Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois

Abstract

For more information on the USGS-the Federal source for science about the Earth, its natural and living resources, natural hazards, and the environment-visit https://www.usgs.gov or call 1-888-ASK-USGS.For an overview of USGS information products, including maps, imagery, and publications, visit https://store.usgs.gov/.Any use of trade, firm, or product names is for descriptive purposes only and does not imply endorsement by the U.S. Government.Although this information product, for the most part, is in the public domain, it also may contain copyrighted materials as noted in the text. Permission to reproduce copyrighted items must be secured from the copyright owner.Suggested citation: Over, T.M., Saito, R.J., Veilleux, A.G., Sharpe, J.B., Soong, D.T., and Ishii, A.L., 2017, Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois (ver. 2.0, November 2017): U.S. Geological Survey Scientific Investigations Report 2016-5050, 50 p. with appendix, https://doi.org/10.3133/ sir20165050. Also published as: Over, T.M., Saito, R.J., Veilleux, A.G., Sharpe, J.B., Soong, D.T., and Ishii, A.L., 2017, Estimation of peak discharge quantiles for selected annual exceedance probabilities in northeastern Illinois: Illinois Center for Transportation Report, FHWA-ICT-16-013, 318 p. with appendix. AbstractThis 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 squaresquantile 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 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 ...

Assessment and significance of the frequency domain for trends in annual peak streamflow

“…where the coefficients, β 0 and β 1 , are determined from the set of lines for all paired samples that can define Q for the distribution of y (Koenker, 2005). Like ordinary linear regression (Serago & Vogel, 2018), quantile regression can be used for causal analysis of nonstationarity by using appropriate covariates (e.g., climate indices, measures of specific flood-generating processes, urban land cover, or binary "intervention" variables, e.g., to represent reservoir construction) (Over et al, 2017;Sankarasubramanian & Lall, 2003), but attribution of trends is not required to estimate flood magnitudes and frequencies that are conditioned on time. At sites where different processes generate floods with distinct frequency domains (Waylen & Woo, 1982;Webb & Betancourt, 1992;Whitfield, 2012), quantile trends can separate the effects of different processes and may indicate which of those processes are changing.…”

“…Quantile regression (Koenker, 2005) provides a unified method for analyzing conditional trends that offers three advantages for flood-frequency analysis: the frequency distributions of peaks do not have to be specified; the record of peaks does not have to be truncated to create a quasi-stationary period for estimating their frequency and magnitudes; and the regression equation can be formulated in terms of time to provide a conditional estimate of a specified quantile for the current year. Quantile regression has been applied to flood frequency analysis and forecasting (Acharya et al, 2020;Ouali et al, 2016;Over et al, 2017) and low-flow trend analysis (Kormos et al, 2016). It is not commonly used to identify flood trends (England Jr. et al, 2018) much less to quantify changes in the variance of at-site flood distributions.…”

Operational Bayesian GLS Regression for Regional Hydrologic Analyses

“…The decision was made based on comparative studies in Australia (Haddad et al, ; Haddad & Rahman, ; Haddad, Rahman, & Ling, ). In the United States, the U.S. Geological Survey (USGS) has recently conducted regional skew studies in several states employing the Bayesian GLS framework suggested in Reis et al () and further developed in Gruber et al () (Eash et al, ; Feaster et al, ; Gotvald et al, ; Gotvald et al, ; Lamontagne et al, ; Mastin et al, ; Olson, ; Over et al, ; Parrett et al, ; Paretti et al, ; Southard & Veilleux, ; Weaver et al, ; Wagner et al, ; Wood et al, ; Zarriello, ).…”

“…The decision was made based on comparative studies in Australia Haddad, Rahman, & Ling, 2015). In the United States, the U.S. Geological Survey (USGS) has recently conducted regional skew studies in several states employing the Bayesian GLS framework suggested in and further developed in Gruber et al ( 2007) (Eash et al, 2013;Feaster et al, 2009;Gotvald et al, 2009;Gotvald et al, 2012;Lamontagne et al, 2012;Mastin et al, 2016;Olson, 2014;Over et al, 2016;Parrett et al, 2011;Paretti et al, 2014;Southard & Veilleux, 2014;Weaver et al, 2009;Wagner et al, 2016;Wood et al, 2016;Zarriello, 2017). This paper starts with the Bayesian GLS model error variance estimator in and develops a complete analysis framework including a range of new regression diagnostic statistics for both B-WLS and B-GLS analyses.…”