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

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 dime...

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Autores principales:	Francisco Gerardo Benavides-Bravo, Dulce Martinez-Peon, Ángela Gabriela Benavides-Ríos, Otoniel Walle-García, Roberto Soto-Villalobos, Mario A. Aguirre-López
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	rainfall data time series long-range dependence Higuchi fractal dimension Hurst exponent clustering Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/060f5489803d40dfba3dcf73e58aeebd
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spelling	oai:doaj.org-article:060f5489803d40dfba3dcf73e58aeebd2021-11-11T18:13:57ZA Climate-Mathematical Clustering of Rainfall Stations in the Río Bravo-San Juan Basin (Mexico) by Using the Higuchi Fractal Dimension and the Hurst Exponent10.3390/math92126562227-7390https://doaj.org/article/060f5489803d40dfba3dcf73e58aeebd2021-10-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/21/2656https://doaj.org/toc/2227-7390When 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.Francisco Gerardo Benavides-BravoDulce Martinez-PeonÁngela Gabriela Benavides-RíosOtoniel Walle-GarcíaRoberto Soto-VillalobosMario A. Aguirre-LópezMDPI AGarticlerainfall datatime serieslong-range dependenceHiguchi fractal dimensionHurst exponentclusteringMathematicsQA1-939ENMathematics, Vol 9, Iss 2656, p 2656 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	rainfall data time series long-range dependence Higuchi fractal dimension Hurst exponent clustering Mathematics QA1-939
spellingShingle	rainfall data time series long-range dependence Higuchi fractal dimension Hurst exponent clustering Mathematics QA1-939 Francisco Gerardo Benavides-Bravo Dulce Martinez-Peon Ángela Gabriela Benavides-Ríos Otoniel Walle-García Roberto Soto-Villalobos Mario A. Aguirre-López 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
description	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.
format	article
author	Francisco Gerardo Benavides-Bravo Dulce Martinez-Peon Ángela Gabriela Benavides-Ríos Otoniel Walle-García Roberto Soto-Villalobos Mario A. Aguirre-López
author_facet	Francisco Gerardo Benavides-Bravo Dulce Martinez-Peon Ángela Gabriela Benavides-Ríos Otoniel Walle-García Roberto Soto-Villalobos Mario A. Aguirre-López
author_sort	Francisco Gerardo Benavides-Bravo
title	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
title_short	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
title_full	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
title_fullStr	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
title_full_unstemmed	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
title_sort	climate-mathematical clustering of rainfall stations in the río bravo-san juan basin (mexico) by using the higuchi fractal dimension and the hurst exponent
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/060f5489803d40dfba3dcf73e58aeebd
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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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