Towards reliable uncertainty quantification for hydrologic predictions, Part I: Development of a particle copula Metropolis Hastings method

Abstract

In this study, a particle copula Metropolis-Hastings (PCMH) approach was developed for reliable uncertainty quantification of hydrological predictions. The proposed PCMH approach employs a mixed particle evolution scheme, which integrates the Gaussian perturbation and copula-based dependent sampling methods. The Metropolis ratio is then employed to determine the acceptance of the candidate samples. The applicability of PCMH is elaborated for a long-term data assimilation case at the River Ouse in UK. Multiple hydrological models and different uncertainty settings in inputs, outputs and sample sizes are tested by the PCMH, particle filter (PF) and particle Markov chain Monte Carlo (PMCMC) approaches. The results indicate that the developed PCMH approach is able to generate more reliable results with less accuracy fluctuation than PF and PMCMC for both deterministic and probabilistic predictions from all the hydrological models. The mean values and the associated variation intervals of NSE over the total 270 runs for PCMH, PF and PMCMC are 0.752 (variation interval of [0.534, 0.866]), 0.661 (variation interval of [0.080, 0.879]), and 0.655 (variation interval of [0.247, 0.824]), respectively. For the probabilistic predictions evaluated by CRPS, the mean values and fluctuation ranges from PCMH, PF and PMCMC are respectively 15.215 ([8.624,31.549]), 18.758 ([8.595, 43.536]), 19.308 ([10.848, 37.799]). These results suggested that the proposed PCMH method would be more robust than PF and PMCMC in generating reliable hydrologic predictions and be less influenced by the hydrologic model structures, uncertainty scenarios, and its inherent randomness. Moreover, the PCMH method can also show better robustness than the copula-based particle filter method since the particle evolution scheme of PCMH would balance extreme samples from copula sampling procedure by mixing samples from Gaussian perturbation and remove unacceptable candidates through the Metropolis acceptance criterion.