AbstractExtreme weather events are generally associated with unusual dynamical conditions, yet the signal-to-noise ratio of the dynamical aspects of climate change that are relevant to extremes appears to be small, and the nature of the change can be highly uncertain. On the other hand, the thermodynamic aspects of climate change are already largely apparent from observations, and are far more certain since they are anchored in agreed-upon physical understanding. The storyline method of extreme event attribution, which has been gaining traction in recent years, quantitatively estimates the magnitude of thermodynamic aspects of climate change, given the dynamical conditions. There are different ways of imposing the dynamical conditions. Here we present and evaluate a method where the dynamical conditions are enforced through global spectral nudging towards reanalysis data of the large-scale vorticity and divergence in the free atmosphere, leaving the lower atmosphere free to respond. We simulate the historical extreme weather event twice: first in the world as we know it, with the events occurring on a background of a changing climate, and second in a ‘counterfactual’ world, where the background is held fixed over the past century. We describe the methodology in detail, and present results for the European 2003 heatwave and the Russian 2010 heatwave as a proof of concept. These show that the conditional attribution can be performed with a high signal-to-noise ratio on daily timescales and at local spatial scales. Our methodology is thus potentially highly useful for realistic stress testing of resilience strategies for climate impacts, when coupled to an impact model.