Estimation of Peak Discharge Quantiles for Selected Annual Exceedance Probabilities in Northeastern Illinois

Scientific Investigations Report 2016-5050
Prepared in cooperation with the Illinois Center for Transportation, the Illinois Department of Transportation, and the Federal Highway Administration
By: , and 



This report provides two sets of equations for estimating peak discharge quantiles at annual exceedance probabilities (AEPs) of 0.50, 0.20, 0.10, 0.04, 0.02, 0.01, 0.005, and 0.002 (recurrence intervals of 2, 5, 10, 25, 50, 100, 200, and 500 years, respectively) for watersheds in Illinois based on annual maximum peak discharge data from 117 watersheds in and near northeastern Illinois. One set of equations was developed through a temporal analysis with a two-step least squares-quantile regression technique that measures the average effect of changes in the urbanization of the watersheds used in the study. The resulting equations can be used to adjust rural peak discharge quantiles for the effect of urbanization, and in this study the equations also were used to adjust the annual maximum peak discharges from the study watersheds to 2010 urbanization conditions.

The other set of equations was developed by a spatial analysis. This analysis used generalized least-squares regression to fit the peak discharge quantiles computed from the urbanization-adjusted annual maximum peak discharges from the study watersheds to drainage-basin characteristics. The peak discharge quantiles were computed by using the Expected Moments Algorithm following the removal of potentially influential low floods defined by a multiple Grubbs-Beck test. To improve the quantile estimates, regional skew coefficients were obtained from a newly developed regional skew model in which the skew increases with the urbanized land use fraction. The skew coefficient values for each streamgage were then computed as the variance-weighted average of at-site and regional skew coefficients. The drainage-basin characteristics used as explanatory variables in the spatial analysis include drainage area, the fraction of developed land, the fraction of land with poorly drained soils or likely water, and the basin slope estimated as the ratio of the basin relief to basin perimeter.

This report also provides the following: (1) examples to illustrate the use of the spatial and urbanization-adjustment equations for estimating peak discharge quantiles at ungaged sites and to improve flood-quantile estimates at and near a gaged site; (2) the urbanization-adjusted annual maximum peak discharges and peak discharge quantile estimates at streamgages from 181 watersheds including the 117 study watersheds and 64 additional watersheds in the study region that were originally considered for use in the study but later deemed to be redundant.

The urbanization-adjustment equations, spatial regression equations, and peak discharge quantile estimates developed in this study will be made available in the web application StreamStats, which provides automated regression-equation solutions for user-selected stream locations. Figures and tables comparing the observed and urbanization-adjusted annual maximum peak discharge records by streamgage are provided at for download.

Suggested Citation

Over, T.M., Saito, R.J., Veilleux, A.G., O’Shea, P.S., Sharpe, J.B., Soong, D.T., and Ishii, A.L., 2021, Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois (ver. 3.0, June 2021): U.S. Geological Survey Scientific Investigations Report 2016–5050, 50 p. with appendix,

ISSN: 2328-0328 (online)

Study Area

Table of Contents

  • Acknowledgments
  • Abstract
  • Introduction
  • Data Development
  • Regional Temporal Regression Analysis and Adjustment
  • Regional Spatial Regression Analyses
  • Applications of Regression Equations
  • Summary
  • References Cited
  • Appendix 1. Northeastern Illinois Regional Skew Analysis
  • References Cited
Publication type Report
Publication Subtype USGS Numbered Series
Title Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois
Series title Scientific Investigations Report
Series number 2016-5050
DOI 10.3133/sir20165050
Edition Version 1.0: June 2016; Version 2.0: November 2017; Version 3.0: June 2021
Year Published 2016
Language English
Publisher U.S. Geological Survey
Publisher location Reston, VA
Contributing office(s) Illinois Water Science Center
Description Report: x, 51 p.; Tables; Companion Files; Version History
Country United States
State Illinois
Online Only (Y/N) Y
Additional Online Files (Y/N) Y
Google Analytic Metrics Metrics page
Additional publication details