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

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 a crucial property for assessing the consequences of an extreme precipitation event, yet most stochastic weather generators do not attempt to capture this property. We model extreme precipitation using a latent Gaussian version of the spatial conditional extremes model. This requires data with Laplace marginal distributions, but precipitation distributions contain point masses at zero that complicate necessary standardisation procedures. We therefore employ two separate models, one for describing extremes of nonzero precipitation and one for describing the probability of precipitation occurrence. Extreme precipitation is simulated by combining simulations from the two models. Nonzero precipitation marginals are modelled using latent Gaussian models with gamma and generalised Pareto likelihoods, and four different precipitation occurrence models are investigated. Fast inference is achieved using integrated nested Laplace approximations (INLA). We model and simulate spatial precipitation extremes in Central Norway, using high-density radar data. Inference on a 6000-dimensional data set is achieved within hours, and the simulations capture the main trends of the observed precipitation well.