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Spatial Variability of the Hurst Exponent for the Daily Scale Rainfall Series in the State of Zacatecas, Mexico

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  • 1 * Centro Nacional de Investigación Disciplinaria en Relación Agua Suelo Planta Atmósfera, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, Gómez Palacio, Durango, Mexico
  • | 2 Campo Experimental Zacatecas, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, Zacatecas, Mexico
  • | 3 Centro de Geología, Universidad Nacional Autónoma de México, Juriquilla, Querétaro, Mexico
  • | 4 Campo Experimental Centro de Jalisco, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, Guadalajara, Jalisco, Mexico
  • | 5 Earth Sciences Department, and Reservoir Characterization Research Group, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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Abstract

The structural pattern of rainfall data exhibits random fluctuations over time and space. Utilizing concepts of fractal theory, it has been possible to identify characteristics of rainfall data beyond simple statistical indicators of their randomness. The objective of this research was to identify the spatial variation of the Hurst exponent, extracted through standard wavelet techniques from time series of daily rainfall data in the state of Zacatecas, Mexico. The Hurst exponent was extracted for 26 locations using the reference techniques for auto-affine traces—in particular, the wavelets method. Results have shown that the Hurst exponents of rainfall time series are negatively influenced by altitude; thus, stations located at higher altitudes were characterized by Hurst exponents indicating more nonpersistent behavior. The trends among geographical variables (west longitude and latitude) and climatic parameters (annual rainfall and number of rainy days) and their relationship with the Hurst exponent were also analyzed.

Corresponding author address: Ignacio Sánchez Cohen, Centro Nacional de Investigación Disciplinaria en Relación Agua Suelo Planta Atmósfera, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, KM 6.5 Margen Derecha Canal de Sacramento, Gómez Palacio, Durango 35140, Mexico. E-mail: sanchez.ignacio@inifap.gob.mx

Abstract

The structural pattern of rainfall data exhibits random fluctuations over time and space. Utilizing concepts of fractal theory, it has been possible to identify characteristics of rainfall data beyond simple statistical indicators of their randomness. The objective of this research was to identify the spatial variation of the Hurst exponent, extracted through standard wavelet techniques from time series of daily rainfall data in the state of Zacatecas, Mexico. The Hurst exponent was extracted for 26 locations using the reference techniques for auto-affine traces—in particular, the wavelets method. Results have shown that the Hurst exponents of rainfall time series are negatively influenced by altitude; thus, stations located at higher altitudes were characterized by Hurst exponents indicating more nonpersistent behavior. The trends among geographical variables (west longitude and latitude) and climatic parameters (annual rainfall and number of rainy days) and their relationship with the Hurst exponent were also analyzed.

Corresponding author address: Ignacio Sánchez Cohen, Centro Nacional de Investigación Disciplinaria en Relación Agua Suelo Planta Atmósfera, Instituto Nacional de Investigaciones Forestales, Agrícolas y Pecuarias, KM 6.5 Margen Derecha Canal de Sacramento, Gómez Palacio, Durango 35140, Mexico. E-mail: sanchez.ignacio@inifap.gob.mx
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