Quantifying the Uncertainty of Design Floods under Nonstationary Conditions

Abstract

Estimating design quantiles for extreme floods in river basins under nonstationary conditions is an emerging field. Nonstationarities could arise from a variety of human and natural factors such as urbanization and climate change. Concepts of return period, design quantile (return level), and risk have already been developed for situations in which increasing or decreasing trends and abrupt shifts in extreme events are present. Because of limited data records, sampling variability, model errors, and the errors in projections into the future, significant uncertainties in the estimates of design floods of future projects will arise. To address the issue of uncertainty resulting from limited sample size of the observations, three methods have been developed for computing confidence intervals for the design quantile corresponding to a desired return period under a nonstationary framework, including (a) delta, (b) bootstrap, and (c) profile likelihood methods. These methods have been developed assuming a generalized extreme value distribution with nonstationary parameters. The applicability and comparison of the proposed methods for determining the confidence interval of quantiles have been demonstrated by using the annual flood maxima of the Assunpink Creek in New Jersey. The delta method, with numerically derived local derivatives, and the approximate bootstrap can be computationally efficient. The profile likelihood method, which is known to be more accurate, is quite burdensome computationally but provides more realistic asymmetric confidence intervals.