Modeling and simulating spatial extremes by combining extreme value theory with generative adversarial networks

Modeling dependencies between climate extremes is important for climate risk assessment, for instance when allocating emergency management funds. In statistics, multivariate extreme value theory is often used to model spatial extremes. However, most commonly used approaches require strong assumptions and are either too simplistic or over-parameterized. From a machine learning perspective, generative adversarial networks (GANs) are a powerful tool to model dependencies in high-dimensional spaces. Yet in the standard setting, GANs do not well represent dependencies in the extremes. Here we combine GANs with extreme value theory (evtGAN) to model spatial dependencies in summer maxima of temperature and winter maxima in precipitation over a large part of western Europe. We use data from a stationary 2000-year climate model simulation to validate the approach and explore its sensitivity to small sample sizes. Our results show that evtGAN outperforms classical GANs and standard statistical approaches to model spatial extremes. Already with about 50 years of data, which corresponds to commonly available climate records, we obtain reasonably good performance. In general, dependencies between temperature extremes are better captured than dependencies between precipitation extremes due to the high spatial coherence in temperature fields. Our approach can be applied to other climate variables and can be used to emulate climate models when running very long simulations to determine dependencies in the extremes is deemed infeasible. Impact Statement Spatially co-occurring climate extremes such as heavy precipitation events or temperature extremes can have devastating impacts on human and natural systems. Modeling complex spatial dependencies between climate extremes in different locations are notoriously difficult and traditional approaches from the field of extreme value theory are relatively inflexible. We show that combining extreme value theory with a deep learning model (generative adversarial networks) can well represent complex spatial dependencies between extremes. Hence, instead of running expensive climate models, the approach can be used to sample many instances of spatially cooccurring extremes with realistic dependence structure, which may be used for climate risk modeling and stress testing of climate-sensitive systems.