Quantifying the uncertainty of return period and risk in hydrologic design

Concepts of risk and uncertainty are commonly used for designing and evaluating flood-related hydraulic structures. A general framework for estimating the uncertainty of the return period and risk is presented based on first-order analysis of uncertainty for determining the variance of the return period and risk of failure and the methods of moments, probability weighted moments, and maximum likelihood. The general method is illustrated using the exponential and Gumbel distributions. The derived variance of the return period is a function of the sample size N and the nonexceedance probability q, while that of the risk is function of N, q, and design life n. Simulation experiments were performed to analyze the behavior of the variance of risk for various values of N, q, and n. They showed that the derived variances of the risk can be applicable for a wide range of conditions, particularly for sample sizes bigger than 50 and design lives smaller or equal to 50. An example is included to illustrate the applicability of the proposed concepts and equations.