Spatial Bayesian hierarchical modeling of precipitation extremes over a large domain

We propose a Bayesian hierarchical model for spatial extremes on a large domain. In the data layer a Gaussian elliptical copula having generalized extreme value (GEV) marginals is applied. Spatial dependence in the GEV parameters is captured with a latent spatial regression with spatially varying coefficients. Using a composite likelihood approach, we are able to efficiently incorporate a large precipitation data set, which includes stations with missing data. The model is demonstrated by application to fall precipitation extremes at approximately 2600 stations covering the western United States, -125 degrees E to -100 degrees E longitude and 30 degrees N-50 degrees N latitude. The hierarchical model provides GEV parameters on a 1/8 degrees grid and, consequently, maps of return levels and associated uncertainty. The model results indicate that return levels and their associated uncertainty have a well-defined spatial structure. Maps of return levels provide information about the spatial variations of the risk of extreme precipitation in the western US and is expected to be useful for infrastructure planning.