Modeling Nonstationary Extreme Dependence With Stationary Max-Stable Processes and Multidimensional Scaling

Abstract

Modeling the joint distribution of extreme events at multiple locations is a challenging task with important applications. In this study, we use max-stable models to study extreme daily precipitation events in Switzerland. The nonstationarity of the spatial process at hand involves important challenges, which are often dealt with by using a stationary model in a so-called climate space, with well-chosen covariates. Here, we instead choose to warp the weather stations under study in a latent space of higher dimension using multidimensional scaling (MDS). Two methods are proposed to define target dissimilarity matrices, based respectively on extremal coefficients and on pairwise likelihoods. Results suggest that the proposed methods allow capturing complex spatial dependences of spatial extreme precipitations, enabling in turn to reliably extrapolate functionals such as extremal coefficients. Supplemental materials for this article are available online.

Keywords:

• Extremal coefficient
• Extreme value theory
• Spatial extremes

Supplementary Materials

A short background in univariate extreme values statistics and more details on MDS methods are provided, together with some details on the tested “classical” max-stable model of Blanchet and Davison (2011). Additional extremal coefficients maps are commented. We also provide a link to download the Fréchet-transformed dataset used in this work, as well as commented R code, allowing one to easily reproduce all of the results and figures in this article. A link for downloading all 219 extremal coefficients maps is also provided. Finally additional diagnostic plots for the proposed models are given. (PDF file)

Acknowledgments

The authors would like to warmly thank Dr. Sophie Fukutome from Meteo-Swiss for useful scientific discussions and for kindly providing the precipitation dataset. The authors also thank Prof. Sebastian Engelke for productive discussions including the key suggestion to investigate Brown-Resnick models, as well as Johanna F. Ziegel for some useful exchanges around proper scoring rules. The authors thank the anonymous associate editor and referees for constructive comments having led to substantial improvements of the paper. Furthermore, D.G. would like to acknowledge support of Idiap Research Institute, his primary affiliation in an early version of this manuscript. C.C. acknowledges funding from the Swiss Mobiliar Insurance.

Additional information

Funding

Part of D.G.’s contributions have taken place within the Swiss National Science Foundation project number 178858.