Aijun Guo

Maximum Entropy-Copula Method for Hydrological Risk Analysis under Uncertainty: A Case Study on the Loess Plateau, China

Copula functions have been extensively used to describe the joint behaviors of extreme hydrological events and to analyze hydrological risk. Advanced marginal distribution inference, for example, the maximum entropy theory, is particularly beneficial for improving the performance of the copulas. The goal of this paper, therefore, is twofold; first, to develop a coupled maximum entropy-copula method for hydrological risk analysis through deriving the bivariate return periods, risk, reliability and bivariate design events; and second, to reveal the impact of marginal distribution selection uncertainty and sampling uncertainty on bivariate design event identification. Particularly, the uncertainties involved in the second goal have not yet received significant consideration. The designed framework for hydrological risk analysis related to flood and extreme precipitation events is exemplarily applied in two catchments of the Loess plateau, China. Results show that (1) distribution derived by the maximum entropy principle outperforms the conventional distributions for the probabilistic modeling of flood and extreme precipitation events; (2) the bivariate return periods, risk, reliability and bivariate design events are able to be derived using the coupled entropy-copula method; (3) uncertainty analysis highlights the fact that appropriate performance of marginal distribution is closely related to bivariate design event identification. Most importantly, sampling uncertainty causes the confidence regions of bivariate design events with return periods of 30 years to be very large, overlapping with the values of flood and extreme precipitation, which have return periods of 10 and 50 years, respectively. The large confidence regions of bivariate design events greatly challenge its application in practical engineering design.

Bivariate frequency analysis of flood and extreme precipitation under changing environment: case study in catchments of the Loess Plateau, China

Floods have changed in a complex manner, triggered by the changing environment (i.e., intensified human activities and global warming). Hence, for better flood control and mitigation in the future, bivariate frequency analysis of flood and extreme precipitation events is of great necessity to be performed within the context of changing environment. Given this, in this paper, the Pettitt test and wavelet coherence transform analysis are used in combination to identify the period with transformed flood-generating mechanism. Subsequently, the primary and secondary return periods of annual maximum flood (AMF) discharge and extreme precipitation (Pr) during the identified period are derived based on the copula. Meanwhile, the conditional probability of occurring different flood discharge magnitudes under various extreme precipitation scenarios are estimated using the joint dependence structure between AMF and Pr. Moreover, Monte Carlo-based algorithm is performed to evaluate the uncertainties of the above copula-based analyses robustly. Two catchments located on the Loess plateau are selected as study regions, which are Weihe River Basin (WRB) and Jinghe River Basin (JRB). Results indicate that: (1) the 1994–2014 and 1981–2014 are identified as periods with transformed flood-generating mechanism in the WRB and JRB, respectively; (2) the primary and secondary return periods for AMF and Pr are examined. Furthermore, chance of occurring different AMF under varying Pr scenarios also be elucidated according to the joint distribution of AMF and Pr. Despite these, one thing to notice is that the associate uncertainties are considerable, thus greatly challenges measures of future flood mitigation. Results of this study offer technical reference for copula-based frequency analysis under changing environment at regional and global scales.