  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.
