A regionalisation approach for rainfall based on extremal dependence

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.

Spatial Dependence of Floods Shaped by Spatiotemporal Variations in Meteorological and Land‐Surface Processes

“…(2015) and Saunders et al. (2019). The F‐madogram v F measures spatial dependence as a function of distance between a pair of stations ( h ; here Euclidean) by comparing the ordering of extreme events between two time series of extreme events ( Z ( x ) and Z ( x + h )) (Cooley et al., 2006): where Z ( x ) are transformed to have Fréchet margins so that .…”

“…Therefore, to identify regions of catchments with similar flood behavior, a third set, the regional event set, is used in conjunction with a clustering procedure relying on the F-madogram as a distance measure as proposed by Bador et al (2015) and Saunders et al (2019). The F-madogram v F measures spatial dependence as a function of distance between a pair of stations (h; here Euclidean) by comparing the ordering of extreme events between two time series of extreme events (Z(x) and Z(x+h)) (Cooley et al, 2006):…”

Sample from copula: a COPPY module

“…The λ-madogram belongs to a family of estimators, namely the madogram, which is of prime interest in environmental sciences, as it is designed to model pairwise dependence between maxima in space, see e.g. [Bernard et al, 2013, Bador et al, 2015, Saunders et al, 2021 where the madogram was used as a dissimilarity measure to perform clustering. Where in several fields, for example econometrics ([Wooldridge, 2007]) or survey theory ( [Boistard et al, 2016]), the MCAR hypothesis appears to be a strong hypothesis, this hypothesis is more realistic in environmental research as the missingness of one observation is usually due to instruments, communication and processing errors that may be reasonably supposed independent of the quantity of interest.…”

A marginal modelling approach for predicting wildfire extremes across the contiguous United States

“…Since we have a large number of grid cell locations (n = 3503) and we wish to expand the available data at each grid cell, we require a technique that designates each location to a cluster, with the number of clusters (k) small in comparison to the number of locations (k n). In this instance, many popular clustering techniques, such as K-medoids, have been shown to be unsuitable, resulting in undesirable features within the clustering allocations (Raykov et al, 2016;Saunders et al, 2021). As such, we utilise divisive hierarchical clustering (Rokach and Maimon, 2005).…”