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

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.

Spatial and temporal Hurst exponent variability of rainfall series based on the climatological distribution in a semiarid region in Mexico

“…An anti-persistent behavior in the rainfall series can hinder the prediction of a new rainfall event. The time of the year that does not present meaningful rainfall events can be the responsible for the anti-persistent behavior in the series (Velásquez et al, 2013). From Table II and Figure 2c, which shows the variation of altitudes in Baja California, it can be observed that the highest altitudes, corresponding to the Sierra Juárez and Sierra San Pedro Mártir, are located in the central area.…”

“…In the case of fractal studies with rainfall approaches, it has been found that the Hurst exponent value is influenced by the altitude of the studied region. A research in Zacatecas, Mexico, showed that altitude causes a negative influence on the Hurst exponent, i.e., climatological stations located at higher altitudes generate an anti-persistent behavior (Velásquez et al, 2013). Furthermore, there have been many studies involving rainfall and fractals, the most noted being an application of the R/S to study the fractal properties of rainfall events from 1921-2010, resulting in time series that showed fractal behavior.…”

Análisis temporal de sequías (1922-2016) en la cuenca alta del río Nazas usando el SPI y su relación con ENSO

“…Siempre es confuso tratar de buscar factores locales que expliquen la repartición espacial de las precipitaciones. Sin embargo, la primera apreciación con respecto a las isoyetas que muestra la Figura 2 permite comprender el rol primordial de la altitud y de la distancia al océano en la distribución de la cantidad de lluvia, como lo señalan Descroix et al (2004) y Velásquez et al (2013). De hecho, de manera paradójica, este rol es más evidente para la vertiente interior (oriental) de la SMO; mientras que para la vertiente del Pacífico, la evolución es inevitablemente más compleja por la simple razón de que la altitud aumenta con el distanciamiento de la costa, haciendo que ambos factores se contrapongan (Descroix et al, 2004).…”

Water Harvesting and Soil Water Retention Practices for Forage Production in Degraded Areas in Arid Lands of Mexico

“…The Mexican desert covers more than 50% of the national surface, which has different degrees of aridity typified by the characteristics of rainfall [6]. In this area, around 18% of the national population is located [7].…”