Abstract
Statistical techniques have been developed for assessing structures to confront extreme events such as floods. Among them are probability distribution functions (PDFs). For example, the waiting time of the first flood exceeding the design flood is geometric, while the number of floods exceeding the design flood in years is binomial. The expected waiting time (EWT) and hydrologic risk of structures are commonly used metrics developed assuming stationarity and independence. And newer techniques include PDFs and project evaluation metrics applicable for nonstationary conditions. This article focuses on first arrival time of th floods exceeding the design flood and associated metrics. The likelihood of first occurrence of 1, 2, 3, etc. floods exceeding the design flood becomes important, as uncertainties of hydrologic regimes increase due to climatic and anthropogenic drivers. We use stationary and nonstationary negative binomial distribution and develop EWT and risk for the th event. They generalize the traditional return period and risk that refer to the occurrence of the first event, i.e., . The newer metrics consider the probability of or more events. We tested by simulation the concepts and derived equations and apply them using annual floods of Assunpink Creek. The results show that the return period and risk functions developed can be helpful in assessing flood related projects.
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Acknowledgments
The first author acknowledges the continuous support of the Department of Civil and Environmental Engineering of Colorado State University. This publication has been sponsored by the Sea Level Solutions Center of the Institute of Water and Environment at Florida International University. We are also thankful to the associate editor and the unknown referees for their valuable comments, which improved the final version of the paper.
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Journal of Hydrologic Engineering
Volume 24 • Issue 10 • October 2019
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©2019 American Society of Civil Engineers.
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Received: Mar 15, 2018
Accepted: Mar 7, 2019
Published online: Jul 18, 2019
Published in print: Oct 1, 2019
Discussion open until: Dec 18, 2019
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