Scientific Investigations Report 2007–5170

Comparison of Peak-Flow Estimation Methods for Small Drainage Basins in Maine

Prepared in cooperation with the Maine Department of Transportation

Scientific Investigations Report 2007–5170

 

By Glenn Hodgkins, Charles Hebson, Pamela Lombard, and Alexander Mann

 

This report is available in PDF Format (956 KB)

Abstract

Understanding the accuracy of commonly used methods for estimating peak streamflows is important because the designs of bridges, culverts, and other river structures are based on these flows. Different methods for estimating peak streamflows were analyzed for small drainage basins in Maine. For the smallest basins, with drainage areas of 0.2 to 1.0 square mile, nine peak streamflows from actual rainfall events at four crest-stage gaging stations were modeled by the Rational Method and the Natural Resource Conservation Service TR-20 method and compared to observed peak flows. The Rational Method had a root mean square error (RMSE) of -69.7 to 230 percent (which means that approximately two thirds of the modeled flows were within -69.7 to 230 percent of the observed flows). The TR-20 method had an RMSE of -98.0 to 5,010 percent. Both the Rational Method and TR-20 underestimated the observed flows in most cases.

For small basins, with drainage areas of 1.0 to 10 square miles, modeled peak flows were compared to observed statistical peak flows with return periods of 2, 50, and 100 years for 17 streams in Maine and adjoining parts of New Hampshire. Peak flows were modeled by the Rational Method, the Natural Resources Conservation Service TR-20 method, U.S. Geological Survey regression equations, and the Probabilistic Rational Method.

The regression equations were the most accurate method of computing peak flows in Maine for streams with drainage areas of 1.0 to 10 square miles with an RMSE of -34.3 to 52.2 percent for 50-year peak flows. The Probabilistic Rational Method was the next most accurate method (-38.5 to 62.6 percent). The Rational Method (-56.1 to 128 percent) and particularly the TR-20 method (-76.4 to 323 percent) had much larger errors. Both the TR-20 and regression methods had similar numbers of underpredictions and overpredictions. The Rational Method overpredicted most peak flows and the Probabilistic Rational Method tended to overpredict peak flows from the smaller (less than 5 square miles) drainage basins and underpredict peak flows from larger drainage basins. The results of this study are consistent with the most comprehensive analysis of observed and modeled peak streamflows in the United States, which analyzed statistical peak flows from 70 drainage basins in the Midwest and the Northwest.

Contents

Abstract

Introduction

Peak Flows at Crest-Stage Gaging Stations with Drainage Areas of 0.2 to 1.0 Square Miles

Field Data Collection

Precipitation Gages

Crest-Stage Gaging Stations

Streamflow Measurements

Observed Peak Flows

Modeled Peak Flows

Rational Method

Runoff Coefficient

Rainfall Intensity

Drainage-Basin Area

TR-20 Method

Comparison of Observed and Modeled Peak Flows

Peak Flows for Selected Return Periods at Streamflow-Gaging Stations with Drainage Areas of 1.0 to 10 Square Miles

Observed Peak Flows

Modeled Peak Flows

Rational Method

TR-20 Method

Regression Equations

Probabilistic Rational Method

Comparison of Observed and Modeled Peak Flows for Selected Return Periods

Summary and Conclusions

References Cited

Appendix 1: Methods for Estimation of Time of Concentration

Appendix 2: Additional Data Used in the Rational Method and Natural Resources Conservation Service TR-20 Methods

Figures

  1. Location of crest-stage gaging stations used in this study with drainage areas from 0.2 to 1.0 square miles.
  2. Location of streamflow-gaging stations used in this study with drainage areas from 1.0 to 10 square miles.
  3. Modeled 50-year peak flows from the Rational Method plotted against observed 50-year peak flows.
  4. Modeled 50-year peak flows from the Natural Resources Conservation Service TR-20 method plotted against observed 50-year peak flows.
  5. Modeled 50-year peak flows from U.S. Geological Survey regression equations plotted against observed 50-year peak flows.
  6. Modeled 50-year peak flows from the Probabilistic Rational Method plotted against observed 50-year peak flows.

Tables

  1. Crest-stage gaging stations established for very small drainage basins in Maine in 1999 and 2000.
  2. Summary of input parameters and modeled peak flows for the Rational Method for basins in Maine with drainage areas of 0.2 to 1.0 square miles.
  3. Summary of input parameters and modeled peak flows for the Natural Resources Conservation Service TR-20 method for basins in Maine with drainage areas of 0.2 to 1.0 square miles.
  4. Observed and modeled peak flows for basins in Maine with drainage areas of 0.2 to 1.0 square miles.
  5. Observed peak flows for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.
  6. Summary of input parameters for the Rational Method for basins with drainage areas of 1.0 to 10 square miles.
  7. Modeled peak flows using the Rational Method for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.
  8. Summary of input parameters for the Natural Resources Conservation Service TR-20 method for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.
  9. Modeled peak flows using the Natural Resources Conservation Service TR-20 method for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.
  10. Modeled peak flows using U.S. Geological Survey regression equations for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.
  11. Probabilistic Rational Method rainfall-runoff coefficients (C) for 2-, 10-, 25-, 50-, and 100-year return periods for 17 U.S. Geological Survey streamflow-gaging stations in Maine.
  12. Modeled peak flows using the Probabilistic Rational Method for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.
  13. Root mean square errors from comparison of modeled and observed peak 2-, 50-, and 100-year streamflows for basins in Maine and New Hampshire with drainage areas of 1.0 to 10 square miles.

 

Suggested citation:
Hodgkins, G.A., Hebson, Charles, Lombard, P.J., and Mann, Alexander, 2007, Comparison of peak-flow estimation methods for small drainage basins in Maine: U.S. Geological Survey Scientific Investigations Report 2007-5170, 32 p.

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