Computationally efficient spatial modeling of annual maximum 24-h precipitation on a fine grid

A computationally efficient statistical method is proposed to obtain distributional properties of annual maximum 24-h precipitation on a 1 by 1km regular grid over Iceland. A covariate based on a local meteorological model that captures information on the physical processes of precipitation is constructed, providing an additional spatial information on maximum precipitation. A latent Gaussian model is built, which takes into account observed maximum precipitation, the covariate based on the local meteorological model, and spatial variations. The observations are assumed to follow the generalized extreme value distribution, where spatial models based on approximate solutions to stochastic partial differential equations are implemented for the location, scale, and shape parameters of the likelihood. An efficient Markov chain Monte Carlo (MCMC) sampler that exploits the sparse matrices induced by the stochastic partial differential equation modeling is implemented, yielding continuous spatial predictions for spatially varying model parameters and quantiles.