Concurrent floods and concurrent droughts in nearby catchments pose challenges to risk assessment and water management. Climate change is affecting extremely high and low discharge, but the complex interplay between changes in individual catchments and in the dependence across catchments make it difficult to provide accurate assessments of the occurrence probabilities of concurrent extremes. In this work, we use a contemporary statistical deep learning model (the deep SPAR framework) to capture concurrent river floods and droughts in four catchments in the Upper Danube basin, based on discharge simulated by a hydrological model driven with large ensemble climate model output. The statistical model is able to accurately capture the multivariate extremes of the simulated discharge, which we assess by making use of the large available sample size. We subsequently use our statistical model to study changes in joint tail behaviour of discharge over time, finding that both compound flooding and drought-like conditions are becoming increasingly likely towards the end of the 21st century under a high-emission scenario. In particular, our results highlight that changes in the dependence structure of extremes strongly contribute to the detected changes, an aspect that would be difficult to capture with traditional approaches. This work paves the way for highly flexible, general inference on compound extremes in hydrological applications, and demonstrates key advantages of using statistical deep learning in this setting.

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