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A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

Author

Listed:
  • Francisco Gerardo Benavides-Bravo

    (Departamento de Ciencias Básicas, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico)

  • Roberto Soto-Villalobos

    (Departamento de Ciencias Básicas, Facultad de Ciencias de la Tierra, Universidad Autónoma de Nuevo León, Linares 67700, Mexico
    These authors contributed equally to this work.)

  • José Roberto Cantú-González

    (Escuela de Sistemas PMRV, Universidad Autónoma de Coahuila, Acuña 26235, Mexico
    These authors contributed equally to this work.)

  • Mario A. Aguirre-López

    (Departamento de Ciencias Básicas, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico)

  • Ángela Gabriela Benavides-Ríos

    (Departamento de Ciencias Básicas, Instituto Tecnológico de Nuevo León, Tecnológico Nacional de México, Guadalupe 67170, Mexico
    These authors contributed equally to this work.)

Abstract

Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect.

Suggested Citation

  • Francisco Gerardo Benavides-Bravo & Roberto Soto-Villalobos & José Roberto Cantú-González & Mario A. Aguirre-López & Ángela Gabriela Benavides-Ríos, 2021. "A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series," Mathematics, MDPI, vol. 9(19), pages 1-20, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2466-:d:649231
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    Citations

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    Cited by:

    1. Huijuan Zhang & Wenkai Liu & Qingfeng Hu & Xiaodong Huang, 2023. "Multi-Scale Integration and Distribution of Soil Organic Matter Spatial Variation in a Coal–Grain Compound Area," Sustainability, MDPI, vol. 15(4), pages 1-17, February.
    2. Alegría, Alfredo & Emery, Xavier, 2024. "Matrix-valued isotropic covariance functions with local extrema," Journal of Multivariate Analysis, Elsevier, vol. 200(C).

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