impervious

Basins grouped by percent area of 

sand and gravel

EXPLANATION

Figure 12. Relation of the magnitude of the 20-percent annual exceedance probability flood determined by regionalized 

equation to impervious area for A, all basins and B, basins grouped by ranges of the basin underlain by sand and gravel.
Factors Affecting Flood Flow Estimates 29

as the AEP decreases was between the most urbanized basin 

(Moshassuck) and the least urbanized basin (Wood River)—

from about 2.6 to 1.3 for 20- to 0.2-percent AEP flood flows, 

respectively. The least amount of change was between the 

two most urbanized basins—from about 1.5 to 1.9 for 20- to 

0.2-percent AEP flood flows, respectively. The reason for these 

relative differences is not clear, but underscores some of the 

differences discussed previously and below.

Adjustments to regional rural flood flow equations to 

account for the influence of urbanization on flood magnitudes have been developed by Sauer and others (1983) for the 

United States. The rural equations were modified by Sauer 

and others to adjust for urbanization by including channel 

slope, basin storage, rainfall, impervious surface, and the basin 

development factor (BDF). The BDF is an index that accounts 

for alterations to the stream channel, sewering, and the extent 

of curbed streets, which often requires extensive field investigation to determine. Sauer and others showed that the urban to 

rural peak discharge ratio increases as impervious surface and 

BDF increase and decreases as the return period of the storm 

increases. For the 2-year storm, the ratio ranged from 1.3 in 

areas with low percent impervious and low BDF to 3.6 in 

basins with high impervious surface and a high BDF. For the 

100-year storm, the ratio of urban to rural flood flow ranged 

from 1.1 in areas of low impervious and low BDF to 2.4 in 

basins with high impervious and high BDF.

A more recent urban adjustment to rural flood flow 

equations was developed by Moglen and Shivers (2006) 

using either imperviousness or population density. The 

principal advantage of this method compared with the method 

developed by Sauer and others (1983) is that the explanatory 

variables can be readily obtained from available geographic 

information. However, the Moglen and Shivers method 

requires a different, time consuming process that involves 

adjusting annual peak flows over time to solve for coefficients 

that minimize an objective function in a nonlinear regression 

model. This analysis was not performed, but the calibrated 

coefficients for simple impervious models determined by 

Moglen and Shivers (2006) from 78 streamgages with 

30 years record from several areas of the country are based 

on the following equations:

UQ20 RQ20 IA 0 862 0 147 2 866 1 % % = × . ( ) + . .

(12)

UQ10 RQ10 IA 0 866 0 128 2 827 1 % % = . × ( ) + . .

(13)

UQ4 4 RQ IA 0 870 0 102 2 965 1 % % = × . ( ) + . .

(14)

UQ2 2 RQ IA 0 873 0 08253 080 1 % % = × . ( ) + . .

(15)

UQ1 1 RQ IA 0 876 0 06283 206 1 % % = . × ( ) + . .

(16)

UQ0 2 RQ0 2 IA 0 883 0 01663 541 1 . .

. .

. % % = × ( ) + (17)

where

UQp% discharge adjusted for urbanization, in cubic 

feet per second, for p-percent AEP;

RQp% rural discharge estimate, in cubic feet per 

second, for p-percent AEP; and

IA impervious area, in percent.

The calibrated equations (12–17) indicate that imperviousness becomes less influential as the AEP decreases. That is, 

imperviousness is more important for floods that occur more 

frequently than for floods that occur less frequently. Equations 

12–17 could be used to adjust the equations (2–8) developed 

in this study for urbanization, but further work is needed to 

determine the applicability of the coefficients.

Separate equations or adjustments to rural equations have 

been developed for urban and rural areas in other geographic 

regions. Adjustments to rural regression equations were 

made using methods similar to Sauer for North Carolina 

from the percent impervious cover (Robbins and Pope, 

1996) and Jefferson County, Kentucky, by the BDF (Martin 

and others, 1997). Urban flood flow equations have been 

developed explicitly for Alabama (Hedgecock and Lee, 2010), 

Georgia (Gotvald and Knaak, 2011), and Missouri (Southard, 

-30

-20

-10

0

10

20

30

40

50

60

70

20 10 4 2 1 0.5 0.2

Annual exceedance probability, in percent

Difference between station, in percent

Moshassuck & Woonasquatucket

Moshassuck & Wood

Woonasquatucket & Wood

EXPLANATION

Figure 13. Ratio of flood magnitudes for select annual 

exceedance probabilities normalized by drainage area between 

streamgages with different extents of basin urbanization. The 

at-site analysis was computed from annual peak records from 

1964–2010 for the Moshassuck River at Providence, RI (01114000), 

Woonasquatucket River at Centerdale, RI, (01114500), and Wood 

River near Arcadia, RI (01117800).
30 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

2010) from either the BDF (Alabama) or the percentage of 

impervious surface (Georgia and Missouri), in addition to 

other basin characteristics. The ratios of urban to rural flood 

flows for 20- and 1-percent AEP were computed from the 

Alabama, Georgia, Kentucky, Missouri, and North Carolina 

studies. The median ratios of urban to rural flood flows were 

1.4 for the 20-percent AEP and 1.2 for the 1-percent AEP, but 

in some cases (Missouri in particular), the ratio drops below 

1.0 (fig. 14). This further underscores the complex effects of 

urbanization and the interaction other basin characteristics can 

have on peak runoff.

Although the effects of urbanization were shown to have 

a relative decrease with the decreasing flood AEP in this and 

other studies, the analysis in this study also indicates that the 

flood magnitude linearly increases in relation to increasing 

imperviousness in some basins with otherwise similar properties. However, there were insufficient data to develop a statistically significant relation, and further research is needed in this 

area, particularly for small, highly developed basins, to better 

assess the effects of urbanization on flood flows. The regionalized equations developed in this study appear to apply reasonably well to basins with less than 37 percent impervious area 

with drainage areas greater than 10 mi2, but the applicability 

of the regional flood flow equations (2–8) in small urbanized 

basins is unknown.

Trends in Annual Peak Flows

Standard methods for calculating the magnitude of floods 

for a given exceedance probability are based on the assumption of stationarity, that is, the annual peak flows exhibit no 

significant trend over time. Milly and others (2008) called 

this assumption into question and advocated for new methods 

to replace models based on stationarity. Several studies have 

documented increases in low and median flows across the 

United States (McCabe and Wolock, 2002; Lins and Slack, 

2005; Small and others, 2006), but trends in peak flows are 

less evident in the literature. In New England, Walter and 

Vogel (2010) found increasing high flows in urbanizing basins, 

but increasing high flows have also been shown by Hodgkins 

and Dudley (2005), Collins (2009), and Huntington and others 

(2009) in basins minimally affected by urbanization. Failing 

to take increasing trends in annual peak flows into account 

in a flood frequency analysis could potentially lead to the 

AL GA KY MO NC

20 1 20 1 20 1 20 1 20 1

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Annual exceedance probability, in percent

Ratio of urban to rural peak discharge

23 36 17 11 31

30 Number of

values

EXPLANATION

90th percentile

75th percentile

Median

25th percentile

10th percentile

Outlier

Outlier

Figure 14. Ratio of urban to rural peak discharges for 20- and 1-percent annual exceedance probability flood 

in five states with separate flood flow equations. The variation of urban to rural flood flow ratios calculated 

in previous studies for Alabama (AL), Georgia (GA), Kentucky (KY), Missouri (MO), and North Carolina (NC) 

underscores the complex interaction of urbanization and other basin characteristics on peak runoff.
Factors Affecting Flood Flow Estimates 31

underestimation of flood magnitudes or incorrect frequency 

of floods of a given magnitude, or both, at some point in 

the future.

Trends in annual peak flows were tested using Kendall’s 

trend test (Helsel and Hirsch, 2002) for the 41 streamgages 

used in the regional flood flow analysis. The test indicated 

76 percent of these streamgages had a statistically significant 

positive trend at the 95-percent confidence level (this includes 

the extended record at 23 streamgages). The Kendall-Theil 

robust line or Theil slope for sites with statistically significant 

trends ranged from 0.6 to 43 percent with a median slope of 

4.0 percent. A subset of streamgages (16 sites) with 70 or more 

years of unregulated systematic record (table 12) indicate all 

but four sites have a statistically significant positive trend at 

the 95-percent confidence level with a Theil slope ranging 

from 3.2 to 28 percent with a median slope of 11 percent. 

Three of the other four streamgages have a statistically 

significant positive trend at about the 90-percent confidence 

level or above; only one streamgage, Little River near 

Hanover, CT (01123000), has a positive trend appreciably less 

than the 90-percent confidence level.

Plots of annual peak flows over time often mask trends 

because of normal variation in the magnitude of flows. An 

example plot (fig. 15A) of annual peak flows for Branch River 

at Forestdale, RI (01111500) shows little evidence of a trend; 

however, when a linear trend line was added (dashed blue line) 

to approximate the Kendall-Theil slope, the positive trend 

becomes apparent. When the annual peaks are identified by 

quartile range (fig. 15B), the plot indicates peaks within the 

interquartile and below the lower quartile have little or no 

trend, but peaks above the upper quartile have an appreciable 

upward trend. Plots of annual peaks at the other 15 long-term 

streamgages with statistically significant trends generally show 

similar patterns.

Table 12. Trends in annual peak flows at streamgages with 70 or more years of unregulated systematic recorded identified by the 

Kendall trend test.

[No., number; TAU, is a function of the number of positive (concordant) pairs minus the number of negative (discordant) pairs; P, is the statistical test for 

significance; light shaded cells indicate trend was not significant above the 95-percent confidence level; dark shading indicates trend was not significant; 

RI, Rhode Island; CT, Connecticut; MA, Massachusetts]

U.S. Geological Survey streamgage Record

TAU P-value Theil slope Number Name Begin End No. of 

years

Rhode Island streamgages

01111500 Branch River at Forestdale, RI 1940 2010 71 0.207 0.011 13.7

01112500 Blackstone River at Woonsocket, RI 1929 2010 82 0.174 0.021 28.5

01117500 Pawcatuck River at Wood River Junction, RI 1940 2010 70 0.233 0.004 14.3

01118000 Wood River at Hope Valley, RI 1941 2010 69 0.247 0.003 6.3

01118500 Pawcatuck River at Westerly, RI 1940 2010 70 0.233 0.004 14.3

01114500 Woonasquatucket River at Centerdale, RI 1941 2010 69 0.268 0.001 6.3

01116000 South Branch Pawtuxet River at Washington, RI 1940 2010 71 0.166 0.042 4.1

01117000 Hunt River near East Greenwich, RI 1940 2010 71 0.334 0.000 3.2

Connecticut streamgages

01119500 Willimantic River near Coventry, CT 1932 2010 79 0.124 0.107 11.2

01123000 Little River near Hanover, CT 1952 2010 61 0.086 0.336 4.5

01121000 Mount Hope River near Warrenville, CT 1941 2010 70 0.233 0.004 8.5

01127500 Yantic River at Yantic, CT 1931 2010 81 0.164 0.031 16. 1

01193500 Salmon River at East Hampton, CT 1929 2010 83 0.233 0.002 22.9

Massachusetts streamgages

01109000 Wading River near Norton, MA 1925 2010 86 0.121 0.103 1.6

01105000 Neponset River at Norwood, MA 1939 2010 71 0.333 0.000 3.7

01176000 Quaboag River at West Brimfield, MA 1912 2010 97 0.126 0.067 3.0
32 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

0

2,000

4,000

6,000

8,000

Discharge, in cubic feet per second 

Annual peak

Detrended peak

A. Annual peaks and detrended annual peaks

0

2,000

4,000

6,000

8,000

1940 1950 1960 1970 1980 1990 2000 2010

Annual peaks

B. Annual peaks by quartile group

Above interquartile

Below interquartile

Interquartile

0

2

4

6

8

10

1941–50 1951–60 1961–70 1971–80 1981–90 1991–00 2001–10

Number of peaks in decade

Above interquartile

Below interquartile

Interquartile

C. Decadal count of annual peak by quartile group

EXPLANATION

EXPLANATION

EXPLANATION

Figure 15. Trends in A, annual peak flows and detrended annual peaks, B, annual peak flows by quartile 

group, and C, decadal count of annual peak flows by quartile group for Branch River at Forestdale, RI 

(01111500).
Factors Affecting Flood Flow Estimates 33

Histograms of the number of annual peak flows within 

each quartile group by decade (fig. 15C) generally indicate an 

increasing number of peaks in the upper quartile range over 

time and a decreasing number of peaks in the lower quartile 

over time. Decades of relatively high annual peaks (2001–10), 

low annual peaks (1941–50), and average annual peaks 

(1951–60 and 1991–2000) are also revealed. Similar patterns 

are seen in histograms (fig. 16) of the average number of 

annual peak flows within each quartile by decade at the 

15 streamgages with statistically significant trends above 

about the 90-percent confidence level (table 12).

Several approaches for incorporating temporal trends 

into a flood frequency analysis have been discussed in the 

literature. One approach is to assume a parametric distribution for annual peak flows to model the parameters of the 

distribution as a function of time using linear regression (Katz 

and others, 2002) or nonlinear methods (Villarini and others, 

2009; Ouarda and El-Adlouni, 2011). Another approach fits 

a locally weighted least squares (LOESS) smoothed curve to 

the annual peaks (Ries and Dillow, 2006). Data are adjusted 

by subtracting the difference between the LOESS line and 

each of the annual peaks from the final value of the LOESS 

curve to “detrend” the data, the hypothesis being that the trend 

is removed but the variance in the data is preserved. This 

effectively rotates the data upward (when the trend is positive) 

around a pivot point at the end of the data record as shown 

in figure 15A. This method appears to unduly affect normal 

cycles of relatively wet and dry periods and was not used to 

adjust peaks in this study.

Walter and Vogel (2010) developed magnification and 

recurrence reduction factors to examine how a linear trend 

would affect flood magnitudes and recurrence intervals at a 

future time. Peak flows at a streamgage were first modeled as 

a function of time using a log-linear regression. The quantile 

function calculates the flood magnitude at a given exceedance 

probability. In the presence of a linear trend, the log-normal 

quantile function may be expressed as a function of time 

by substituting the regression equation into the cumulative 

distribution function. The magnification factor is the ratio of 

the quantile function at a future time to the quantile function at 

present. After simplification of terms, the magnification factor 

can be expressed as a function of the slope of the regression 

and the time period, as follows:

M e t = β×∆ , (18)

where

M is the flood modification factor, that is, 

the change in flood magnitude over a 

specified time;

	 β is the slope of the lognormal regression of 

annual peak flow and time; and

	 ∆t is the projected time period.

The method assumes that the linear trend persists at the 

same rate over the projected time period and can be used to 

calculate the amount by which a given flood flow must be 

multiplied to represent a flood of the same exceedance probability over that time interval.

0

1

2

3

4

5

6

7

1931–40 1941–50 1951–60 1961–70 1971–80 1981–90 1991–00 2001–10

Average number of peaks

Above interquartile

Below interquartile

Interquartile

EXPLANATION

Figure 16. Average number of annual peak flows by decade by quartile range among 15 streamgages with statistically significant 

trends above about the 90-percent confidence level.
34 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

The flood magnification factors (equation 18) were 

calculated at 15 unregulated streamgages with long-term 

records (table 12) with statistically significant trends. Flood 

magnification factors determined for 10-, 20-, and 30-year 

projections had computed means of 1.06, 1.13, and 1.21 

respectively. In other words, if the linear trend in annual peak 

flows persists, the flood with a given exceedance probability 

will, on average, be 6, 13, and 21 percent greater in magnitude 

in 10, 20, and 30 years, respectively. The distribution of the 

flood magnification factors at the 15 streamgages projected for 

10, 20, and 30 years out in the future are shown in figure 17A 

with values ranging from 0.14 to 12 percent, 2.8 to 25 percent, 

and 4.3 to 39 percent for 10, 20, and 30 years out from 2010, 

respectively. The range in flood magnification factors can be 

applied to floods of any exceedance probability.

Alternatively, a recurrence reduction factor computes the 

change in the expected average return time of a flood based 

on a persistent linear trend. An increasing trend causes the 

average return time of a given magnitude flood to decrease 

in the future. Walter and Vogel (2010) define the recurrence 

reduction factor as the ratio of the return period of a given 

magnitude flood at some point in the future to the return 

period of the same magnitude flood at present. The return 

period of a flood is often misinterpreted, and therefore, its use 

EXPLANATION

90th percentile

75th percentile

Median

25th percentile

25th percentile

Mean

Number of years in the future from 2010

100

20

60

0

40

80

Reduction factor, in percent

10 20 30

1-percent annual exceedance probability

0.2-percent annual exceedance probability 

n = 15

B. Recurrence-Reduction Factor

n = 15

Number of years in the future from 2010

10 20 30

Magnification factor, in percent

10

20

30

0

40

A. Flood-Magnification Factor

Figure 17. Projected influence of trends 

in annual peak flows at 15 long-term 

streamgages by the A, flood magnification 

factor and B, recurrence reduction factor.
Application of Methods and Significance of Results 35

has diminished in recent flood frequency analyses but is used 

here for illustrative purposes. The recurrence reduction factor 

is the increase in frequency for a given magnitude flood in the 

presence of a trend derived by equating the quantile function 

for the present condition at a given exceedance probability to 

the quantile at a future period. For example, a 0.5 recurrence 

reduction factor during a 10-year period would mean that a 

100-year flood (1-percent AEP) would become a 50-year flood 

(2-percent AEP) in 10 years time. That is, a flood magnitude 

for a given AEP will likely occur twice as frequently if the 

trend persists at the 0.5 reduction factor rate.

Recurrence reduction factors calculated for 100- and 

500-year floods were projected out for the 10-, 20-, and 

30-year periods (fig. 17B). The trend at the 15 unregulated 

streamgages with long-term records (table 12) with statistically significant trends, on average, indicate that a 100-year 

flood at present (2010) would have an average return period 

of 73, 55, and 43 years when projected 10, 20, and 30 years in 

the future. A 500-year flood at present would have an average return period of 344, 245, and 182 years when projected 

10, 20, and 30 years in the future. While these results can 

be unsettling, it should be emphasized that the change factors computed by the methods of Walter and Vogel (2010) 

assume the same linear trend, which may not continue over the 

projected time periods. True trends can only be determined by 

continued monitoring of streamflow. Statistical procedures for 

nonstationarity are in their infancy, and the trends observed in 

the data used in this study and its effects on flood frequency 

will require further work as this science evolves.

Application of Methods and 

Significance of Results

Floods are considered random events that have inherent uncertainties associated with the data, or lack thereof, 

and various errors and limitations of the statistical methods 

used to estimate the magnitude of floods for a given AEP. 

Our understanding of flood flows and the associated risks can 

be improved by applying the information gained from the 

streamgage flood frequency and the regional regression analyses. The analyses can also improve our understanding of flood 

flows at short-term streamgages not used in the analyses and 

exceedance probability of the 2010 flood in Rhode Island.

Weighted Estimates of Flood Flows at 

Streamgages

Flood flow estimates for a given AEP at streamgages, 

particularly those with short records, can be improved by 

a weighted average of two independent estimates from the 

streamgage analyses and the regional regression equations. 

The procedure assumes that the estimates are independent, 

which is considered true in most practical instances by 

Bulletin 17B. Exceptions may include regional regression 

equations based on clusters of streamgages in close proximity 

or with uniformly short periods of record; this does not appear 

to be a factor in this analysis. If the at-site and regression 

flood flow statistics are not independent, then the variance of 

a weighted estimate will be larger than the variance of each 

estimate. Also note that if basin characteristics are outside 

the range of characteristics used in the regional regression or 

if the high flows at a streamgage are appreciably affected by 

regulation, then a weighted estimate should not be made.

In the past, the weights for flood flow estimates were 

often made based on the number of years of record used 

to determine the at-site estimate and the equivalent years 

of record for the regression equation. The equivalent years 

of record is an approximation of the gage record needed to 

achieve accuracy comparable with that of the regression 

model (Tasker and Stedinger, 1989). This approach often fails 

to account for the true variance of the respective flood flow 

estimate and the information content provided by the regional 

skew. For example, the variance of the annual peak flow 

record will determine the reliability of the probability distribution even for streamgage records of equal length.

A weighted estimate can be calculated from the variance 

of independent estimates, which can be viewed as a measure 

of the uncertainty. When the variance corresponding to one of 

the estimates is high, the uncertainty is high and the weight 

applied to that estimate should be relatively small. Conversely, 

when the variance is low, the uncertainty is low and the weight 

applied to that estimate should be relatively large. Thus, the 

optimum weight is inversely proportional to the variance of 

each flood flow estimate, which is described in Bulletin 17B 

and can be calculated from the log10 of flood flows and variances as follows:

Q V V wgt

site reg

= +

(Qsite × Vreg) + (Qreg × Vsite)

, (19)

where

Qwgt is the weighted flow estimate for a given AEP,

Qsite is the at-site flow estimate for a given AEP,

Qreg is the regional regression flood flow estimate 

for a given AEP,

Vsite is the variance of the at-site estimate for a 

given AEP, and

Vreg is the variance of the regional regression 

estimate for a given AEP.

Similarly, a weighted variance can be calculated from the 

inverse variances of each flood flow estimate by:

V

V V

V V wgt

site reg

site reg

= ×

+

. (20)
36 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

There are a number of variables needed to calculate 

the variance of the at-site and regional regression flood flow 

estimates. The at-site variance is based on the number of peak 

flow observations and the log10 values of the mean, standard 

deviation, and skew determined by the B17B or the EMA 

analysis and the RMSE of the regional skew used. In this 

analysis, the regional regression variance is determined from 

the standard error of the model, the number of explanatory 

variables, and the covariance matrix (U) of the explanatory 

variables used in equation. To facilitate the computation of 

the weighted estimate (equation 19), the USGS developed the 

Weighted Independent Estimator (WIE) program (Cohn and 

others, 2012).

Weighted estimates of 20-, 10-, 4-, 2-, 1-, 0.5-, and 

0.2-percent AEP flood flows were calculated using the WIE 

and are reported in table 13 (in back of report) for the Rhode 

Island streamgages reported in table 7 (in back of report); the 

WIE values in table 13 (in back of report) are the arithmetic 

transformation of the log10 values of flow computed in equation 19. For comparison, the at-site and regression flood flows 

along with the percent difference between the at-site value and 

WIE values also are reported. A positive difference indicates 

the weighted estimate is greater than the at-site estimate, and 

conversely, a negative value indicates the weighted estimate 

is smaller than the at-site estimate. Differences between the 

magnitude of floods determined from the at-site and weighted 

estimates progressively increase as the exceedance probability decreases (fig. 18); differences at the 0.2-percent AEP 

flows were largest and ranged from -45 to 23 percent. A flood 

with a 20-percent AEP has an interquartile range of -1.0 to 

1.4 percent, whereas a flood with a 0.2-percent AEP has an 

interquartile range of -16 to 5.8 percent. The increasing difference with decreasing flood probability is attributed to the 

greater uncertainty of flood flows as the AEP decreases.

Flood Flows at Streamgages with Limited 

Record

Flood magnitudes determined at streamgages with 

short records are subject to greater inaccuracies because the 

statistical properties of the record are less likely to reflect long 

term conditions. This is referred to as the sampling error of 

the true population, and the effects of the sampling error are 

mitigated to some extent by a skew weighted to the generalized skew representative of the region. The weighted skew 

is inversely proportional to the variance of each estimate as 

described in Bulletin 17B; however, this procedure is not 

without flaws because the true variance may not be accurately 

represented, particularly for streamgages with short records. 

Streamgages with short records can be extended using MOVE 

to better reflect long-term conditions, as was done for 23 of 

streamgages used in the study; however, the extrapolated 

record is made with less confidence as the concurrent shortand long-term streamgage record decreases. The regional flood 

frequency analysis did not include all the available short-term 

streamgages initially complied for the study because of the 

greater uncertainties associated with these streamgages and 

because of the limited number of index stations available 

for record extension. Still, flood flow estimates at short-term 

40

20

0

-20

-40

-60

Percent difference

20 10 4 2 1 0.1 0.2

Annual exceedance probability

EXPLANATION

Outlier

90th percentile

75th percentile

Median

Outlier

10th percentile

25th percentile

Figure 18. Range of differences between flood flows calculated from at-site analysis of annual peak 

flows and weighted independent estimate for selected annual exceedance probabilities.
Application of Methods and Significance of Results 37

streamgages provide additional information for flood insurance studies, infrastructure design, and other purposes 

in basins with short-term streamgages not used in the 

regional analysis.

In preparation of the Johnson and Laraway (1977) 

flood frequency study, 20 streamgages were established 

in Rhode Island that generally ran between the mid-1960s 

and mid-1970s. The drainage area for these streams ranged 

from 0.5 to 7.33 mi2 with a median of 3.1 mi2 (table 14). 

While data for small basins are generally lacking, the record 

at these streamgages has a median length of 9 years. Three 

streamgages established later for other purposes have been 

in operation 10, 12, and 16 years with drainage areas of 3.6, 

20, and 5.0 mi2, respectively (table 14). In 2010, 17 other 

streamgages were in operation in Rhode Island that were not 

compiled because they have a record of less than 6 years, but 

could be of value in future flood frequency studies.

The distribution of flood flows was estimated at 19 of the 

short-term streamgages using B17B analysis of the systematic 

record, B17B and EMA analysis of the extended record, and 

the regional regression equation regardless of its applicability 

to the site (table 15, in back of report). That is, many of these 

short-term streamgages had basin characteristics outside the 

range applicable to the regional flood flow equations, particularly drainage area size. Four of the short-term streamgages 

(Metacomt Brook at East Providence, RI–01109300; Mowry 

Painc Brook near Chepachet, RI–01111450; Shippee Brook 

tributary at North Foster, RI–01115200; Furnace Hill Brook 

at Cranston, RI–01116870) were not included in the analysis 

because of suspect data quality (for example, the annual peak 

flows are excessively large for drainage basins of that size and 

showed little variation over the period data was collected). 

Thirteen of the 19 streamgages have basin characteristics 

outside of the range of characteristics used to develop the 

Table 14. Streamgages with short-term records in Rhode Island that were not used in the regional flood frequency analysis.

[DA, drainage area; mi2, square miles; STRDEN, stream density; mi/mi2, miles per square mile; StorNHD, storage; trib, tributary; --, not determined; 17 other 

streamgages are in the U.S. Geological Survey peak-flow database but with no greater than 6 years record]

U.S. Geological Survey streamgage Record DA

(mi2)

STRDEN 

(mi/mi2)

StorNHD

Number Name Begin End Years (percent)

01106100 Cold Brook near Adamsville, RI 1966 1973 9 1.15 2.86 5.64

01109300 Metacomt Brook at E. Providence, RIa 1966 1973 9 0.82 -- --

01111250 Dry Arm Brook near Wallum Lake, RI 1966 1978 13 1.74 2.20 14.69

01111450 Mowry Painc Brook near Chepachet, RIa 1966 1973 9 1.87 -- --

01112700 Blackstone River trib 1 at Woonsocket, RI 1965 1974 10 2.31 1.97 2.88

01113600 Blackstone River trib 2 at Berkeley, RI 1966 1978 13 1.04 1.56 5.25

01113695 Catamint Brook at Cumberland, RI 2000 2010 10 3.55 2.29 5.99

01115098 Peeptoad Brook near North Scituate, RI 1994 2010 16 4.96 1.68 17.15

01115100 Mosquitohawk Brook near North Scituate, RI 1965 1974 9 3.06 2.41 17.18

01115200 Shippee Brook trib at North Foster, RIa 1966 1974 9 2.42 -- --

01115300 Wilbur Hollow Brook near Clayville, RI 1966 1978 13 4.61 2.26 8.27

01115770 Carr River near Nooseneck, RI 1964 1980 20 7.33 1.88 8.78

01115830 Bear Brook near Coventry, RI 1966 1978 13 3.98 1.68 1.76

01116300 Furnace Hill Brook at Cranston, RIa 1965 1974 9 4.19 2.39 5.29

01116600 Pocasset River near North Scituate, RI 1966 1978 13 1.34 3.10 10.66

01116650 Hardig Brook near W. Warwick, RI 1966 1973 9 3.19 2.00 1.48

01116870 Frenchtown Brook near Davisville, RI 1966 1973 9 3.12 2.15 6.75

01117250 Browns Brook at Wakefield, RI 1966 1973 9 0.5 0.53 13.30

01117370 Queen River at Liberty, RI 1998 2010 12 19.6 1.73 4.42

01117600 Meadow Brook near Carolina, RI 1965 1974 11 5.53 1.67 9.15

01117820 Wood River trib near Arcadia, RI 1966 1973 9 0.77 1.46 1.87

01118020 Perry Healy Brook near Bradford, RI 1966 1973 9 1.82 1.48 12.84

01126200 Bucks Horn Brook at Greene, RI 1965 1974 9 5.52 2.32 9.78

a

Suspect peak flow record.
38 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

regional regression equations, mostly because drainage areas 

were about 20 to 90 percent smaller than the minimum drainage area (4.0 mi2

) used in the regional regression. At these 

streamgages, regional regression estimates were reported, but 

no uncertainty limits or weighted estimates are given because 

the equations were applied to basins outside the appropriate 

limits of the equations.

Results indicate a wide variation between the flood 

estimates by method and by site with similar drainage areas. 

Generally, flood flows differed less between the period of 

record and extended record estimates than between extended 

record and regression estimates. Differences between the 

period of record and extended record estimates ranged from 

-46 to 37 percent and from -64 to 251 percent for 20- and 

0.2-percent AEPs, respectively. Differences between the 

extended record and regression estimates ranged from -83 

to 345 percent and from -89 to 541 percent for 20- and 

0.2-percent AEPs, respectively. Differences between methods 

at a site tended to be consistent across the range of AEP 

flows. Generally, the flood flow information from the shortterm streamgage can be used with greater confidence when 

the differences between methods are small. The results also 

indicate the need for additional data in small basins.

The streamgage at Carr River near Nooseneck, RI 

(01116600) was established in 1964, discontinued in 

1980, and reactivated in 2006. Collectively, the Carr River 

streamgage has 20 years of annual peak flows that provide 

a reasonable length of record to independently verify the 

regional regression equations for a small basin; the drainage 

area at the streamgage is 6.74 mi2. The same regional skew 

(0.52) and RMSE (0.46) applied elsewhere this study was 

used in this at-site analysis. The magnitude of flood flows 

determined by a B17B analysis for the period of record 

on average was 37 greater than that determined from the 

extended record analysis; flows ranged from 27 to 45 percent 

greater for 20- and 0.2-percent AEP, respectively. Carr 

River records were extended back to 1941 using MOVE 

and the Hunt River near East Greenwich, RI (01117000) as 

the index streamgage; the MOVE fit reasonably well with a 

correlation coefficient of 0.89 and an RMSE of 60 ft3/s. Flood 

magnitudes derived from the regional regression equation 

were consistently less than those computed from the period 

of record B17B analysis; flows ranged from 18 to 71 percent 

less for 20- and 0.2-percent AEP, respectively. On the other 

hand, the regression equation flood magnitudes compared with 

the extended record B17B analysis were 13 percent greater 

at the 20-percent AEP, matched the 10-percent AEP, and 

were progressively smaller (14 to 48 percent) from the 4- to 

0.2-percent AEP, respectively. All but the 0.5- and 0.2-percent 

AEP regional regression flows for this streamgage were within 

the percent average standard error of prediction.

Flood Flows at an Ungaged Site on a Gaged 

Stream

Estimates of flood flows on a stream above or below a 

gaged location, within limits, can be improved by combining the streamgage information with the regional regression 

equation. Verdi and Dixon (2011) present a method for better 

estimating flows at an ungaged site on a gaged stream from 

Sauer (1974) for streamgages with a record of 10 or more 

years (equation 21). To obtain a weighted peak-flow estimate 

(QP(u)w) for an AEP at the ungaged site, the flood flow estimate 

for an upstream or downstream gaged (QP(g)w) must first be 

determined by the at-site analysis (table 7, in back of report) 

adjusted by the WIE analysis reported in table 13 (in back of 

report). Streamgages in Rhode Island with short records not 

included in the regional analysis are listed in table 14, but 

most should not be used because they have drainage areas outside the applicable limits of the regional regression equations. 

The weighted estimate for the ungaged site (QP(u)w) on a gaged 

stream is then computed as follows:

QP(u)w

2ΔDA

DAg

QP(u)r

QP(g)w

QP(g)r

2ΔDA

DAg

1– , (21)

where

QP(u)w is the flow estimate for the selected P-percent 

AEP at the ungaged site, in cubic feet per 

second;

ΔDA is the absolute difference between the 

drainage areas at the gaged and ungaged 

sites, in square miles;

DAg is the drainage area for the gaged site, in 

square miles;

QP(g)w is the weighted flow at the streamgage 

derived from at-site analysis and regional 

regression equations for the selected 

P-percent AEP (table 13, in back of report), 

in cubic feet per second;

QP(g)r is the flow estimate derived from the 

applicable regional equations 2–8 for the 

selected P-percent AEP at the gaged site, in 

cubic feet per second; and

QP(u)r is the flow estimate derived from the 

applicable regional equations 2–8 for the 

selected P-percent AEP at the ungaged site, 

in cubic feet per second.

Use of equation 21 gives no weight to the at-site estimate when the drainage area ratio between the gaged and 

ungaged sites are less than 0.5 or greater than 1.5 and gives 

increased weight to the at-site estimate as the drainage area 

ratio approaches 1. The weighting procedure should not be 

used when hydrologic characteristics abruptly change, such as 

a large instream impoundment between the sites.
Application of Methods and Significance of Results 39

An example application of this procedure is the computation of the weighted 1-percent AEP flow, for a hypothetical 

site on the Wood River above Hope Valley, RI (01117500) 

streamgage. For simplicity and comparative purposes, the 

example assumes the ungaged site is the streamgage at Wood 

River at Arcadia, RI (01117800). It also should be noted that 

the Wood River at Arcadia streamgage was not used in the 

development of the regionalized flood flow equations because 

of its high correlation with the downstream streamgage at 

Hope Valley.

1. Obtain the value of Q1%(g)w for the streamgage in 

table 13 (in back of report) (= 3,160 ft3/s)

2. Obtain the ΔDA between the gaged and ungaged 

sites (=74.53 – 35.14 = 39.39 mi2)

3. Compute the regional regression (Q1%(u)r) for the 

ungaged site using equation 6

(= 10 2 623 0 852 35 14 0 792 1 35 0 941 10 10 ( . +( . ×log ( . )) ( + . l × og ( . ))−( . ×log ( . ))) 10 7 84

= 1,590 ft3/s)

4. Compute the regional regression (Q1%(g)r) for the 

gaged site using equation 5 (= 3,200 ft3/s) and

5. Compute the weighted estimate for the ungaged site 

(Q1%(u)w) using equation 21

2 × -39.39

74.53

3,160

3,200

2 × -39.39

74.53 1,590

= 1,590 ft3/s.

The adjusted discharge (1,590 ft3/s) at the “ungaged” site 

determined by equation 21 is no different than the computed 

value from the regional regression (1,590 ft3/s) because the 

drainage area at the “ungaged” site is under the lower limit 

of the drainage area ratio (0.47); thus, all the weight is put on 

regional regression flow value.

A similar, but simpler approach used in StreamStats (an 

interactive online tool for solving regionalized equations; Ries 

and others, 2008) is used to adjust flood flows on the basis of 

the drainage area ratio at the gaged and ungaged sites on the 

same stream. The weighting procedure should not be applied 

when the drainage area ratio is less than 0.5 or greater than 1.5 

or when hydrologic characteristics abruptly change between 

the sites. The adjustment method for a site above or below a 

gaged location in StreamStats goes at least a far back as the 

Elements of Applied Hydrology (Johnstone and Cross, 1949):

b

QP u( )w = QP g( )w

DAu

DAg

, (22)

where

QP(u)w is the flow estimate for the selected P-percent 

AEP at the ungaged site, in cubic feet per 

second;

DAu is the drainage area at the ungaged site, in 

square miles;

DAg is the drainage area at the streamgage, in 

square miles;

QP(g)w is the weighted flow estimate for the selected 

P-percent AEP at the ungaged site, in cubic 

feet per second; and

b is the exponent of drainage area from the 

appropriate regression equations.

Exponents from regional flood flow equations derived 

from WREG using a GLS analysis of drainage area range from 

0.76 to 0.80 (table 16). The average exponent b over the range 

of exceedance probabilities (0.78 in this study) is used by 

some in equation 22 to obtain a weighted estimate of a flood 

flow at an ungaged site on a gaged stream for any exceedance probability flood. Solving equation 22 for Wood River at 

Arcadia (the “ungaged” site) yields a discharge of 1,770 ft3/s 

(= [35.14/74.53]0.77 × 3,160) for the 1-percent AEP flow. The 

adjusted 1-percent AEP flow is about 11 percent larger than 

the computed magnitude from the regional regression equation (1,590 ft3

/s) and about 8 percent larger than the weighted 

at-site flood magnitude (1,640 ft3/s).

Table 16. Regional exponent for drainage area adjustment of a 

flood flows at an ungaged site on gaged stream determined from 

the regional regression of drainage area.

[Note, the constant is not used in the drainage area ratio adjustment but could 

be used to estimate flood flows at ungaged site from drainage area only]

Percent annual 

exceedance 

probability

Exponent b Constant

20 0.81 1.76

10 0.80 1.88

4 0.79 2.04

2 0.78 2.14

1 0.77 2.23

0.5 0.77 2.32

0.2 0.76 2.42
40 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

In some instances, equation 21 can produce flows that do 

not increase in the downstream direction when the change in 

drainage area is small and the change in basin storage is large. 

This is because, in the underlying regional regression used 

in equation 21 (equations 2–8), basin storage (StorNHD) is a 

negative term, which causes the flood quantile to decrease as 

StorNHD increases. Although, this can be true, some applications require flows increase in the downstream direction and 

care should be taken to ensure the desired result. A hybrid of 

equations 21 and 22 presented by Guimaraes and Bohman 

(1992) and Stamey and Hess (1993) can be used to ensure 

increasing flow in the downstream direction:

 

QP(u)w

2ΔDA

DAg

QP(u)r QP(u)r

DAu

DAg

2ΔDA

DAg

1– . (23)

Similar to the other methods, this method only applies 

when the ungaged site is within 0.5 and 1.5 times the drainage area of the streamgage and there is no major change in 

basin characteristics between sites. Using the same example as 

before, equation 23 yields an adjusted discharge of 1,580 ft3/s, 

which is about 4 percent less than the WIE flow (1,640 ft3/s) 

at Wood River at Arcadia, RI (01117800) determined from the 

at-site analysis weighted by the regional regression equation 

(table 13, in back of report).

A spreadsheet for solving the flood flows for a given 

exceedance probability on a stream above or below a gaged 

location by these methods can be accessed through a hyperlink 

in appendix 3. The equation 21 requires user specified drainage area at the gaged and ungaged sites, regional regression 

estimated flood magnitudes for the ungaged and gaged sites 

for a given exceedance probability, and flood magnitude determined from the streamgage analysis for the same exceedance 

probability. Equation 23 is solved simultaneously with equation 21, but does not require the regional regression estimated 

flood magnitude at the streamgage. The drainage area ratio 

method (equation 22) only requires user specified drainage 

areas at the gaged site and flood magnitude determined from 

the streamgage analysis for a given exceedance probability at 

the gaged site. In this test example, the “ungaged” site, which 

is actually a long-term streamgage, the more complex method 

(equation 23) was marginally closer to the at-site flood flow 

estimate than the simpler method (equation 22).

For an ungaged site that is between two gaged sites on 

the same stream, two flow estimates can be made using the 

methods and criteria outlined above, but additional hydrologic 

judgment may be necessary to determine which method and 

estimates (or some interpolation thereof) are most appropriate. Only a few rivers in Rhode Island have multiple gages to 

apply multiple adjusted estimates of flood flows at an ungaged 

site on a gaged stream, such as Pawcatuck River between 

Westerly and Wood River Junction and Wood River between 

Hope Valley and Arcadia. Other factors that should be considered when evaluating the two estimates include differences in 

the length of record for the two streamgages and the quality of 

the peak flow record.

Comparison with a Previous Rhode Island Flood 

Study

With the development of updated at-site flood statistics 

and regional regression relations, a question that arises is how 

have results changed between previous and updated analyses. 

Comparisons were made for flood magnitudes at the 10-, 1-, 

and 0.2-percent exceedance probabilities using the 18 Rhode 

Island streamgages in this study (table 7, in back of report), 10 

of which had been used in the previous study by Johnson and 

Laraway (1977), which was intended for use in small drainage 

basins (less than about 10 mi2) and for frequent floods (the 

data used in that study only spanned 6 years of record from 

1966–71). Regression equations had been developed for 50- 

and 20-percent AEP floods and were then extrapolated to 10-, 

4-, and 2-percent AEP floods using factors presented by Green 

(1964). Further extrapolations were made to a 1-percent AEP 

flood when the equations were incorporated into the NFF 

program (Jennings and others, 1994) and to a 0.2-percent AEP 

flood when NFF was replaced by the National Streamflow 

Statistics (NSS) program (Ries and Crouse, 2002).

Comparisons were made between the flood magnitudes obtained from the at-site analyses determined from the 

weighted skew coefficient and the regional regression equations in this report. A second comparison was made between 

the at-site flows and those calculated from the previous Rhode 

Island flood flow equations, and a third comparison was made 

between the updated and previous flood flow equations. The 

distribution of the differences between the at-site analyses, 

the updated equations, and the previous regional equations are 

shown by boxplots in figure 19.

Positive differences indicate that the updated regression 

equation results are greater than the at-site results or previous regression equation results; negative percentage differences indicate that the updated regression equation results are 

smaller than the at-site results or previous regression equation 

results. Most notable is that the median difference in values 

between of the updated regional equation and the at-site 
Application of Methods and Significance of Results 41

analyses are near zero, whereas the median difference between 

the previous regional equation and the at-site analyses are 

appreciably higher than zero. Hence, the previous equations 

generally produce larger flows than the updated equations, particularly as the exceedance probability decreases, underscoring 

the limitation of how the previous regression equations were 

developed. At the 1- and 0.2-percent AEP, the median differences between the at-site analyses and previous flood equations are about 43 and 55 percent, respectively, and the lower 

quartile is above the zero line. Generally, the large differences 

between the updated and previous flood flow equations can be 

explained by the additional record used in the analyses and the 

disproportional number of the highest peaks in the years following the end of the record used in the previous study. These 

differences highlight the need to periodically update flood flow 

statistics and regional regression equations.

Annual Exceedance Probability of the 2010 

Flood in Rhode Island

One of the purposes of this study was to determine the 

annual exceedance probability of the 2010 flood in Rhode 

Island. Of the 21 active streamgages in Rhode Island in 

2010, 18 set new record peak flows (table 17) with AEPs 

ranging from 2 to 0.2 percent (50- to 500-year return interval, 

respectively). Most 2010 peak flows were between a 0.5- and 

0.2-percent AEP except for streamgages in the Blackstone 

River Basin, which lie in the northern part of Rhode Island 

and in Massachusetts and did not set new record peak flows 

during the 2010 flood; the AEP of the peak flows at these 

streamgages ranged from 4 and 2 percent (25- to 50-year 

return interval, respectively).

200

150

100

50

0

-50

10 percent 1 percent 0.2 percent

Percent difference

At-site and new regional equation

At-site and old regional equation

New and old regional equations

Flood exceedance probability

Difference between values calculated from: EXPLANATION

90th percentilet

75th percentile

Median

25th percentile

10th percentile

Outlier

Figure 19. Differences from at-site analyses and regional regression equations in this study and regression equations 

from previous study by Johnson and Laraway (1977) for 18 streamgages in Rhode Island (table 7) for 10-, 1-, and 

0.2-percent annual exceedance probability floods.
42 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 17. March–April 2010 flood peak and annual exceedance probability at active streamgages in Rhode Island.

[Values in bold typeface indicate new peak of record. AEP, annual exceedance probability determined from weighted estimates in table 7. ft3/s, cubic feet per 

second; %, percent; R, river; Ave., Avenue; Rd., Road; RI, Rhode Island; nr, near; --, not determined]

U.S. Geological Survey streamgage Start of 

record

2010 Flood peak Previous record peak

Date

Gage 

height,

(feet)

Discharge

(ft3/s)

AEP

(%)

Discharge

(ft3/s) Date Number Name

Ten Mile River Basin

01109403 Ten Mile R, Pawtucket Ave. at East Providence, RI 1986 03/31/2010 10.79 2,600 1 2,190 10/16/2005

Blackstone River Basin

01111300 Nipmuc River near Harrisville, RI 1964 03/30/2010 8.29 1,800 2 1,870 10/15/2005

01111500 Branch River at Forestdale, RI 1940 03/31/2010 12.05 5,260 4 6,290 10/15/2005

01112500 Blackstone River at Woonsocket, RI 1929 03/31/2010 14.50 14,900 4 32,900a 08/19/1955

Pawtuxet, Woonasquatucket, Moshassuck, and Hunt River Basins

01114000 Moshassuck River at Providence, RI 1963 03/30/2010 6.26 2,040 1 1,990 10/15/2005

01114500 Woonasquatucket River at Centerdale, RI 1941 03/30/2010 9.00 1,750 2 1,530 10/15/2005

01115098 Peeptoad Brook at Elmdale Rd. nr North Scituate, RI 1994 03/30/2010 2.55 249 4 180 10/20/1996

01115187 Ponaganset River at South Foster, RI 1994 03/14/2010 6.57 1,330 2 1,110 06/17/2001

01115630 Nooseneck River at Nooseneck, RI 1964b 03/30/2010 5.32 1,020 0.2 762 08/11/2008

01116000 South Branch Pawtuxet River at Washington, RI 1940 03/31/2010 9.22 5,480 0 1,980 06/06/1982

01116500 Pawtuxet River at Cranston, RI 1939 03/31/2010 20.79 14,900 0.2c 5,440 06/07/1982

01117000 Hunt River near East Greenwich, RI 1940 03/30/2010 5.61 2,380 0.2 1,680 10/15/2005

Pawcatuck River Basin

01117350 Chipuxet River at West Kingston, RI 1973 03/31/2010 9.78 748 0.2 306 10/16/2005

01117370 Queen River at Liberty Rd. at Liberty, RI 1998 03/30/2010 8.44 1,830 0.2c 713 10/15/2005

01117420 Usquepaug River near Usquepaug, RI 1976 03/31/2010 11.16 2,070 0.5 1,060 06/06/1982

01117430 Pawcatuck River at Kenyon, RI 2002 04/01/2010 7.21 2,510 -- 885 04/17/2007

01117468 Beaver River near Usquepaug, RI 1974 03/30/2010 6.41 901 0.2 329 06/06/1982

01117500 Pawcatuck River at Wood River Junction, RI 1940 04/01/2010 11.16 3,490 0.2 1,860 06/07/1982

01117800 Wood River near Arcadia, RI 1964 03/31/2010 10.56 2,650 0 1480 06/06/1982

01118000 Wood River at Hope Valley, RI 1941 03/30/2010 13.72 5,470 0 2,390 06/06/1982

01118500 Pawcatuck River at Westerly, RI 1940 03/30/2010 15.38 10,800 0.2 7,070 06/06/1982

a

Previously coded as a dam break, but recent inspection of the record indicates this had little effect on the peak.

b

Ended in 1981 and restarted in 2007.

c

Determined from at-site flood analysis.
Summary and Conclusions 43

Summary and Conclusions

A statewide disaster was declared for Rhode Island by the 

President on March 30, 2010, following heavy persistent rains 

from late February through March 2010 that caused severe 

flooding and set, or nearly set, record streamflows and water 

levels at many long-term streamgages in the state. Following 

floods of this severity, updating and documenting the magnitude of annual exceedance probability (AEP) floods is important for flood plain management, transportation infrastructure 

design, and flood insurance studies to help minimize future 

flood damages and risks. In August 2010, the U.S. Geological 

Survey (USGS) entered into an agreement with the Federal 

Emergency Management Agency to document and characterize the March–April 2010 flood. As part of that agreement, 

a study was conducted to estimate the magnitude of flood 

flows at selected AEPs at streamgages in Rhode Island and 

to develop statewide regional equations for estimating flood 

flows at ungaged locations.

To better represent the Rhode Island region, the magnitude of floods were determined at 43 streamgages including 20 

in Rhode Island, 14 in eastern Connecticut, and 9 in southeastern and south central Massachusetts. At-site analyses were 

made using the standard Bulletin 17B (Interagency Committee 

on Water Data, 1981) log-Pearson type III (B17B) methods 

as implemented in PeakFQ (Flynn and others, 2006) and by 

the expected moments algorithm (EMA) for 20-, 10-, 4-, 2-, 

1-, 0.5-, and 0.2-percent AEP floods. The B17B and EMA 

methods use the same statistical moments (mean, standard 

deviation, and skew) of the logs of the annual peak flows to fit 

the data to a log-Pearson type III probability distribution. The 

difference is that the B17B method fits the data point values, 

whereas the EMA method uses point and interval data to better 

utilize available information. The inverse of the AEP is an 

approximation of the recurrence interval of a flood, which for 

the AEPs listed are 5-, 10-, 25-, 50-, 100-, 200-, and 500-year 

return intervals, respectively.

The at-site AEP flood magnitudes were computed using 

a weighted skew determined from the average skews at 

40 streamgages. Annual peak flow records were extended at 

22 of the 40 streamgages using the maintenance of variance 

extension (MOVE) procedure to best represent the generalized skew for the region by incorporating the largest number 

of streamgages and longest period possible. After adjustments 

for low outliers, historic data, and uncertainties in the annual 

peak flows, an average skew of 0.52 was determined for the 

region with a root mean square error of 0.46. At 18 long-term 

streamgages used in the skew analysis, high outliers were 

detected (annual peaks that far exceed other annual peaks) that 

were caused by four large independent events. Skews at these 

18 streamgages averaged 0.93 and were 79 percent larger 

than the average skew determined from the 40 streamgages. It 

could be argued that because the high outliers are caused by 

independent events, the higher average skew values are more 

representative of the regional long-term population distribution. A change in the regional skew from 0.52 to 0.93 resulted 

in an average increase in the magnitude of 1- and 0.2-percent 

AEP floods by about 7 and 13 percent, respectively, but had 

progressively less effect on successively higher probability 

floods (more frequent floods).

Flood magnitudes were reported at selected AEPs at 

43 streamgages, which included three additional streamgages 

in Rhode Island that were not used in the regional skew analysis because of regulation, an atypical large negative skew, and 

redundancy with a longer term downstream gage. In addition 

to flood flow estimates for selected AEPs, the magnitude of 

the 95-percent confidence interval was determined at each 

streamgage. The confidence interval determined by the EMA 

is considered more robust and a more accurate measure of the 

possible flood magnitudes for a given AEP than those determined by the standard B17B method. Regression equations to 

estimate magnitude of floods at selected AEPs at ungaged sites 

were developed from 41 of these streamgages; two of the three 

additional streamgages in Rhode Island were not used in the 

regional regression equation development because of regulation or redundancy.

Regional regression equations were developed to estimate 

magnitude of floods at selected AEPs at ungaged sites from atsite flood quantiles and their respective basin characteristics. 

A total of 55 basin characteristics were evaluated as potential 

explanatory variables in the regression; however, only three 

characteristics were statistically significant—drainage area 

(DA) in square miles, stream density (STRDEN) in miles 

per square mile, and basin storage (StorNHD) in percent. 

Stream density and storage were derived from the 1:24:000 

National Hydrography Dataset (NHD). Storage is the total 

area of wetlands and water over the basin. All values used in 

the regression were transformed to base 10 logarithms. The 

final regression equations were developed using the USGS 

Weighted Multiple Linear Regression (WREG) program determined by the Generalized Least Squares (GLS) method, which 

is considered the most applicable for regional analysis because 

it accounts for streamgage record lengths and correlation 

between streamgages. The pseudo coefficient of determination 

(pseudo R2) indicates that the explanatory variables explain 

95 to 96 percent of the variance in the flood magnitude from 

20- to 0.2-percent AEPs at the 41 streamgages used to develop 

the regression equations. Flood flows at the 95-percent confidence level for each exceedance probability derived from 

the regional regression equation model error variance and the 

covariance matrix are also reported.

Flood flow estimates for a given AEP at gaged sites, 

particularly at sites with short records, can be improved by a 

weighted average of two independent estimates of the at-site 

analysis and the regional regression equations. The weighted 

estimate is based on the magnitude of the flood and uncertainty associated with each estimate. Differences between 

the magnitude of floods determined from the at-site estimate 

and the weighted estimate ranged from -44 to 28 percent; a 

positive value indicates the weighted estimate is greater than 

the at-site estimate, and conversely, a negative value indicates 

the weighted estimate is smaller than the at-site estimate. 
44 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

The progressive increase in difference with decreasing flood 

probability is attributed to the greater uncertainty of the flood 

magnitude as the exceedance probability decreases. Estimates 

of flood flows on a stream above or below a gaged location, within limits, also can be improved by combining the 

streamgage information with the regional regression equation. 

A weighting procedure is applicable when the ungaged to 

gaged drainage area ratio is between 0.5 and 1.5 and hydrologic characteristics of the basin do not abruptly change.

Effects of urbanization on flood flows also were examined because impervious cover is generally considered an 

important factor, and this region has a long history of urban 

development. The imperviousness of the streamgage basins 

used in the regression analysis ranged from 0.5 to 37 percent 

with a mean of 5.2 percent, and although imperviousness 

provided some explanatory power in the regression, it was not 

statistically significant at the 95-percent confidence level for 

any of the exceedance probabilities examined. Stratified datasets indicated a linear relation for 20-percent AEP floods that 

increase with increasing imperviousness, but only for basins 

underlain by 40 percent or more sand and gravel. The magnitude of the 20-percent AEP flood flow appears to be unrelated 

to imperviousness for basins underlain by less than 20 percent 

sand and gravel. For flood flows with lower AEPs, the relation 

between surficial deposits and imperviousness progressively 

weakened. This result is confirmed by analysis of three longterm streamgages in close proximity to each other with similar 

characteristics except for the percentage of imperviousness. 

Although regional flood studies in other areas of the country 

have found urbanization to be an important factor, results from 

this study indicate a complex interaction with other characteristics that confounds a statistical portrayal of urban effects on 

flood flows. Further research is needed in this area, particularly for small, highly developed basins where little data exist.

Standard methods for calculating the magnitude of floods 

for given exceedance probabilities are based on the assumption of stationarity, that is, annual peak flows exhibit no significant trend over time. A subset of 16 streamgages with 70 or 

more years of unregulated systematic record indicates all but 4 

have a statistically significant positive trend at the 95-percent 

confidence level; three streamgages had a significant positive 

trend between the about 90- and 95-percent confidence level. 

The Theil slope of the 15 streamgages with statistical significance ranged from 3.2 to 28 percent with a median slope of 

11 percent. If this trend continued linearly in time, then the 

magnitude of a flood with a given exceedance probability, on 

average, would be 6, 13, and 21 percent greater in 10, 20, and 

30 years, respectively. Trends and their effects can only be 

ascertained by continued monitoring of streamflow and the 

continued development of the science of nonstationarity in 

flood frequency analysis.

One of the purposes of updating the flood frequency 

information for Rhode Island was to assess the AEP of the 

2010 flood. Of the 21 active streamgages in Rhode Island in 

2010, 18 set new record peaks with AEPs ranging from 2 and 

0.2 percent (50- to 500-year return interval, respectively). 

Most 2010 peak flows were between a 0.5- and 0.2-percent 

AEP except for streamgages in the Blackstone River Basin, 

which ranged between a 4- and 2-percent AEP.

Acknowledgments

The authors gratefully acknowledge Timothy A. Cohn 

and Julie E. Kiang of the U.S. Geological Survey (USGS) for 

their valuable assistance and guidance through the labyrinth 

of statistical procedures used in flood frequency analysis and 

regionalization. The authors also acknowledge Charles E. 

Berenbrock of the USGS for his assistance with the weighted 

independent estimates program.

Selected References

Alexander, T.W., and Wilson, G.L., 1995, Technique for estimating the 2- to 500-year flood discharges on unregulated 

streams in rural Missouri: U.S. Geological Survey WaterResources Investigations Report 95–4231, 33 p.

Benson, M.A., 1962, Factors influencing the occurrence of 

floods in a humid region of diverse terrain: U.S. Geological 

Survey Water-Supply Paper 1580–B, 30 p.

Bogart, D.B., 1960, Floods of August–October 1955, New 

England to North Carolina: U.S. Geological Survey WaterSupply Paper 1420, 854 p.

Cohn, T.A., Berenbrock, Charles, Kiang, J.E., and Mason, 

R.R., Jr., 2012, Calculating weighted estimates of peak 

streamflow statistics: U.S. Geological Survey Fact Sheet 

2012–3038, 4 p., at http://pubs.usgs.gov/fs/2012/3038/.

Cohn, T.A., Lane, W.M., and Baier, W.G., 1997, An algorithm 

for computing moments-based flood quantile estimates 

when historical flood information is available: Water 

Resources Research, v. 33, no. 9, p. 2089–2096.

Cohn, T.A., Lane, W.M., and Stedinger, J.R., 2001, Confidence intervals for expected moments algorithm flood 

quantile estimates: Water Resources Research, v. 37, no. 6, 

p. 1695–1706.

Collins, M.J., 2009, Evidence for changing flood risk in New 

England since the late 20th century: Journal of the American Water Resources Association, v. 45, no. 2, p. 279–290.

Denny, C.S., 1982, Geomorphology of New England: U.S. 

Geological Survey Professional Paper 1208, 18 p.
Selected References 45

Eng, Ken, Chen, Yin-Yu, and Kiang, J.E., 2009, User’s guide 

to the weighted-multiple-linear-regression program (WREG 

version 1.0): U.S. Geological Survey Techniques and 

Methods, book 4, chap. A8, 21 p., at http://pubs.usgs.gov/

tm/tm4a8/.

Federal Emergency Management Agency, 1981, Flood insurance study, City of Warwick, Rhode Island, Kent County, 

September 15, 1981: Federal Emergency Management 

Agency community no. 445409, 16 p., 2 pls.

Flynn, K.M., Kirby, W.H., and Hummel, P.R., 2006, 

User’s manual for PeakFQ, annual flood frequency analysis using bulletin 17B guidelines: U.S. Geological Survey 

Techniques and Methods Report, book 4, chap. B4, 42 p., 

at http://pubs.usgs.gov/tm/2006/tm4b4/.

Gotvald, A.J., Feaster, T.D., and Weaver, J.C., 2009, Magnitude and frequency of rural floods in the southeastern 

United States, 2006—Volume 1, Georgia: U.S. Geological 

Survey Scientific Investigations Report 2009–5043, 120 p., 

at http://pubs.usgs.gov/sir/2009/5043/.

Gotvald, A.J., and Knaak, A.E., 2011, Magnitude and frequency of floods for urban and small rural streams in 

Georgia, 2008: U.S. Geological Survey Scientific Investigations Report 2011–5042, 39 p., at http://pubs.usgs.gov/

sir/2011/5042/.

Green, A.R., 1964, Magnitude and frequency of floods in the 

United States—Part 1A, North Atlantic slope basins, Maine 

to Connecticut: U.S. Geological Survey Water-Supply Paper 

1671, 260 p.

Griffis, V.W., and Stedinger, J.R., 2007, The use of GLS 

regression in regional hydrologic analyses: Journal of 

Hydrology, v. 344, p. 82–95.

Griffis, V.W., and Stedinger, J.R., 2009, Log-Pearson Type 3 

distribution and its application in flood frequency analysis. 

III—Sample skew and weighted skew estimators: Journal of 

Hydrologic Engineering, v. 14, no. 2, p. 121–130.

Griffis, V.W., Stedinger, J.R., and Cohn, T.A., 2004, Log 

Pearson Type 3 quantile estimators with regional skew 

information and low outlier adjustments: Water Resources 

Research, v. 40, W07503, 17 p.

Grover, N.C., 1937, The floods of March 1936—Part 1. New 

England rivers: U.S. Geological Survey Water-Supply Paper 

798, 466 p.

Grubbs, F.E., and Beck, Glen, 1972, Extension of sample 

sizes and percentage points for significance tests of outlying 

observations: Technometrics, v. 14, no. 2, p. 847–854.

Gruber, A.M., Dirceu, S.R., Jr., and Stedinger, J.R., 2007, 

Models of regional skew based on Bayesian GLS regression, in Kabbes, K.C., ed., Proceedings of the World Environmental and Water Resources Congress 2007—Restoring 

our Natural Habitat, Tampa, Florida, May 15–19, 2007: 

Reston, Virginia, American Society of Civil Engineers, 

paper 40927–3285, 10 p.

Gruber, A.M., and Stedinger, J.R., 2008, Models of LP3 

regional skew, data selection, and Bayesian GLS regression, 

in Babcock, R.W., Jr., and Walton, Raymond, eds., World 

Environmental and Water Resources Congress 2008—

Ahupua’a, Honolulu, Hawaii, May 12–16, 2008: Reston, 

Va., American Society of Civil Engineers, paper 596, 10 p.

Guimaraes, W.B., and Bohman, L.R., 1992, Techniques for 

estimating magnitude and frequency of floods in South 

Carolina, 1988: U.S. Geological Survey Water-Resources 

Investigations Report 91–4157, 175 p.

Hedgecock, T.S., and Feaster, T.D., 2007, Magnitude and frequency of floods in Alabama, 2003: U.S. Geological Survey 

Scientific Investigations Report 2007–5204, 28 p., at 

http://pubs.usgs.gov/sir/2007/5204/.

Hedgecock, T.S., and Lee, K.G., 2010, Magnitude and frequency of floods for urban streams in Alabama, 2007: U.S. 

Geological Survey Scientific Investigations Report 2010–

5012, 17 p., at http://pubs.usgs.gov/sir/2010/5012/.

Helsel, D.R., and Hirsch, R.M., 2002, Statistical methods in 

water resources: U.S. Geological Survey Techniques of 

Water-Resources Investigations, book 4, chap. A3, 523 p.

Hirsch, R.M., 1982, A comparison of four streamflow record 

extension techniques: Water Resource Research, v. 18, 

no. 4, p. 1081–1088.

Hodgkins, G.A., and Dudley, R.W., 2005, Changes in the 

magnitude of annual and monthly streamflows in 

New England, 1902–2002: U.S. Geological Survey 

Scientific Investigations Report 2005–5135, 37 p., at 

http://pubs.usgs.gov/sir/2005/5135/.

Hollis, G.E., 1975, The effect of urbanization on floods of different recurrence interval: Water Resources Research, v. 11, 

no. 3, p. 431–435.

Huntington, T.G., Richardson, A.D., McGuire, K.J., and 

Hayhoe, Katharine, 2009, Climate and hydrological changes 

in the northeastern United States—Recent trends and 

implications for forested and aquatic ecosystems: Canadian 

Journal of Forest Research, v. 39, no. 2, p. 199–212.

Interagency Advisory Committee on Water Data, 1981, 

Guidelines for determining flood flow frequency: Bulletin 

17B of the Hydrology Subcommittee, Office of Water Data 

Coordination, U.S. Geological Survey, Reston, Va., revised 

March 1982, 183 p.
46 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Jennings, M.E., Thomas, W.O., Jr., and Riggs, H.C., 1994, 

Nationwide summary of U.S. Geological Survey regional 

regression equations for estimating magnitude and frequency of floods for ungaged sites, 1993: U.S. Geological 

Survey Water-Resources Investigations Report 94–4002, 

196 p. [Superseded by Water-Resources Investigations 

Report 02–4168.]

Johnson, C.G., and Laraway, G.A., 1977, Flood magnitude 

and frequency of small Rhode Island streams—Preliminary 

estimating relations: U.S. Geological Survey Open-File 

Report 76–883, 20 p.

Johnstone, Don, and Cross, W.P., 1949, Elements of applied 

hydrology: New York, N.Y., Ronald Press Co., 276 p.

Katz, R.W., Parlange, M.B., and Naveau, Philippe, 2002, 

Statistics of extremes in hydrology: Advances in Water 

Resources v. 25, p. 1287–1304.

Kinnison, H.B., 1930, The New England flood of November of 1927: U.S. Geological Survey Water-Supply Paper 

636–C, 330 p.

Konrad, C.P., 2003, Effects of urban development on floods: 

U.S. Geological Survey Fact Sheet 076–03, 4 p.

Konrad, C.P., and Booth, D.B., 2002, Hydrologic trends 

associated with urban development for selected streams in 

the Puget Sound Basin, western Washington: U.S. Geological Survey Water-Resources Investigations Report 02–4040, 

40 p., at http://pubs.usgs.gov/wri/wri024040/pdf/

WRIR02-4040.pdf.

Lins, H.F., and Slack, J.R., 2005, Seasonal and regional characteristics of U.S. streamflow trends in the United States 

from 1940 to 1999: Physical Geography, v. 26, no. 6, 

p. 489–501.

Ludwig, A.H., and Tasker, G.D., 1993, Regionalization of 

low-flow characteristics of Arkansas streams: U.S. Geological Survey Water-Resources Investigations Report 93–4013, 

19 p.

Martin, G.R., Ruhl, K.J., Moore, B.L., and Rose, M.F., 1997, 

Estimation of peak discharge frequency of urban streams in 

Jefferson County, Kentucky: U.S. Geological Survey WaterResources Investigations Report 97–4219, 40 p.

Martins, E.S., and Stedinger, J.R., 2002, Cross-correlation 

among estimators of shape: Water Resources Research, 

v. 38, no. 11, 7 p., at http://www.agu.org/journals/wr/

wr0211/2002WR001589/2002WR001589.pdf.

McCabe, G.J., and Wolock, D.M., 2002, A step increase in 

streamflow in the conterminous United States: Geophysical 

Research Letters, v. 29, no. 24, p. 2185–2189, at 

http://www.agu.org/journals/gl/gl0224/2002GL015999/

2002GL015999.pdf.

Milly, P.C.D., Betancourt, Julio, Falkenmark, Malin, Hirsch, 

R.M., Kundzewicz, Z.W., Lettenmaier, D.P., and Stouffer, 

R.L., 2008, Stationarity is dead—Whither Water Management?: Science, v. 319, no. 5863, p. 573–574.

Moglen, G.E., and Shivers, D.E., 2006, Methods for 

adjusting U.S. Geological Survey rural regression peak 

discharges in urban settings: U.S. Geological Survey 

Scientific Investigations Report 2006–5270, 55 p., at 

http://pubs.usgs.gov/sir/2006/5270/.

Murphy, P.J., 2001a, Estimating equation for mixed populations of floods in Massachusetts: Journal of Hydrologic 

Engineering, v. 6, no. 1, p. 72–74.

Murphy, P.J., 2001b, Evaluation of mixed-population flood 

frequency analysis: Journal of Hydrologic Engineering, v. 6, 

no. 1, p. 62–70.

National Oceanic and Atmospheric Administration, 2002, 

Rhode Island, sec. 37 of Monthly station normals of temperature, precipitation, and heating and cooling degree days 

1971–2000: Climatography of the United States, no. 82, 

accessed March 3, 2012, at http://cdo.ncdc.noaa.gov/

climatenormals/clim81/RInorm.pdf.

National Oceanic and Atmospheric Administration, [undated], 

Historical hurricane tracks: National Oceanic and 

Atmospheric Administration, accessed May 4, 2012, at 

http://www.csc.noaa.gov/hurricanes/.

Ouarda, T.B.M.J., and El-Adlouni, S., 2011, Bayesian nonstationary frequency analysis of hydrological variables: 

Journal of the American Water Resources Association, v. 47, 

no. 3, p. 496–505.

Parker, G.W., Ries, K.G., III, and Socolow, R.S., 1998, The 

flood of June 1998 in Massachusetts and Rhode Island: 

U.S. Geological Survey Fact Sheet 110–98, 4 p., at 

http://pubs.usgs.gov/fs/fs110-98/.

Paulsen, C.G., Bigwood, B.L., Harrington, A.W., Hartwell, 

O.W., and Kinnison, H.B., 1940, Hurricane floods of 

September 1938: U.S. Geological Survey Water-Supply 

Paper 867, 562 p.

Perley, Sidney, 1891, Historic storms of New England: Salem, 

Mass., Salem Press, 341 p.

Reis, D.S., Jr., Stedinger, J.R., and Martins, E.S., 2005, 

Bayesian generalized least squares regression with application to log Pearson Type 3 regional skew estimation: Water 

Resources Research, v. 41, W10419, 14 p.

Ries, K.G., III, 2007, The National streamflow statistics 

program—A computer program for estimating streamflow 

statistics for ungaged sites: U.S. Geological Survey 

Techniques and Methods, book 4, chap. A6, 37 p., at 

http://pubs.usgs.gov/tm/2006/tm4a6/.
Selected References 47

Ries, K.G., III, and Atkins, J.B., 2002, The National flood 

frequency program, version 3—A computer program for 

estimating magnitude and frequency of floods for 

ungaged sites, 2002: U.S. Geological Survey WaterResources Investigations Report 02–4168, 42 p., at 

http://pubs.usgs.gov/wri/wri024168/.

Ries, K.G., III, and Crouse, M.Y., comps., 2002, The National 

Flood Frequency Program, version 3—A computer program for estimating magnitude and frequency of floods 

for ungaged sites, 2002: U.S. Geological Survey WaterResources Investigations Report 02–4168, 53 p., at 

http://pubs.usgs.gov/wri/wri024168/.

Ries, K.G., III, and Dillow, J.J.A., 2006, Magnitude and 

frequency of floods on nontidal streams in Delaware: 

U.S. Geological Survey Scientific Investigations Report 

2006–5146, 59 p., at pubs.usgs.gov/sir/2006/5146/pdf/

sir2006-5146.pdf.

Ries, K.G., III, Guthrie, J.D., Rea, A.H., Steeves, P.A., 

and Stewart, D.W., 2008, StreamStats—A water resources 

web application: U.S. Geological Survey Fact Sheet 2008–

3067, 6 p., at http://pubs.usgs.gov/fs/2008/3067/pdf/

fs-2008-3067-508.pdf.

Robbins, J.C., and Pope, B.F., III, 1996, Estimation of 

flood frequency characteristics of small urban streams 

in North Carolina: U.S. Geological Survey WaterResources Investigations Report 96–4084, 21 p., at 

http://pubs.usgs.gov/wri/1996/4084/report.pdf.

Sauer, V.B., 1974, Flood characteristics of Oklahoma 

streams—Techniques for calculating magnitude and 

frequency of floods in Oklahoma, with compilations of 

flood data through 1971: U.S. Geological Survey WaterResources Investigations Report 52–73, 301 p.

Sauer, V.B., Thomas, W.O., Stricker, V.A., and Wilson, K.V., 

1983, Flood characteristics of urban watersheds in the 

United States: U.S. Geological Survey Water-Supply Paper 

2207, 69 p.

Sherwood, J.M., 1994, Estimation of volume-durationfrequency relations of ungaged small urban streams in Ohio: 

Water Resources Bulletin, v. 30, no. 2, p. 261–269.

Small, David, Islam, Shafiqul, and Vogel, R.M., 2006, Trends 

in precipitation and streamflow in the eastern U.S.—Paradox or perception?: Geophysical Research Letters L03403, 

v. 33, 4 p.

Southard, R.E., 2010, Estimation of the magnitude and frequency of floods in urban areas in Missouri: U.S. Geological Survey Scientific Investigations Report 2010–5073, 

27 p., at http://pubs.usgs.gov/sir/2010/5073/.

Stamey, T.C., and Hess, G.W., 1993, Techniques for estimating 

magnitude and frequency of floods in rural basins of Georgia: U.S. Geological Survey Water-Resources Investigations 

Report 93–4016, 69 p.

Stedinger, J.R., and Tasker, G.D., 1985, Regional hydrologic 

analysis—1. Ordinary, weighted, and generalized least 

squares compared: Water Resources Research, v. 21, no. 9, 

p. 1421–1432.

Stedinger, J.R., and Tasker, G.D., 1986, Regional hydrologic 

analysis—2. Model-error estimators, estimation of sigma 

and log-Pearson type 3 distributions: Water Resources 

Research, v. 22, no. 10, p. 1487–1499.

Tasker, G.D., and Stedinger, J.R., 1989, An operational GLS 

model for hydrologic regression: Journal of Hydrology, 

v. 111, p. 361–375.

Thomas, W.O., and Kirby, W.H., 2002, Estimation of extreme 

floods, in Ries, K.G., III, and Crouse, M.Y., eds., The 

National Flood Frequency Program, version 3—A computer 

program for estimating magnitude and frequency of 

floods for ungaged sites: U.S. Geological Survey WaterResources Investigations Report 02–4168, p. 12–14, at 

http://pubs.usgs.gov/wri/wri024168/.

Thomson, M.T., Cannon, W.B., Thomas, M.P., and Hayes, 

S.S., 1964, Historical floods in New England: U.S. Geological Survey Water-Supply Paper 1779–M, 105 p.

U.S. Army Corps of Engineers, 1958, Frequency of New 

England floods: U.S. Army Corps of Engineers Civil Works 

Investigations Project CW–l51, 10 p.

U.S. Geological Survey, 2012, Peak streamflow for the Nation, 

in National Water Information System: U.S. Geological 

Survey, accessed May 4, 2012, at http://nwis.waterdata.

usgs.gov/usa/nwis/peak/.

Verdi, R.J., and Dixon, J.F., 2011, Magnitude and frequency 

of floods for rural streams in Florida, 2006: U.S. Geological 

Survey Scientific Investigations Report 2011–5034, 69 p., 

1 pl., at http://pubs.usgs.gov/sir/2011/5034/.

Villarini, Gabriele, Smith, J.A., Serinaldi, Francesco, Bales, 

Jerad, Bates, P.D., and Krajewski, W.F., 2009, Flood frequency analysis for nonstationary annual peak records in an 

urban drainage basin: Advances in Water Resources, v. 23, 

p. 1255–1266.

Walker, P.N., 1991, Rhode Island floods and droughts, with a 

section on General climatology, by R.E. Lautzenheiser, in

National water summary 1988–89—Floods and droughts: 

U.S. Geological Survey Water-Supply Paper 2375, 

p. 483–488.
48 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Walter, Meghan, and Vogel, R.M., 2010, Increasing 

trends in peak flows in the northeastern United States 

and their impacts on design, in Joint Federal Interagency 

Conference, 2d, Las Vegas, Nevada, June 27–July 1, 2010, 

Proceedings: Advisory Committee on Water Information, 

16 p., at http://acwi.gov/sos/pubs/2ndJFIC/Contents/

2F_Walter_03_01_10.pdf.

Watson, K.M., and Schopp, R.D., 2009, Methodology for 

estimation of flood magnitude and frequency for New 

Jersey streams: U.S. Geological Survey Scientific Investigations Report 2009–5167, 51 p., at http://pubs.usgs.gov/

sir/2009/5167/.

Wood, G.K., Swallow, L.A., Johnson, C.G., and Searles, G.H., 

1970, Flood of March 1968 in eastern Massachusetts and 

Rhode Island: U.S. Geological Survey Open-File Report 

70–373, 81 p.
Glossary 49

Glossary

adjusted r-squared (adj-R2) The adjusted 

coefficient of determination (adj-R2), a 

measure of the percentage of the variation 

explained by the explanatory variables of 

the equation adjusted for the number of 

parameters in the equation.

annual exceedance probability (AEP)

The expected annual probability of a flood, 

previously referred to in terms of return 

period of a flood. The probability, often 

expressed as a decimal fraction less than 

1.0, that an annual peak discharge will be 

exceeded in a 1-year period. The reciprocal 

of the exceedance probability is referred to 

as the recurrence interval or return period 

in years.

annual peak The maximum instantaneous 

discharge occurring during a water year.

average standard error of prediction

The square root of the average spread or 

dispersion of the predicted value from the 

observed mean.

average variance of prediction (AVP)

The average spread or dispersion of the 

predicted value from the observed mean.

confidence interval The range of an 

estimated parameter value in which the 

true value lies for a specified probability 

(95-percent confidence level, α = 5 percent, 

is generally used throughout this report).

covariance A measure of how much two 

random variables change together. Positive 

values indicate variables tend to show similar 

behavior, whereas negative values indicate 

the greater value of one variable correspond 

to the smaller value of the other variable. In 

multiple variable regression, covariance is 

expressed in matrix form sized according to 

the number of variables in the regression.

expected moments algorithm (EMA) Method 

for fitting a probability distribution to annual 

peak discharge data using a generalized 

method of moments, similar to the standard 

log-Pearson type III (LPIII) method described 

in Bulletin 17B (Interagency Advisory 

Committee on Water Data, 1981), except the 

expected moments algorithm (EMA) can also 

use interval data, whereas LPIII is restricted 

to point data. Interval data provide additional 

information that cannot be represented by 

point data, such as the potential range of 

annual peak flows outside of the systematic 

and historic record and the uncertainties 

around recorded peaks used in the analysis.

generalized least squares (GLS)

A regression method that accounts for 

differences in the variances and cross 

correlations of the errors associated with 

different recorded discharges; known as 

GLS. Differences in variances can result 

from differences in the length of record for 

each site, whereas cross correlations among 

concurrent annual peak discharges results 

in cross correlation between estimated 

flood statistics, such as quantiles and 

skew coefficients.

historic flood Magnitude of a flood 

recorded, or estimated, outside the systematic 

period of record.

log-Pearson type III (LPIII) A frequency 

distribution determined from the statistical 

moments of the annual peak flow mean, 

standard deviation, and skew.

maintenance of variation extension 

(MOVE) A linear regression technique 

used for filling in missing streamflow data 

measurements or producing a unique extended 

streamflow sequence that maintains the mean 

and variance for the sample.

Mallow’s Cp An estimate of the standardized 

mean square error of prediction; this is 

a compromise between maximizing the 

explained variance by including all relevant 

variables and minimizing the standard error 

by keeping the number of variables as small 

as possible.

mean square error (MSE) The average 

of the squares of the differences between 

the estimated values and the measured 

values. This metric represents how closely, 

on average, an estimated value matches a 

measured value.
50 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

multicolinearity A statistical phenomenon 

in which two or more predictor variables 

in a multiple regression model are highly 

correlated, in which case the regression 

coefficients may change erratically in 

response to small changes in the model or 

the data.

ordinary least squares (OLS) Linear 

regression method is standard approach 

to the “least squares” solution of fitting 

and independent variable to one or more 

dependent variables.

outlier A data point that departs from the 

trend of the rest of a dataset as described 

by a distribution or other mathematical 

relationship.

100-year flood An annual peak discharge 

having an average recurrence interval of 

100 years, corresponding to an annual 

exceedance probability of 1 percent.

predicted residual sum of squares 

(PRESS) A validation type estimator of 

error. Predicted residual sum of squares 

(PRESS) uses n-1 observations to develop 

the equation and then estimates the value of 

the observation that was left out. The process 

is repeated for each observation, and the 

prediction errors are squared and summed.

pseudo-R-squared (pseudo-R2) A statistic 

generated by GLS regression, the pseudo 

coefficient of determination (pseudo-R2) is 

similar to the adj-R2 in that it is a measure of 

the predictive strength of the regression model 

except that it removes the time sampling error.

root mean square error (RMSE)

The square root of the sum of the squares 

of the differences between estimated and 

the measured values divided by the number 

of observations minus one. This metric 

represents the magnitude of the differences 

between the estimated and measured values. 

Of particular concern in this report is the root 

mean square error (RMSE) of the regional 

skew estimate.

skew (γ) A statistical measure of the data 

symmetry or lack thereof used to compute 

the flood frequency distribution. The skew 

generally is computed from the logarithms 

of annual peak discharges at the streamgage. 

Because the skew is sensitive to outliers, 

it may be an unreliable estimate of the true 

skew, especially for small samples; Bulletin 

17B (Interagency Committee on Water 

Data, 1981) recommends that the skew is 

weighted with a regional, or generalized, 

skew that is based on data from many longterm streamgages to produce at-site flood 

frequency estimates.

standard error of estimate (SE) Also 

referred to as the root mean squared error of 

the residuals, it is the standard deviation of 

observed values about the regression line. 

It is computed by dividing the unexplained 

variation or the error sum of squares by its 

degrees of freedom. In this study, the standard 

error is based on one standard deviation.

variance A measure of the spread or 

dispersion of a set of values around their 

mean calculated by the mean of the squares 

of the deviation of the value from the 

mean, which is equal to the square of the 

standard deviation.

variance inflation factor (VIF) Expresses 

the ratio of the actual variance of the 

coefficient of the explanatory variable to 

its variance if it were independent of the 

explanatory variables. A variance inflation 

factor greater than 5 to 10 generally indicates 

multicolinearity, a serious problem in the 

regression models.

variance of prediction (VP) A measure of 

the likely difference between the prediction 

provided by a regression model and the actual 

value of the variable.

weighted independent estimator (WIE)

A software program that weights two 

independent estimates inversely proportional 

to the uncertainty of the individual estimates.

weighted least squares (WLS) A regression 

method that accounts for the variation in 

the errors caused by unequal record lengths 

at streamgages used to estimate the flood 

characteristics of interest. Weighted least 

squares regression incorporates weights 

associated with each data point into the fitting 

criterion. The size of the weights corresponds 

to the precision of the information contained 

in the record.
Tables 7, 13, and 15
52 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Rhode Island streamgages

Adamville Brook at Adamville, RI (01106000)

1941–1978, 1987a

20 5 220 200 250 220 -- -- -- 220 190 250

10 10 260 230 300 250 -- -- -- 250 220 300

4 25 310 270 370 290 -- -- -- 300 250 390

2 50 340 290 420 310 -- -- -- 330 280 480

1 100 380 320 470 330 -- -- -- 360 300 580

0.5 200 410 340 520 340 -- -- -- 400 320 700

0.2 500 450 380 590 360 -- -- -- 440 340 900 a

EMA analysis detected and conditioned six low ouliers.

Beaver River near Usquepaug, RI (01117468)

1976–2010 1942–2010a,b

20 5 230 190 290 230 190 170 210 190 160 230

10 10 320 260 410 320 250 220 300 250 210 340

4 25 460 360 650 470 350 300 430 350 280 580

2 50 590 450 880 610 450 370 570 450 330 880

1 100 750 550 1,200 790 560 460 740 560 400 1,320

0.5 200 950 670 1,600 1,000 700 560 950 700 470 2,010

0.2 500 1,300 850 2,240 1,370 930 710 1,310 920 570 3,500 a

Actual records 1942–1975 extended using Wood River at Hope Valley, RI (01118000).

b

Error of ±6% assigned to 1968 peak for EMA analysis.

Blackstone River at Woonsocket, RI (01112500)

1929–2010

20 5 9,160 8,290 10,300 9,180 -- -- -- 9,160 8,030 10,800

10 10 11,800 10,500 13,600 11,800 -- -- -- 11,800 10,100 14,900

4 25 15,800 13,800 18,800 15,700 -- -- -- 15,800 13,000 22,300

2 50 19,300 16,400 23,500 19,100 -- -- -- 19,300 15,300 30,200

1 100 23,100 19,400 28,900 22,800 -- -- -- 23,100 17,700 40,600

0.5 200 27,500 22,700 35,100 27,100 -- -- -- 27,500 20,200 54,400

0.2 500 34,200 27,500 44,900 33,400 -- -- -- 34,200 23,700 79,600

Branch River at Forestdale, RI (01111500)

1940–2010 (1936 Historic peak)

20 5 2,890 2,560 3,320 2,830 -- -- -- 2,820 2,430 3,400

10 10 3,800 3,310 4,490 3,670 -- -- -- 3,680 3,100 4,730

4 25 5,160 4,380 6,330 4,880 -- -- -- 4,960 4,010 7,180

2 50 6,320 5,260 7,980 5,880 -- -- -- 6,040 4,720 9,740

1 100 7,630 6,230 9,900 6,990 -- -- -- 7,250 5,450 13,100

0.5 200 9,100 7,290 12,100 8,200 -- -- -- 8,600 6,200 17,500

0.2 500 11,300 8,860 15,600 9,990 -- -- -- 10,600 7,240 25,500

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.

[AEP, annual exceedance probability, in percent. Period of record analysis, the systematic record and historic peaks if present. Extended record analysis, includes 

the period of record plus records estimated by maintenance of variance extension (MOVE). Length of record used in the analysis is shown below each streamgage. 

B17B, flood frequency analysis made using Bulletin 17B (Interagency Committee on Water Data, 1981) guidelines. EMA, expected moments algorithm; the 

EMA analysis is for the period of record for stations were the record is not extended. Values in bold typeface are values used in the regional analysis. All values 

are in cubic feet per second (ft3/s). All values except for the systematic peak were computed from a weighted skew of 0.52 and root mean square error of 0.46. %, 

percent; --, station record was not extended; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]
Table 7 53

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Rhode Island streamgages—Continued

Chepachet River at Chepachet, RI (01111400)

1965–1975 1940–2010a

20 5 -- -- -- 520 520 470 600 520 450 630

10 10 -- -- -- 680 680 600 800 680 570 880

4 25 -- -- -- 910 920 780 1,120 920 740 1,340

2 50 -- -- -- 1,100 1,120 940 1,400 1,120 870 1,820

1 100 -- -- -- 1,310 1,350 1,110 1,730 1,350 1,010 2,470

0.5 200 -- -- -- 1,540 1,600 1,290 2,110 1,600 1,150 3,340

0.2 500 -- -- -- 1,900 1,990 1,570 2,710 1,990 1,350 4,920 a

Actual records 1965–75 extended using Branch River at Forestdale, RI (01111500).

Chipuxet River at West Kingston, RI (01117350)

1974–2010 1941–2010a,b

20 5 180 160 220 150 140 130 160 140 120 180

10 10 250 210 320 200 190 170 230 190 160 270

4 25 360 290 490 280 270 230 330 270 210 460

2 50 460 360 670 360 350 290 440 350 260 700

1 100 580 440 890 450 440 360 570 440 310 1,080

0.5 200 730 530 1,170 560 550 430 740 550 360 1,660

0.2 500 980 680 1,670 750 730 560 1,030 730 450 2,980 a

Actual records 1974–2010 extended using Hunt River at East Greenwich, RI (01117000).

b

Error of ±8% assigned to 1968 and 1970 peaks for EMA analysis.

Hunt River near East Greenwich, RI (01117000)

1941–2010

20 5 610 550 690 610 -- -- -- 610 530 750

10 10 810 710 940 810 -- -- -- 810 680 1,080

4 25 1,110 957 1,350 1,140 -- -- -- 1,110 880 1,780

2 50 1,390 1,170 1,740 1,450 -- -- -- 1,390 1,060 2,610

1 100 1,720 1,420 2,220 1,820 -- -- -- 1,720 1,240 3,850

0.5 200 2,120 1,700 2,810 2,280 -- -- -- 2,120 1,450 5,710

0.2 500 2,750 2,140 3,800 3,040 -- -- -- 2,750 1,750 9,620 a

Set high threshold (1,748 ft3/s) to reflect that 1938 peak was large but less than 2010 peak (2,380 ft3/s), 1938 stage only and reflects storm surge.

Moshassuck River at Providence, RI (01114000)

1964–2010 1942–2010a

20 5 1,210 1,120 1,320 1,140 1,120 1,050 1,220 1,130 1,030 1,260

10 10 1,400 1,290 1,560 1,320 1,320 1,220 1,450 1,320 1,190 1,540

4 25 1,660 1,500 1,910 1,540 1,570 1,430 1,770 1,580 1,390 1,970

2 50 1,870 1,660 2,190 1,690 1,770 1,590 2,030 1,770 1,530 2,360

1 100 2,090 1,830 2,500 1,840 1,980 1,750 2,300 1,970 1,660 2,800

0.5 200 2,320 2,000 2,820 1,990 2,190 1,920 2,590 2,180 1,790 3,320

0.2 500 2,640 2,240 3,300 2,180 2,490 2,150 3,000 2,460 1,960 4,130 a

Actual records 1964–2010 extended using Woonasquatucket River at Centerdale, RI (01114500).

Nipmuc River near Harrisville, RI (01111300)

1965–2010 1940–2010a,b

20 5 880 740 1,100 730 730 640 850 730 620 900

10 10 1,200 980 1,520 980 990 850 1,180 990 810 1,310

4 25 1,640 1,300 2,210 1,360 1,380 1,150 1,720 1,380 1,080 2,100

2 50 2,020 1,570 2,840 1,680 1,720 1,410 2,220 1,720 1,300 2,980

1 100 2,450 1,860 3,580 2,050 2,120 1,700 2,820 2,120 1,530 4,190

0.5 200 2,930 2,170 4,430 2,470 2,580 2,020 3,530 2,580 1,780 5,850

0.2 500 3,650 2,630 5,760 3,100 3,290 2,510 4,660 3,280 2,120 9,020 a

Actual records 1965–2010 extended using Branch River at Forestdale, RI (01111500).

b

Error of ±5% assigned to 1954 and 1955 peaks for EMA analysis.

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
54 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Rhode Island streamgages—Continued

Nooseneck River at Nooseneck, RI (01115630)

1965–1975 1942–2010a,b

20 5 430 340 590 330 330 290 370 330 280 400

10 10 600 450 880 430 430 380 500 430 360 560

4 25 860 620 1,400 580 580 500 710 580 470 890

2 50 1,100 760 1,930 720 720 600 910 720 550 1,260

1 100 1,380 920 2,600 880 880 720 1,140 880 650 1,780

0.5 200 1,710 1,100 3,450 1,070 1,060 850 1,420 1,060 750 2,500

0.2 500 2,240 1,380 4,920 1,350 1,350 1,050 1,860 1,350 890 3,930 a

Actual record 1965–75 extended using Wood River at Hope Valley, RI (01118000).

b

Error of ±16% assigned to 1982 peak.

Pawtuxet River at Cranston, RI (01116500)

1940–2010a

20 5 2,830 2,570 3,170 2,830 -- -- -- 2,900 2,400 3,420

10 10 3,740 3,330 4,300 3,740 -- -- -- 3,840 3,220 4,840

4 25 5,230 4,520 6,290 5,230 -- -- -- 5,420 4,330 8,340

2 50 6,640 5,600 8,260 6,640 -- -- -- 6,940 5,290 14,100

1 100 8,370 6,880 10,800 8,370 -- -- -- 8,820 6,370 24,000

0.5 200 10,500 8,400 13,900 10,500 -- -- -- 11,100 7,590 38,200

0.2 500 14,000 10,800 19,400 14,000 -- -- -- 15,000 9,450 70,700 a

Station skew is used because of upstream regulation; historical peaks of 1886 and 1938 are included in analysis. Streamgage not used in regionalization analysis 

because of upstream regulation by Scituate Reservoir.

Pawcatuck River at Westerly, RI (01118500)

1941–2010 (Historical peaks 1927 and 1936b)

20 5 3,300 3,040 3,620 3,310 -- -- -- 3,400 3,030 3,940

10 10 4,080 3,710 4,570 4,160 -- -- -- 4,230 3,680 5,200

4 25 5,230 4,650 6,060 5,480 -- -- -- 5,460 4,560 7,550

2 50 6,220 5,440 7,390 6,680 -- -- -- 6,530 5,260 10,100

1 100 7,340 6,310 8,930 8,070 -- -- -- 7,730 6,000 13,500

0.5 200 8,610 7,270 10,700 9,700 -- -- -- 9,100 6,790 18,100

0.2 500 10,600 8,700 13,600 12,300 -- -- -- 11,200 7,910 26,700 a

Set high threshold (7,625 ft3/s) above 1936 historical peak (3,150 ft3/s) to reflect that 1938 peak was likely larger.

Pawcatuck River at Wood River Junction, RI (01117500)

1941–2010

20 5 1,030 950 1,140 1,020 -- -- -- 1,030 910 1,210

10 10 1,280 1,160 1,450 1,290 -- -- -- 1,280 1,110 1,620

4 25 1,660 1,470 1,940 1,690 -- -- -- 1,660 1,380 2,420

2 50 1,990 1,730 2,380 2,050 -- -- -- 1,990 1,590 3,300

1 100 2,370 2,020 2,900 2,470 -- -- -- 2,370 1,820 4,510

0.5 200 2,790 2,340 3,510 2,950 -- -- -- 2,790 2,060 6,190

0.2 500 3,440 2,810 4,470 3,720 -- -- -- 3,440 2,400 9,410

Ponaganset River at South Foster, RI (01115187)a

1995–2010 1940–2010a,b

20 5 940 750 1,280 760 760 680 860 760 660 890

10 10 1,200 940 1,770 960 960 850 1,120 960 820 1,200

4 25 1,580 1,180 2,550 1,230 1,260 1,080 1,510 1,260 1,040 1,740

2 50 1,890 1,370 3,260 1,460 1,500 1,270 1,850 1,500 1,200 2,280

1 100 2,220 1,560 4,100 1,690 1,760 1,470 2,220 1,770 1,370 2,960

0.5 200 2,590 1,770 5,080 1,940 2,050 1,680 2,640 2,050 1,530 3,820

0.2 500 3,130 2,050 6,620 2,300 2,470 1,990 3,280 2,480 1,760 5,290 a

Actual records 1995-2010 extended using Branch River at Forestdale, RI (01111500).

b

Error of ±5% assigned to 1955, 1968, 1979, and 1982 peak for EMA analysis.

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
Table 7 55

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Rhode Island streamgages—Continued

South Branch Pawtuxet River at Washington, RI (01116000)

1941–2010 (Historical peak 1936)

20 5 1,090 970 1,260 1,100 -- -- -- 1,120 940 1,380

10 10 1,470 1,280 1,740 1,480 -- -- -- 1,500 1,240 2,030

4 25 2,060 1,740 2,540 2,100 -- -- -- 2,130 1,660 3,360

2 50 2,600 2,140 3,320 2,660 -- -- -- 2,700 2,000 4,930

1 100 3,230 2,610 4,260 3,340 -- -- -- 3,370 2,380 7,230

0.5 200 3,980 3,140 5,410 4,150 -- -- -- 4,170 2,800 10,600

0.2 500 5,170 3,960 7,310 5,450 -- -- -- 5,450 3,410 17,500 a

Set high threshold (3,568 ft3/s) above 1936 historical peak (1,000 ft3/s) to reflect that 1938 peak was larger but less than 2010 peak (5,480 ft3/s).

Ten Mile River at Pawtucket Avenue at East Providence, RI (01109403)

1987–2010 1926–2010a,b

20 5 1,270 1,060 1,610 1,120 1,120 1,020 1,240 1,120 1,000 1,290

10 10 1,640 1,340 2,190 1,400 1,400 1,260 1,590 1,400 1,230 1,700

4 25 2,180 1,710 3,140 1,780 1,800 1,590 2,100 1,800 1,530 2,390

2 50 2,640 2,010 4,010 2,100 2,130 1,860 2,540 2,130 1,750 3,070

1 100 3,160 2,340 5,050 2,430 2,490 2,140 3,020 2,490 1,980 3,910

0.5 200 3,740 2,690 6,280 2,790 2,880 2,440 3,560 2,880 2,220 4,960

0.2 500 4,620 3,200 8,250 3,320 3,450 2,870 4,370 3,460 2,540 6,740 a

Actual records 1987–2010 extended using Wading River near Norton, MA (01109000).

b

Error of ±3% assigned to 1931, 1936, 1938, 1946, 1954–55, 1968–70, 1978–79, and 1983–84 peaks for EMA analysis.

Usquepaug River near Usquepaug, RI (01117420)

1976–2010 1941–2010a,b

20 5 660 570 800 550 550 500 610 550 480 660

10 10 860 720 1,090 710 710 630 810 710 600 920

4 25 1,170 950 1,570 960 950 820 1,130 950 770 1,450

2 50 1,440 1,140 2,030 1,180 1,160 980 1,420 1,170 904 2,040

1 100 1,750 1,340 2,570 1,440 1,400 1,170 1,770 1,410 1,050 2,890

0.5 200 2,110 1,570 3,220 1,750 1,680 1,380 2,190 1,700 1,200 4,100

0.2 500 2,660 1,910 4,290 2,240 2,130 1,690 2,860 2,150 1,430 6,500 a

Records extended using Pawcatuck River at Wood River Junction, RI (01117500).

b

Error of ±4% assigned to 1968 peak for EMA analysis.

Wood River near Arcadia, RI (01117800)

1964–2010 1942–2010a

20 5 700 610 820 620 620 560 700 620 540 760

10 10 920 790 1,120 820 810 720 940 820 680 1,100

4 25 1,280 1,060 1,640 1,140 1,100 950 1,330 1,120 890 1,800

2 50 1,610 1,300 2,150 1,450 1,370 1,160 1,700 1,400 1,060 2,650

1 100 2,000 1,570 2,780 1,820 1,680 1,390 2,160 1,740 1,250 3,910

0.5 200 2,460 1,880 3,560 2,260 2,050 1,650 2,700 2,120 1,460 5,800

0.2 500 3,200 2,360 4,880 2,990 2,630 2,060 3,600 2,750 1,760 9,780 a

Actual records for 1964–2010 extended using Wood River at Hope Valley, RI (01118000); includes use of 1936 historical peak. Streamgage not used in regional 

analysis because of high correlation of annual peaks to downstream streamgage at Hope Valley.

Wood River at Hope Valley, RI (01118000)

1942–2010 (Historical peak 1936a)

20 5 1,310 1,200 1,450 1,300 -- -- -- 1,310 1,160 1,540

10 10 1,650 1,490 1,870 1,670 -- -- -- 1,650 1,420 2,100

4 25 2,170 1,910 2,550 2,250 -- -- -- 2,170 1,780 3,170

2 50 2,630 2,270 3,180 2,790 -- -- -- 2,630 2,080 4,380

1 100 3,160 2,670 3,920 3,440 -- -- -- 3,160 2,390 6,080

0.5 200 3,760 3,120 4,800 4,200 -- -- -- 3,760 2,730 8,460

0.2 500 4,710 3,810 6,220 5,450 -- -- -- 4,700 3,210 13,100 a

Set high threshold (2,500 ft3/s) above 1936 historical peak (1,540 ft3/s) to reflect that the 1938 peak was likely larger.

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
56 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Rhode Island streamgages—Continued

Woonasquatucket River at Centerdale, RI (01114500)

1942–2010 (Historical peak 1936a)

20 5 920 820 1,040 920 -- -- -- 910 800 1,060

10 10 1,150 1,020 1,340 1,150 -- -- -- 1,150 990 1,400

4 25 1,470 1,270 1,760 1,440 -- -- -- 1,460 1,230 1,940

2 50 1,720 1,460 2,110 1,670 -- -- -- 1,720 1,400 2,450

1 100 1,990 1,670 2,490 1,900 -- -- -- 1,980 1,570 3,070

0.5 200 2,270 1,880 2,900 2,130 -- -- -- 2,270 1,740 3,810

0.2 500 2,670 2,170 3,500 2,460 -- -- -- 2,670 1,960 5,020 a

Set high threshold (1,500 ft3/s) above 1936 historical peak (1,000 ft3/s) to reflect that the 1938 peak was likely larger.

Massachusetts streamgages

Kettle Brook at Worcester, MA (01109500)

1924–1980

20 5 730 610 900 720 -- -- -- 730 570 1,000

10 10 1,080 880 1,400 1,080 -- -- -- 1,080 810 1,740

4 25 1,720 1,330 2,380 1,730 -- -- -- 1,720 1,190 3,580

2 50 2,350 1,760 3,430 2,390 -- -- -- 2,350 1,540 6,230

1 100 3,170 2,300 4,850 3,230 -- -- -- 3,170 1,930 10,900

0.5 200 4,200 2,940 6,760 4,320 -- -- -- 4,200 2,380 19,000

0.2 500 6,000 4,020 10,300 6,230 -- -- -- 6,000 3,070 39,800

Little River near Oxford, MA (01124500)

1940–2010 1913–2010a

20 5 830 600 1,300 670 700 630 800 700 600 870

10 10 1,340 920 2,370 1,010 1,010 890 1,180 1,010 820 1,400

4 25 2,360 1,480 4,980 1,680 1,570 1,330 1,920 1,570 1,190 2,670

2 50 3,510 2,050 8,450 2,460 2,140 1,760 2,720 2,140 1,520 4,400

1 100 5,120 2,790 14,000 3,560 2,890 2,310 3,810 2,890 1,920 7,280

0.5 200 7,360 3,740 23,000 5,140 3,860 3,010 5,280 3,860 2,380 12,100

0.2 500 11,700 5,440 43,200 8,310 5,610 4,210 8,040 5,610 3,140 23,900 a

Records extended 1913–39 and after 1959 using Quaboag River at West Brimfield, MA (01176000). Records after 1959 were extended because of flood control 

regulation.

Mumford River at East Douglas, MA (01111000)

1939–1951, 1955, 2004–2010 1940–2010

20 5 680 510 1,000 700 690 600 810 690 580 870

10 10 1,000 720 1,640 960 960 820 1,170 960 780 1,320

4 25 1,570 1,060 2,980 1,380 1,390 1,150 1,770 1,390 1,070 2,250

2 50 2,140 1,360 4,530 1,760 1,790 1,440 2,360 1,790 1,310 3,350

1 100 2,880 1,730 6,760 2,210 2,260 1,780 3,080 2,260 1,570 4,950

0.5 200 3,810 2,170 9,930 2,740 2,820 2,160 3,960 2,820 1,860 7,270

0.2 500 5,440 2,890 16,200 3,580 3,710 2,760 5,430 3,710 2,280 12,000 a

Actual record 1939–51, 2004–10 extended using Branch River at Forestdale, RI (01111500).

Neponset River at Norwood, MA (01105000)

1939–2010

20 5 600 540 670 600 -- -- -- 600 520 710

10 10 770 680 890 770 -- -- -- 770 650 990

4 25 1,020 890 1,220 1,020 -- -- -- 1,020 830 1,510

2 50 1,240 1,060 1,520 1,240 -- -- -- 1,240 970 2,080

1 100 1,490 1,240 1,870 1,490 -- -- -- 1,490 1,120 2,860

0.5 200 1,770 1,450 2,280 1,770 -- -- -- 1,780 1,280 3,940

0.2 500 2,200 1,760 2,930 2,200 -- -- -- 2,220 1,510 5,990

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
Table 7 57

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Massachusetts streamgages—Continued

Quaboag River at West Brimfield, MA (01176000)

1913–2010

20 5 1,870 1,710 2,060 1,790 -- -- -- 1,870 1,640 2,210

10 10 2,470 2,230 2,780 2,450 -- -- -- 2,470 2,110 3,170

4 25 3,460 3,040 4,040 3,660 -- -- -- 3,460 2,790 5,210

2 50 4,390 3,780 5,270 4,920 -- -- -- 4,390 3,370 7,640

1 100 5,530 4,660 6,830 6,600 -- -- -- 5,530 4,030 11,300

0.5 200 6,910 5,710 8,780 8,820 -- -- -- 6,910 4,770 16,700

0.2 500 9,220 7,400 12,100 12,900 -- -- -- 9,220 5,890 28,200

Sevenmile River near Spencer, MA (01175760)

1961–2010 1913–2010a,b

20 5 290 250 340 280 300 260 330 300 250 370

10 10 360 310 440 420 420 370 490 420 340 580

4 25 470 390 580 690 650 550 790 650 490 1,100

2 50 550 450 710 990 880 730 1,110 880 630 1,790

1 100 640 520 840 1,400 1,180 940 1,540 1,180 790 2,930

0.5 200 730 580 990 1,980 1,560 1,220 2,120 1,570 980 4,810

0.2 500 860 680 1,200 3,110 2,240 1,690 3,180 2,260 1,280 9,340 a

Actual records 1961–2010 extended using Quaboag River at West Brimfield, MA (01176000).

b

Error of ±11% assigned to 1936, 1938, and 1955 peaks for EMA analysis.

Taunton River near Bridgewater, MA (01108000)

1931–76, 85–89, 96, 98–2010 1926–2010a,b

20 5 3,200 2,980 3,470 3,210 3,160 2,970 3,400 3,150 2,910 3,460

10 10 3,710 3,420 4,090 3,670 3,670 3,420 4,000 3,660 3,350 4,130

4 25 4,350 3,960 4,900 4,210 4,320 3,960 4,790 4,300 3,860 5,120

2 50 4,840 4,350 5,530 4,580 4,800 4,370 5,400 4,780 4,220 5,960

1 100 5,320 4,740 6,180 4,930 5,290 4,770 6,020 5,260 4,550 6,880

0.5 200 5,820 5,140 6,850 5,260 5,780 5,170 6,660 5,750 4,870 7,900

0.2 500 6,500 5,660 7,770 5,680 6,450 5,700 7,540 6,410 5,270 9,430 a

Actual record 1931–76, 1985–89, 1996, 1998–2010 extended using Wading River near Norton, MA (01109000).

b

Error of ±15% assigned to 1979, 1983, and 1984 peaks.

Threemile River near North Dighton, MA (01109060)

1967–2010 1926–2010a,b

20 5 1,640 1,440 1,930 1,430 1,420 1,300 1,580 1,420 1,270 1,630

10 10 2,050 1,760 2,490 1,760 1,760 1,590 1,990 1,760 1,550 2,110

4 25 2,600 2,180 3,280 2,200 2,230 1,980 2,590 2,240 1,910 2,890

2 50 3,030 2,500 3,940 2,550 2,610 2,280 3,090 2,620 2,180 3,630

1 100 3,490 2,820 4,640 2,920 3,010 2,600 3,630 3,020 2,440 4,530

0.5 200 3,960 3,160 5,400 3,300 3,440 2,930 4,220 3,460 2,710 5,600

0.2 500 4,620 3,610 6,500 3,840 4,060 3,400 5,080 4,080 3,060 7,360 a

Actual records 1967–2010 extended using Wading River near Norton, MA (01109000).

b

Error of ±2% assigned to 1931, 1936, and 1955 peaks for EMA analysis.

Wading River near Norton, MA (01109000)

1926–2010

20 5 720 660 790 720 -- -- -- 720 640 820

10 10 900 810 1,010 890 -- -- -- 900 780 1,080

4 25 1,150 1,020 1,330 1,140 -- -- -- 1,150 970 1,520

2 50 1,360 1,180 1,610 1,330 -- -- -- 1,360 1,120 1,940

1 100 1,580 1,360 1,910 1,540 -- -- -- 1,580 1,260 2,470

0.5 200 1,830 1,550 2,250 1,770 -- -- -- 1,830 1,410 3,130

0.2 500 2,180 1,820 2,760 2,100 -- -- -- 2,180 1,610 4,250

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
58 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Connecticut streamgages

Blackwell Brook near Brooklyn, CT (01126600)

1962-1976 1952–2010a

20 5 920 680 1,400 950 950 820 1,120 950 790 1,180

10 10 1,270 900 2,160 1,240 1,260 1,060 1,540 1,260 1,030 1,660

4 25 1,810 1,220 3,520 1,630 1,700 1,400 2,170 1,700 1,340 2,550

2 50 2,300 1,480 4,890 1,940 2,070 1,670 2,720 2,070 1,580 3,460

1 100 2,850 1,760 6,640 2,260 2,470 1,960 3,350 2,480 1,820 4,630

0.5 200 3,490 2,070 8,830 2,600 2,920 2,270 4,050 2,920 2,060 6,140

0.2 500 4,470 2,520 12,600 3,070 3,560 2,710 5,120 3,580 2,370 8,800 a

Actual records 1962–76 extended using Little River near Hanover, CT (01123000) to 1952–1961 and 1977–2010.

Fivemile River at Killingly, CT (01126000)

1938–1984 1938–2010a

20 5 1,060 930 1,250 1,060 1,060 960 1,190 1,060 930 1,240

10 10 1,370 1,180 1,660 1,330 1,340 1,190 1,540 1,330 1,150 1,640

4 25 1,830 1,530 2,320 1,700 1,720 1,500 2,050 1,720 1,440 2,330

2 50 2,220 1,810 2,900 1,990 2,040 1,750 2,480 2,040 1,650 3,000

1 100 2,650 2,120 3,580 2,300 2,390 2,010 2,970 2,380 1,870 3,840

0.5 200 3,130 2,450 4,370 2,630 2,760 2,290 3,500 2,750 2,090 4,880

0.2 500 3,850 2,940 5,600 3,090 3,300 2,690 4,290 3,290 2,380 6,640 a

Actual records 1938–1984 extended using Little River near Hanover, CT (01123000).

Hop River near Columbia, CT (01120000)

1933–1984 1933–2010a

20 5 3,360 2,920 3,960 3,380 3,370 3,040 3,810 3,370 2,950 3,970

10 10 4,460 3,800 5,460 4,310 4,330 3,830 5,010 4,330 3,710 5,390

4 25 6,140 5,060 7,900 5,620 5,710 4,940 6,820 5,710 4,720 7,880

2 50 7,620 6,130 10,200 6,690 6,860 5,830 8,400 6,860 5,490 10,400

1 100 9,300 7,310 12,800 7,840 8,120 6,800 10,200 8,120 6,280 13,600

0.5 200 11,200 8,620 16,000 9,090 9,510 7,830 12,200 9,520 7,090 17,600

0.2 500 14,200 10,600 21,100 10,900 11,600 9,330 15,200 11,600 8,190 24,700 a

Actual records 1933–1984 extended using Salmon River near East Hampton, CT (01193500). 

Little River near Hanover, CT (01123000)

1952–2010a

20 5 1,410 1,240 1,630 1,410 -- -- -- 1,370 1,180 1,620

10 10 1,810 1,570 2,170 1,800 -- -- -- 1,760 1,500 2,200

4 25 2,390 2,020 2,980 2,340 -- -- -- 2,320 1,910 3,200

2 50 2,870 2,370 3,680 2,770 -- -- -- 2,780 2,220 4,200

1 100 3,390 2,750 4,460 3,220 -- -- -- 3,280 2,530 5,470

0.5 200 3,960 3,160 5,330 3,710 -- -- -- 3,820 2,840 7,060

0.2 500 4,780 3,730 6,640 4,400 -- -- -- 4,620 3,260 9,790 a

61 years of actual record, but "historical" record spanned 75 years; Lower perception threshold of 1,450 ft3/s used in EMA from 1937–51.

Moosup River at Moosup, CT (01126500)

1933–1984 1933–2010a

20 5 2,230 1,990 2,560 2,280 2,280 2,060 2,560 2,290 2,020 2,650

10 10 2,820 2,460 3,330 2,810 2,840 2,540 3,250 2,860 2,490 3,450

4 25 3,640 3,110 4,490 3,510 3,600 3,160 4,240 3,630 3,070 4,750

2 50 4,330 3,620 5,490 4,040 4,210 3,630 5,060 4,240 3,500 5,960

1 100 5,080 4,170 6,620 4,580 4,850 4,130 5,930 4,880 3,910 7,400

0.5 200 5,910 4,760 7,900 5,140 5,520 4,640 6,870 5,560 4,320 9,110

0.2 500 7,120 5,600 9,840 5,910 6,460 5,350 8,230 6,520 4,840 11,900 a

Actual records 1933–1984 extended using Yantic River at Yantic, CT (01127500).

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
Table 7 59

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Connecticut streamgages—Continued

Mount Hope River near Warrenville, CT (01121000)

1941–2010

20 5 1,760 1,560 2,020 1,760 -- -- -- 1,730 1,490 2,090

10 10 2,370 2,060 2,810 2,370 -- -- -- 2,270 1,910 2,940

4 25 3,340 2,810 4,140 3,350 -- -- -- 3,090 2,480 4,560

2 50 4,220 3,480 5,410 4,260 -- -- -- 3,800 2,940 6,320

1 100 5,270 4,240 6,970 5,330 -- -- -- 4,610 3,420 8,720

0.5 200 6,500 5,110 8,870 6,600 -- -- -- 5,530 3,930 12,000

0.2 500 8,480 6,470 12,000 8,650 -- -- -- 6,950 4,650 18,100 b

Lower confidence limits set 12 peaks above 2,250 ft3/s (average -18.4%) for EMA analysis.

Natchaug River at Willimantic, CT (01122000)

1931–1951 (pre-flood control) 1931–2010a,b

20 5 6,030 4,730 8,290 6,620 6,690 5,930 7,660 6,350 5,460 7,700

10 10 8,660 6,550 13,000 9,350 9,320 8,100 11,000 8,510 7,100 11,200

4 25 13,300 9,440 22,500 14,100 13,800 11,600 17,100 11,900 9,470 18,300

2 50 17,900 12,100 33,300 18,900 18,100 14,800 23,300 15,000 11,400 26,400

1 100 23,800 15,300 48,500 25,000 23,500 18,800 31,300 18,700 13,600 38,200

0.5 200 31,200 19,100 69,800 32,800 30,200 23,400 41,600 23,000 15,900 55,100

0.2 500 44,300 25,400 111,000 46,400 41,400 31,200 59,800 30,000 19,300 89,200 a

Actual pre-flood control records 1931–1951 extended using Willimantic River near Coventry, CT (01119500). 

b

Lower confidence limits set 18 peaks above 5,370 ft3/s by an average -18% for EMA analysis.

Pendleton Brook Hill near Clark Falls, CT (01118300)

1959–2010 1942–2010a,b

20 5 220 190 260 200 200 180 230 200 170 230

10 10 280 240 340 260 260 220 300 250 210 320

4 25 370 310 470 340 340 290 420 330 270 470

2 50 450 370 580 410 420 350 520 400 320 620

1 100 530 430 710 480 500 410 640 470 360 820

0.5 200 620 490 860 570 590 480 780 550 410 1070

0.2 500 760 580 1080 690 730 570 990 670 470 1520 a

Actual records 1959–2010 extended using Wood River at Hope Valley, RI (01118000). 

b

Error of -31% assigned to 2010 peak for EMA analysis.

Quinebaug River at Quinebaug, CT (01124000)

1932–1959 (pre-flood control) 1919–2010a

20 5 4,820 3,620 6,920 4,190 4,270 3,720 4,980 4,250 3,520 5,420

10 10 7,950 5,700 12,600 6,460 6,440 5,490 7,790 6,320 5,020 8,970

4 25 14,400 9,560 26,200 10,900 10,500 8,600 13,400 10,100 7,440 17,400

2 50 21,900 13,600 44,300 15,800 14,800 11,700 19,600 13,900 9,670 28,700

1 100 32,700 19,100 73,500 22,700 20,500 15,800 28,400 18,900 12,300 47,400

0.5 200 48,200 26,400 120,000 32,300 28,100 21,000 40,500 25,500 15,400 78,200

0.2 500 79,000 39,900 226,000 50,700 42,000 30,100 63,800 37,100 20,400 151,000 a

Pre-flood control records (1932–59) extended using Quinebaug River at Jewett City, CT (01127000) from 1919–31 and post-flood control records extended using 

Willimantic River at Coventry, CT (01119500) from 1960–2010.

b

Lower confidence limits set 1955 and 2006 peaks of -30 and -7.1%, respectively, for EMA analysis.

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
60 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

AEP

(%)

Return 

interval 

(years) 

Period of record analysis

Systematic 

peak flow 

estimate

Extended record analysis

B17B B17B EMA

Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper

Connecticut streamgages—Continued

Safford Brook near Woodstock Valley, CT (01120500)

1951–1981 1941–2010a,b

20 5 520 440 630 430 430 400 480 400 360 470

10 10 660 550 840 540 550 490 620 490 430 600

4 25 870 710 1,170 700 710 620 830 620 530 830

2 50 1,000 830 1,480 840 840 720 1,020 720 600 1,050

1 100 1,200 960 1,830 983 990 840 1,230 830 670 1,330

0.5 200 1,500 1,100 2,240 1,140 1,160 960 1,470 950 740 1,670

0.2 500 1,800 1,310 2,900 1,390 1,400 1,140 1,840 1,120 830 2,240 a

Actual records 1951–1981 extended using Mount Hope River near Warrenville, CT (01121000).

b

Lower confidence limits set for 1951–81 peaks from 0 to -45% (-19.4% average) for EMA analysis.

Salmon River near East Hampton, CT (01193500)

1929–2010

20 5 5,140 4,570 5,870 5,140 -- -- -- 5,060 4,350 6,100

10 10 6,970 6,080 8,200 6,970 -- -- -- 6,770 5,670 8,750

4 25 9,870 8,370 12,100 9,850 -- -- -- 9,400 7,530 13,800

2 50 12,500 10,400 15,800 12,500 -- -- -- 11,700 9,030 19,400

1 100 15,600 12,700 20,300 15,600 -- -- -- 14,400 10,600 26,900

0.5 200 19,300 15,300 25,800 19,200 -- -- -- 17,500 12,400 37,300

0.2 500 25,100 19,400 34,800 24,900 -- -- -- 22,400 14,800 57,000 b

Lower confidence limits set 1956, 1973, 1974, 1979, and 1982 peaks of -12, -21, -12, -26, and -20%, respectively, for EMA analysis.

Shetucket River near Willimantic, CT (01122500)

1904–51 (pre-flood control) 1904–2010a

20 5 11,000 9,040 14,000 12,800 12,700 11,400 14,300 11,600 9,910 14,100

10 10 15,300 12,200 20,800 17,800 17,200 15,200 20,000 16,500 13,700 21,500

4 25 22,600 17,200 33,700 26,500 24,800 21,200 30,000 24,600 19,300 36,600

2 50 29,800 21,800 47,700 35,200 32,000 26,800 40,000 32,200 24,200 54,000

1 100 38,800 27,200 66,500 46,100 40,700 33,300 52,500 41,400 29,600 79,200

0.5 200 50,000 33,600 91,700 60,000 51,300 41,000 68,200 52,400 35,600 115,000

0.2 500 69,200 44,000 139,000 84,100 69,000 53,400 95,400 70,500 44,600 188,000 a

Actual pre-flood control records 1904–1906, 1920–1921, 1929–1951, after 1951 record extended using Willimantic River near Coventry, CT (01119500).

b

87 years of actual record, but “historical” record spanned 107 years; Lower confidence limits for 1955 and 2006 peaks of -5.3 and -5.4%, respectively, for EMA 

analysis; Lower perception threshold of 3,500 ft3/s used in EMA during record gaps from 1907–19 and 1922–28.

Willimantic River near Coventry, CT (01119500)

1932–2010

20 5 3,990 3,510 4,620 3,960 -- -- -- 3,970 3,330 4,990

10 10 5,670 4,880 6,800 5,680 -- -- -- 5,590 4,520 7,760

4 25 8,560 7,110 10,800 8,730 -- -- -- 8,320 6,330 13,800

2 50 11,400 9,210 14,900 11,800 -- -- -- 11,000 7,900 21,300

1 100 15,000 11,800 20,300 15,700 -- -- -- 14,200 9,670 32,900

0.5 200 19,400 14,800 27,300 20,800 -- -- -- 18,200 11,700 50,700

0.2 500 27,000 20,000 39,900 29,600 -- -- -- 25,000 14,700 89,700 b

Errors of -11, -12, -5 and -8% assigned to 1936, 1955, 1982, and 2006 peaks, respectively, for EMA analysis.

Yantic River at Yantic, CT (01127500)

1931–2010

20 5 4,410 3,940 5,010 4,420 -- -- -- 4,380 3,800 5,200

10 10 5,800 5,090 6,770 5,780 -- -- -- 5,710 4,850 7,180

4 25 7,870 6,740 9,520 7,770 -- -- -- 7,660 6,270 10,700

2 50 9,660 8,120 12,000 9,460 -- -- -- 9,310 7,370 14,300

1 100 11,700 9,630 14,900 11,300 -- -- -- 11,100 8,500 19,000

0.5 200 13,900 11,300 18,200 13,400 -- -- -- 13,200 9,670 25,000

0.2 500 17,400 13,800 23,400 16,600 -- -- -- 16,200 11,300 35,700 b

Lower confidence limit set 1938 peak for EMA analysis.

Table 7. Estimated magnitude of flood flows and confidence limits for selected annual exceedance probabilities at selected 

streamgages in Rhode Island, Connecticut, and Massachusetts for the period of record through 2010.—Continued
Table 13 61

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Rhode Island streamgages

Adamville Brook at Adamville, RI (01106000)

20 220 0.001 220 0.015 220 0.001 0.0

10 250 0.001 280 0.013 250 0.001 0.0

4 300 0.002 380 0.011 300 0.002 0.0

2 330 0.002 460 0.012 350 0.002 6.1

1 360 0.003 540 0.012 400 0.003 11.1

0.5 400 0.004 630 0.014 440 0.003 10.0

0.2 440 0.006 750 0.017 510 0.005 15.9

Beaver River near Usquepaug, RI (01117468)

20 190 0.001 280 0.014 200 0.001 5.3

10 250 0.003 370 0.013 270 0.002 8.0

4 350 0.005 510 0.011 400 0.003 14.3

2 450 0.008 620 0.012 510 0.005 13.3

1 560 0.012 740 0.012 650 0.006 16.1

0.5 700 0.016 870 0.014 790 0.008 12.9

0.2 930 0.024 1,050 0.017 1,000 0.010 7.5

Blackstone River at Woonsocket, RI (01112500)

20 9,160 0.001 9,530 0.014 9,180 0.001 0.2

10 11,800 0.002 12,500 0.013 11,900 0.001 0.8

4 15,800 0.003 16,700 0.011 16,000 0.002 1.3

2 19,300 0.004 20,000 0.011 19,500 0.003 1.0

1 23,100 0.006 23,400 0.011 23,200 0.004 0.4

0.5 27,500 0.009 27,400 0.013 27,500 0.005 0.0

0.2 34,200 0.012 33,100 0.016 33,700 0.007 -1.5

Branch River at Forestdale, RI (01111500)

20 2,890 0.001 2,240 0.012 2,820 0.001 -2.4

10 3,800 0.002 2,910 0.011 3,660 0.002 -3.7

4 5,160 0.004 3,930 0.010 4,800 0.003 -7.0

2 6,320 0.005 4,730 0.010 5,720 0.003 -9.5

1 7,630 0.007 5,580 0.010 6,660 0.004 -12.7

0.5 9,100 0.010 6,500 0.011 7,780 0.005 -14.5

0.2 11,300 0.015 7,830 0.014 9,400 0.007 -16.8

Chepachet River at Chepachet, RI (01111400)

20 520 0.001 380 0.013 510 0.001 -1.9

10 680 0.002 490 0.012 650 0.002 -4.4

4 920 0.003 670 0.010 850 0.003 -7.6

2 1,120 0.005 810 0.011 1,010 0.003 -9.8

1 1,350 0.007 960 0.010 1,170 0.004 -13.3

0.5 1,600 0.010 1,110 0.012 1,360 0.005 -15.0

0.2 1,990 0.014 1,320 0.015 1,630 0.007 -18.1
62 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Rhode Island streamgages—Continued

Chipuxet River at West Kingston, RI (01117350)

20 140 0.001 220 0.014 150 0.001 7.1

10 190 0.003 290 0.013 210 0.002 10.5

4 270 0.005 390 0.011 310 0.004 14.8

2 350 0.008 480 0.012 400 0.005 14.3

1 440 0.012 570 0.011 500 0.006 13.6

0.5 550 0.017 660 0.014 610 0.008 10.9

0.2 730 0.026 790 0.017 770 0.010 5.5

Hunt River near East Greenwich, RI (01117000)

20 610 0.001 590 0.013 610 0.001 0.0

10 810 0.002 760 0.011 800 0.002 -1.2

4 1,110 0.004 1,030 0.010 1,090 0.003 -1.8

2 1,390 0.007 1,250 0.010 1,330 0.004 -4.3

1 1,720 0.010 1,490 0.010 1,600 0.005 -7.0

0.5 2,120 0.014 1,730 0.012 1,890 0.006 -10.8

0.2 2,750 0.021 2,080 0.014 2,330 0.009 -15.3

Moshassuck River at Providence, RI (01114000)

20 1,120 0.000 980 0.014 1,120 0.000 0.0

10 1,320 0.001 1,300 0.013 1,320 0.001 0.0

4 1,570 0.001 1,790 0.011 1,590 0.001 1.3

2 1,770 0.002 2,200 0.012 1,820 0.002 2.8

1 1,980 0.003 2,620 0.011 2,080 0.002 5.1

0.5 2,190 0.004 3,110 0.014 2,350 0.003 7.3

0.2 2,490 0.005 3,810 0.017 2,740 0.004 10.0

Nipmuc River near Harrisville, RI (01111300)

20 730 0.002 890 0.013 750 0.001 2.7

10 990 0.002 1,180 0.012 1,020 0.002 3.0

4 1,380 0.004 1,640 0.011 1,450 0.003 5.1

2 1,720 0.006 2,020 0.011 1,830 0.004 6.4

1 2,120 0.009 2,410 0.011 2,250 0.005 6.1

0.5 2,580 0.012 2,880 0.013 2,720 0.006 5.4

0.2 3,290 0.018 3,530 0.016 3,410 0.008 3.6

Nooseneck River at Nooseneck, RI (01115630)

20 330 0.001 350 0.016 330 0.001 0.0

10 430 0.002 460 0.015 430 0.002 0.0

4 580 0.004 640 0.014 600 0.003 3.4

2 720 0.006 800 0.014 740 0.004 2.8

1 880 0.009 960 0.015 910 0.005 3.4

0.5 1,060 0.012 1,130 0.017 1,090 0.007 2.8

0.2 1,350 0.017 1,390 0.021 1,370 0.010 1.5
Table 13 63

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Rhode Island streamgages—Continued

Pawcatuck River at Westerly, RI (01118500)

20 3,300 0.001 3,300 0.014 3,300 0.001 0.0

10 4,080 0.001 4,190 0.013 4,090 0.001 0.2

4 5,230 0.003 5,510 0.011 5,290 0.002 1.1

2 6,220 0.004 6,540 0.011 6,320 0.003 1.6

1 7,340 0.006 7,690 0.011 7,480 0.004 1.9

0.5 8,610 0.008 8,760 0.013 8,690 0.005 0.9

0.2 10,600 0.012 10,400 0.016 10,500 0.007 -0.9

Pawcatuck River at Wood River Junction, RI (01117500)

20 1,030 0.001 960 0.015 1,020 0.001 -1.0

10 1,280 0.001 1,200 0.013 1,280 0.001 0.0

4 1,660 0.003 1,580 0.011 1,650 0.002 -0.6

2 1,990 0.004 1,880 0.012 1,960 0.003 -1.5

1 2,370 0.007 2,220 0.012 2,310 0.004 -2.5

0.5 2,790 0.009 2,500 0.014 2,670 0.006 -4.3

0.2 3,440 0.013 2,940 0.018 3,220 0.008 -6.4

Ponaganset River at South Foster, RI (01115187)

20 760 0.001 540 0.013 740 0.001 -2.6

10 960 0.002 710 0.012 930 0.001 -3.1

4 1,260 0.003 980 0.010 1,190 0.002 -5.6

2 1,500 0.004 1,190 0.010 1,410 0.003 -6.0

1 1,760 0.006 1,420 0.010 1,630 0.004 -7.4

0.5 2,050 0.007 1,670 0.012 1,890 0.005 -7.8

0.2 2,470 0.011 2,020 0.015 2,270 0.006 -8.1

South Branch Pawtuxet River at Washington, RI (01116000)

20 1,090 0.002 1,260 0.013 1,110 0.001 1.8

10 1,470 0.002 1,630 0.012 1,500 0.002 2.0

4 2,060 0.005 2,200 0.010 2,100 0.003 1.9

2 2,600 0.007 2,650 0.010 2,620 0.004 0.8

1 3,230 0.010 3,140 0.010 3,180 0.005 -1.5

0.5 3,980 0.014 3,630 0.012 3,790 0.007 -4.8

0.2 5,170 0.021 4,360 0.015 4,680 0.009 -9.5

Ten Mile River at Pawtucket Avenue at East Providence, RI, (01109403)

20 1,120 0.001 1,450 0.012 1,140 0.001 1.8

10 1,400 0.001 1,890 0.011 1,440 0.001 2.9

4 1,800 0.002 2,560 0.009 1,920 0.002 6.7

2 2,130 0.003 3,090 0.010 2,330 0.002 9.4

1 2,490 0.004 3,660 0.009 2,820 0.003 13.3

0.5 2,880 0.006 4,280 0.011 3,300 0.004 14.6

0.2 3,450 0.009 5,160 0.014 4,030 0.005 16.8
64 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Rhode Island streamgages—Continued

Usquepaug River near Usquepaug, RI (01117420)

20 550 0.001 870 0.013 570 0.001 3.6

10 710 0.002 1,130 0.012 750 0.002 5.6

4 950 0.004 1,540 0.010 1,070 0.003 12.6

2 1,160 0.006 1,870 0.011 1,360 0.004 17.2

1 1,400 0.008 2,220 0.011 1,710 0.005 22.1

0.5 1,680 0.011 2,580 0.013 2,060 0.006 22.6

0.2 2,130 0.016 3,110 0.015 2,580 0.008 21.1

Wood River near Arcadia, RI (01117800)

20 620 0.001 640 0.061 620 0.001 0.0

10 810 0.002 820 0.059 810 0.002 0.0

4 1,100 0.004 1,110 0.058 1,100 0.004 0.0

2 1,370 0.007 1,340 0.064 1,360 0.006 -0.7

1 1,680 0.010 1,590 0.072 1,640 0.009 -2.4

0.5 2,050 0.014 1,830 0.081 1,940 0.012 -5.4

0.2 2,630 0.020 2,200 0.101 2,390 0.017 -9.1

Wood River at Hope Valley, RI (01118000)

20 1,310 0.001 1,290 0.014 1,310 0.001 0.0

10 1,650 0.002 1,670 0.012 1,650 0.001 0.0

4 2,170 0.003 2,240 0.011 2,190 0.002 0.9

2 2,630 0.005 2,700 0.011 2,650 0.004 0.8

1 3,160 0.007 3,200 0.011 3,180 0.004 0.6

0.5 3,760 0.011 3,690 0.013 3,730 0.006 -0.8

0.2 4,710 0.016 4,410 0.016 4,570 0.008 -3.0

Woonasquatucket River at Centerdale, RI (01114500)

20 920 0.001 830 0.013 910 0.001 -1.1

10 1,150 0.001 1,070 0.011 1,140 0.001 -0.9

4 1,470 0.002 1,440 0.010 1,460 0.002 -0.7

2 1,720 0.003 1,720 0.010 1,720 0.002 0.0

1 1,990 0.005 2,040 0.010 2,000 0.003 0.5

0.5 2,270 0.006 2,360 0.012 2,300 0.004 1.3

0.2 2,670 0.009 2,820 0.014 2,720 0.005 1.9

Massachusetts streamgages

Kettle Brook at Worcester, MA (01109500)

20 730 0.004 990 0.013 780 0.003 6.8

10 1,080 0.006 1,290 0.012 1,150 0.004 6.5

4 1,720 0.011 1,750 0.010 1,740 0.005 1.2

2 2,350 0.016 2,110 0.011 2,200 0.006 -6.4

1 3,170 0.023 2,500 0.010 2,690 0.007 -15.1

0.5 4,200 0.032 2,930 0.012 3,230 0.009 -23.1

0.2 6,000 0.046 3,530 0.015 4,020 0.011 -33.0
Table 13 65

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Massachusetts streamgages—Continued

Little River near Oxford, MA (01124500)

20 700 0.002 740 0.014 710 0.001 1.4

10 1,010 0.003 950 0.012 1,000 0.002 -1.0

4 1,570 0.006 1,280 0.011 1,460 0.004 -7.0

2 2,140 0.010 1,540 0.011 1,830 0.005 -14.5

1 2,890 0.015 1,820 0.011 2,200 0.006 -23.9

0.5 3,860 0.022 2,120 0.013 2,640 0.008 -31.6

0.2 5,610 0.033 2,540 0.016 3,280 0.011 -41.5

Mumford River at East Douglas, MA (01111000)

20 690 0.002 680 0.013 690 0.002 0.0

10 960 0.003 880 0.012 950 0.002 -1.0

4 1,390 0.005 1,190 0.010 1,320 0.003 -5.0

2 1,790 0.008 1,420 0.010 1,620 0.005 -9.5

1 2,260 0.012 1,690 0.010 1,930 0.005 -14.6

0.5 2,820 0.016 1,950 0.012 2,290 0.007 -18.8

0.2 3,710 0.023 2,340 0.014 2,800 0.009 -24.5

Neponset River at Norwood, MA (01105000)

20 600 0.001 670 0.013 610 0.001 1.7

10 770 0.002 850 0.012 780 0.002 1.3

4 1,020 0.003 1,150 0.010 1,050 0.002 2.9

2 1,240 0.005 1,380 0.010 1,280 0.003 3.2

1 1,490 0.007 1,640 0.010 1,550 0.004 4.0

0.5 1,770 0.010 1,890 0.012 1,820 0.005 2.8

0.2 2,200 0.014 2,250 0.014 2,220 0.007 0.9

Quaboag River at West Brimfield, MA (01176000)

20 1,870 0.001 3,860 0.013 1,960 0.001 4.8

10 2,470 0.002 5,030 0.012 2,700 0.002 9.3

4 3,460 0.004 6,750 0.010 4,120 0.003 19.1

2 4,390 0.006 8,080 0.011 5,460 0.004 24.4

1 5,530 0.009 9,490 0.010 7,120 0.005 28.8

0.5 6,910 0.013 11,100 0.012 8,800 0.006 27.4

0.2 9,220 0.020 13,400 0.015 11,400 0.009 23.6

Sevenmile River near Spencer, MA (01175760)

20 300 0.002 440 0.014 310 0.001 3.3

10 420 0.003 580 0.012 450 0.002 7.1

4 650 0.006 800 0.011 700 0.004 7.7

2 880 0.010 980 0.011 930 0.005 5.7

1 1,180 0.015 1,170 0.011 1,180 0.006 0.0

0.5 1,560 0.021 1,390 0.013 1,450 0.008 -7.1

0.2 2,240 0.031 1,700 0.016 1,860 0.011 -17.0
66 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Massachusetts streamgages—Continued

Taunton River near Bridgewater, MA (01108000)

20 3,160 0.000 2,640 0.014 3,160 0.000 0.0

10 3,670 0.000 3,330 0.013 3,660 0.000 -0.3

4 4,320 0.001 4,340 0.011 4,320 0.001 0.0

2 4,800 0.001 5,100 0.011 4,830 0.001 0.6

1 5,290 0.002 5,980 0.011 5,380 0.001 1.7

0.5 5,780 0.002 6,760 0.013 5,920 0.002 2.4

0.2 6,450 0.003 7,940 0.016 6,690 0.003 3.7

Threemile River near North Dighton, MA (01109060)

20 1,420 0.001 1,470 0.013 1,430 0.001 0.7

10 1,760 0.001 1,880 0.012 1,770 0.001 0.6

4 2,230 0.002 2,510 0.010 2,270 0.001 1.8

2 2,610 0.003 2,990 0.010 2,680 0.002 2.7

1 3,010 0.004 3,530 0.010 3,150 0.003 4.7

0.5 3,440 0.005 4,060 0.012 3,620 0.003 5.2

0.2 4,060 0.007 4,830 0.014 4,300 0.005 5.9

Wading River near Norton, MA (01109000)

20 720 0.001 770 0.013 720 0.001 0.0

10 900 0.001 990 0.012 900 0.001 0.0

4 1,150 0.002 1,320 0.010 1,170 0.002 1.7

2 1,360 0.003 1,580 0.010 1,400 0.002 2.9

1 1,580 0.004 1,880 0.010 1,660 0.003 5.1

0.5 1,830 0.006 2,150 0.012 1,920 0.004 4.9

0.2 2,180 0.008 2,560 0.014 2,310 0.005 6.0

Connecticut streamgages

Blackwell Brook near Brooklyn, CT (01126600)

20 950 0.002 590 0.013 890 0.002 -6.3

10 1,260 0.002 770 0.012 1,150 0.002 -8.7

4 1,700 0.004 1,050 0.010 1,480 0.003 -12.9

2 2,070 0.006 1,270 0.010 1,740 0.004 -15.9

1 2,470 0.008 1,510 0.010 1,980 0.004 -19.8

0.5 2,920 0.011 1,770 0.012 2,300 0.006 -21.2

0.2 3,560 0.015 2,140 0.015 2,750 0.007 -22.8

Fivemile River at Killingly, CT (01126000)

20 1,060 0.001 1,260 0.013 1,070 0.001 0.9

10 1,340 0.001 1,630 0.012 1,360 0.001 1.5

4 1,720 0.002 2,190 0.010 1,810 0.002 5.2

2 2,040 0.003 2,620 0.010 2,180 0.003 6.9

1 2,390 0.005 3,090 0.010 2,600 0.003 8.8

0.5 2,760 0.007 3,570 0.012 3,030 0.004 9.8

0.2 3,300 0.010 4,270 0.014 3,660 0.006 10.9
Table 13 67

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Connecticut streamgages—Continued

Hop River near Columbia, CT (01120000)

20 3,370 0.001 2,600 0.013 3,310 0.001 -1.8

10 4,330 0.002 3,430 0.012 4,220 0.001 -2.5

4 5,710 0.003 4,670 0.010 5,480 0.002 -4.0

2 6,860 0.004 5,670 0.011 6,520 0.003 -5.0

1 8,120 0.006 6,700 0.010 7,600 0.004 -6.4

0.5 9,510 0.008 7,910 0.012 8,880 0.005 -6.6

0.2 11,600 0.011 9,630 0.015 10,700 0.006 -7.8

Little River near Hanover, CT (01123000)

20 1,410 0.001 1,320 0.014 1,400 0.001 -0.7

10 1,810 0.002 1,740 0.012 1,800 0.002 -0.6

4 2,390 0.003 2,380 0.011 2,390 0.003 0.0

2 2,870 0.005 2,890 0.011 2,880 0.003 0.3

1 3,390 0.007 3,410 0.011 3,400 0.004 0.3

0.5 3,960 0.009 4,040 0.013 4,000 0.005 1.0

0.2 4,780 0.013 4,920 0.016 4,840 0.007 1.3

Moosup River at Moosup, CT (01126500)

20 2,280 0.001 2,430 0.013 2,290 0.001 0.4

10 2,840 0.001 3,180 0.012 2,870 0.001 1.1

4 3,600 0.002 4,320 0.010 3,710 0.002 3.1

2 4,210 0.003 5,230 0.010 4,400 0.002 4.5

1 4,850 0.004 6,180 0.010 5,180 0.003 6.8

0.5 5,520 0.005 7,260 0.012 5,990 0.004 8.5

0.2 6,460 0.007 8,800 0.015 7,160 0.005 10.8

Mount Hope River near Warrenville, CT (01121000)

20 1,730 0.001 1,610 0.014 1,720 0.001 -0.6

10 2,270 0.002 2,140 0.013 2,260 0.002 -0.4

4 3,090 0.004 2,960 0.011 3,060 0.003 -1.0

2 3,800 0.006 3,610 0.012 3,740 0.004 -1.6

1 4,610 0.008 4,270 0.011 4,480 0.005 -2.8

0.5 5,530 0.011 5,100 0.014 5,350 0.006 -3.3

0.2 6,950 0.016 6,250 0.017 6,620 0.008 -4.7

Natchaug River at Willimantic, CT (01122000)

20 6,350 0.001 6,160 0.014 6,320 0.001 -0.5

10 8,510 0.002 8,150 0.013 8,440 0.002 -0.8

4 11,900 0.004 11,000 0.011 11,700 0.003 -1.7

2 15,000 0.006 13,300 0.012 14,400 0.004 -4.0

1 18,700 0.009 15,600 0.011 17,200 0.005 -8.0

0.5 23,000 0.013 18,500 0.014 20,700 0.007 -10.0

0.2 30,000 0.019 22,500 0.017 25,700 0.009 -14.3
68 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Connecticut streamgages—Continued

Pendleton Brook Hill near Clark Falls, CT (01118300)

20 200 0.001 140 0.015 190 0.001 -5.0

10 250 0.002 180 0.014 240 0.002 -4.0

4 330 0.003 250 0.012 310 0.002 -6.1

2 400 0.004 310 0.013 370 0.003 -7.5

1 470 0.006 370 0.013 440 0.004 -6.4

0.5 550 0.008 430 0.015 510 0.005 -7.3

0.2 670 0.012 520 0.018 610 0.007 -9.0

Quinebaug River at Quinebaug, CT (01124000)

20 4,250 0.002 4,370 0.013 4,260 0.002 0.2

10 6,320 0.004 5,720 0.012 6,170 0.003 -2.4

4 10,100 0.007 7,700 0.010 9,010 0.004 -10.8

2 13,900 0.011 9,230 0.011 11,300 0.006 -18.7

1 18,900 0.017 10,800 0.011 13,500 0.006 -28.6

0.5 25,500 0.023 12,700 0.013 16,200 0.008 -36.5

0.2 37,100 0.035 15,400 0.016 20,200 0.011 -45.6

Safford Brook near Woodstock Valley, CT (01120500)

20 400 0.001 340 0.015 400 0.001 0.0

10 490 0.001 460 0.014 490 0.001 0.0

4 620 0.002 640 0.012 620 0.002 0.0

2 720 0.003 800 0.013 740 0.002 2.8

1 830 0.004 960 0.012 860 0.003 3.6

0.5 950 0.006 1,160 0.015 1,000 0.004 5.3

0.2 1,120 0.008 1,430 0.018 1,210 0.006 8.0

Salmon River near East Hampton, CT (01193500)

20 5,060 0.001 3,140 0.013 4,840 0.001 -4.3

10 6,770 0.002 4,130 0.012 6,280 0.002 -7.2

4 9,400 0.004 5,610 0.010 8,170 0.003 -13.1

2 11,700 0.006 6,790 0.010 9,690 0.004 -17.2

1 14,400 0.008 8,010 0.010 11,100 0.004 -22.9

0.5 17,500 0.011 9,430 0.012 13,100 0.006 -25.1

0.2 22,400 0.016 11,400 0.015 15,800 0.008 -29.5

Shetucket River near Willimantic, CT (01122500)

20 12,700 0.001 13,000 0.015 12,700 0.001 0.0

10 17,200 0.002 17,300 0.013 17,300 0.002 0.6

4 24,800 0.005 23,300 0.012 24,400 0.003 -1.6

2 32,000 0.007 28,000 0.012 30,500 0.005 -4.7

1 40,700 0.011 32,800 0.012 36,800 0.006 -9.6

0.5 51,300 0.015 38,800 0.015 44,500 0.007 -13.3

0.2 69,000 0.022 47,300 0.018 55,900 0.010 -19.0
Table 13 69

Table 13. Magnitude and variance of 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probability floods determined from 

at-site analyses, regional regression equations, and weighted independent estimates.—Continued

[At-site, Bulletin 17B or expected moments algorithm results highlighted in table 7; Values may not exactly match because of rounding; ft3/s, cubic feet per 

second; RI, Rhode Island; MA, Massachusetts; CT, Connecticut]

Annual 

exceedance 

probability 

(percent)

At-site Regional regression Weighted Percent 

difference 

at site and 

weighted flow

Flow 

(ft3/s) Variance Flow (ft3/s) Variance Flow (ft3/s) Variance

Connecticut streamgages—Continued

Willimantic River near Coventry, CT (01119500)

20 3,970 0.002 5,170 0.014 4,100 0.002 3.3

10 5,590 0.003 6,880 0.013 5,820 0.002 4.1

4 8,320 0.006 9,390 0.011 8,690 0.004 4.4

2 11,000 0.009 11,400 0.012 11,200 0.005 1.8

1 14,200 0.013 13,400 0.011 13,800 0.006 -2.8

0.5 18,200 0.019 16,000 0.014 16,900 0.008 -7.1

0.2 25,000 0.027 19,500 0.017 21,500 0.010 -14.0

Yantic River at Yantic, CT (01127500)

20 4,380 0.001 2,770 0.013 4,220 0.001 -3.7

10 5,710 0.002 3,640 0.012 5,390 0.001 -5.6

4 7,660 0.003 4,930 0.010 6,920 0.002 -9.7

2 9,310 0.004 5,940 0.010 8,140 0.003 -12.6

1 11,100 0.006 7,000 0.010 9,330 0.004 -15.9

0.5 13,200 0.008 8,220 0.012 10,800 0.005 -18.2

0.2 16,200 0.012 9,950 0.015 13,000 0.007 -19.8
70 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010 AEP Return interval (years) Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Bear Brook near Coventry, RI (csg) (01115830) (3.98 mi2

)

b

1966–78 1942–2010a

20 5 150 130 190 160 150 170 160 140 180 410 -- -- -- -- --10 10 170 150 220 190 180 220 190 170 240 560 -- -- -- -- --

4 25 200 170 270 250 220 280 250 210 350 790 -- -- -- -- --2 50 220 180 310 290 250 340 290 240 460 1,000 -- -- -- -- --1 100 240 190 360 340 290 410 340 270 620 1,210 -- -- -- -- --0.5 200 260 210 400 390 340 480 390 300 830 1,470 -- -- -- -- --0.2 500 280 220 460 480 400 610 480 340 1,200 1,840 -- -- -- -- -- aRecord extended with Wood River at Hope Valley, RI (01118000).

bBasin storage (StorNHD) is 50% less than the range of values used to develop regional regression equation.

Blackstone River Tributary at Woonsocket, RI (01112700) (2.07 mi2

)

1966–74 1926–2010a

20 5 190 150 310 160 150 180 160 150 190 170 -- -- -- -- --10 10 250 180 450 200 180 230 200 180 240 230 -- -- -- -- --

4 25 330 230 690 260 230 300 260 220 340 330 -- -- -- -- --2 50 400 260 940 300 270 360 300 250 430 410 -- -- -- -- --1 100 470 300 1,200 350 300 430 350 280 540 490 -- -- -- -- --0.5 200 550 340 1,600 410 340 500 410 320 680 590 -- -- -- -- --0.2 500 670 390 2,300 480 400 610 480 360 910 740 -- -- -- --

– aRecord extended with Wading River near Norton, MA (01109000).

Blackstone River Tributary No. 2 at Berkeley, RI (csg) (01113600) (1.11 mi2

)

1966–78 1926–2010a

20 5 43 37 52 41 37 46 41 36 47 49 -- -- -- -- --10 10 50 42 64 52 46 59 52 45 62 65 -- -- -- -- --

4 25 60 49 83 66 58 77 66 56 85 91 -- -- -- -- --2 50 67 54 100 77 67 92 77 64 110 110 -- -- -- -- --1 100 76 60 120 89 76 110 89 72 130 140 -- -- -- -- --0.5 200 84 65 140 100 86 130 100 79 160 160 -- -- -- -- --0.2 500 97 72 170 120 99 150 120 89 210 200 -- -- -- -- -- aRecord extended with Wading River near Norton, MA (01109000).

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.[AEP, annual exceedance probability, in percent; Period of record analysis, is the systematic record; Extended record analysis, includes the period of record plus records estimated by MOVE; record length indicated below each station; B17B, flood frequency analysis made using Bulletin 17B guidelines; EMA, expected moments algorithm; All values in cubic feet per second (ft3/s); All at-site analysis made using a weighted regional skew of 0.52 and root mean square error of 0.46; --, indicates analysis not made because basin characteristics were out of range of the characteristics used to develop regional regression equation; csg, crest stage gage; Values in red color indicate one or more of the streamgage basin characteristics outside the range of values used to develop regional regression equation, most commonly the basin drainage area, which is provided following the station name; %, percent; RI, Rhode Island]
Table 15 71

AEP

Return 

interval 

(years) 

Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA

Peak 

flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper

Browns Brook at Wakefield, RI (csg) (01117250) (0.44 mi2)

1966–74 1959–2010a

20 5 19 16 24 26 23 30 26 22 34 4 -- -- -- -- --10 10 22 18 30 35 30 42 35 28 52 5 -- -- -- -- --

4 25 25 21 38 49 41 62 49 37 94 7 -- -- -- -- --2 50 28 22 45 63 51 82 63 45 150 9 -- -- -- -- --1 100 31 24 52 79 62 110 79 53 240 11 -- -- -- -- --0.5 200 33 26 60 98 76 140 98 63 390 12 -- -- -- -- --0.2 500 37 28 71 130 97 200 130 77 680 14 -- -- -- -- --

aRecord extended with Pendleton Hill Brook near Clark Falls, CT (01118300).

Bucks Horn Brook at Greene, RI (01126200) (5.49 mi2)

1966–74 1940–2010a 1940–2010a

20 5 270 200 460 230 210 270 230 200 280 160 93 270 200 180 23010 10 360 250 690 300 260 350 300 260 380 210 120 340 250 210 290

4 25 480 320 1,100 400 340 480 400 330 560 280 180 450 320 260 3902 50 580 370 1,500 480 400 590 480 380 750 340 210 550 370 290 4701 100 700 430 2,100 570 470 720 570 430 1,000 410 250 660 250 220 3000.5 200 830 480 2,700 670 550 870 670 490 1,300 470 280 800 490 350 6800.2 500 1,000 570 3,800 820 650 1,100 820 570 1,900 570 320 1,010 580 390 860

aRecord extended with Branch River at Forestdale, RI (01111500).

Carr River near Nooseneck, RI (01115770) (6.74 mi2)

1964–79; 2007–10 1941–2010a 1941–2010a

20 5 220 170 330 160 140 190 160 130 210 180 100 300 160 130 20010 10 340 240 550 230 200 280 230 180 350 230 140 380 230 180 310

4 25 550 370 1,000 360 290 460 360 260 690 310 200 500 350 240 5102 50 770 490 1,600 480 380 650 480 330 1,200 380 230 620 460 390 7401 100 1,100 640 2,500 640 500 900 640 410 2,000 460 280 730 590 340 1,0200.5 200 1,500 820 3,800 850 640 1,200 850 500 3,500 530 310 890 744 390 1,4100.2 500 2,200 1,100 6,400 1,200 870 1,900 1,200 650 7,300 630 350 1,130 980 460 2,100

aRecord extended with Hunt River near East Greenwich, RI (01117000).

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.—Continued
72 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010 AEP Return interval (years) Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Catamint Brook at Cumberland, RI (01113695) (3.55 mi2

)

2000–10 1940–2010a

20 5 120 100 170 100 93 110 99 90 110 160 -- -- -- -- --10 10 150 120 220 120 110 130 120 100 140 210 -- -- -- -- --

4 25 180 140 290 140 130 160 140 120 180 300 -- -- -- -- --2 50 200 150 350 160 140 190 160 140 220 370 -- -- -- -- --1 100 230 170 430 180 160 210 180 150 260 440 -- -- -- -- --0.5 200 250 180 510 200 180 240 200 160 310 520 -- -- -- -- --0.2 500 290 200 630 230 200 280 230 180 390 630 -- -- -- -- -- aRecord extended with Branch River at Forestdale, RI (01111500).

Cold Brook near Adamsville, RI (csg) (01106100) (1.17 mi2

)

1966–1974 1940–2010a

20 5 0 0 0 78 69 90 78 66 97 78 -- -- -- -- --10 10 0 0 0 110 92 130 110 87 140 100 -- -- -- -- --

4 25 0 0 0 150 130 190 150 120 250 150 -- -- -- -- --2 50 0 0 0 190 160 250 190 140 370 180 -- -- -- -- --1 100 0 0 0 240 190 320 240 170 550 220 -- -- -- -- --0.5 200 0 0 0 300 240 410 300 200 830 260 -- -- -- -- --0.2 500 0 0 0 400 300 570 400 250 1,400 320 -- -- -- -- -- aRecord extended with Branch River at Forestdale, RI (01111500) to 1940–65 and Nipmuc River near Harrisville, RI (01111300) to 1975–2010.

Dry Arm Brook near Wallum Lake, RI (csg) (01111250) (1.45 mi2

)

1966–1978 1940–2010a

20 5 84 66 120 78 69 90 78 67 94 34 -- -- -- -- --10 10 110 81 160 100 88 120 100 86 130 43 -- -- -- -- --

4 25 130 99 230 140 120 170 140 110 200 59 -- -- -- -- --2 50 160 110 290 170 140 210 170 130 260 71 -- -- -- -- --1 100 180 130 360 200 160 260 200 150 350 86 -- -- -- -- --0.5 200 210 140 430 230 190 310 230 170 460 98 -- -- -- -- --0.2 500 240 160 550 290 230 390 290 200 660 120 -- -- -- -- -- aRecord extended with Branch River at Forestdale, RI (01111500).

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.—Continued
Table 15 73

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.—Continued

AEP

Return 

interval 

(years) 

Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA

Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper

Frenchtown Brook near Davisville, RI (csg) (01116870) (2.96 mi2)

1966–1974 1941–2010a

20 5 88 64 150 99 86 110 99 82 130 120 -- -- -- -- --10 10 120 82 230 140 120 170 140 110 200 160 -- -- -- -- --

4 25 160 110 390 210 170 260 210 160 370 220 -- -- -- -- --2 50 200 130 560 270 220 360 270 190 590 270 -- -- -- -- --1 100 250 150 780 360 280 490 360 240 960 320 -- -- -- -- --0.5 200 300 170 1,100 460 350 650 460 290 1,600 380 -- -- -- -- --0.2 500 380 200 1,600 630 460 950 630 360 3,000 460 -- -- -- -- --

aRecord extended with Hunt River near East Greenwich, RI (01117000).

Hardig Brook near West Warwick, RI (csg) (01116650) (3.25 mi2)

1966–1974 1942–2010a

20 5 250 210 330 260 240 290 260 240 310 450 -- -- -- -- --10 10 290 240 410 330 300 370 330 280 410 620 -- -- -- -- --

4 25 340 280 540 420 370 490 420 350 600 900 -- -- -- -- --2 50 390 300 650 500 440 590 500 400 810 1,130 -- -- -- -- --1 100 430 330 770 590 500 720 590 460 1,100 1,370 -- -- -- -- --0.5 200 480 360 920 690 580 860 690 510 1,490 1,680 -- -- -- -- --0.2 500 540 390 1,140 840 700 1,080 840 600 2,230 2,120 -- -- -- -- --

aRecord extended with Wood River at Hope Valley, RI (01118000).

Meadow Brook near Carolina, RI (01117600) (4.76 mi2)

1966–1974 1942–2010a 1942–2010a

20 5 92 73 130 97 87 110 97 83 120 120 67 200 97 82 12010 10 120 90 180 130 110 150 130 110 180 150 88 250 130 100 160

4 25 150 110 280 180 150 220 180 140 300 200 120 330 180 130 2402 50 190 130 370 230 190 290 230 170 450 250 150 410 230 160 3301 100 220 150 490 280 230 370 280 200 690 300 180 490 290 180 4400.5 200 270 170 640 350 280 470 350 230 1,060 340 200 590 350 210 5900.2 500 330 200 900 460 360 650 460 290 1,870 410 220 750 450 240 840

aRecord extended with Wood River at Hope Valley, RI (01118000).
74 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010 AEP Return interval (years) Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Mosquitohawk Brook near North Scituate, RI (01115100) (3.09 mi2

)

1966–1974 1940–2010a

20 5 370 240 730 300 260 360 300 250 380 61 -- -- -- -- --10 10 530 330 1,270 420 360 520 420 340 580 77 -- -- -- -- --

4 25 790 460 2,400 610 500 788 610 470 977 110 -- -- -- -- --2 50 1,040 570 3,690 790 630 1,040 790 580 1,430 130 -- -- -- -- --1 100 1,320 680 5,500 990 770 1,360 990 690 2,080 150 -- -- -- -- --0.5 200 1,650 810 8,000 1,220 930 1,730 1,220 810 2,990 170 -- -- -- -- --0.2 500 2,190 1,000 12,700 1,600 1,180 2,350 1,600 990 4,800 200 -- -- -- -- -- aRecord extended with Branch River at Forestdale, RI (01115000).

Peeptoad Brook at Elmdale Road near North Scituate, RI (01115098) (4.83 mi2

)

1995–2010 1940–2010a 1940–2010a

20 5 180 150 220 150 140 170 150 140 170 68 38 120 150 130 17010 10 210 180 280 180 170 210 180 160 220 86 49 150 180 160 210

4 25 250 210 360 230 200 270 230 200 300 120 69 200 230 190 2702 50 290 230 430 270 230 320 270 220 380 140 81 240 260 210 3301 100 320 250 500 310 260 370 310 250 470 170 96 290 300 220 3900.5 200 360 270 570 350 300 430 350 270 590 190 100 340 330 240 4600.2 500 410 300 690 400 340 510 410 300 770 220 120 430 390 270 560 aRecord extended with Branch River at Forestdale, RI (01115000).

Perry Healy Brook near Bradford, RI (csg) (01118020) (1.78 mi2

)

1966–74 1940–2010a

20 5 60 42 110 56 49 64 56 48 67 33 -- -- -- -- --10 10 84 56 180 73 64 86 73 61 96 42 -- -- -- -- --

4 25 120 77 330 100 85 120 100 80 150 58 -- -- -- -- --2 50 160 94 510 120 100 160 120 95 210 70 -- -- -- -- --1 100 210 110 760 150 120 200 150 110 290 85 -- -- -- -- --0.5 200 260 130 1,120 180 140 240 180 130 400 97 -- -- -- -- --0.2 500 350 170 1,820 230 180 310 230 150 610 110 -- -- -- -- -- aRecord extended with Branch River at Forestdale, RI (01115000).

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.—Continued
Table 15 75

AEP

Return 

interval 

(years) 

Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA

Peak 

flow 

estimate

95% confidence Peak flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence Peak 

flow 

estimate

95% confidence

Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper

Pocasset River near North Scituate, RI (csg) (01116600) (1.22 mi2)

1966–74 1940–2010a

20 5 45 36 65 44 40 49 44 38 51 50 -- -- -- -- --10 10 58 44 90 55 49 63 55 47 68 64 -- -- -- -- --

4 25 76 55 130 71 62 84 71 59 97 89 -- -- -- -- --2 50 90 64 170 84 72 100 84 68 130 110 -- -- -- -- --1 100 110 72 220 98 83 120 98 77 160 130 -- -- -- -- --0.5 200 120 81 270 110 94 140 110 86 210 150 -- -- -- -- --0.2 500 150 94 350 140 110 180 140 98 290 180 -- -- -- -- --

aRecord extended with Branch River at Forestdale, RI (01115000).

Queen River at Liberty, RI (01117370) (19.8 mi2)

1999–2010 1940–2010a 1940–2010a

20 5 710 500 1,190 380 340 440 380 330 480 760 450 1,290 8,390 330 46010 10 1,040 700 2,030 520 450 600 520 430 710 1,010 610 1,660 530 420 660

4 25 1,620 1,010 3,850 730 620 890 730 570 1,230 1,390 880 2,200 770 563 1,0502 50 2,190 1,280 6,030 930 770 1,180 940 690 1,880 1,710 1,050 2,760 1,000 680 1,4601 100 2,900 1,600 9,230 1,170 946 1,540 1,180 820 2,880 2,040 1,260 3,270 1,280 820 2,0100.5 200 3,810 1,970 13,900 1,460 1,150 1,980 1,480 970 4,440 2,410 1,430 4,050 1,600 950 2,7100.2 500 5,350 2,560 23,200 1,940 1,480 2,750 1,960 1,200 7,900 2,940 1,640 5,220 2,120 1,140 3,960

aRecord extended with Hunt River at East Greenwich, RI (01117000) 1941–75 and Usquepaug River near Usquepaug (01117420) 1976–1998.

Wilbur Hollow Brook near Clayville, RI (csg) (01115300) (4.57 mi2)

1966–1978 1940–2010a

20 5 220 180 290 200 180 230 200 180 230 150 90 260 200 180 23010 10 270 210 390 250 220 280 250 220 280 200 120 330 249 210 290

4 25 330 250 530 320 280 370 320 280 370 270 170 440 310 260 3802 50 390 290 660 370 320 440 370 320 440 330 200 540 370 290 4701 100 440 320 810 430 360 520 430 360 520 400 250 650 420 320 5700.5 200 500 350 970 490 410 610 490 410 610 470 280 790 490 350 6800.2 500 590 400 1,220 580 480 740 580 480 740 560 320 1,010 580 390 860

aRecord extended with Branch River at Forestdale, RI (01115000).

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.—Continued
76 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010 AEP Return interval (years) Period of record analysis Extended record analysis Regional regression Weighted average B17B B17B EMA Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Peak flow estimate 95% confidence Lower Upper Lower Upper Lower Upper Lower Upper Lower Upper Wood River Tributary near Arcadia, RI (csg) (01117820) (0.84 mi2

)

1966–1974 1940–2010a

20 5 20 16 27 20 19 22 20 18 24 89 -- -- -- -- --10 10 23 18 35 25 23 28 25 22 31 120 -- -- -- -- --

4 25 28 22 48 32 28 37 32 27 46 180 -- -- -- -- --2 50 32 24 59 38 33 45 38 30 63 220 -- -- -- -- --1 100 36 26 71 45 38 55 45 35 85 270 -- -- -- -- --0.5 200 40 28 85 52 44 66 52 39 120 330 -- -- -- -- --0.2 500 46 31 110 64 53 83 64 45 180 410 -- -- -- -- -- aRecord extended with Wood River at Hope Valley, RI (01118000).

Table 15. Estimated magnitude of flood flows and confidence limits for annual exceedance probabilities at short-term streamgages in Rhode Island.—Continued
Appendixes 1–3
78 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

Table 1–1. Basin characteristics tested for use as explanatory variables in regionalized regression equations for estimated flood 

flows at ungaged sites.—Continued

[ft, foot; ft/mi, feet per mile; mi, mile; mi/mi, miles per mile; mi/mi2, miles per square mile; mi2, square mile; °F, degrees Fahrenheit]

Basin characteristic Name Unit Notes

Shape

Source: Basin boundaries covers (internal)

Drainage area DA mi2

X-coordinate at center of basin centroid_x ft Rhode Island State plane coordinates

Y-coordinate at center of basin centroid_y ft Rhode Island State plane coordinates

X-coordinate at outlet of basin outlet_x ft Rhode Island State plane coordinates

Y-coordinate at outlet of basin outlet_y ft Rhode Island State plane coordinates

Basin perimeter BP mi2

Compactness ratio CR None Calculated: BP/2 (pi × DA)0.5

Basin length BL mi Distance from outlet to headwater along main axis

Effective width BW mi Calculated: DA/BL

Elongation ratio ER None Calculated: [4 × DA/pi × BL2]0.5 = 1.13(1/SF)0.5

Shape factor SF None Calculated: BL/BW

Rotundity RB None Calculated: [π × BL2] / 4 DA = 0.785 × SF

Land cover

Source: National Land Cover Dataset (NLCD) 2006 

http://www.epa.gov/mrlc/nlcd-2006.html

Area of open water Water Percent

Area of open urban OpenUrb Percent

Area of low density development LowDen Percent

Area of moderate density development ModDen Percent

Area of high density development HiDen Percent

Area of moderate to high density development ModHiUrb Percent Calculated: ModDen + HiDen

Total urban area AllUrban Percent Calculated: LowDen + MpdDen + HiDen

Area of deciduous forests DecFor Percent

Area of coniferous forests ConFor Percent

Area of mixed forests MixFor Percent

Total forest area Forest Percent Calculated: DecFor + ConFor + MixFor

Total forest and low density development area Forest2 Percent Calculated: Forest + ForWet + LowDen

Area of barren land Barren Percent

Area of shrub land Shrub Percent

Total open area Open Percent Calculated: Barren + Srub

Area of grassland Grass Percent

Area of pasture Pature Percent

Area of cropland Crop Percent

Total agriculture area Agr Percent Calculated: Grass + Pasture + Crop

Area of forested wetlands ForWet Percent

Area of nonforest wetlands Wetland Percent

Total wetland area AllWet Percent Calculated: ForWet + Wetland

Storage area of lakes, ponds, and wetlands StorNLCD Percent Calculated: Water + AllWet

Appendix 1. Basin Characteristics Considered for Use in the Regional 

Regression Analysis
Appendix 1 79

Table 1–1. Basin characteristics tested for use as explanatory variables in regionalized regression equations for estimated flood 

flows at ungaged sites.—Continued

[ft, foot; ft/mi, feet per mile; mi, mile; mi/mi, miles per mile; mi/mi2, miles per square mile; mi2, square mile; °F, degrees Fahrenheit]

Basin characteristic Name Unit Notes

Land cover—Continued

Source: National Land Cover Dataset (NLCD) 2001 impervous surface layer

http://www.csc.noaa.gov/digitalcoast/data/nlcd-impervious/index.html

Area of impervious land IMPERV Percent NLCD 2001 Impervious Surface

Source: National Hydrography Dataset (NHD) 1:24,000

http://nhd.usgs.gov/

Storage area of lakes, ponds, and wetlands StorNHD Percent Calculated from 1:24,000 NHD

Terrain

Source: National Elevation Dataset (NED) 10-meter resolution

http://seamless.usgs.gov/ned13.php

Mean basin slope MBslp Percent

Mean basin elevation ELEV ft

Maximum basin elevation ELEVmax ft

Minimum basin elevation ELEVmin ft

Basin relief RELIEF ft

Basin outlet elevation OUTLETELEV ft

Infiltration

Source: State GIS portals

http://www.mass.gov/mgis/sg24k.htm

http://www.edc.uri.edu/rigis/data/data.aspx?ISO=geoscientificInformation

http://www.ct.gov/dep/cwp/view.asp?a=2698&q=322898

Area of sand and gravel deposits SG Percent

Area of till deposits Till Percent

Source: Natural Resource Conservation Service (NRCS) SSURGO data

http://soildatamart.nrcs.usda.gov/Default.aspx

Area of hydrologic soils group A SoilA Percent

Area of hydrologic soils group B SoilB Percent

Area of hydrologic soils group C SoilC Percent

Area of hydrologic soils group D SoilD Percent

Climate

Source: DAYMET - daily surface weather data and climatological summaries

http://www.daymet.org/default.jsp

Mean annual total precipitation PRECIP Inches

Mean maximum daily temperature MTempF °F

Stream network

Source: National Hydrography Dataset (NHD) 1:24,000

http://nhd.usgs.gov/

Total length of streams STRMTOT mi2

Main channel slope MCslp ft/mi Calculated: 10 and 85 percent of main channel distance.

Main channel sinuosity SINOUS mi/mi Calculated: MCL/BL

Stream density STRDEN mi/mi2 Calculated: STRMTOT/DA
80 Magnitude of Floods for Selected Annual Exceedance Probabilities in Rhode Island Through 2010

The accuracy of a regression depends on the model error 

and the sampling error. Model error measures the ability of the 

explanatory variables to estimate the flood flows calculated 

from the streamgage records. The model error depends on the 

number and predictive power of the explanatory variables in 

a regression equation. Sampling error measures the ability of 

a finite number of streamgages with a finite record to describe 

the true characteristics of flood flows. The sampling error 

depends on the number and record length of streamgages used 

in the analysis, which decreases as the number of streamgages 

and record lengths increase.

A measure of the uncertainty in a regression equation 

estimate for a site, i, is the variance of prediction, Vp,i. The Vp,i

is the sum of the model error variance and sampling error 

variance and is computed using the following equation 

(Eng and others, 2009):

V

p,i

 = γ2 + MSEs,i , (2–1)

where

	 γ2 model error variance, and

MSEs,i sampling mean square error for site i.

Appendix 2. Measurement of Regression Error

Assuming that the explanatory variables for the 

streamgages in a regression analysis are representative of all 

streamgages in the region, the average accuracy of prediction 

for a regression equation is determined by computing the average variance of prediction, AVP, for n number of streamgages:

AVP = γ2 + MSEs,i

1

n (2–2)

A more traditional measure of the accuracy is the 

standard error of prediction, Sp, which is simply the square 

root of the variance of prediction. The average standard error 

of prediction for a regression equation can be computed 

in percent error using AVP, in log units, and the following 

transformation:

Sp,ave = 100 [102.3026(AVP) – 1]0.5 (2–3)

where

Sp,ave is the average standard error of prediction, 

in percent.
Appendix 3 81

[Click on worksheet title below to link to spreadsheet]

Regional-FFQ Computes annual-exceedance probability 

(AEP) flood flows and 95-percent confidence interval from 

regional regression equations developed for ungaged sites in 

Rhode Island.

US-DS Flow Equations for improving estimates of flood 

flows, within certain limits, at an ungaged site on a stream 

above or below a gaged location in Rhode Island.

Appendix 3. Link to Spreadsheet RI_Flood-Flow-Equations.xls
Prepared by the Pembroke Publishing Service Center.

For more information concerning this report, contact:

Director

U.S. Geological Survey

Massachusetts-Rhode Island Water Science Center

10 Bearfoot Road

Northborough, MA 01532

dc_ma@usgs.gov

or visit our Web site at:

http://ma.water.usgs.gov
Zarriello and others—Magnitude of Flood Flows for Selected Annual Exceedance Probabilities in Rhode Island Through 2010—SIR 2012–5019