Statistical modelling of spatiotemporal processes with applications to extreme rainfall in Denmark

Sub-daily precipitation events can trigger severe pluvial and urban flooding, resulting in significant social and economic losses. Cities are particularly vulnerable due to impervious surfaces and limited drainage capacity. Projections from the Intergovernmental Panel on Climate Change (IPCC) indicate that northern Europe is likely to experience an increased risk of intense rainfall and urban flooding in the coming decades. Effective climate adaptation in cities, therefore, depends on accurate assessments of how precipitation patterns may evolve, enabling planners to mitigate the growing frequency and severity of flood events.

Denmark has a long tradition of developing guidelines for urban drainage design, including recommendations for design rainfall intensities. Since 1999, a regional model has been used to estimate these intensities. While the model has undergone several updates, recent advances in automated precipitation measurements have significantly increased the availability of high-resolution, sub-hourly data, potentially improving the analysis of short-duration extreme rainfall events.

To develop reliable recommendations for design rainfall intensities, it is essential to examine regional variability and identify the factors that drive these differences. Moreover, an extreme value statistical modelling framework is needed to incorporate both regional and temporal explanatory variables, assess their importance, and estimate design rainfall characteristics at multiple locations. Both objectives are central to this thesis.

The first step in this work was to improve the understanding of the physical drivers of extreme precipitation in Denmark. It was demonstrated that relatively simple statistical approaches can provide meaningful insights into the relationship between meteorological drivers and the occurrence of extreme rainfall events. Moreover, well-established regression techniques have been shown to achieve predic-tive performance comparable to that of machine learning methods when applied appropriately. Atmospheric instability and moisture content were identified as key explanatory variables, and large-scale circulation patterns were also found to play a significant role.

Building on this, a spatiotemporal modelling approach was developed to analyze extreme rainfall frequencies, addressing common challenges in count data such as overdispersion and zero inflation. Applied to a dense network of rain gauges, the model revealed distinct regional patterns in extreme event frequency and highlighted the influence of both climatological and geographical factors. Then, the framework was extended to a two-stage structure that models both event frequency and rainfall intensity, enabling the estimation of return levels and their associated uncertainties.

In both models, a spatial hierarchical statistical framework was used in which residual spatial correlation is captured by a latent Gaussian random field. Spatial dependence was handled through the stochastic partial differential approximation of Matérn Gaussian fields, together with integrated nested Laplace approximations for fast inference. It was demonstrated that complex hierarchical spatial models are well-suited for analyzing extreme precipitation data and yield robust results within a reasonable computational time.

Finally, comparisons with the Danish national model indicated broad agreement in return levels for long-duration rainfall, while revealing notable differences in both return levels and their spatial patterns for shorter durations relevant for pluvial flooding in particular.

Overall, this PhD study provides a deeper understanding of the statistical and physical characteristics of extreme precipitation in Denmark, with direct relevance for hydrological design and climate adaptation. The statistical approaches developed are flexible and can serve as a foundation for investigating extreme events in a variety of environmental settings.