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

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 climate model outputs and notably convection permitting model outputs. A focus was notably on whether findings are consistent with Clausius-Clapeyron relation. Here we investigate more generally how rainfall variability across scales change with temperature, relying on the scale invariant framework of the Universal Multifractals. Extremes, which can be derived from multifractal features are embedded in the study. Rainfall and temperature data from three high resolution measurement campaigns that took place in Northern France between 2016 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 d). Then we find that across both ranges of scales, the scale invariant maximum observable singularity is positively associated with sample-mean surface temperature, with weak individual-sample correlations and with seasonality that cannot be fully disentangled from temperature. This provides a scale-invariant observational complement to the existing multifractal-extremes literature on climate-forced rainfall changes. It provides a framework to interpret previously commonly reported trends of a scale dependence of the rate of increase of extremes with temperature.