Space Time Modelling of Precipitation Using Hidden Markov Models

In this paper, we propose a new hidden Markov model (HMM) for the space-time evolution of daily rainfall. The hidden Markov chain represents the different meteorological regimes (“weather types”) and it is assumed that this variable explains the dynamics of the precipitation. The spatial structure within hidden weather types is modelled by censored power-transformed Gaussian distributions. It provides flexible and interpretable multivariate models for the mixed discretecontinuous variables that describe both precipitation, when it occurs, and no precipitation. The model is fitted to rainfall data from a small network of stations in New Zealand encompassing a diverse range of orographic effects and it is shown that the proposed model provides a better description of the spatial structure of precipitation than a more conventional HMM commonly used in the literature.