Bayesian calibration and uncertainty analysis of hydrological models: A comparison of adaptive Metropolis and sequential Monte Carlo samplers

Bayesian statistical inference implemented by stochastic algorithms such as Markov chain Monte Carlo (MCMC) provides a flexible probabilistic framework for model calibration that accounts for both model and parameter uncertainties. The effectiveness of such Monte Carlo algorithms depends strongly on the user-specified proposal or sampling distribution. In this article, a sequential Monte Carlo (SMC) approach is used to obtain posterior parameter estimates of a conceptual hydrologic model using data from selected catchments in eastern Australia. The results are evaluated against the popular adaptive Metropolis MCMC sampling approach. Both methods display robustness and convergence, but the SMC displays greater efficiency in exploring the parameter space in catchments where the optimal solutions lie in the tails of the prescribed prior distribution. The SMC method is also able to identify a different set of parameters with an overall improvement in likelihood and Nash-Sutcliffe efficiency for selected catchments. As a result of its population-based sampling mechanism, the SMC method is shown to offer improved efficiency in identifying parameter optimization and to provide sampling robustness, in particular in identifying global posterior modes.