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.

Geological Modeling for Nahr Umr Formation in Subba Oil Field, Southern Iraq

Geological modeling is very important in reservoir study, where it is described the framework of the structure and provided a distribution of petrophysical properties, the geological model helps to comprehend the fluid flow behavior affected by the heterogeneity of reservoir, also it is used to calculate oil initially in place and to choose the new well location in reservoir management. In this study, a geological model is built for Nahr Umr Formation based on data of 11 wells (SU-2, SU-3, SU-4, SU-5, SU-6, SU-7, SU-9, SU-10, SU-11, SU-13, and SU-14), including the location of wells, well tops, also contour map of the Nahr Umr Formation in Subba oil field is utilized. The structural model is constructed for the Nahr Umr Formation, which consists of two domes. The formation is composed of sandstone mainly interbedded with shale. The formation is divided into four units (B1, B2, C1, and C2) depending on well log data, each unit is divided into layers for getting better distribution of petrophysical properties, where unit B2 is divided to the number of layers is higher than other units due to its heterogeneity. The variogram is used as a geostatistical method to predict the petrophysical properties at unsampled locations, experimental variogram is calculated from well log data in a horizontal and vertical direction. The spherical variogram model shows a good fitting with the experimental variogram. Sequential Gaussian algorithm is used in distribution of petrophysical properties in a geological model which shows good petrophysical properties in unit B2 and unit B1, while units C1 and C2 are highly saturated with water.

Geostatistical analysis of static level evolution between 1995-2005 and 2007-2017 in San Luis Potosí Aquifer, México

Knowing the piezometric levels evolution of an aquifer is essential for planning the use of water resources in the cities of central México, such as San Luis Potosí, whose population depends almost entirely on groundwater. Applying geostatistical methods from georeferenced data can reliably provide information on the spatial variability of valley piezometry. The objective of this study is to evaluate the evolution of the static levels of the aquifer in San Luis Potosí Valley, through an interpolation analysis by the kriging method. For both periods, the experimental variogram was adjusted to the Gaussian model and the method with the best results was ordinary kriging. From this analysis it was obtained that the decay of the static levels is more critical in the central zone of the valley, while the zones of the northwest and towards the south, the aquifer levels have shown an important recovery; the important values for the decrease in static levels coincide with the areas where the population density is greater.

Analysis of Fracture Networks of the Black Volta Catchment in Côte D’ivoire

A good knowledge of fracturing leads to a better exploitation of the groundwater of the areas in crystalline basement. This study area of interests the catchment of Black Volta area in north eastern Côte d’Ivoire. Its aims to characterize the fracture networks of the catchment of Black Volta. Various methods were used notably mapping using satellite image processing, statistical and geostatistical analysis. The results showed that fracturing of Black Volta area is dense and homogeneous. Statistical analysis of geometric parameter of the fracturing such as fracture lengths and spacing are distributed respectively according to power law and gamma law. The deployment of the fracturing in this area is organized and the experimental variogram is characterized by two nested elementary structures. The practical ranges of these two elementary variograms are respectively 34, 5 km to 60 km. Results indicate that the fracturing of Black Volta area reached a stage of advanced development and is complex. Fracturing of Black Volta area is now well known and the groundwater modeling can be undertaking.

Calculation and Fitting Methods of Variogram

Calculation and fitting of variogram is a very important problem in the study of geostatistics. With the need of practical application, variogarm with multiform definition has appeared. But, the study of variogram is mainly focus on the calculation and fitting of theoretical variogram, and less on the experimental variogram, more a lack of research on the automatic calculation. There is little research on experimental variogram. To strengthen the study of experimental variogram is the future trend of development.

Spatial Distribution of Heavy Metals in Surface Soil of Zhejiang Pinghu

In this paper, the spatial structure of heavy metals were quantitatively described to soil in Zhejiang Pinghu City based on statistical methods, and the main factors of the spatial structure of heavy metals were discussed in the study region. The results showed that the soil experimental variogram model fitted better in the study area in the 7 heavy metals of As, Cr, Cd, Cu, Ni, Pb, and Zn. Principal component analysis reflected the elements Pb, Zn, Cu, As, Cr and Ni distribution in a same component; and elemental Hg and Cd each a separate component.

VARIABILIDADE ESPACIAL DA UMIDADE DO SOLO EM IRRIGAÇÃO POR GOTEJAMENTO SOB CULTIVO PROTEGIDO

VARIABILIDADE ESPACIAL DA UMIDADE DO SOLO EM IRRIGAÇÃO POR GOTEJAMENTO SOB CULTIVO PROTEGIDO[1] Ivana Fúrio BatistaCélia Regina Lopes ZimbackJuliana Aguiar VettoratoDepartamento de Recursos Naturais, Faculdade de Ciências Agronômicas, Universidade Estadual Paulista, Botucatu, CP 237, CEP 18603-970. E-mail: [email protected] 1 RESUMO Foi estudada a variabilidade espacial da umidade do solo num sistema de irrigação por gotejamento em uma estufa (5,0 x 20,0m) na Fazenda Experimental São Manuel, da Faculdade de Ciências Agronômicas, Universidade Estadual Paulista, Estado de São Paulo, Brasil. Foi estabelecida a malha de amostragem no espaçamento de 1,0 x 0,5m, acrescida de quatro adensamentos de 0,25m. Foram utilizados dados da umidade do solo em 178 pontos. A análise da dependência espacial foi obtida com o auxílio do Programa GS+. Foi construído o variograma experimental e definido o modelo de ajuste, de modo que a curva que melhor se ajustou aos pontos obtidos representasse a magnitude, alcance e intensidade da variabilidade espacial da variável estudada. A umidade do solo apresentou distribuição espacial anisotrópica. Para a direção 0°, pode-se notar uma dependência espacial caracterizada como alta, com o alcance de aproximadamente 3,30m, no sentido do comprimento da estufa. Entretanto, no sentido da largura da estufa, não foi possível ajustar modelos. Utilizando a representação gráfica da superfície, a área estudada apresentou um maior teor de água na parte inicial e menor na parte final das linhas de distribuição de água. A krigagem mostrou-se um bom interpolador para mapeamento da umidade do solo. UNITERMOS: geoestatística, dependência espacial, umidade do solo, irrigação por gotejamento, cultivo protegido. BATISTA, I.F.; ZIMBACK, C.R.L.; VETTORATO, J.A. SPATIAL VARIABILITY OF SOIL MOISTURE IN A DRIP IRRIGATION SYSTEM UNDER GREENHOUSE 2 ABSTRACT Soil moisture spatial variability in a drip irrigation system was studied in a greenhouse (5.0 x 20.0m) at São Manuel Experimental Farm, FCA/UNESP, Botucatu – SP, Brazil. Sampling was established in a 1.0 x 0.5m grid, increased 0.25m thickening. Soil moisture data were used in 178 points. The spatial dependence analysis was obtained with the aid of the GS+ Program. The experimental variogram was built and the setting model defined, so that the curve better fitted to the obtained points represented the spatial variability magnitude, range and intensity of the studied variable. Soil moisture presented anisotropic spatial distribution. Spatial dependence was noticed for 0° direction, characterized as high, with approximately 3.30m range in the greenhouse length ward. However, in the greenhouse width ward, it was not possible to fit models. Using the surface graphic representation, the studied area presented higher water content in the initial part and a lower one in the final part of water distribution lines. Kriging was shown to be a good interpolator for soil moisture mapping. KEYWORDS: geostatistics, spatial dependence, soil moisture, drip irrigation, greenhouse.