Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho

Scientific Investigations Report 2016-5083

Prepared in cooperation with Idaho Transportation Department
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The U.S. Geological Survey, in cooperation with the Idaho Transportation Department, updated regional regression equations to estimate peak-flow statistics at ungaged sites on Idaho streams using recent streamflow (flow) data and new statistical techniques. Peak-flow statistics with 80-, 67-, 50-, 43-, 20-, 10-, 4-, 2-, 1-, 0.5-, and 0.2-percent annual exceedance probabilities (1.25-, 1.50-, 2.00-, 2.33-, 5.00-, 10.0-, 25.0-, 50.0-, 100-, 200-, and 500-year recurrence intervals, respectively) were estimated for 192 streamgages in Idaho and bordering States with at least 10 years of annual peak-flow record through water year 2013. The streamgages were selected from drainage basins with little or no flow diversion or regulation. The peak-flow statistics were estimated by fitting a log-Pearson type III distribution to records of annual peak flows and applying two additional statistical methods: (1) the Expected Moments Algorithm to help describe uncertainty in annual peak flows and to better represent missing and historical record; and (2) the generalized Multiple Grubbs Beck Test to screen out potentially influential low outliers and to better fit the upper end of the peak-flow distribution. Additionally, a new regional skew was estimated for the Pacific Northwest and used to weight at-station skew at most streamgages. The streamgages were grouped into six regions (numbered 1_2, 3, 4, 5, 6_8, and 7, to maintain consistency in region numbering with a previous study), and the estimated peak-flow statistics were related to basin and climatic characteristics to develop regional regression equations using a generalized least squares procedure. Four out of 24 evaluated basin and climatic characteristics were selected for use in the final regional peak-flow regression equations.

Overall, the standard error of prediction for the regional peak-flow regression equations ranged from 22 to 132 percent. Among all regions, regression model fit was best for region 4 in west-central Idaho (average standard error of prediction=46.4 percent; pseudo-R2>92 percent) and region 5 in central Idaho (average standard error of prediction=30.3 percent; pseudo-R2>95 percent). Regression model fit was poor for region 7 in southern Idaho (average standard error of prediction=103 percent; pseudo-R2<78 percent) compared to other regions because few streamgages in region 7 met the criteria for inclusion in the study, and the region’s semi-arid climate and associated variability in precipitation patterns causes substantial variability in peak flows.

A drainage area ratio-adjustment method, using ratio exponents estimated using generalized least-squares regression, was presented as an alternative to the regional regression equations if peak-flow estimates are desired at an ungaged site that is close to a streamgage selected for inclusion in this study. The alternative drainage area ratio-adjustment method is appropriate for use when the drainage area ratio between the ungaged and gaged sites is between 0.5 and 1.5.

The updated regional peak-flow regression equations had lower total error (standard error of prediction) than all regression equations presented in a 1982 study and in four of six regions presented in 2002 and 2003 studies in Idaho. A more extensive streamgage screening process used in the current study resulted in fewer streamgages used in the current study than in the 1982, 2002, and 2003 studies. Fewer streamgages used and the selection of different explanatory variables were likely causes of increased error in some regions compared to previous studies, but overall, regional peak‑flow regression model fit was generally improved for Idaho. The revised statistical procedures and increased streamgage screening applied in the current study most likely resulted in a more accurate representation of natural peak-flow conditions.

The updated, regional peak-flow regression equations will be integrated in the U.S. Geological Survey StreamStats program to allow users to estimate basin and climatic characteristics and peak-flow statistics at ungaged locations of interest. StreamStats estimates peak-flow statistics with quantifiable certainty only when used at sites with basin and climatic characteristics within the range of input variables used to develop the regional regression equations. Both the regional regression equations and StreamStats should be used to estimate peak-flow statistics only in naturally flowing, relatively unregulated streams without substantial local influences to flow, such as large seeps, springs, or other groundwater-surface water interactions that are not widespread or characteristic of the respective region.

Suggested Citation

Wood, M.S., Fosness, R.L., Skinner, K.D., and Veilleux, A.G., 2016, Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho: U.S. Geological Survey Scientific Investigations Report 2016–5083, 56 p.,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Abstract
  • Introduction
  • Data Screening and Compilation
  • Estimating Peak-Flow Frequency Statistics at Selected Gaged Sites
  • Estimating Peak-Flow Frequency Statistics at Ungaged Sites Through a Regional Regression Analysis
  • Comparison of Results from Previous Studies
  • Estimating Flow Statistics Using StreamStats
  • Potential Areas for Further Study
  • Summary
  • Acknowledgments
  • References Cited
  • Appendix A-B

Additional publication details

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USGS Numbered Series
Estimating peak-flow frequency statistics for selected gaged and ungaged sites in naturally flowing streams and rivers in Idaho
Series title:
Scientific Investigations Report
Series number:
Year Published:
U.S. Geological Survey
Publisher location:
Reston, VA
Contributing office(s):
Idaho Water Science Center
Report: vi, 56 p.; Appendix A
United States
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