A Universal Multifractals perspective into the link between rainfall extremes and temperature

Abstract. The link between rainfall extremes, usually defined as a given percentile or for a given return period, and temperature has been widely investigated using measurement data and/or convection permitting model outputs. A focus was notably on whether findings are consistent with Clausius-Clapeyron relation. A scale dependence of the rate of increase with temperature is commonly reported. Here we investigate how rainfall extremes and more generally variability across scales change with temperature, relying on the scale invariant framework of the Universal Multifractals. Rainfall and temperature data from three high resolution measurement campaigns that took place in France between 2018 and 2025 are used. Scaling behaviour is confirmed on two distinct ranges of scales, first at event scale (30 s – 1 h) and then up to synoptic scale (roughly 11 days). Then we find that across both ranges of scales, the scale invariant maximum observable singularity increases on average with greater temperature, which provides a framework to interpret previously observed trends.