A fundamental goal in climate attribution is to estimate how forced climate change contributes to observed extreme weather events. The storyline attribution method compares an observed weather event, conditional on its atmospheric dynamic state (i.e., atmospheric circulation), in the current, 'factual' climate to an event with very similar circulation conditions in a hypothetical, 'counterfactual' climate. However, physical climate models cannot directly transfer these storyline counterfactuals across different climate forcing states. Statistical and machine learning techniques may overcome this limitation; yet, emulating circulation-conditional extreme events under different climate states is challenging. Here, we demonstrate distributional autoencoders (DAEs) as a versatile method for generating climate counterfactuals. They model the full distribution of spatially resolved European temperature fields conditional on the atmospheric circulation state and the mean global warming level. These distributions allow for deriving meaningful conditional probability ratios, which is a particular advantage of the DAE-based storyline approach. We train DAEs on fully coupled climate model simulations and we evaluate the modelled distributions across different factual and storyline-based counterfactual climate model simulations. In an illustrative case study, we revisit the 2003 European heatwave and we generate counterfactuals for a hypothetical `2003-like European heatwave' using ERA5 circulation, which we hypothesize to occur a quarter century (2028) and a half century (2053) after 2003. The conditional intensity would increase from 29.3 °C in 2003, to 30.3 °C and 32.1 °C in 2028 and 2053, respectively and conditional probability ratios would be 2.1 and 3.2 when compared to 2003.

翻译：气候变化归因的一个基本目标是估计人为强迫气候变化如何影响观测到的极端天气事件。情景归因方法通过比较当前"事实气候"中给定大气动力状态（即大气环流）条件下的观测天气事件，与假设"反事实气候"中具有相似环流条件的事件。然而，物理气候模型无法直接在不同气候强迫状态间传递这些情景反事实。统计与机器学习技术可克服这一局限，但在不同气候状态下模拟环流条件极端事件仍具挑战性。本文证明分布自编码器（DAEs）是生成气候反事实的一种通用方法。该模型基于大气环流状态和全球平均增暖水平，模拟了欧陆空间解析温度场的完整分布。这些分布可推导有意义的条件概率比，这是基于DAE的情景归因方法的独特优势。我们在全耦合气候模型模拟上训练DAE，并在不同事实气候与基于情景反事实的气候模型模拟中评估其模拟分布。通过案例研究，我们重新审视2003年欧洲热浪事件，利用ERA5环流数据生成假设"2003型欧洲热浪"在2003年后25年（2028年）和50年（2053年）的反事实情景。条件强度将从2003年的29.3°C分别增至2028年的30.3°C和2053年的32.1°C，与2003年相比条件概率比分别为2.1和3.2。