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Scientific Investigations Report 2013–5086

Prepared in cooperation with the Iowa Department of Transportation and the Iowa Highway Research Board (Project TR-519)

Methods for Estimating Annual Exceedance-Probability Discharges for Streams in Iowa, Based on Data through Water Year 2010

By David A. Eash, Kimberlee K. Barnes, and Andrea G. Veilleux

Thumbnail of and link to report PDF (7.42 MB)Abstract

A statewide study was performed to develop regional regression equations for estimating selected annual exceedance-probability statistics for ungaged stream sites in Iowa. The study area comprises streamgages located within Iowa and 50 miles beyond the State’s borders. Annual exceedance-probability estimates were computed for 518 streamgages by using the expected moments algorithm to fit a Pearson Type III distribution to the logarithms of annual peak discharges for each streamgage using annual peak-discharge data through 2010. The estimation of the selected statistics included a Bayesian weighted least-squares/generalized least-squares regression analysis to update regional skew coefficients for the 518 streamgages. Low-outlier and historic information were incorporated into the annual exceedance-probability analyses, and a generalized Grubbs-Beck test was used to detect multiple potentially influential low flows. Also, geographic information system software was used to measure 59 selected basin characteristics for each streamgage.

Regional regression analysis, using generalized least-squares regression, was used to develop a set of equations for each flood region in Iowa for estimating discharges for ungaged stream sites with 50-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities, which are equivalent to annual flood-frequency recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively. A total of 394 streamgages were included in the development of regional regression equations for three flood regions (regions 1, 2, and 3) that were defined for Iowa based on landform regions and soil regions.

Average standard errors of prediction range from 31.8 to 45.2 percent for flood region 1, 19.4 to 46.8 percent for flood region 2, and 26.5 to 43.1 percent for flood region 3. The pseudo coefficients of determination for the generalized least-squares equations range from 90.8 to 96.2 percent for flood region 1, 91.5 to 97.9 percent for flood region 2, and 92.4 to 96.0 percent for flood region 3. The regression equations are applicable only to stream sites in Iowa with flows not significantly affected by regulation, diversion, channelization, backwater, or urbanization and with basin characteristics within the range of those used to develop the equations.

These regression equations will be implemented within the U.S. Geological Survey StreamStats Web-based geographic information system tool. StreamStats allows users to click on any ungaged site on a river and compute estimates of the eight selected statistics; in addition, 90-percent prediction intervals and the measured basin characteristics for the ungaged sites also are provided by the Web-based tool. StreamStats also allows users to click on any streamgage in Iowa and estimates computed for these eight selected statistics are provided for the streamgage.

First posted May 8, 2013

For additional information contact:
Director, Iowa Water Science Center
U.S. Geological Survey
P.O. Box 1230
Iowa City, IA 52244

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Suggested citation:

Eash, D.A., Barnes, K.K., and Veilleux, A.G., 2013, Methods for estimating annual exceedance-probability discharges for streams in Iowa, based on data through water year 2010: U.S. Geological Survey Scientific Investigations Report 2013-5086, 63 p. with appendix.,




Methods for Dataset Development for Streamgages

Regional Regression Analyses to Estimate Annual Exceedance-Probability Discharges for Ungaged Stream Sites

Weighted Method to Estimate Annual Exceedance-Probability Discharges for Streamgages

Weighted Methods to Estimate Annual Exceedance-Probability Discharges for Ungaged Sites on Gaged Streams

Weighted Method to Estimate Annual Exceedance-Probability Discharges for Ungaged Sites Draining More Than One Flood Region

Region-of-Influence Method to Estimate Annual Exceedance-Probability Discharges for Ungaged Stream Sites

Comparison of Annual Exceedance-Probability Discharges


Maximum Floods in Iowa



References Cited


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