Fast spatial simulation of extreme high-resolution radar precipitation data using INLA

We develop a methodology for modelling and simulating high-dimensional spatial precipitation extremes, using a combination of the spatial conditional extremes model, latent Gaussian models and integrated nested Laplace approximations (INLA). The spatial conditional extremes model requires data with Laplace marginal distributions, but precipitation distributions contain point masses at zero that complicate necessary standardisation procedures. We propose to model conditional extremes of nonzero precipitation only, while separately modelling precipitation occurrences. The two models are then combined to create a complete model for extreme precipitation. Nonzero precipitation marginals are modelled using a combination of latent Gaussian models with gamma and generalised Pareto likelihoods. Four different models for precipitation occurrence are investigated. New empirical diagnostics and parametric models are developed for describing components of the spatial conditional extremes model. We apply our framework to simulate spatial precipitation extremes over a water catchment in Central Norway, using high-density radar data. Inference on a 6000-dimensional data set is performed within hours, and the simulated data capture the main trends of the observed data well.