A Dimension-Reduced Multivariate Spatial Model for Extreme Events: Balancing Flexibility and Scalability

TL;DR

This paper introduces a scalable, flexible spatial extreme value model using dimension reduction, improving the analysis of rare environmental events like extreme precipitation and temperature across large regions.

Contribution

The novel JLS-GEV framework incorporates a dimension-reduced latent spatial process, enhancing flexibility and scalability in modeling complex spatial and cross-variable dependencies of extremes.

Findings

JLS-GEV outperforms baseline models in simulations

Effective in capturing nonstationary spatial behaviors

Practical for real-world climate data analysis

Abstract

Modeling extreme precipitation and temperature is vital for understanding the impacts of climate change, as hazards like intense rainfall and record-breaking temperatures can result in severe consequences, including floods, droughts, and wildfires. Gaining insight into the spatial variation and interactions between these extremes is critical for effective risk management, early warning systems, and informed policy-making. However, challenges such as the rarity of extreme events, spatial dependencies, and complex cross-variable interactions hinder accurate modeling. We introduce a novel framework for modeling spatial extremes, building upon spatial generalized extreme value (GEV) models. Our approach incorporates a dimension-reduced latent spatial process to improve scalability and flexibility, particularly in capturing asymmetry in cross-covariance structures. This Joint Latent Spatial GEV model (JLS-GEV) overcomes key limitations of existing methods by providing a more flexible framework for inter-variable dependencies. In addition to addressing event rarity, spatial dependence and cross-variable interactions, JLS-GEV supports nonstationary spatial behaviors and independently collected data sources, while maintaining practical fitting times through dimension reduction. We validate JLS-GEV through extensive simulation studies, demonstrating its superior performance in capturing spatial extremes compared to baseline modeling approaches. Application to real-world data on extreme precipitation and temperature in the southeastern United States highlights its practical utility. While primarily motivated by environmental challenges, this framework is broadly applicable to interdisciplinary studies of spatial extremes in interdependent natural processes.