Universal Multifractals characterization of high-resolution rainfall in the Paris region

Rainfall exhibits strong variability, intermittency and a heavy-tailed distributions across a wide range of scales. Understanding and characterizing these features is needed for numerous applications such as quantifying the extremes or merging measurements from various sensors operating at different space-time scales. 

This study presents a comprehensive multifractal analysis of high-resolution (30 s) 1D rainfall time series from the Paris region (2018 – 2024) using the Universal Multifractals (UM) framework. The data was collected with the help of optical disdrometers installed on the campus of Ecole nationale des Ponts et chausséee campus (https://hmco.enpc.fr/portfolio-archive/taranis-observatory/) UM framework has been widely used to characterize and simulate rainfall across wide range of scales with the help of only three parameters: the mean intermittency C₁, the multifractality index α and  the non-conservation parameter H. 

Spectral analysis identifies a clear scale break around 1 h, separating two distinct regimes. Coarse scales (>1h) are characterized by smooth, low-intermittency variability (spectral slope β ≈ 0.4), while fine scales (<1h) exhibit stronger spectral slope (β > 1). Accordingly, a regime-dependent analysis strategy is adopted: actual rainfall series are used at coarse scales to preserve large scale structure, while absolute values of fluctuation series are preferred at fine scales to reduce to study underlying conservative field and obtain cleaner scaling behaviour.

Analyses reveal strong multifractality (α ≈ 1.6 –1.7) and moderate intermittency (C₁ ≈ 0.12 – 0.45) at fine scale regimes. At coarser scale regimes, rainfall exhibits smoother variability with moderate multifractality (α < 1)and lower intermittency (C₁ ≈ 0.15–0.18). The UM parameters display good inter annual stability over 2018 – 2024, mild seasonal modulation (slightly higher C₁ in summer), and individual rain-event analyses were performed to examine event-to-event variability, indicating substantial heterogeneity between events.  

These results demonstrate the relevance of the UM framework for quantitatively characterizing rainfall variability in the Paris region. Initial attempts to interpret the observed differences between fine and coarse scales regimes using a unique model will be presented. 

Authors acknowledge partial financial support by the European Union as part of the Horizon Europe programme, Marie Skłodowska-Curie Actions, call COFUND-2022 and under grant agreement number 101126720; the France-Taiwan Ra2DW project (grant number by the French National Research Agency – ANR-23-CE01-0019-01).