Development of a copula-based particle filter (CopPF) approach for hydrologic data assimilation under consideration of parameter interdependence

In this study, a copula-based particle filter (CopPF) approach was developed for sequential hydrological data assimilation by considering parameter correlation structures. In CopPF, multivariate copulas are proposed to reflect parameter interdependence before the resampling procedure with new particles then being sampled from the obtained copulas. Such a process can overcome both particle degeneration and sample impoverishment. The applicability of CopPF is illustrated with three case studies using a two-parameter simplified model and two conceptual hydrologic models. The results for the simplified model indicate that model parameters are highly correlated in the data assimilation process, suggesting a demand for full description of their dependence structure. Synthetic experiments on hydrologic data assimilation indicate that CopPF can rejuvenate particle evolution in large spaces and thus achieve good performances with low sample size scenarios. The applicability of CopPF is further illustrated through two real-case studies. It is shown that, compared with traditional particle filter (PF) and particle Markov chain Monte Carlo (PMCMC) approaches, the proposed method can provide more accurate results for both deterministic and probabilistic prediction with a sample size of 100. Furthermore, the sample size would not significantly influence the performance of CopPF. Also, the copula resampling approach dominates parameter evolution in CopPF, with more than 50% of particles sampled by copulas in most sample size scenarios.