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

Abstract

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.

Geo-Hydrological Events and Temporal Trends in CAPE and TCWV over the Main Cities Facing the Mediterranean Sea in the Period 1979–2018

“…The Hurst exponent method [36] gives an estimation of a time series autocorrelation and it is a powerful tool to study persistence and long-range dependence [37,38]. It is widely used in many research fields, from climate science [39][40][41][42] to hydrology and water resources [38,43,44] and economics [35,45]. In this research, the rescaled range (R/S) analysis [36] provides the estimation of the Hurst exponent.…”

On the Spatial Scale Dependence of Long‐Term Persistence in Global Annual Precipitation Data and the Hurst Phenomenon

“…(2020); Adarsh and Priya (2021); Benavides‐Bravo et al. (2021); Dimitriadis, Iliopoulou, et al. (2021); Dimitriadis, Koutsoyiannis, et al.…”

“…The work of Hurst has been used to characterize LTP across multiple disciplines, ranging from climate science to the analysis of internet traffic and the flow of blood in human arteries (O'Connell et al, 2016). Recent research on Hurst behavior in the climate and hydrology fields is reported by Adarsh et al (2020); Adarsh and Priya (2021); Benavides-Bravo et al (2021); ; ; Legates and Outcalt (2022); Pal et al (2020); Rahmani and Fattahi (2021, 2022c, 2022a, 2022b. The hypothesis of long-term persistence (LTP) in annual precipitation has been explored in a number of studies of point and grid scale data.…”

Statistical Analysis of PM10 Concentration in the Monterrey Metropolitan Area, Mexico (2010–2018)

“…Additionally, Nikolopoulos et al [23] used the HFD algorithm to study PM 10 time series, indicating fractality and long-term memory in the behavior of the records from the studied stations. However, none of these exponents have been calculated to compare them with geographic parameters, such as latitude, longitude, and altitude, despite the fact that those relations have been found for other meteorological variables [27][28][29][30].…”