Imprecise probabilistic estimation of design floods with epistemic uncertainties

An imprecise probabilistic framework for design flood estimation is proposed on the basis of the Dempster-Shafer theory to handle different epistemic uncertainties from data, probability distribution functions, and probability distribution parameters. These uncertainties are incorporated in cost-benefit analysis to generate the lower and upper bounds of the total cost for flood control, thus presenting improved information for decision making on design floods. Within the total cost bounds, a new robustness criterion is proposed to select a design flood that can tolerate higher levels of uncertainty. A variance decomposition approach is used to quantify individual and interactive impacts of the uncertainty sources on total cost. Results from three case studies, with 127, 104, and 54 year flood data sets, respectively, show that the imprecise probabilistic approach effectively combines aleatory and epistemic uncertainties from the various sources and provides upper and lower bounds of the total cost. Between the total cost and the robustness of design floods, a clear trade-off which is beyond the information that can be provided by the conventional minimum cost criterion is identified. The interactions among data, distributions, and parameters have a much higher contribution than parameters to the estimate of the total cost. It is found that the contributions of the various uncertainty sources and their interactions vary with different flood magnitude, but remain roughly the same with different return periods. This study demonstrates that the proposed methodology can effectively incorporate epistemic uncertainties in cost-benefit analysis of design floods.