Análisis de conglomerados en estaciones pluviométricas mediante el exponente de Hurst y Variogramas en la cuenca del río San Juan

Un tema importante en el estudio del comportamiento de las series temporales y, en particular, series de tiempo meteorologicas, es la dependencia a largo plazo. En esta tesis se ´ analiza el comportamiento de las variaciones de precipitacion en diferentes per ´ ´ıodos, utilizando el analisis de las correlaciones de largo alcance. Variogramas y exponente de Hurst se ´ aplicaron a los datos historicos de diferentes estaciones pluviom ´ etricas de la cuenca del r ´ ´ıo San Juan, en la region hidrogr ´ afica RH-24 M ´ exico. La base de datos fue proporcionada por ´ la Comision Nacional del Agua (CONAGUA). A los variogramas, se les obtuvo el exponente ´ de Hurst y se utilizo como una entrada para llevar a cabo un an ´ alisis de agrupamiento de ´ estaciones de lluvia. Grupos de muestras homogeneas que pueden ser ´ utiles en un an ´ alisis ´ de frecuencia regional se obtuvieron a traves del proceso

Procesos aleatorios en modelación matemática

Repasamos brevemente un modelo simple de caminata aleatoria para modelar el comportamiento colectivo de muchas partículas y el problema asociado con la causalidad de la ecuación de difusión obtenida en el límite difusivo

Outcomes from elective colorectal cancer surgery during the SARS-CoV-2 pandemic

This study aimed to describe the change in surgical practice and the impact of SARS-CoV-2 on mortality after surgical resection of colorectal cancer during the initial phases of the SARS-CoV-2 pandemic

A New Deterministic Gasket Fractal Based on Ball Sets

F.H.-Z. thanks FCFM-UNACH and the support from CONACyT through the program “Investi gadoras e investigadores por México”, Cátedra 873. M.A.A.-L. thanks CONACyT for the postdoc toral grant 839412 and FCFM-UNACH for sup porting his research stay.In this paper, we propose a new gasket fractal constructed in a deterministic iterated function system (IFS) way by means of interacting ball and square sets in R 2 . The gasket consists of the ball sets generated by the IFS, possessing also exact self-similarity. All this leads to a direct deduction of other properties and a clear construction methodology, including a dynamic geometry procedure with an open-source construction protocol. We also develop an extended version of the fractal in Rn. Some resulting config urations consisting of stacked 2D-fractals are plotted. We discuss about potential applications of them in some areas of science, focusing mainly on percolation models. Guidelines for future work are also provided

A Quadratic–Exponential Model of Variogram Based on Knowing the Maximal Variability: Application to a Rainfall Time Series

Variogram models are a valuable tool used to analyze the variability of a time series; such variability usually entails a spherical or exponential behavior, and so, models based on such functions are commonly used to fit and explain a time series. Variograms have a quasi-periodic structure for rainfall cases, and some extra steps are required to analyze their entire behavior. In this work, we detailed a procedure for a complete analysis of rainfall time series, from the construction of the experimental variogram to curve fitting with well-known spherical and exponential models, and finally proposed a novel model: quadratic–exponential. Our model was developed based on the analysis of 6 out of 30 rainfall stations from our case study: the Río Bravo–San Juan basin, and was constructed from the exponential model while introducing a quadratic behavior near to the origin and taking into account the fact that the maximal variability of the process is known. Considering a sample with diverse Hurst exponents, the stations were selected. The results obtained show robustness in our proposed model, reaching a good fit with and without the nugget effect for different Hurst exponents. This contrasts to previous models, which show good outcomes only without the nugget effect

Clustering of Rainfall Stations in RH-24 Mexico Region Using the Hurst Exponent in Semivariograms

An important topic in the study of the time series behavior and, in particular, meteorological time series is the long-range dependence. This paper explores the behavior of rainfall variations in different periods, using long-range correlations analysis. Semivariograms and Hurst exponent were applied to historical data in different pluviometric stations of the Río Bravo-San Juan watershed, at the hydrographic RH-24 Mexico region. The database was provided by the Water National Commission (CONAGUA). Using the semivariograms, the Hurst exponent was obtained and used as an input to perform a cluster analysis of rainfall stations. Groups of homogeneous samples that might be useful in a regional frequency analysis were obtained through the process

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 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

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

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

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

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