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

This study investigates the applicability and accuracy of Copula models constructed using the Principle of Maximum Entropy (POME) for simulating flood peak discharge and flood volume, and compares their performance with that of traditional Copula models to assess the potential of POME in developing objective probability models under multiple statistical constraints. Using annual maximum daily mean discharge (Q) and the corresponding maximum three-day flood volume (W) data from two hydrological stations as case studies, 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 comprehensively assessed using the Akaike Information Criterion (AIC), Root Mean Square Error (RMSE), and relative errors of statistical parameters. Results indicate that for marginal distribution fitting, the MaxEnt distribution exhibits superior performance in terms of RMSE, particularly in the upper tail region of the cumulative distribution function. For Copula fitting, the Gaussian Copula demonstrates the best performance in joint probability distribution modeling, whereas the MaxEnt Copula shows relatively weaker performance. Among the four schemes, M4 achieves the optimal simulation results for statistical parameters and linear correlation coefficients. By incorporating multiple statistical constraints, the POME offers an objective modeling framework for both marginal and joint distributions without the need for preassumed distributional forms, making it particularly suitable for capturing the complexity and uncertainty of hydrological events and enabling flexible stochastic modeling of interdependent hydrological variables.