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.

Air-quality monitoring and analysis are initial parts of a comprehensive strategy to prevent air pollution in cities. In such a context, statistical tools play an important role in determining the time-series trends, locating areas with high pollutant concentrations, and building predictive models. In this work, we analyzed the spatio-temporal behavior of the pollutant PM₁₀ in the Monterrey Metropolitan Area (MMA), Mexico during the period 2010–2018 by applying statistical analysis to the time series of seven environmental stations. First, we used experimental variograms and scientific visualization to determine the general trends and variability in time. Then, fractal exponents (the Hurst rescaled range and Higuchi algorithm) were used to analyze the long-term dependence of the time series and characterize the study area by correlating that dependence with the geographical parameters of each environmental station. The results suggest a linear decrease in PM₁₀ concentration, which showed an annual cyclicity. The autumn-winter period was the most polluted and the spring-summer period was the least. Furthermore, it was found that the highest average concentrations are located in the western and high-altitude zones of the MMA, and that average concentration is related in a quadratic way to the Hurst and Higuchi exponents, which in turn are related to some geographic parameters. Therefore, in addition to the results for the MMA, the present paper shows three practical statistical methods for analyzing the spatio-temporal behavior of air quality.

This paper addresses the problem of characterizing the randomness of wind speed in urban areas. The study proposes two diffusion models to characterize the behavior of the random component of wind speed in an urban area from time series measured hourly by fourteen meteorological stations during the time period 2022–2023. In particular, a basic criterion is established to categorize these stations based on the variance of the underlying stochastic process for the stationary case in order to reduce the number of mathematical models. Kernel-based regression (KBR) was used to estimate the Karmers–Moyal (KM) coefficients associated with the drift and diffusion terms. The numerical solution of the proposed Langevin equation was employed to calculate the statistical properties of the process, taking into account the variance values for station classification. The results show that from the variance values expressed in \(m^{2}/s^{2}\), the weather stations can be classified into two types-the former with a variance of less than one and the latter with a variance greater than one. Therefore, only two Langevin models are obtained. This shows that model reduction using basic statistical properties of the time series is feasible when a geographical classification is not possible.