A Dynamic Spatio-temporal Precipitation Model

A spatio-temporal model for precipitation is presented. Modeling the continuous and the discrete part of rainfall together, it is assumed that precipitation has a censored and powertransformed normal distribution. The mean of this distribution is linked to covariates. Spatio-temporal correlations are accounted for by a latent Gaussian variable that follows a Markovian temporal evolution combined with spatially correlated innovations. We propose to specify the temporal evolution using a vector autoregression that is motivated by an autoregressive convolution approach. Exploiting in a natural way the unidirectional flow of time, the model allows for non-separable covariance structures. Furthermore, the Markovian structure offers computational benefits. The model is space as well as time resolution consistent. We apply the model to three-hourly Swiss rainfall data, collected at 26 stations. As a side result, we introduce a new tool, the primary posterior predictive density, for assessing the fit of Bayesian models.

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