Regression Equations for Estimating Flood Flows for the 2-, 10-, 25-, 50-, 100-, and 500-Year Recurrence Intervals in Connecticut

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

Scientific Investigations Reports 2004-5160


By Elizabeth A. Ahearn


In cooperation with the Connecticut Department of Transportation and the Connecticut Department of Environmental Protection


This report is also available as a pdf.



Multiple linear-regression equations were developed to estimate the magnitudes of floods in Connecticut for recurrence intervals ranging from 2 to 500 years. The equations can be used for nonurban, unregulated stream sites in Connecticut with drainage areas ranging from about 2 to 715 square miles. Flood-frequency data and hydrologic characteristics from 70 streamflow-gaging stations and the upstream drainage basins were used to develop the equations. The hydrologic characteristics—drainage area, mean basin elevation, and 24-hour rainfall—are used in the equations to estimate the magnitude of floods. Average standard errors of prediction for the equations are 31.8, 32.7, 34.4, 35.9, 37.6 and 45.0 percent for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals, respectively. Simplified equations using only one hydrologic characteristic—drainage area—also were developed. The regression analysis is based on generalized least-squares regression techniques.

Observed flows (log-Pearson Type III analysis of the annual maximum flows) from five streamflow-gaging stations in urban basins in Connecticut were compared to flows estimated from national three-parameter and seven-parameter urban regression equations. The comparison shows that the three- and seven- parameter equations used in conjunction with the new statewide equations generally provide reasonable estimates of flood flows for urban sites in Connecticut, although a national urban flood-frequency study indicated that the three-parameter equations significantly underestimated flood flows in many regions of the country. Verification of the accuracy of the three-parameter or seven-parameter national regression equations using new data from Connecticut stations was beyond the scope of this study.

A technique for calculating flood flows at streamflow-gaging stations using a weighted average also is described. Two estimates of flood flows—one estimate based on the log-Pearson Type III analyses of the annual maximum flows at the gaging station, and the other estimate from the regression equation—are weighted together based on the years of record at the gaging station and the equivalent years of record value determined from the regression. Weighted averages of flood flows for the 2-, 10-, 25-, 50-, 100-, and 500-year recurrence intervals are tabulated for the 70 streamflow-gaging stations used in the regression analysis. Generally, weighted averages give the most accurate estimate of flood flows at gaging stations.

An evaluation of the Connecticut's streamflow-gaging network was performed to determine whether the spatial coverage and range of geographic and hydrologic conditions are adequately represented for transferring flood characteristics from gaged to ungaged sites. Fifty-one of 54 stations in the current (2004) network support one or more flood needs of federal, state, and local agencies. Twenty-five of 54 stations in the current network are considered high-priority stations by the U.S. Geological Survey because of their contribution to the longterm understanding of floods, and their application for regionalflood analysis. Enhancements to the network to improve overall effectiveness for regionalization can be made by increasing the spatial coverage of gaging stations, establishing stations in regions of the state that are not well-represented, and adding stations in basins with drainage area sizes not represented. Additionally, the usefulness of the network for characterizing floods can be maintained and improved by continuing operation at the current stations because flood flows can be more accurately estimated at stations with continuous, long-term record.




Purpose and Scope

Previous Studies

Description of the Study Area

Estimating Flood Flows at Stream Sites in Nonurban Basins

Data Used in the Regression Analysis

Analytical Procedures for Regression Analysis

Correlations Between Explanatory Variables

Regression Analysis Using Ordinary-Least-Squares

Regression Analysis Using Generalized-Least-Squares

Diagnostic Evaluation of the Regression Models

Evaluation of Possible Hydrologic Subregions

Results of the Regression Analysis

Accuracy of the Regression Equations

Limitations of the Regression Equations

Simplified Regression Equations

Web Application for Solving the Regression Equation

Estimating Flood Flows at Stream Sites in Urban Basins

Definitions of Equation Variables

Accuracy and Limitations of the National Urban Regression Equations

Comparison of Flood-Flow Estimates From the Urban Equations to Observed Flows in Connecticut

Weighted Averages of Flood Flow for Streamflow-Gaging Stations

Evaluation of the Streamflow-Gaging Network for Characterizing Flood Flows

Spatial Coverage

Record Lengths

Drainage-Basin Characteristics


Summary and Conclusions

Selected References


1. Peak-flow frequency estimates for streams in Connecticut for selected recurrence intervals

2. Hydrologic characteristics for streamflow-gaging stations used in the regression analysis for


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