Combining large model ensembles with extreme value statistics to improve attribution statements of rare events

• Improved quantification of weather extremes by reconciling extreme value theory (EVT) with large model ensembles.
• A methodological combination provides more objective parameter choices for EVT and ensemble simulations.
• A case study of weather extremes in the unusual winter 2013/14 in Europe is presented.
• A robust warming of the coldest winter temperatures is found across Europe in 2013/14.
• Heavy precipitation has consistently increased in Northern Europe but remains effectively unchanged elsewhere.

Gaining a better understanding of rare weather events is a major research challenge and of crucial relevance for societal preparedness in the face of a changing climate. The main focus of previous studies has been to apply a range of relatively distinct methodologies to constrain changes in the odds of those events, including both parametric statistics (extreme value theory, EVT) and empirical approaches based on large numbers of dynamical model simulations.In this study, the applicability of EVT in the context of probabilistic event attribution is explored and potential combinations of both methodological frameworks are investigated. In particular, this study compares empirical return time estimates derived from a large model ensemble with parametric inferences from the same data set in order to assess whether statements made about events in the tails are similar. Our analysis is illustrated using a case study of cold extremes and heavy rainfall in winter 2013/14 in Europe (focussing on two regions: North-West Russia and the Iberian Peninsula) for a present-day (including ‘anthropogenic’ influences) and an alternative ‘non-industrial’ climate scenario.We show that parametric inferences made about rare ‘extremes’ can differ considerably from estimates based on large ensembles. This highlights the importance of an appropriate choice of block and sample sizes for parametric inferences of the tails of climatological variables. For example, inferences based on annual extremes of daily variables are often insufficient to characterize rare events due to small sample sizes (i.e. with return periods >100>100 years). Hence, we illustrate how a combination of large numerical simulations with EVT might enable a more objective assessment of EVT parameters, such as block and sample size, for any given variable, region and return period of interest.By combining both methodologies, our case study reveals that a distinct warming of cold extremes in winter has occurred throughout Europe in the ‘anthropogenic’ relative to the non-industrial climates for given sea surface temperatures in winter 2013/14. Moreover, heavy rainfall events have become significantly more frequent and more pronounced in North and North-East Europe, while other regions demonstrate no discernible changes.In conclusion, our study shows that EVT and empirical estimates based on numerical simulations can indeed be used to productively inform each other, for instance to derive appropriate EVT parameters for short observational time series. Further, the combination of ensemble simulations with EVT allows us to significantly reduce the number of simulations needed for statements about the tails.