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

A new hidden Markov model (HMM) 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 using a Monte Carlo EM algorithm whose use and performance are discussed using 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 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 HMM commonly used in the literature. However the fitted model, like the standard HMM, cannot fully reproduce the local dynamics and underestimates the lag-one autocorrelations.