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

Abstract

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.

Advancing our understanding of compound weather and climate events via large ensemble model simulations

“…We would like to note that alternative to SMILEs exist. For example, climate emulators 99,100 simulate large sample sizes at low-computational cost; however, despite some exceptions 86 , they are…”

“…Building on a perfect-model approach, SMILEs offer a powerful testbed for new and existing methodologies 22,74 . This can be particularly useful for assessing the skills of novel methods in compound event research, which can be very complex given the need of modelling multiple inter-variable relationships and multivariate extremes 85,86 . In a perfect-model approach, the climate represented by the large ensemble simulations of one climate model can be used as pseudo reality and the statistical model can be calibrated to data of a single ensemble member, representing the observations that are limited in sample size.…”

Machine learning applications for weather and climate need greater focus on extremes

“…Five out of six studies used at least 10 years of training data. Three studies obtained reasonable evaluation results for extreme events with estimated return periods much longer than the training dataset, indicating that generalisation to more extreme events is possible (Boulaguiem et al 2022, Frame et al 2022, Lopez-Gomez et al 2022. However, it still seems wise to plan to require large training datasets to develop models for such cases.…”

Inference and Sampling for Archimax Copulas

“…However, these techniques are largely used for modeling the bulk of a distribution and may not extrapolate well to out-of-distribution samples or samples within the tails, as discussed in [57]. Some methods have been proposed to represent only the tails, for example in [1,6]. However, these methods are used only for sampling, and do not provide a way of quantifying the dependence of the observation.…”

“…The inference results are given in Table 2 of the main paper. We plot the samples in Figure 13, 20 coordinates at a time, with coordinates (0, 1,2,3,4,5,6,7,8,9,20,21,22,23,24,25,26,27,28,29) in Figure 13 (a) and coordinates (0, 10,20,30,40,50,60,70,80,90,9,19,29,39,49,59,69,79,89,99) in Figure 13 (b). The generated samples are in blue above the diagonal, the true samples are in black below the diagonal.…”