Spatiotemporal analyses of extreme rainfall frequencies in Denmark via Bayesian hierarchical modelling using SPDE with INLA

Abstract This study proposes a Bayesian hierarchical model to analyze spatiotemporal patterns of extreme rainfall frequencies across Denmark, with a focus on understanding the underlying factors driving these patterns. Covariates and spatial information are incorporated through a generalized additive modeling framework. To handle the spatial correlation in the data, the model employs a Markovian representation of the Matérn covariance function via the stochastic partial differential equations (SPDE) approach. The model fits within the framework of latent Gaussian models, enabling efficient inference using the Integrated Nested Laplace Approximation (INLA). Results indicate that extreme rainfall frequencies are clustered in space, and there are both meteorological factors (i.e., atmospheric water content, vertical instability) and topographical features (i.e., distance to open sea) that explain a significant part of the spatial variability. Our method explicitly models the spatiotemporal correlation structure inherent in extreme rainfall data while remaining computationally efficient, improving our understanding of extreme rainfall patterns.