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

Francisco Gerardo Benavides-Bravo, Roberto Soto-Villalobos, José Roberto Cantú-González, Mario A. Aguirre-López and Ángela Gabriela Benavides-Ríos
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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
José Roberto Cantú-González: Escuela de Sistemas PMRV, Universidad Autónoma de Coahuila, Acuña 26235, Mexico
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

Mathematics, 2021, vol. 9, issue 19, 1-20

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.

Keywords: variogram; rainfall data; exponential model; maximal variability; nugget effect; Hurst exponent; curve fitting; Río Bravo–San Juan basin; Monterrey metropolitan area (MMA) (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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