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Scientific Investigations Report 2009–5267

Prepared in cooperation with the Oklahoma Water Resources Board

Methods for Estimating Flow-Duration and Annual Mean-Flow Statistics for Ungaged Streams in Oklahoma

By Rachel A. Esralew and S. Jerrod Smith


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Flow statistics can be used to provide decision makers with surface-water information needed for activities such as water-supply permitting, flow regulation, and other water rights issues. Flow statistics could be needed at any location along a stream. Most often, streamflow statistics are needed at ungaged sites, where no flow data are available to compute the statistics. Methods are presented in this report for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma.

Flow statistics included the (1) annual (period of record), (2) seasonal (summer-autumn and winter-spring), and (3) 12 monthly duration statistics, including the 20th, 50th, 80th, 90th, and 95th percentile flow exceedances, and the annual mean-flow (mean of daily flows for the period of record). Flow statistics were calculated from daily streamflow information collected from 235 streamflow-gaging stations throughout Oklahoma and areas in adjacent states.

A drainage-area ratio method is the preferred method for estimating flow statistics at an ungaged location that is on a stream near a gage. The method generally is reliable only if the drainage-area ratio of the two sites is between 0.5 and 1.5.

Regression equations that relate flow statistics to drainage-basin characteristics were developed for the purpose of estimating selected flow-duration and annual mean-flow statistics for ungaged streams that are not near gaging stations on the same stream. Regression equations were developed from flow statistics and drainage-basin characteristics for 113 unregulated gaging stations.

Separate regression equations were developed by using U.S. Geological Survey streamflow-gaging stations in regions with similar drainage-basin characteristics. These equations can increase the accuracy of regression equations used for estimating flow-duration and annual mean-flow statistics at ungaged stream locations in Oklahoma. Streamflow-gaging stations were grouped by selected drainage-basin characteristics by using a k-means cluster analysis. Three regions were identified for Oklahoma on the basis of the clustering of gaging stations and a manual delineation of distinguishable hydrologic and geologic boundaries: Region 1 (western Oklahoma excluding the Oklahoma and Texas Panhandles), Region 2 (north- and south-central Oklahoma), and Region 3 (eastern and central Oklahoma).

A total of 228 regression equations (225 flow-duration regressions and three annual mean-flow regressions) were developed using ordinary least-squares and left-censored (Tobit) multiple-regression techniques. These equations can be used to estimate 75 flow-duration statistics and annual mean-flow for ungaged streams in the three regions. Drainage-basin characteristics that were statistically significant independent variables in the regression analyses were (1) contributing drainage area; (2) station elevation; (3) mean drainage-basin elevation; (4) channel slope; (5) percentage of forested canopy; (6) mean drainage-basin hillslope; (7) soil permeability; and (8) mean annual, seasonal, and monthly precipitation.

The accuracy of flow-duration regression equations generally decreased from high-flow exceedance (low-exceedance probability) to low-flow exceedance (high-exceedance probability) . This decrease may have happened because a greater uncertainty exists for low-flow estimates and low-flow is largely affected by localized geology that was not quantified by the drainage-basin characteristics selected.

The standard errors of estimate of regression equations for Region 1 (western Oklahoma) were substantially larger than those standard errors for other regions, especially for low-flow exceedances. These errors may be a result of greater variability in low flow because of increased irrigation activities in this region.

Regression equations may not be reliable for sites where the drainage-basin characteristics are outside the range of values of independent variables used to develop the equations. The equations are not accurate for streams that are regulated by water-supply reservoirs, streams that are affected by local irrigation activity, or streams that are affected by urban change.

First posted May 10, 2010

For additional information contact:

Director, U.S. Geological Survey
202 NW 66th Street, Building 7
Oklahoma City, OK 73116

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Suggested citation:

Esralew, R.A., Smith, S.J., 2010, Methods for estimating flow-duration and annual mean-flow statistics for ungaged streams in Oklahoma: U.S. Geological Survey Scientific Investigations Report 2009-5267, 131 p.




Description of Study Area and Factors that Affect Streamflow in the Study Area

Calculation of Flow-Duration and Annual Mean-flow Statistics at Gaging Stations

Methods of Estimating Flow-Duration and Annual Mean-Flow Statistics at Ungaged
Stream Locations

Development of Regression Equations to Estimate Flow-Duration and Annual Mean-
Flow Statistics at Unregulated Ungaged Stream Locations in Oklahoma

Results of Regression Analysis to Estimate Flow-Duration and Annual Mean-Flow
Statistics for Unregulated Ungaged Stream Locations in Oklahoma


References Cited


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