  Spatial maps of extreme precipitation are a critical component of flood
estimation in hydrological modeling, as well as in the planning and design of
important infrastructure. This is particularly relevant in countries such as
Norway that have a high density of hydrological power generating facilities and
are exposed to significant risk of infrastructure damage due to flooding. In
this work, we estimate a spatially coherent map of the distribution of extreme
hourly precipitation in Norway, in terms of return levels, by linking
generalized extreme value (GEV) distributions with latent Gaussian fields in a
Bayesian hierarchical model. Generalized linear models on the parameters of the
GEV distribution are able to incorporate location-specific geographic and
meteorological information and thereby accommodate these effects on extreme
precipitation. A Gaussian field on the GEV parameters captures additional
unexplained spatial heterogeneity and overcomes the sparse grid on which
observations are collected. We conduct an extensive analysis of the factors
that affect the GEV parameters and show that our combination is able to
appropriately characterize both the spatial variability of the distribution of
extreme hourly precipitation in Norway, and the associated uncertainty in these
estimates.
