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• Analyse the impact of climate change on rail transport systems. • Explore the uncertainties in climate risk data. • Develop new climate risk analysis methods using advanced uncertainty modelling. • Develop a risk prediction tool to reduce climate impact on rails. • Conduct a UK national wide empirical study to provide useful insights for rail network adaptation to climate change. Climate change poses critical challenges for rail infrastructure and operations. However, the systematic analysis of climate risks and the associated costs of tackling them, particularly from a quantitative perspective, is still at an embryonic phase due to the kaleidoscopic nature of climate change impacts and lack of precise climatic data. To cope with such challenges, an advanced Fuzzy Bayesian Reasoning (FBR) model is applied in this paper to understand climate threats of the railway system. This model ranks climate risks under high uncertainty in data and comprehensively evaluates these risks by taking account of infrastructure resilience and specific aspects of severity of consequence. Through conducting a nationwide survey on the British railway system, it dissects the status quo of primary climate risks. The survey implies that the top potential climate threats are heavy precipitation and floods. The primary risks caused by the climate threats are bridges collapsing and bridge foundation damage due to flooding and landslips. The findings can aid transport planners to prioritise climate risks and develop rational adaptation measures and strategies. [ABSTRACT FROM AUTHOR]