Imprecise probabilistic estimation of design floods with epistemic uncertainties
Water Resources Research
American Geophysical Union (AGU)
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.
This study was supported by the National Natural Science Foundation of China (Grant No. 51320105010 and 51279021). The first author gratefully acknowledges the financial support provided by the China Scholarship Council. The authors are deeply indebted to editors, Dr Francesco Serinaldi and another anonymous reviewer for their valuable time and constructive suggestions that greatly improved the quality of this paper. The data of Three Gorges were obtained from the China Three Gorges Corporation. The data of Biliu were obtained from the Biliu reservoir administration. The data of Harbin were obtained from the Harbin hydrology bureau. These data are available as in Supporting Information Data Set which includes Data Set S1, Data Set S2 and Data Set S3. Data Set S1 corresponds to Three Gorges; Data Set S2 corresponds to Biliu; Data Set S3 corresponds to Harbin.
This is the author accepted manuscript. The final version is available from the publisher via the DOI in this record.