We use a storyline approach to model the impacts of extreme flood events in Switzerland in a warmer climate. We find a non-linear relationship between the increase in precipitation and the increase in discharge, which is, among other factors, due to the increasing precipitation intensity. We find a strongly non-linear relationship between the increase in discharge and the increase in damages, which is due to the geometry of the riverbeds, the relative position of the exposure to the rivers, and the discharge exceeding the upper limit of the protective infrastructure.