Space-time modelling of precipitation by using a hidden Markov model and censored Gaussian distributions

A new hidden Markov model for the space-time evolution of daily rainfall is developed which models precipitation within hidden regional weather types by censored power-transformed Gaussian distributions. The latter provide flexible and interpretable multivariate models for the mixed discrete-continuous variables that describe both precipitation, when it occurs, and no precipitation. Parameter estimation is performed by using a Monte Carlo EM algorithm whose use and performance are evaluated by simulation studies. The model is fitted to rainfall data from a small network of stations in New Zealand encompassing a diverse range of orographic effects. The results that are obtained show that the marginal distributions and spatial structure of the data are well described by the fitted model which provides a better description of the spatial structure of precipitation than a standard hidden Markov model that is commonly used in the literature. However, the fitted model, like the standard hidden Markov model, cannot fully reproduce the local dynamics and underestimates the lag 1 auto-correlations.