A regionalisation approach for rainfall based on extremal dependence
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A regionalisation approach for rainfall based on extremal dependence K. R. Saunders1
· A. G. Stephenson2 · D. J. Karoly3,4
Received: 15 June 2019 / Revised: 28 August 2020 / Accepted: 4 September 2020 / © The Author(s) 2020
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. Keywords Clustering · Climate extremes · Spatial dependence · Extremal dependence AMS 2000 Subject Classifications 60G70 · 62P12 · 62G32 · 62D05
K. R. Saunders
[email protected] 1
Delft Institute of Applied Mathematics, Delft University of Technology, Delft, Netherlands
2
Data61, CSIRO, Clayton, Victoria, Australia
3
School of Earth Sciences, The University of Melbourne, Parkville, Victoria, Australia
4
NESP Earth Systems and Climate Change Hub, CSIRO, Aspendale, Victoria, Australia
K.R. Saunders et al.
1 Introduction The impacts of extreme rainfall and associated flooding can be observed on a scale that covers hundreds of kilometres. For example, the 2011 floods in Australia affected an area the size of France and Germany (Queensland Floods Commission of Inquiry 2012). Flooding on this scale is also not unprecedented, with further evidence that extreme rainfall and associated flooding can occur across large geographical scales given in Fig. 1. These historical instances establish the need to understand the spatial range of potential impacts from extreme rainfall. However, for many countries this understanding is lacking, particularly on daily and sub-daily scales. 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). Of particular interest are max-stable processes, which provide a natural extension of univariate extreme value theory to extremes in continuous space with dependence (de Haan 1984; Schlather 2002). Modelling rainfall extremes in continuous space is desirable as the risk at locations without stations can be assessed. Max-stable processes also have strong mathematical justification for extrapolating outside the range
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