A Bayesian spatial framework for modeling sub-hourly to daily extreme precipitation in Denmark using SPDE with INLA

We present a new methodology for regional modeling extreme sub-daily precipitation events, aimed at producing spatially continuous return level maps with associated uncertainties. The approach is implemented within a Bayesian generalized additive modeling framework using a two-stage modeling procedure. In the first stage, exceedance frequencies are modeled with the Negative Binomial distribution. In the second, exceedance magnitudes are modeled with the Generalized Pareto distribution. Both stages contain latent spatial random effects modeled as Gaussian random fields. Bayesian inference is performed using the Integrated Nested Laplace Approximation (INLA), a fast and accurate alternative to MCMC for latent Gaussian models. We apply the methodology to a dataset of sub-hourly precipitation time series from stations across Denmark. The model captures spatial variation in both the frequency and magnitude of extremes, and produces high-resolution return level maps with associated uncertainty. In addition, sensitivity analyses with synthetic gauge networks show that wide spatial coverage of an area is more important than station density for predictive skill, highlighting the crucial role of network structure and design in reliable extreme rainfall modeling. Our two-stage Bayesian model provides a flexible alternative to the model currently used in Denmark. For longer durations (360 and 1440 min), the two models show good agreement, whereas for shorter durations (30 and 60 min), notable differences appear in both spatial variability and uncertainty. The methodology presented in this work can be adapted to different studies on extremes and can be extended to include additional covariates