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Nonstationary Flood Frequency Analysis Using Regression in the North-Central United States

Scientific Investigations Report 2025-5034
Prepared in cooperation with the Illinois Department of Transportation, Iowa Department of Transportation, Michigan Department of Transportation, Minnesota Department of Transportation, Missouri Department of Transportation, Montana Department of Natural Resources and Conservation, North Dakota Department of Water Resources, South Dakota Department of Transportation, and Wisconsin Department of Transportation
By:
https://doi.org/10.3133/sir20255034

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Abstract

Traditional flood frequency methods assume that the statistical properties of peak streamflow do not change with time and may not be appropriate for many areas in the north-central United States. This study examines a nonstationary flood frequency analysis method that uses ordinary least squares linear regression to estimate flood magnitudes at U.S. Geological Survey streamgages that exhibit trends and change points in a nine-State region including Montana, North Dakota, South Dakota, Minnesota, Illinois, Iowa, Wisconsin, Missouri, and Michigan. Additionally, an extension of this method is introduced, which enables nonstationary flood frequency based on a statistical relation with a stochastic climate predictor.

Estimates of the 1-percent annual exceedance probability flood using regression equations to adjust for conditions in 2020 were computed at U.S. Geological Survey streamgages across the study area. Regression equations used either a time index or a climate variable as the explanatory variable for changes in peak streamflow. Of 153 candidate streamgages, the assumptions of time-adjusted analyses were met at 137 streamgages. Climate-adjusted flood frequency analyses were applicable at 98 streamgages based on annual precipitation, annual temperature, or annual snowfall. Time- and climate-adjusted methods produced similar estimates of the 1-percent annual exceedance probability flood magnitude at streamgages where both methods were applicable. Nonstationary estimates of the 1-percent annual exceedance probability flood were primarily greater than stationary estimates in eastern North and South Dakota, Minnesota, Iowa, Illinois, and parts of Missouri and less than stationary estimates in Montana, western North and South Dakota, and Wisconsin. The largest differences between stationary and nonstationary flood estimates were in North and South Dakota and Minnesota.

Suggested Citation

Levin, S.B., 2025, Nonstationary flood frequency analysis using regression in the north-central United States: U.S. Geological Survey Scientific Investigations Report 2025–5034, 33 p., https://doi.org/10.3133/sir20255034.

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Acknowledgments
  • Abstract
  • Introduction
  • Purpose and Scope
  • Data and Site Selection
  • Flood Frequency Methods
  • Estimation of Flood Frequency at Candidate Streamgages
  • Regional Applicability of Using Linear Regression in Nonstationary Flood Frequency
  • Summary
  • References Cited
Publication type Report
Publication Subtype USGS Numbered Series
Title Nonstationary flood frequency analysis using regression in the north-central United States
Series title Scientific Investigations Report
Series number 2025-5034
DOI 10.3133/sir20255034
Publication Date May 02, 2025
Year Published 2025
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Upper Midwest Water Science Center
Description Report: viii, 33 p.; Dataset
Country United States
State Illinois, Iowa, Michigan, Minnesota, Missouri, Montana, North Dakota, South Dakota, Wisconsin
Online Only (Y/N) Y
Additional Online Files (Y/N) N
Additional publication details