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Scientific Investigations Report 2010–5217

Prepared in cooperation with the Kentucky Energy and Environment Cabinet, Division of Water

Methods for Estimating Selected Low-Flow Frequency Statistics for Unregulated Streams in Kentucky

By Gary R. Martin and Leslie D. Arihood


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This report provides estimates of, and presents methods for estimating, selected low-flow frequency statistics for unregulated streams in Kentucky including the 30-day mean low flows for recurrence intervals of 2 and 5 years (30Q2 and 30Q5) and the 7-day mean low flows for recurrence intervals of 5, 10, and 20 years (7Q2, 7Q10, and 7Q20). Estimates of these statistics are provided for 121 U.S. Geological Survey streamflow-gaging stations with data through the 2006 climate year, which is the 12-month period ending March 31 of each year. Data were screened to identify the periods of homogeneous, unregulated flows for use in the analyses.

Logistic-regression equations are presented for estimating the annual probability of the selected low-flow frequency statistics being equal to zero. Weighted-least-squares regression equations were developed for estimating the magnitude of the nonzero 30Q2, 30Q5, 7Q2, 7Q10, and 7Q20 low flows. Three low-flow regions were defined for estimating the 7-day low-flow frequency statistics.

The explicit explanatory variables in the regression equations include total drainage area and the mapped streamflow-variability index measured from a revised statewide coverage of this characteristic. The percentage of the station low-flow statistics correctly classified as zero or nonzero by use of the logistic-regression equations ranged from 87.5 to 93.8 percent. The average standard errors of prediction of the weighted-least-squares regression equations ranged from 108 to 226 percent. The 30Q2 regression equations have the smallest standard errors of prediction, and the 7Q20 regression equations have the largest standard errors of prediction.

The regression equations are applicable only to stream sites with low flows unaffected by regulation from reservoirs and local diversions of flow and to drainage basins in specified ranges of basin characteristics. Caution is advised when applying the equations for basins with characteristics near the applicable limits and for basins with karst drainage features.

Posted December 21, 2010

For additional information contact:
Director, Kentucky Water Science Center
U.S. Geological Survey
9818 Bluegrass Parkway
Louisville, KY 40299–1906

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Suggested citation:

Martin, G.R., and Arihood, L.D., 2010, Methods for estimating selected low-flow frequency statistics for unregulated streams in Kentucky: U.S. Geological Survey Scientific Investigations Report 2010–5217, 83 p., plus 2 pl.




Methods for Data-Collection Stations

Methods for Ungaged Stream Sites


References Cited


Appendix 1.  Trend Tests of Long-Term Climate Data for Kentucky During 1895–2004

Appendix 2.  Trend-Test Screening of Annual 7-Day Low Flows for Selected Long-Term Continuous-Record Streamflow-Gaging Stations in Kentucky for Various Periods of Record

Appendix 3.  Double-Mass Curves Showing Relations of Cumulative Annual 7-Day Low Flows among Selected Hydro-Climate Data Network, Hydrologic Benchmark Network, and
                  Reference Streamflow-Gaging Stations in and surrounding Kentucky

Appendix 4.  A Procedure for Detrending Annual Low-Flow Data for Frequency Analysis

Appendix 5.  Classification Tables for Logistic-Regression Equations for Estimating the Probability of Zero Flow For Selected Low-Flow Frequencies in Kentucky

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