A Framework of Dependence Modeling and Evaluation System for Compound Flood Events

Abstract

The coincidence and superposition of flood processes from different rivers and regions tend to form compound flood events, determined by spatial relationship between diverse flood processes that cannot be accurately depicted and evaluated by existing dependence analysis methods. A framework, integrating multi‐dimensional vine copula model and dependence evaluation system, was developed with a testing‐oriented application to explore underlying dependence between two kinds of extreme runoff series (peak discharge and flood volume) extracted from the identified compound flood events in the upper reaches of the Yangtze River. Multi‐dimensional regular vine (R‐vine) copula models were established to depict the complex and diverse dependence, and corresponding vine structure was specified by the vine structure array that can reflect the sequence of tributaries flowing into the main stream and the spatial locations of different hydrometric stations. Dependence magnitude and association status were calculated and compared according to the optimal R‐vine copula models and information theory. Comparison with existing methods demonstrated that dependence evaluation system could reflect nonlinear and local dependence characteristics and eliminate the effect of extreme runoff series from other hydrometric station on the dependence. The association status between different extreme runoff series of the upper Yangtze River and its tributaries were diverse in view of the impact of tributary flood inflow. The proposed framework can be regarded as an effective way for dependence modeling and evaluation of compound floods, thus providing a scientific reference for the risk analysis of water resources systems.

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“…Vine copulas provide a generic approach to construct multivariate joint distributions based on pair‐copula constructions, with the basic idea of decomposing the n ‐dimensional multivariate density function into $$$ n\left(n-1\right)/2 $$$ unconditional bivariate copulas and conditional bivariate copulas (Wang & Shen, 2023a). Since the introduction of R‐vine to arrange $$$ n\left(n-1\right)/2 $$$ pair‐copulas into $$$ n-1 $$$ nested trees $$$ {T}_i $$$ ($$$ i\in \left[1,n-1\right] $$$) with $$$ \left(n+2\right)\left(n-1\right)/2 $$$ nodes joined by $$$ n\left(n-1\right)/2 $$$ edges (Bedford & Cooke, 2002), the optimal pair‐copula construction can be determined according to certain evaluation criteria (e.g., Kendall's tau).…”

“…Vine copulas provide a generic approach to construct multivariate joint distributions based on pair-copula constructions, with the basic idea of decomposing the n-dimensional multivariate density function into n nÀ 1 ð Þ=2 unconditional bivariate copulas and conditional bivariate copulas (Wang & Shen, 2023a). Since the introduction of R-vine (Bedford & Cooke, 2002), the optimal pair-copula construction can be determined according to certain evaluation criteria (e.g., Kendall's tau).…”