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

Abstract: Aiming to deliver improved precipitation simulations for hydrological impact assessment studies, we develop a methodology for modelling and simulating high-dimensional spatial precipitation extremes, focusing on both their marginal distributions and tail dependence structures. Tail dependence is crucial for assessing the consequences of extreme precipitation events, yet most stochastic weather generators do not attempt to capture this property. The spatial distribution of precipitation occurrences is modelled with four competing models, while the spatial distribution of nonzero extreme precipitation intensities are modelled with a latent Gaussian version of the spatial conditional extremes model. Nonzero precipitation marginal distributions are modelled using latent Gaussian models with gamma and generalised Pareto likelihoods. Fast inference is achieved using integrated nested Laplace approximations (INLA). We model and simulate spatial precipitation extremes in Central Norway, using 13 years of hourly radar data with a spatial resolution of $1 \times 1$~km$^2$, over an area of size $6461$~km$^2$, to describe the behaviour of extreme precipitation over a small drainage area. Inference on this high-dimensional data set is achieved within hours, and the simulations capture the main trends of the observed precipitation well.