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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" di...

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Main Authors: Alvaro Alberto López-Lambraño, Carlos Fuentes, Yeraldin Serpa-Usta, Neila María González Tejada, Alvaro López-Ramos
Format: Article
Language:English
Published: MDPI AG 2025-05-01
Series:Atmosphere
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Online Access:https://www.mdpi.com/2073-4433/16/6/639
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author Alvaro Alberto López-Lambraño
Carlos Fuentes
Yeraldin Serpa-Usta
Neila María González Tejada
Alvaro López-Ramos
author_facet Alvaro Alberto López-Lambraño
Carlos Fuentes
Yeraldin Serpa-Usta
Neila María González Tejada
Alvaro López-Ramos
author_sort Alvaro Alberto López-Lambraño
collection DOAJ
description 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mo>(</mo><mi>q</mi></mrow></semantics></math></inline-formula>) 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.
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spelling doaj-art-d31b8bbbc4d64c3188a7d19def4689352025-08-20T03:26:17ZengMDPI AGAtmosphere2073-44332025-05-0116663910.3390/atmos16060639Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican PlateauAlvaro Alberto López-Lambraño0Carlos Fuentes1Yeraldin Serpa-Usta2Neila María González Tejada3Alvaro López-Ramos4School of Engineering, Architecture and Design, Universidad Autónoma de Baja California, Ensenada 22860, MexicoInstituto Mexicano de Tecnología del Agua, Jiutepec 62550, MexicoSchool of Engineering, Architecture and Design, Universidad Autónoma de Baja California, Ensenada 22860, MexicoGICA Group, Department of Civil Engineering, Universidad Pontificia Bolivariana Campus Montería, Montería 230002, ColombiaGICA Group, Department of Civil Engineering, Universidad Pontificia Bolivariana Campus Montería, Montería 230002, ColombiaA 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>q</mi><mo>)</mo></mrow></semantics></math></inline-formula>, 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>h</mi><mo>(</mo><mi>q</mi></mrow></semantics></math></inline-formula>) 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.https://www.mdpi.com/2073-4433/16/6/639multifractal analysisLegendre transformationsingularity spectrum
spellingShingle Alvaro Alberto López-Lambraño
Carlos Fuentes
Yeraldin Serpa-Usta
Neila María González Tejada
Alvaro López-Ramos
Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau
Atmosphere
multifractal analysis
Legendre transformation
singularity spectrum
title Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau
title_full Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau
title_fullStr Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau
title_full_unstemmed Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau
title_short Multifractal Measures and Singularity Analysis of Rainfall Time Series in the Semi-Arid Central Mexican Plateau
title_sort multifractal measures and singularity analysis of rainfall time series in the semi arid central mexican plateau
topic multifractal analysis
Legendre transformation
singularity spectrum
url https://www.mdpi.com/2073-4433/16/6/639
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