Multifractal correlation of rainfall extremes and temperature

Multifractal processes describe complex systems characterized by variability that spans across multiple scales and intensities, governed by scale-invariant distributions of extreme values. Universal Multifractals (UM) provide a robust framework for modelling and understanding the inherent extreme variability and scaling properties of various geophysical phenomena. It is a parsimonious framework that relies on only 3 parameters with physical interpretation, C₁ the mean intermittency, α the multifractality index and H the non-conservation parameter.

 

Rainfall, inherently variable across spatial and temporal domains, has been widely studied in the framework of UM, with techniques like Trace Moment (TM) and Double Trace Moment (DTM) applied to characterize its scaling properties. Based on this framework, this study aims to assess the correlation between rainfall scaling features and extremes, and temperature ones, relying on multifractal analysis such as DTM and TM. High resolution simultaneously collected rainfall data from disdrometers and temperature data from meteorological stations is used. Data was collected during various measurement campaigns operated by the TARANIS observatory of HM&Co laboratory of Enpc (https://hmco.enpc.fr/portfolio-archive/taranis-observatory/). Data collected both in an urban area and on a meteorological mast located on a wind farm is used. For the disdrometer data, it was collected with 30 seconds time steps, As for the temperature, the meteorological station measures the temperature at 1Hz, so to match their time series it was necessary to take averages of the temperature data at each 30s.

 

Initially, the study explores the correlation between the primary multifractal parameters (C₁, α, H) of rainfall and the average temperature at the rainfall event scale. Subsequently, a comparative analysis was conducted between these rainfall parameters and their counterparts derived from temperature fluctuations. This two-step approach aimed to uncover not only direct correlations between rainfall and temperature but also the extent to which the multifractal properties of rainfall mirror those observed in temperature dynamics. In a second part of the study, similar analysis on longer periods of typically one month are used to complement event based analysis by accounting for dry periods.

 

Authors acknowledge the ANR PRCI Ra2DW project supported by the French National Research Agency – ANR-23-CE01-0019-01 for partial financial support.