Hierarchical Space-Time Modeling of Asymptotically Independent Exceedances With an Application to Precipitation Data

Abstract

The statistical modeling of space-time extremes in environmental applications is key to understanding complex dependence structures in original event data and to generating realistic scenarios for impact models. In this context of high-dimensional data, we propose a novel hierarchical model for high threshold exceedances defined over continuous space and time by embedding a space-time Gamma process convolution for the rate of an exponential variable, leading to asymptotic independence in space and time. Its physically motivated anisotropic dependence structure is based on geometric objects moving through space-time according to a velocity vector. We demonstrate that inference based on weighted pairwise likelihood is fast and accurate. The usefulness of our model is illustrated by an application to hourly precipitation data from a study region in Southern France, where it clearly improves on an alternative censored Gaussian space-time random field model. While classical limit models based on threshold-stability fail to appropriately capture relatively fast joint tail decay rates between asymptotic dependence and classical independence, strong empirical evidence from our application and other recent case studies motivates the use of more realistic asymptotic independence models such as ours. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.

Keywords:

• Asymptotic independence
• Composite likelihood
• Gamma random fields
• Hourly precipitation
• Space-time convolution
• Space-time extremes

Acknowledgments

The authors express their gratitude toward two anonymous referees and the associate editor for many useful comments that have helped improving earlier versions of the article. The authors thank Julie Carreau (IRD HydroSciences, Montpellier, France) for helping them in collecting the data from the Meteo France database.

Notes

1 The code is open source and can be downloaded from http://github.com/chraibi/EEOver.

Additional information

Funding

The work of the authors was supported by the French National Programme LEFE/INSU and by the LabEx NUMEV. Thomas Opitz acknowledges financial support from Ca’ Foscari University, Venice, Italy.