Parameter Uncertainty and Sensitivity Evaluation of Copula-Based Multivariate Hydroclimatic Risk Assessment

Abstract

Extensive uncertainties exist in hydroclimatic risk analysis. Especially in multivariate hydrologic risk inferences, uncertainties in individual hydroclimatic extremes such as floods and their dependence structure may lead to bias and uncertainty in future hydrologic risk predictions. In this study, a parameter uncertainty and sensitivity evaluation (PUSE) framework is proposed to quantify parameter uncertainties and then reveal their contributions to the multivariate hydroclimatic risk predictions. The predictive risks are finally generated by “integrating†the values over the posterior distributions of the parameters. The proposed approach was applied for bivariate risk analysis of compound floods at the Xiangxi River to characterize the concurrence probabilities of flood peaks and volumes. The results demonstrate that the proposed approach can quantify uncertainties in a copula-based multivariate risk analysis and characterize effects and contributions of parameters in marginal and dependence structures on the multivariate hydroclimatic risk predictions. In terms of the bivariate risk for flood peak and volume at the Xiangxi River, uncertainties in model parameters would lead to noticeable uncertainties even for moderate floods. The performances of the copula model for flood peak-volume at Xiangxi River are mainly affected by the uncertainties in location parameters of the two individual flood variables. Also, parameter uncertainty in the dependence structure (i.e., copula) would also poses explicit impacts on performance of the copula-based risk analyses model. These uncertainties would result into higher bivariate predictive risks than the values obtained by “optimal/deterministic†predictions. This indicates that uncertain- ties are required to be considered to provide reliable multivariate hydroclimatic risk predictions.

Keywords: Hydroclimatic risk, Copula, MCMC, factorial analysis, global sensitivity analysis