Spatio-temporal generation of precipitation using a Hidden Markov Model, extended extreme distributions and conditional Gaussian fields

Current weather generators struggle to capture large-scale spatio-temporal variability in rainfall occurrence and intensity. To address this challenge, this study develops a spatio-temporal weather generator for daily precipitation across multiple stations by extending the classical multivariate hidden Markov model to a spatial framework. Both occurrence and intensity processes are driven by spatio-temporal latent fields with distinct covariance structures, allowing for different dynamical behaviours. The rainfall intensity process is simulated conditionally on the occurrence process, ensuring continuity between dry and wet conditions in both time and space. Model inference relies on a novel hybrid Expectation-Maximisation algorithm designed to address the intractability of the complete likelihood, while achieving substantial computational gains compared to compositelikelihood EM approaches. The generator is applied to 51 years of daily precipitation data from 37 weather stations across France. Four interpretable hidden states are identified, whose most probable temporal sequence is consistent with known meteorological patterns. The generator is assessed through several model-agnostic metrics, targeting marginal, pairwise, spatial, and spatiotemporal properties. Results demonstrate that the proposed generator accurately reproduces rainfall statistics across a wide range of spatial and temporal scales, including droughts and extreme precipitation events, validating its relevance for climate impact assessment.