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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2025-05-01
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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. |
| format | Article |
| id | doaj-art-d31b8bbbc4d64c3188a7d19def468935 |
| institution | Kabale University |
| issn | 2073-4433 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atmosphere |
| 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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