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Regression Method for Estimating Long-Term Mean Annual Ground-Water Recharge Rates from Base Flow in Pennsylvania

U.S. Geological Survey Scientific Investigations Report 2008-5185

Prepared in cooperation with the Pennsylvania Department of Conservation and Natural Resources,
Bureau of Topographic and Geologic Survey

By Dennis W. Risser, Ronald E. Thompson, and Marla H. Stuckey

View the report in Portable Document Format (PDF) SIR 2008-5185 (3.75 MB)


A method was developed for making estimates of long-term, mean annual ground-water recharge from streamflow data at 80 streamflow-gaging stations in Pennsylvania. The method relates mean annual base-flow yield derived from the streamflow data (as a proxy for recharge) to the climatic, geologic, hydrologic, and physiographic characteristics of the basins (basin characteristics) by use of a regression equation.

Base-flow yield is the base flow of a stream divided by the drainage area of the basin, expressed in inches of water basinwide. Mean annual base-flow yield was computed for the period of available streamflow record at continuous streamflow-gaging stations by use of the computer program PART, which separates base flow from direct runoff on the streamflow hydrograph. Base flow provides a reasonable estimate of recharge for basins where streamflow is mostly unaffected by upstream regulation, diversion, or mining.

Twenty-eight basin characteristics were included in the exploratory regression analysis as possible predictors of base-flow yield. Basin characteristics found to be statistically significant predictors of mean annual base-flow yield during 1971–2000 at the 95-percent confidence level were (1) mean annual precipitation, (2) average maximum daily temperature, (3) percentage of sand in the soil, (4) percentage of carbonate bedrock in the basin, and (5) stream channel slope. The equation for predicting recharge was developed using ordinary least-squares regression. The standard error of prediction for the equation on log-transformed data was 9.7 percent, and the coefficient of determination was 0.80.

The equation can be used to predict long-term, mean annual recharge rates for ungaged basins, providing that the explanatory basin characteristics can be determined and that the underlying assumption is accepted that base-flow yield derived from PART is a reasonable estimate of ground-water recharge rates. For example, application of the equation for 370 hydrologic units in Pennsylvania predicted a range of ground-water recharge from about 6.0 to 22 inches per year. A map of the predicted recharge illustrates the general magnitude and variability of recharge throughout Pennsylvania.

Table of Contents

     Base-Flow Yield and Recharge
     Previous Investigations
     Purpose and Scope
Regression Method for Estimating Recharge Rates
     Determining Base-Flow Yield for Basins
     Basin Characteristics
     Regression Techniques
     Sensitivity of Predictions
     Limitations of Regression Equations
     Example Calculation
Recharge Estimates for Basins in Pennsylvania
References Cited

Suggested citation:
Risser, D.W., Thompson, R.E., and Stuckey, M.H., 2008, Regression method for estimating long-term mean annual ground-water recharge rates from base flow in Pennsylvania: U.S. Geological Survey Scientific Investigations Report 2008-5185, 23 p.

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View the report in Portable Document Format (PDF) SIR 2008-5185 (3.75 MB)

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