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

Benavides-Bravo, Francisco Gerardo; Soto-Villalobos, Roberto; Cantú-González, José Roberto; Aguirre-López, Mario A.; Benavides-Ríos, Ángela Gabriela

doi:10.3390/math9192466

Cited by 7 publications

(4 citation statements)

References 36 publications

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“…Indeed, aided by the division of background colors in the charts of Figure 2, greater PM 10 concentrations can be observed in the autumn-winter period than in the spring-summer period for all of the MMA. This suggests that the quasi-periodic behavior of the time series is a natural phenomenon of the region that could be related to other environmental factors that have been reported with the same cyclical characteristics for the study area, such as the seasonal rains of the region [55].…”

Section: Time Series and Semi-variogramssupporting

confidence: 62%

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

et al. 2022

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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 [d=R1]time-series trendstrend of time series, locating areas with high [d=R1]pollutant concentrationsconcentration of pollutants, 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. [d=R1]First, weWe 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[d=R1]. The, with the autumn-winter period [d=R1]wasas the most polluted and the spring-summer period [d=R1]wasas 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, [d=R1]in additionadditionally to the results for the MMA, the present paper shows three [d=R1]practicaluseful statistical methods for analyzing the spatio-temporal behavior of air quality.

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Section: Time Series and Semi-variogramssupporting

confidence: 62%

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

et al. 2022

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“…Este modelo apresenta aplicabilidade quando não há significativa relação espacial entre as estações pluviométricas (Subyani, 2019). Houve um baixo desempenho deste modelo para Minas Gerais, mesmo existindo aplicabilidade deste nos climas semiárido (Oliveira et al, 2022) e amazônico (Millán-Vega et al, 2020), assim como no estado do Tocantins (Neto et al, 2020b) e do Mato Grasso (Cerón et al, 2021), e em outros países (Machiwal et al, 2020;Benavides-Bravo et al, 2021;Bati et al, 2022).…”

Section: Modelounclassified

Comparação de modelos geoestatísticos para estimativa de precipitação em Minas Gerais, Brasil, entre os anos hidrológicos de 2000 e 2021

Guimarães

Alves²

2023

Rev. Bras. Geog. Fis.

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A gestão integrada dos recursos hídricos no Brasil e no mundo tem passado por desafios provenientes de processos naturais e antrópicos. Assim, o conhecimento preciso das condições quantitativas e qualitativas dos recursos hídricos é de fundamental importância, sendo o monitoramento pluviométrico por estações pluviométricas distribuídas no estado um componente central deste, no que diz respeito ao entendimento da dinâmica espacial e temporal da precipitação. Em Minas Gerais, tais estações estão concentradas em determinadas áreas, dificultando o processo de tomada de decisão pelos agentes gestores. As técnicas de geoestatística têm se mostrado acuradas para estimativa de precipitação em espaços sem estações pluviométricas, sendo que tal trabalho visou aplicá-las no estado, nos anos hidrológicos de outubro de 2000 a setembro de 2021. Verificou-se o potencial dos modelos Circular, Gaussiano, Esférico, Tetraesférico, Pentaesférico e Exponencial, e o Grau de Dependência Espacial entre as variáveis, utilizando-se do tratamento de dados por linguagem de programação Python e R e por técnicas de geoprocessamento. Os resultados apontaram para maior aplicabilidade do modelo Gaussiano em toda série histórica, sendo sucedido pelo modelo Exponencial em períodos chuvosos, e pelo modelo Circular na estação seca. Os modelos Pentaesférico, Esférico e Tetraesférico foram os menos aplicados. Viu-se também uma relação irregular entre o desempenho dos modelos e o Grau de Dependência Espacial das variáveis.Palavras-chave: krigagem, dependência espacial, estações pluviométricas, gestão integrada dos recursos hídricos. Comparison of geostatistical models for rainfall forecast in Minas Gerais, Brazil, between 2000 and 2021 hydrological years A B S T R A C TThe integrated water resources management in Brazil and worldwide had been through challenges from anthropic activities and natural processes. In that regard, the precise knowledge of water resources quality and quantity conditions has major importance, with the rainfall monitoring network by rainfall stations as a core component for understanding the precipitation spatial and temporal dynamics. These stations are concentrated in a few sites within Minas Gerais, which makes the decision-making process difficult for the manager agents. Geostatistical analysis has been shown as an accurate method for rainfall forecast in spaces with lack of rainfall stations, and this work aimed to apply it in Minas Gerais, between October 2000 and September 2021 hydrological years. It was checked Circular, Gaussian, Spherical, Tetraspherical, Pentaspherical, and Exponential models potential, and the degree of spatial dependence, using data treatment by Python and R programming language and geoprocessing tools. The results showed that Gaussian model has greater applicability in the time series, being succeed by Exponential model in wet season, and Circular model in dry season. Pentaspherical, Spherical, and Tetraspherical models were the least applied. It was found an irregular relationship between models’ performance and the degree of spatial dependence.Keywords: kriging, degree of spatial dependence, rainfall stations, integrated water resources management.

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“…Some scholars have shown that at least 4-8 variogram maps should be calculated to determine whether soil properties are isotropic or anisotropic by comparing the magnitudes of the principal and secondary variograms. If the ratio of the principal variogram to the secondary variogram is 1 or close to 1, then it is isotropic, indicating that regionalized variables have the same or similar changes in different directions [54]. Anisotropy needs to be converted to isotropy according to the linear proportion relationship.…”

Section: Spatial Structure Analysis Of Som At Different Scalesmentioning

confidence: 99%

Multi-Scale Integration and Distribution of Soil Organic Matter Spatial Variation in a Coal–Grain Compound Area

Zhang

Liu

et al. 2023

Sustainability

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Soil organic matter (SOM) scale effects are critical for crop growth and food security, especially in coal–grain complexes. However, few studies describe the spatial variation in SOM and its influencing factors at different sampling scales. Here, geostatistical theory and mathematical statistical methods were adopted to analyze the spatial variation characteristics of and structural differences in SOM in the coal mining subsidence area at Zhaogu No. 2 Mine at different sampling scales. The results showed that SOM varied spatially at large, medium, and small scales, and the coefficients of variation were 28.07%, 14.93%, and 14.31%, respectively, which are moderate values. The characteristic functions of the SOM content at different sampling scales differed, and the spatial structure scale effect was obvious. The spatial distribution of the SOM content fitted by the multiscale fitting model method was generally the same as the spatial distribution law of the SOM content fitted by the single scale kriging interpolation method; however, in terms of the detailed expression and spatial distribution of small-scale SOM content, the fitting model method was more accurate, and the accuracy increased by 36%. At the different sampling scales, sample size and soil type had specific effects on the SOM spatial distribution. These results provide research concepts and technical countermeasures for improving food security and the ecological environment in the coal–grain complex and help ensure sustainable agricultural lands.

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

Cited by 7 publications

References 36 publications

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

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

Comparação de modelos geoestatísticos para estimativa de precipitação em Minas Gerais, Brasil, entre os anos hidrológicos de 2000 e 2021

Multi-Scale Integration and Distribution of Soil Organic Matter Spatial Variation in a Coal–Grain Compound Area

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