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<p>This study investigates the applicability of Maximum Entropy (MaxEnt) Copula models constructed by the Principle of Maximum Entropy (POME) for simulating flood peak discharge and flood volume, and compares their performance with traditional Copula models. Using annual maximum daily mean discharge (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\:Q\)</EquationSource> </InlineEquation>) and corresponding maximum three-day flood volume (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\:W\)</EquationSource> </InlineEquation>) data from two hydrological stations, four modeling schemes were designed: M1 (traditional marginals + traditional Copula), M2 (MaxEnt marginals + MaxEnt Copula), M3 (traditional marginals + MaxEnt Copula), and M4 (MaxEnt marginals + traditional Copula). Model performance was evaluated by Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and relative errors of key statistical characteristics. This is the first systematic comparison of MaxEnt Copula and traditional Copula combined schemes. Results show that the MaxEnt distribution outperforms traditional ones in marginal fitting by RMSE, especially in the upper tail of the cumulative distribution function (CDF). For dependence modeling, the Gaussian Copula best represents the joint distribution, while the MaxEnt Copula performs relatively weakly. Scheme M4 provides the most accurate estimates for statistical characteristics and linear correlation. POME offers an objective framework without predefined distribution forms, providing a flexible approach for stochastic modeling of interdependent hydrological variables.</p>

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A Comparative Study of Maximum Entropy Based and Traditional Copula Models for Joint Simulation of Bivariate Flood

  • 期刊论文

  • 发表日期：

    2026年5月28日

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  • Kuang Wang,
  • Fan Li

摘要

This study investigates the applicability of Maximum Entropy (MaxEnt) Copula models constructed by the Principle of Maximum Entropy (POME) for simulating flood peak discharge and flood volume, and compares their performance with traditional Copula models. Using annual maximum daily mean discharge ( \(\:Q\) ) and corresponding maximum three-day flood volume ( \(\:W\) ) data from two hydrological stations, four modeling schemes were designed: M1 (traditional marginals + traditional Copula), M2 (MaxEnt marginals + MaxEnt Copula), M3 (traditional marginals + MaxEnt Copula), and M4 (MaxEnt marginals + traditional Copula). Model performance was evaluated by Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and relative errors of key statistical characteristics. This is the first systematic comparison of MaxEnt Copula and traditional Copula combined schemes. Results show that the MaxEnt distribution outperforms traditional ones in marginal fitting by RMSE, especially in the upper tail of the cumulative distribution function (CDF). For dependence modeling, the Gaussian Copula best represents the joint distribution, while the MaxEnt Copula performs relatively weakly. Scheme M4 provides the most accurate estimates for statistical characteristics and linear correlation. POME offers an objective framework without predefined distribution forms, providing a flexible approach for stochastic modeling of interdependent hydrological variables.