Entropy–Copula in Hydrology and Climatology

Amir AghaKouchak Center for Hydrometeorology and Remote Sensing, Department of Civil and Environmental Engineering, University of California, Irvine, Irvine, California

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Abstract

The entropy theory has been widely applied in hydrology for probability inference based on incomplete information and the principle of maximum entropy. Meanwhile, copulas have been extensively used for multivariate analysis and modeling the dependence structure between hydrologic and climatic variables. The underlying assumption of the principle of maximum entropy is that the entropy variables are mutually independent from each other. The principle of maximum entropy can be combined with the copula concept for describing the probability distribution function of multiple dependent variables and their dependence structure. Recently, efforts have been made to integrate the entropy and copula concepts (hereafter, entropy–copula) in various forms to take advantage of the strengths of both methods. Combining the two concepts provides new insight into the probability inference; however, limited studies have utilized the entropy–copula methods in hydrology and climatology. In this paper, the currently available entropy–copula models are reviewed and categorized into three main groups based on their model structures. Then, a simple numerical example is used to illustrate the formulation and implementation of each type of the entropy–copula model. The potential applications of entropy–copula models in hydrology and climatology are discussed. Finally, an example application to flood frequency analysis is presented.

Denotes Open Access content.

Corresponding author address: Amir AghaKouchak, E/4130 Engineering Gateway, University of California, Irvine, Irvine, CA 92617. E-mail: amir.a@uci.edu

Abstract

The entropy theory has been widely applied in hydrology for probability inference based on incomplete information and the principle of maximum entropy. Meanwhile, copulas have been extensively used for multivariate analysis and modeling the dependence structure between hydrologic and climatic variables. The underlying assumption of the principle of maximum entropy is that the entropy variables are mutually independent from each other. The principle of maximum entropy can be combined with the copula concept for describing the probability distribution function of multiple dependent variables and their dependence structure. Recently, efforts have been made to integrate the entropy and copula concepts (hereafter, entropy–copula) in various forms to take advantage of the strengths of both methods. Combining the two concepts provides new insight into the probability inference; however, limited studies have utilized the entropy–copula methods in hydrology and climatology. In this paper, the currently available entropy–copula models are reviewed and categorized into three main groups based on their model structures. Then, a simple numerical example is used to illustrate the formulation and implementation of each type of the entropy–copula model. The potential applications of entropy–copula models in hydrology and climatology are discussed. Finally, an example application to flood frequency analysis is presented.

Denotes Open Access content.

Corresponding author address: Amir AghaKouchak, E/4130 Engineering Gateway, University of California, Irvine, Irvine, CA 92617. E-mail: amir.a@uci.edu
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