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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, Version 1.1

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

Thumbnail of and link to report PDF (11 MB)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.

Revised March 27, 2013

First posted June 25, 2012

  • Appendix 3 XLS (156 kB)

    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.

For additional information contact:
Office Chief
U.S. Geological Survey
New England Water Science Center
Massachusetts-Rhode Island Office
10 Bearfoot Road
Northborough, MA 01532
(508) 490-5000

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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 (ver. 1.2, revised March 27, 2013): U.S. Geological Survey Scientific Investigations Report 2012–5109, 81 p. (Also available at




Data Compilation

Magnitude of Flood Flows at Streamgages

Magnitude of Flood Flows at Ungaged Streams

Factors Affecting Flood Flow Estimate

Application of Methods and Significance of Results

Summary and Conclusions


Selected References


Tables 7, 13, and 15

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

Appendix 2. Measurement of Regression Error

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

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