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Heat waves such as the one in Europe 2003 have severe consequences for the economy, society, and ecosystems. It is unclear whether temperatures could have exceeded these anomalies even without further climate change. Developing storylines and quantifying highest possible temperature levels is challenging given the lack of long homogeneous time series and methodological framework to assess them. Here, we address this challenge by analysing summer temperatures in a nearly 5000-year pre-industrial climate model simulation, performed with the Community Earth System Model CESM1. To assess how anomalous temperatures could get, we compare storylines, generated by three different methods: (1) a return-level estimate, deduced from a generalized extreme value distribution, (2) a regression model, based on dynamic and thermodynamic heat wave drivers, and (3) a novel ensemble boosting method, generating large samples of re-initialized extreme heat waves in the long climate simulation.All methods provide consistent temperature estimates, suggesting that historical exceptional heat waves as in Chicago 1995, Europe 2003 and Russia 2010 could have been substantially exceeded even in the absence of further global warming. These estimated unseen heat waves are caused by the same drivers as moderate observed events, but with more anomalous patterns. Moreover, altered contributions of circulation and soil moisture to temperature anomalies include amplified feedbacks in the surface energy budget. The methodological framework of combining different storyline approaches of heat waves with magnitudes beyond the observational record may ultimately contribute to adaptation and to the stress testing of ecosystems or socio-economic systems to increase resilience to extreme climate stressors.

Model projections of regional changes in heavy rainfall are uncertain. On timescales of few decades, internal variability plays an important role and therefore poses a challenge to detect robust model response in heavy rainfall to rising temperatures. We use spatial aggregation to reduce the major role of internal variability and evaluate the heavy rainfall response to warming temperatures with observations. We show that in the regions with high rainfall intensity and for which gridded observations exist, most of the models underestimate the historical scaling of heavy rainfall and the land fraction with significant positive heavy rainfall scalings during the historical period. The historical behavior is correlated with the projected heavy rainfall intensification across models allowing to apply an observational constraint, i.e., to calibrate multimodel ensembles with observations in order to narrow the range of projections. The constraint suggests a substantially stronger intensification of future heavy rainfall than the multimodel mean.

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