Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau

A multifractal formalism relates multiscale quantities to the multifractal spectrum. The multifractal framework provides significant analytical advantages by incorporating a wide range of statistical moment orders (q), thereby enabling a more comprehensive characterization of the intrinsic structural variability embedded in the dataset. The scaling properties of the analyzed rainfall time series was studied using Legendre transformation. This tool is effective for detecting multifractality in the time series of interest and for extracting information on scaling behavior. The obtained parameters may ultimately aid in performing multifractal modeling. The 50-year-long daily rainfall time series shows multifractal properties. The analysis of the generalized Hurst exponent h(q) enabled the classification of time series’ temporal dynamics, distinguishing between persistent, anti-persistent, and uncorrelated behavior. The multifractal analysis proves to be an effective and robust tool to characterize precipitation time series in the context of climate change research. Ultimately, the parameters and features derived from the multifractal spectrum—such as singularity strengths and spectrum width—serve as both quantitative and qualitative metrics for characterizing the spatiotemporal dynamics of rainfall in the semi-arid region of the Central Mexican Plateau.