Copula-Based Bayesian Inference Approaches for Uncertainty Quantification for Hydrological Simulation

In this study, an advanced copula-based Bayesian inference framework is proposed to characterize probabilistic features in hydrological simulations. Specifically, a Copula–Metropolis–Hastings (CopMH) algorithm is developed through integrating copula functions into the conventional Metropolis–Hastings (MH) algorithm within an interdependence-sampling framework. In CopMH, the interdependence structure among model parameters is quantified using copula functions, which are subsequently employed to generate proposal candidates. The proposed approach is then applied to uncertainty analysis in hydrological simulations of the Ruihe River watershed in Northwest China. The results indicate that, compared with the traditional MH, incorporating copula-based proposal distributions significantly improves convergence efficiency and simulation accuracy, as inter-parameter dependence is more effectively captured. All algorithms are independently repeated 15 times, and CopMH exhibits more robust and stable performance than MH. Furthermore, the intercorrelation analysis of hydrological model parameters reveals that interactive effects among parameters are ubiquitous. These findings highlight that consideration of the interrelationship among the parameters in hydrologic models is meaningful and necessary for uncertainty quantification of hydrological simulation. This study demonstrates the strong potential of the proposed CopMH approach for effectively quantifying and reducing parameter uncertainty in hydrological simulations.