A hidden Markov model for modelling long-term persistence in multi-site rainfall time series 1. Model calibration using a Bayesian approach

A Bayesian approach for calibrating a hidden Markov model (HMM) to long-term multi-site rainfall time series is presented. Using a HMM approach for simulating long-term persistence is attractive because it has an explicit mechanism to produce long-term wet and dry periods which are a feature of many long-term hydrological time series. The ability to fully evaluate parameter uncertainty for the multi-site HMM represents an advance in the stochastic modelling of long-term persistence in multi-site hydrological time series. The challenges in applying the Bayesian Markov chain Monte Carlo (MCMC) method known as the Gibbs sampler to infer the posterior distribution of the multi-site HMM parameters are fully outlined. The specification of appropriate prior distributions was found to be crucial for the successful implementation of the Gibbs sampler. It is described how using synthetic data led to the development of an appropriate prior specification. Further synthetic data analysis showed how the benefits of space-for-time substitution for identifying the long-term persistence structure are dependent on the spatial correlation that exists in multi-site data. A methodology for handling missing data is also described. This study highlights the important role of the priors in Bayesian analysis using MCMC methods by illustrating that misleading inferences can result if the priors are inappropriately specified.