Uncertainty quantification and propagation in bivariate design flood estimation using a Bayesian information-theoretic approach

Abstract

Copula-based statistical model has been extensively used to characterize the joint probability behaviors of extreme hydro-climatic design events, such as bivariate design floods. However, parameter uncertainty, not desirably but inevitably, accompanies the copula-based design flood estimation (CDFE) model which makes the inference results of design flood ambiguous. In this paper, we develop a Bayesian information-theoretic (BIT) approach to disclose design flood uncertainty arising from parameter uncertainty in CDFE model and furthermore examine how the parameter uncertainty is propagated to design flood estimation. Two catchments located in the Yellow River Basin, China, are selected as study regions. The research we have done indicates that design flood uncertainty is considerably large under parameter uncertainty. Worse still, the uncertainty in design flood increases along with the return period, thus making the design flood inference more ambiguous. Specifically, shape and scale parameters of marginal distributions have the largest contribution to the design flood uncertainty, followed by copula parameter, finally the location parameter of marginal distribution. Furthermore, the interaction between some parameters has dominant effect on design flood uncertainty compared with the individual effect of these parameters. These findings will enable better understanding the design flood uncertainty under parameter uncertainty. Moreover, the proposed BIT approach also offers a promising technical reference for design estimation of other types of extreme hydrological events, not limited to the design flood.