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Improvements in computing power, data gathering and our understanding of atmospheric dynamics have lead to the availability of spatially and temporally extensive sets of data on the atmospheric processes that a ect precipitation. However, these two processes (atmospheric circulation and precipitation) operate on very di erent spatial scales. Recently, considerable e ort has been devoted to developing \downscaling" models which condition local precipitation on broad-scale atmospheric circulation. In this article, we develop a stochastic model for relating precipitation occurrences at multiple rain gauge stations to atmospheric circulation patterns.The proposed model is an example of a nonhomogeneous hidden Markov model, and generalizes existing downscaling models in the literature. The model assumes that atmospheric circulation can be classi ed into a small number of (unobserved) discrete patterns (called \weather states"). The weather states are assumed to follow a Markov chain in which the transition probabilities depend on observable characteristics of the atmosphere (e.g. mean sea-level pressure). Precipitation is assumed to be conditionally temporally, but not spatially, independent g i v en the weather state. An autologistic model for multivariate binary data is used to model rainfall occurrences and capture local spatial dependencies. However, the usual approach to estimation in hidden Markov models | exact likelihood using the EM algorithm | is computationally intractable if there are large numbers of rain gauge stations. Therefore, two alternative estimation procedures are developed which c o m bine (an approximation to) the usual E-step with a modi ed M-step based on either maximum pseudolikelihood or Monte Carlo maximum likelihood. Both techniques yield models which t the data well, although the pseudolikelihood is seen to be ill-behaved in certain situations. This approach i s u s e d t o m o d e l a 1 5 y ear sequence of winter data from 30 rain stations in southwestern Australia. The rst 10 years of data are used for model development and the remaining 5 years are used for model evaluation. The tted model is able to accurately reproduce the observed rainfall statistics in the reserved 1 data, even in the face of a small non-stationary shift in atmospheric circulation (and, consequently, rainfall) between the two periods. The tted model also provides some useful insights into the processes driving rainfall in this region. We discuss the role that models such as this might play in assessing the impact of climate change.

Geostatistical approaches to modeling spatio-temporal data rely on parametric covariance models and rather stringent assumptions, such as stationarity, separability and full symmetry. This paper reviews recent advances in the literature on space-time covariance functions in light of the aforementioned notions, which are illustrated using wind data from Ireland. Experiments with time-forward kriging predictors suggest that the use of more complex and more realistic covariance models results in improved predictive performance.

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