Bayesian spatial clustering of extremal behaviour for hydrological variables

TL;DR

This paper introduces a Bayesian spatial clustering method for extremal hydrological data that jointly models tail behavior and spatial dependence, improving inference accuracy for extreme events.

Contribution

It presents the first spatial clustering approach for extreme values that accounts for both tail similarity and spatial dependence within a Bayesian framework.

Findings

Effective clustering of hydrological extremes demonstrated in simulations.

Improved marginal tail estimation by incorporating spatial dependence.

Application to real data shows meaningful spatial clusters in precipitation and river flow.

Abstract

To address the need for efficient inference for a range of hydrological extreme value problems, spatial pooling of information is the standard approach for marginal tail estimation. We propose the first extreme value spatial clustering methods which account for both the similarity of the marginal tails and the spatial dependence structure of the data to determine the appropriate level of pooling. Spatial dependence is incorporated in two ways: to determine the cluster selection and to account for dependence of the data over sites within a cluster when making the marginal inference. We introduce a statistical model for the pairwise extremal dependence which incorporates distance between sites, and accommodates our belief that sites within the same cluster tend to exhibit a higher degree of dependence than sites in different clusters. We use a Bayesian framework which learns about both the number of clusters and their spatial structure, and that enables the inference of site-specific marginal distributions of extremes to incorporate uncertainty in the clustering allocation. The approach is illustrated using simulations, the analysis of daily precipitation levels in Norway and daily river flow levels in the UK.