Combining regional estimation and historical floods: a multivariate semi-parametric peaks-over-threshold model with censored data

TL;DR

This paper develops a semi-parametric multivariate peaks-over-threshold model combining regional estimation and historical flood data, accounting for censored observations, to improve extreme flood quantile estimation across multiple sites.

Contribution

It introduces a novel semi-parametric Dirichlet Mixture model that integrates regional and historical flood data with censored observations for multivariate extreme value analysis.

Findings

Historical data significantly affect return level estimates.

Catchments show notable asymptotic dependence in extreme floods.

Model comparison reveals differences based on regionalization and historical data inclusion.

Abstract

The estimation of extreme flood quantiles is challenging due to the relative scarcity of extreme data compared to typical target return periods. Several approaches have been developed over the years to face this challenge, including regional estimation and the use of historical flood data. This paper investigates the combination of both approaches using a multivariate peaks-over-threshold model, that allows estimating altogether the intersite dependence structure and the marginal distributions at each site. The joint distribution of extremes at several sites is constructed using a semi-parametric Dirichlet Mixture model. The existence of partially missing and censored observations (historical data) is accounted for within a data augmentation scheme. This model is applied to a case study involving four catchments in Southern France, for which historical data are available since 1604. The comparison of marginal estimates from four versions of the model (with or without regionalizing the shape parameter; using or ignoring historical floods) highlights significant differences in terms of return level estimates. Moreover, the availability of historical data on several nearby catchments allows investigating the asymptotic dependence properties of extreme floods. Catchments display a a significant amount of asymptotic dependence, calling for adapted multivariate statistical models.