Semivariogram Parameters Research Articles

Relationships Between Tillage and Spatial Patterns of Heterodera glycines

ABSTRACT The dynamics of Heterodera glycines spatial patterns were studied under different tillage systems in two naturally infested soybean fields in Iowa from 1994 to 1997. At each location, there were four different tillage treatments (conventional tillage, reduced tillage, ridge tillage, and no tillage). Soil samples were taken from 98 contiguous quadrats (5.2 m(2)) per plot in the fall of 1994, before any tillage was performed, and in the spring of the following 3 years shortly after planting. Cysts were extracted from soil samples by elutriation and counted, and eggs were extracted from cysts and enumerated. Spatial patterns of H. glycines populations were characterized by geostatistical analysis and variance-to-mean (VM) ratios. Semivariance values were calculated for cyst and egg densities and semivariograms were constructed. In general, there was greater spatial dependence among cyst populations than egg populations. In one field with a strongly aggregated initial H. glycines population, tillage practices resulted in changes in spatial patterns of H. glycines populations, characterized by spherical-model semivariogram parameters (sill, nugget effect, and range of spatial dependence). These parameters indicated increasing aggregation over time in no tillage and ridge tillage treatments, but decreasing aggregation in reduced and conventional tillage treatments. There was an increase of 350% in sill values (maximum semivariance) for cyst populations after 3 years of no tillage, but in the conventional tillage treatment, sill values remained unchanged or decreased over time as tillage was implemented. Semivariograms for cyst and egg population densities revealed strong anisotropy (directional spatial dependence) along soybean rows, coincident with the direction of tillage practices. VM ratios for cyst counts increased each year in the no tillage and ridge tillage treatments, but decreased for 2 years in reduced tillage and conventional tillage treatments. Final VM ratios for cyst and egg counts were highest in the no tillage treatment. In a second field, with low initial aggregation of H. glycines populations, there was little measurable change in semivariogram parameters after 3 years of no tillage, but in the conventional tillage treatment, populations became less aggregated, as the range, sill, and the proportion of the sill explained by spatial dependence decreased for cyst population densities. Our results indicated that in soybean fields with initially aggregated populations of H. glycines, no tillage and ridge tillage systems promoted aggregation of the nematode population, whereas conventional and reduced tillage systems resulted in a less aggregated spatial pattern.

Anisotropic Autocorrelation in House Prices

This paper examines anisotropic spatial autocorrelation in single-family house prices and in hedonic house price equation residuals using a spherical semivariogram and transactions data for one county in the Philadelphia, Pennsylvania MSA. Isotropic semivariograms model spatial relationships as a function of the distance separating properties in space. Anisotropic semivariograms model spatial relationships as a function of both the distance and the direction separating observations in space. The goals of this paper are: (1) to determine whether there is spatial autocorrelation in hedonic house price equation residuals; and (2) to empirically examine the validity of the isotropy assumption. We estimate the parameters of spherical semivariograms for house prices and for hedonic house price equation residuals for 21 housing submarkets within Montgomery County, Pennsylvania. These housing submarkets are constructed by dividing the county into 21 groupings of economically similar adjacent census tracts. Census tracts are grouped according to 1990 census tract median house prices and according to characteristics of the housing stock. We fit the residuals of each submarket hedonic house price equation to both isotropic and anisotropic sepherical semivariograms. We find evidence of spatial autocorrelation in the hedonic residuals in spite of a very elaborate hedonic specification. Additionally, we have determined that, in some submarkets, the spatial autocorrelation in the hedonic residuals is anisotropic rather than isotropic. The empirical results suggest that the spatial autocorrelation in Montgomery County single-family house price equation residuals is anisotropic in submarkets where residents typically commmute to a regional or local Central Businss District (CBD).

Variabilidade espacial da rugosidade superficial do solo medida com rugosímetros de agulhas e laser

A variabilidade espacial da rugosidade superficial do solo foi estudada a partir de uma grade de dados pontuais medidos com instrumentos de diferentes graus de precisão. Para a medição da rugosidade utilizou-se um rugosímetro laser, em condições de laboratório, sendo as leituras realizadas antes e após a aplicação de diferentes quantidades de chuva (0 mm, 10 mm, 55 mm, 85 mm). Nas condições de campo (pastagem e superfície arada) utilizou-se um rugosimetro de agulhas, e as leituras foram realizadas em quatro datas distintas. Verificou-se alta dependência espacial para a rugosidade superficial, com os dados obtidos em ambos os métodos e em todos os tratamentos. Os parâmetros dos semivariogramas obtidos com os dados do rugosímetro de agulhas apresentaram grandes variações nas diferentes datas, devido à forma de distribuição e ao tamanho dos agregados. Isso indica a dificuldade de encontrar um modelo tridimensional, representativo do microrrelevo, em condições de campo. Verificou-se grande semelhança em todos os semivariogramas obtidos a partir dos dados do rugosímetro laser (superfície simulada) indicando que, apesar das alterações na rugosidade superficial, não foram observadas modificações no comportamento da dependência espacial com a aplicação de diferentes quantidades de chuva.

A Composite Likelihood Approach to Semivariogram Estimation

This article proposes the use of estimating functions based on composite likelihood for the estimation of isotropic as well as geometrically anisotropic semivariogram parameters. The composite likelihood approach is objective, eliminating the specification of distance lags and lag tolerances associated with the commonly used moment estimator. Extensions to the geometric anisotropy case include a parameterized transformed distance function, which eliminates the subjective estimation of the parameters of geometric anisotropy. The composite likelihood approach requires no matrix inversions and the estimators are shown to be consistent in a fashion similar to maximum likelihood and restricted maximum likelihood but without reliance on strong distributional assumptions. Predictions based on composite likelihood estimates performed very well using isotropic and geometric anisotropic simulated data and compared favorably to predictions based on the traditional approach in the isotropic case. Comparisons were also made using data collected on iron-ore measurements where previous analyses determined a geometric anisotropic semivariogram model to be appropriate.

3D Conditional Simulation of Porosity For a Heterogeneous Core

Abstract Conditional simulated annealing, sequential Gaussian simulation and kriging were used to simulate the three-dimensional (3D) porosity distribution for a heterogeneous anisotropic core from the Fenn-Big Valley Field in Alberta, Canada. The 3D porosity distribution was known from previous X-ray computerized tomography experiments. The ability of each method to model the experimental porosity distribution was examined. The conditional data sets were selected from the complete set of known values. The remaining data were assumed to be unknown and were simulated. The simulated values were then compared to the experimental values. Simulated annealing can exactly reproduce the specified semivariograms. For this problem simulated annealing is more efficient if only objective-reducing swaps are accepted. A more convenient way to treat the anisotropies in the semivariogram parameters, sill and range, is presented. Introduction Geostatistical techniques are becoming common tools for engineers and geologists in the petroleum industry. For a variety of problems such as reservoir simulation, reservoir characterization, seal analysis and reserve estimation, the practicing engineer or geologist is constantly working with incomplete data sets. In order to solve these problems one must make some estimate of the unknown data. Often one also needs an estimate of the uncertainties associated with these estimates. Geostastical techniques can provide both estimates of the unknown parameters and estimates of the associated uncertainties. There are a variety of geostatistical techniques available, with new approaches and techniques continually being developed. These techniques are often difficult to evaluate because the "correct" answer is seldom, if ever, known for the field problems to which they are applied. This paper examines three common, but very different techniques, on a laboratory problem where the "answer" has been determined. These techniques are explained and compared, and some new suggestions are made on the implementation of one of these techniques. A better understanding of the predictions made with these techniques can aid the engineer or geologist in understanding the advantages and limitations in applying a geostatistical technique to solve problems such as reservoir simulation and the characterization of cores, reservoirs, and seal rocks. Kriging, sequential Gaussian simulation (SGS), and simulated annealing simulation (SAS) are three often-used geostatistical methods for reservoir characterization with SAS gaining more attention because of its capability to accurately reproduce semivariograms and its ability to incorporate data from different sources. In this study, kriging, conditional SGS and SAS are used to model the porosity distribution of two- and three-dimensional heterogeneous anisotropic core samples. The results from each method are examined and compared. SAS is better than kriging and SGS in reproducing the semivariogram, especially for anisotropic cases, but it suffers considerably from computational intensity. To make SAS more efficient, different annealing schedules are investigated, and different patterns of lag vectors are considered for the objective function. Also, to achieve a better representation of the spatial structures of simulated attributes, a more convenient treatment of anisotropies of the semivariogram sill and range is examined. Core Data A 102 mm long, 98 mm diameter core section from the Fenn-Big Valley in Alberta, Canada is the subject of this study except when stated otherwise.

Bayesian Modeling and Inference for Geometrically Anisotropic Spatial Data

A geometrically anisotropic spatial process can be viewed as being a linear transformation of an isotropic spatial process. Customary semivariogram estimation techniques often involve ad hoc selection of the linear transformation to reduce the region to isotropy and then fitting a valid parametric semivariogram to the data under the transformed coordinates. We propose a Bayesian methodology which simultaneously estimates the linear transformation and the other semivariogram parameters. In addition, the Bayesian paradigm allows full inference for any characteristic of the geometrically anisotropic model rather than merely providing a point estimate. Our work is motivated by a dataset of scallop catches in the Atlantic Ocean in 1990 and also in 1993. The 1990 data provide useful prior information about the nature of the anisotropy of the process. Exploratory data analysis (EDA) techniques such as directional empirical semivariograms and the rose diagram are widely used by practitioners. We recommend a suitable contour plot to detect departures from isotropy. We then present a fully Bayesian analysis of the 1993 scallop data, demonstrating the range of inferential possibilities.

Estimation of semivariogram parameters and evaluation of the effects of data sparsity

Semivariogram parameters are estimated by a weighted least-squares method and a jackknife kriging method. The weighted least-squares method is investigated by differing the lag increment and maximum lag used in the fit. The jackknife kriging method minimizes the variance of the jackknifing error as a function of semivariogram parameters. The effects of data sparsity and the presence of a trend are investigated by using 400-, 200-, and 100-point synthetic data sets. When the two methods yield significantly different results, more data may be needed to determine reliably the semivariogram parameters, or a trend may be present in the data.

Geostatistical analysis of soil properties in a secondary tropical dry forest, St. Lucia, West Indies

Spatial variability of soil properties directly influences forest growth. However, spatial variation in soil properties has not been studied within tropical dry forests. As such, it is unclear whether soil properties, like moisture and N availability, display spatial variation at scales similar to that of other ecosystems. To gain insight into this variation, we established a 56 × 56 m sampling grid in tropical dry forest on the Caribbean island of St. Lucia. Samples collected at 4-m intervals were analyzed for forest floor mass, soil texture, pH, organic C, net N mineralization, net nitrification and available P. Geostatistical procedures were used to determine spatial autocorrelation of the aforementioned properties and processes. Semivariogram parameters were used in a block kriging procedure to produce spatial maps of soil properties. At the scale of our study, most soil properties exhibited spatial autocorrelation at distances of 24 m or less. Varying degrees of similarity were found between patterns of forest floor mass, organic C, net N mineralization, net nitrification and available P. No similarity was found between soil texture or pH and other properties. Fine-scale spatial patterns of net N mineralization and net nitrification are likely driven by overstory litter inputs, rather than variation in soil texture and water availability.

Fuzzy‐c‐Means and Kriging for Mapping Soil as a Continuous System

AbstractEven though soil has long been recognized as a continous system in both the geographical and taxonomic context, there has been no practical approach to mapping soil as a continuum. Fuzzy set theory and the regionalized variable theory provide for such an approach. A predetermined optimal sampling scheme was used for sampling of pedons in an area of 627 by 375 m. The fuzzy‐c‐means (FCM) algorithm was first used to quantify the pedons into intragrade and extragrade classes by minimization of the fuzzy objective function. The resulting matrix of membership coefficients was used to determine membership semivariograms for the c + 1 continuous soil classes. The resulting semivariogram parameters were further used for kriging of the membership coefficients, yielding an isarithmic map for each of the c + 1 fuzzy soil classes. A composite map that presents the core areas of the continuous classification units was produced by overlaying of the isarithmic maps of the c + 1 classes. The significance of this approach to geographical (or soil) information systems is the associated minimum loss of information if fuzzy logic and operations are integrated into the systems.

A Comparison of Spatial Semivariogram Estimators and Corresponding Ordinary Kriging Predictors

Predicting values of a spatially distributed variable, such as the concentration of a mineral throughout an ore body or the level of contamination around a toxic-waste dump, can be accomplished by a regression procedure known as kriging. Kriging and other types of statistical inference for spatially distributed variables are based on models of stochastic processes {Y t: t ∊ D} called random-field models. A commonly used class of random-field models are the intrinsic models, for which the mean is constant, and half of the variance of Yt , – Ys . is a function, called the semivariogram, of the difference t – s. The type of kriging corresponding to an intrinsic model is called ordinary kriging. The semivariogram, which typically is taken to depend on one or more unknown parameters, must be estimated prior to ordinary kriging. Various estimators of the semivariogram's parameters have been proposed. For two Gaussian intrinsic random-field models, we compare, by a Monte Carlo simulation study, the performance o...