A Bayesian spatial framework for modeling extreme sub-daily precipitation in Denmark

We present a new methodology for modeling the intensities of extreme sub-daily precipitation events aimed at generating spatially continuous return level maps with associated uncertainties. This supports a comprehensive understanding of extreme precipitation events, which is important for climate adaptation planning. Our approach is built within a Bayesian generalized additive modeling framework designed to capture complex trends in marginal extremes over space.

The modeling strategy follows a two-step procedure. In the first step, the frequency of exceedances over a threshold is modeled using a spatially varying Negative Binomial distribution. In the second step, the magnitudes of these exceedances are modeled using the Generalized Pareto distribution. Here, the scale parameter is allowed to vary across space while the shape parameter is assumed to remain constant over the spatial domain.

The latent random effects are modeled using Gaussian process priors, which provide high flexibility and interpretability. Inference is performed using the Integrated Nested Laplace Approximation (the INLA system), which provides a fast and accurate alternative to traditional Markov chain Monte Carlo methods, making the framework computationally feasible for high-resolution spatial modeling.

We apply the proposed methodology to a dataset of sub-daily precipitation time series with >25 years of operational service at 50 stations across Denmark. The model successfully captures spatial variation in both the rate and magnitude of extreme events and efficiently produces high-resolution maps of return levels along with credible intervals that quantify uncertainty.

Our two-step Bayesian model offers a robust alternative to the current state-of-the-art method used in Denmark for estimating the intensities of extreme sub-daily precipitation events. The results are consistent with existing approaches but show a more detailed uncertainty quantification. By explicitly modeling spatial variation, the framework enables predictions at unsampled locations, enhancing the understanding of extreme precipitation patterns.