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

Aijun Guo,Jianxia Chang,Zhihui Guo,Qiang Huang,Yimin Wang

doi:10.3390/e19110609

Aijun Guo, Jianxia Chang + Show 3 more

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https://doi.org/10.3390/e19110609

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Abstract

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.

Highlights

Extreme hydrological events have had disastrous effects on society and the environment in recent years
Previous studies have paid considerably less attention to the impact of uncertainty on hydrological risk analysis [34,35,36]. Another contribution of this paper is to present a framework aiming to reveal the impact of marginal distribution selection uncertainty and sampling uncertainty on hydrological risk analysis
The present study primarily aims to advance the coupled maximum entropy principle (MEP)-copula model for study primarily aims to advance the coupled MEP-copula model for bivariateConsequently, risk analysis, the andpresent to reveal the impact of the marginal distribution selection uncertainty and bivariate risk analysis, and to reveal the impact of the marginal distribution selection uncertainty and sampling uncertainty on hydrological risk analysis

Summary

Introduction

Extreme hydrological events (e.g., floods, rainstorms, droughts) have had disastrous effects on society and the environment in recent years. Floods, as one of the most frequent and costly natural disasters, have posed a serious threat to the human life and economic development [1,2,3]. A report issued by UNISDR (2015) highlights the fact that, between 1995 and 2015, floods affected. Flood risk analysis can provide extremely valuable information by estimating the occurrence of floods for flood control and disaster mitigation, hydraulic structure design, reservoir management, and so on [6,7]. It is widely known that, in rain-dominant watersheds, river floods are commonly triggered by extreme precipitation events [8,9].

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