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A Climate-Mathematical Clustering of Rainfall Stations in the Río Bravo-San Juan Basin (Mexico) by Using the Higuchi Fractal Dimension and the Hurst Exponent

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  • Francisco Gerardo Benavides-Bravo

    (Department of Basic Sciences, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico)

  • Dulce Martinez-Peon

    (Department of Electrical and Electronics Engineering, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico)

  • Ángela Gabriela Benavides-Ríos

    (Department of Basic Sciences, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico)

  • Otoniel Walle-García

    (Departamento de Ciencias Básicas, Facultad de Ciencias de la Tierra, Universidad Autónoma de Nuevo León, Linares 67700, Mexico)

  • Roberto Soto-Villalobos

    (Departamento de Ciencias Básicas, Facultad de Ciencias de la Tierra, Universidad Autónoma de Nuevo León, Linares 67700, Mexico)

  • Mario A. Aguirre-López

    (Department of Basic Sciences, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico
    Current address: Facultad de Ciencias en Física y Matemáticas, Universidad Autónoma de Chiapas, Tuxtla Gutiérrez 29050, Mexico.)

Abstract

When conducting an analysis of nature’s time series, such as meteorological ones, an important matter is a long-range dependence to quantify the global behavior of the series and connect it with other physical characteristics of the region of study. In this paper, we applied the Higuchi fractal dimension and the Hurst exponent (rescaled range) to quantify the relative trend underlying the time series of historical data from 17 of the 34 weather stations located in the Río Bravo-San Juan Basin, Mexico; these data were provided by the National Water Commission CONAGUA) in Mexico. In this way, this work aims to perform a comparative study about the level of persistency obtained by using the Higuchi fractal dimension and Hurst exponent for each station of the basin. The comparison is supported by a climate clustering of the stations, according to the Köppen classification. Results showed a better fitting between the climate of each station and its Higuchi fractal dimension obtained than when using the Hurst exponent. In fact, we found that the more the aridity of the zone the more the persistency of rainfall, according to Higuchi’s values. In turn, we found more relation between the Hurst exponent and the accumulated amount of rainfall. These are relations between the climate and the long-term persistency of rainfall in the basin that could help to better understand and complete the climatological models of the study region. Trends between the fractal exponents used and the accumulated annual rainfall were also analyzed.

Suggested Citation

  • Francisco Gerardo Benavides-Bravo & Dulce Martinez-Peon & Ángela Gabriela Benavides-Ríos & Otoniel Walle-García & Roberto Soto-Villalobos & Mario A. Aguirre-López, 2021. "A Climate-Mathematical Clustering of Rainfall Stations in the Río Bravo-San Juan Basin (Mexico) by Using the Higuchi Fractal Dimension and the Hurst Exponent," Mathematics, MDPI, vol. 9(21), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:21:p:2656-:d:660825
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    References listed on IDEAS

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