Abstract
To mitigate the risk posed by extreme rainfall events, we require statistical models that reliably capture extremes in continuous space with dependence. However, assuming a stationary dependence structure in such models is often erroneous, particularly over large geographical domains. Furthermore, there are limitations on the ability to fit existing models, such as max-stable processes, to a large number of locations. To address these modelling challenges, we present a regionalisation method that partitions stations into regions of similar extremal dependence using clustering. To demonstrate our regionalisation approach, we consider a study region of Australia and discuss the results with respect to known climate and topographic features. To visualise and evaluate the effectiveness of the partitioning, we fit max-stable models to each of the regions. This work serves as a prelude to how one might consider undertaking a project where spatial dependence is non-stationary and is modelled on a large geographical scale.
Highlights
The impacts of extreme rainfall and associated flooding can be observed on a scale that covers hundreds of kilometres
We provided the necessary information about estimating the F-madogram distances and understanding the physical meaning behind the clustering structure
Hierarchical clustering is performed in F-madogram space, for most applications the regions need to be defined in Euclidean space
Summary
The impacts of extreme rainfall and associated flooding can be observed on a scale that covers hundreds of kilometres. Statistical models can be used to assess the spatial range of dependence between rainfall extremes, with a summary of some common statistical methods given in Davison et al (2012). Assuming a fixed parametric dependence structure is unlikely to yield meaningful results This presents an obstacle to creating a parsimonious statistical model and reliably identifying which regions are likely to experience similar impacts from extreme rainfall. We propose using hierarchical clustering instead with the F-madogram distance This ensures the clusters obtained are not affected by station density and are well informed by extremal dependence. We demonstrate how the different clustering methods perform using daily rainfall stations in Australia. The resulting regionalisation generates valuable insights into the dependence of Australian rainfall extremes We demonstrate this through a range of examples, highlighting features of climate and topography.
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