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The socio-economic impacts of rare extreme events, such as droughts, are one of the main ways in which climate affects humanity. A key challenge is to quantify the changing risk of once-in-a-decade or even once-in-a-century events under global warming, while leaning heavily on comparatively short observation spans. The predictive power of classical statistical methods from extreme value theory (EVT) often remains limited to uncorrelated events with short return periods. This is mainly due to their strong assumption of an underlying exponential family distribution of the variable in question. Standard EVT is therefore at odds with the rich and large-scale correlations found in various surface climate parameters such as local temperatures, as well as the more complex shape of empirical distributions. Here, we turn to recent developments in machine learning, namely to conditional normalizing flows, which are flexible neural networks for modeling highly-correlated unknown distributions. Given a short time series, we show how such networks can model the posterior probability of events whose return periods are much longer than the observation span. The necessary correlations and patterns can be extracted from a paired set of inputs, i.e. time series, and outputs, i.e. return periods. To evaluate this approach in a controlled setting, we generate synthetic training data by sampling temporally autoregressive processes with a non-trivial covariance structure. We compare the results to a baseline analysis using EVT. In this work, we focus on the prediction of return periods of rare statistical events. However, we expect the same potential for a wide range of statistical measures, such as the power spectrum and rate functions. Future work should also investigate its applicability to compound and spatially extended events, as well as changing conditions under warming scenarios.

Tracing the spatio-temporal distribution of water isotopologues (e.g., H216O, H218O,HD16O, D216O), in the atmosphere allows insights in to the hydrological cycle and surface-atmosphere interactions. Strong relationships between atmospheric circulation and isotopologue variability exist, mitigated by fractionation during phase transitions of water. Isotopic gradients correlate with precipitation amount, temperature, with distance to source areas of evaporation and often follow topographic features. Isotope-enabled general circulation models (iGCMs) have been established to explicitly simulate the processes that lead to these distributions, in response to the changes in radiative forcing, boundary conditions, and including effects of internal variability of the climate system. However, few of these iGCMs1,2 of varying complexity exist to date and isotopic tracers decrease their computational efficiency.Here, we evaluate the potential of replacing the explicit simulation of the isotopic component in the water cycle by statistical learning for offline model evaluation at interannual to multi-millennial timescales. This is challenging. While the relevant fractionation processes are well understood, the climate system is a chaotic, nonstationary system of high dimensionality. Therefore, successful statistical prediction requires the (so far elusive) understanding of the timescale-dependent relationships in the climate system. We present a case study on the feasibility of this approach.We focus on the impact of variable selection (primarily surface temperature, precipitation and sea-level pressure) and boundary conditions (CO2 concentrations, ice sheet distribution). We also compare different approaches to dimensionality reduction, and compare the performance of different machine-learning approaches including simple linear regression, random forests, Gaussian Processes and different types of neural networks. The accuracy of the predictions is evaluated using regional and global area-weighted mean squared errors across training and evaluation data from individual GCM simulations and across climatic states. We find a high spatial variability of prediction accuracy, modest in many locations with the presently employed approaches. We obtain encouraging results for the prediction of isotope variability in Greenland and the Antarctic.References[1] Tindall, J. C., P. J. Valdes, and Louise C. Sime. "Stable water isotopes in HadCM3: Isotopic signature of El Niño–Southern Oscillation and the tropical amount effect." Journal of Geophysical Research: Atmospheres 114.D4 (2009)[2] Werner, Martin, et al. "Glacial–interglacial changes in H 2 18 O, HDO and deuterium excess–results from the fully coupled ECHAM5/MPI-OM Earth system model." Geoscientific Model Development 9.2 (2016): 647-670.