The analysis of ranked observations of soil structure using indicator geostatistics

Structure is an important physical feature of the soil that is associated with water movement, the soil atmosphere, microorganism activity and nutrient uptake. A soil without any obvious organisation of its components is known as apedal and this state can have marked effects on several soil processes. Accurate maps of topsoil and subsoil structure are desirable for a wide range of models that aim to predict erosion, solute transport, or flow of water through the soil. Also such maps would be useful to precision farmers when deciding how to apply nutrients and pesticides in a site-specific way, and to target subsoiling and soil structure stabilization procedures. Typically, soil structure is inferred from bulk density or penetrometer resistance measurements and more recently from soil resistivity and conductivity surveys. To measure the former is both time-consuming and costly, whereas observations made by the latter methods can be made automatically and swiftly using a vehicle-mounted penetrometer or resistivity and conductivity sensors. The results of each of these methods, however, are affected by other soil properties, in particular moisture content at the time of sampling, texture, and the presence of stones. Traditional methods of observing soil structure identify the type of ped and its degree of development. Methods of ranking such observations from good to poor for different soil textures have been developed. Indicator variograms can be computed for each category or rank of structure and these can be summed to give the sum of indicator variograms (SIV). Observations of the topsoil and subsoil structure were made at four field sites where the soil had developed on different parent materials. The observations were ranked by four methods and indicator and the sum of indicator variograms were computed and modelled for each method of ranking. The individual indicators were then kriged with the parameters of the appropriate indicator variogram model to map the probability of encountering soil with the structure represented by that indicator. The model parameters of the SIVs for each ranking system were used with the data to krige the soil structure classes, and the results are compared with those for the individual indicators. The relations between maps of soil structure and selected wavebands from aerial photographs are examined as basis for planning surveys of soil structure. (C) 2007 Elsevier B.V. All rights reserved.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial analysis of the distribution of Spodoptera frugiperda (J.E. Smith) (Lepidoptera: Noctuidae) and losses in maize crop productivity using geostatistics

A lagarta-do-cartucho, Spodoptera frugiperda (J.E. Smith), é uma das principais pragas do milho nas Américas. O estudo de sua distribuição espacial é fundamental para a utilização de estratégias de controle, otimização de técnicas de amostragens, determinação de danos econômicos e incorporação de um programa de agricultura de precisão. em uma área cultivada com milho foram realizadas amostragens com intervalo semanal, correspondendo ao estádio vegetativo que compreende desde a germinação até o pendoamento. Foram amostradas 10 plantas ao acaso por parcela, no total de 2000 plantas em cada amostragem. A produtividade foi obtida através da colheita de todas as parcelas que eram pesadas separadamente no campo e em cada parcela foram coletadas 15 espigas aleatoriamente para estimar o comprimento e o diâmetro médio. As análises espaciais, utilizando geoestatística, mostraram que o modelo esférico apresentou o melhor ajuste às lagartas pequenas. À medida que as lagartas foram se desenvolvendo sua distribuição foi tornando aleatória, representada por um modelo ajustado por uma reta, não tendo sido detectado nenhum tipo de dependência espacial nos pontos de amostragem. A produtividade e o diâmetro e comprimento da espiga foram descritos por modelos esféricos, indicando uma variabilidade espacial nos parâmetros de produtividade na área cultivada. A geoestatística mostrou-se promissora para a aplicação de métodos precisos no controle integrado de pragas.

Comparing three indices of catch per unit effort using Bayesian geostatistics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Geostatistics and remote sensing methods in the classification of images of areas cultivated with citrus

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Spatial intra-annual variability of precipitation based on geostatistics. a case study for the Paraiba do Sul Basin, southeastern Brazil

The emphasis in this research is to evaluate the spatial distribution of the precipitation using a geostatistics approach. Seasonal time scales records considering DJF, MAM, JJA e SON periods performed the analysis. Procedures to evaluate the variogram selection and to produce kriging maps were performed in a GIS environment (ArcGIS®). The results showed that kriging method was very suitable to detect both large changes in the whole area as those local small and subtle changes. Kriging demonstrated be a powerful statistical interpolation method that might be very useful in regions with great complexity in climatology and geomorphology.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Exchanging uncertainty: interoperable geostatistics?

Traditionally, geostatistical algorithms are contained within specialist GIS and spatial statistics software. Such packages are often expensive, with relatively complex user interfaces and steep learning curves, and cannot be easily integrated into more complex process chains. In contrast, Service Oriented Architectures (SOAs) promote interoperability and loose coupling within distributed systems, typically using XML (eXtensible Markup Language) and Web services. Web services provide a mechanism for a user to discover and consume a particular process, often as part of a larger process chain, with minimal knowledge of how it works. Wrapping current geostatistical algorithms with a Web service layer would thus increase their accessibility, but raises several complex issues. This paper discusses a solution to providing interoperable, automatic geostatistical processing through the use of Web services, developed in the INTAMAP project (INTeroperability and Automated MAPping). The project builds upon Open Geospatial Consortium standards for describing observations, typically used within sensor webs, and employs Geography Markup Language (GML) to describe the spatial aspect of the problem domain. Thus the interpolation service is extremely flexible, being able to support a range of observation types, and can cope with issues such as change of support and differing error characteristics of sensors (by utilising descriptions of the observation process provided by SensorML). XML is accepted as the de facto standard for describing Web services, due to its expressive capabilities which allow automatic discovery and consumption by ‘naive’ users. Any XML schema employed must therefore be capable of describing every aspect of a service and its processes. However, no schema currently exists that can define the complex uncertainties and modelling choices that are often present within geostatistical analysis. We show a solution to this problem, developing a family of XML schemata to enable the description of a full range of uncertainty types. These types will range from simple statistics, such as the kriging mean and variances, through to a range of probability distributions and non-parametric models, such as realisations from a conditional simulation. By employing these schemata within a Web Processing Service (WPS) we show a prototype moving towards a truly interoperable geostatistical software architecture.

Parallel geostatistics for sparse and dense datasets

Very large spatially-referenced datasets, for example, those derived from satellite-based sensors which sample across the globe or large monitoring networks of individual sensors, are becoming increasingly common and more widely available for use in environmental decision making. In large or dense sensor networks, huge quantities of data can be collected over small time periods. In many applications the generation of maps, or predictions at specific locations, from the data in (near) real-time is crucial. Geostatistical operations such as interpolation are vital in this map-generation process and in emergency situations, the resulting predictions need to be available almost instantly, so that decision makers can make informed decisions and define risk and evacuation zones. It is also helpful when analysing data in less time critical applications, for example when interacting directly with the data for exploratory analysis, that the algorithms are responsive within a reasonable time frame. Performing geostatistical analysis on such large spatial datasets can present a number of problems, particularly in the case where maximum likelihood. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively. Most modern commodity hardware has at least 2 processor cores if not more. Other mechanisms for allowing parallel computation such as Grid based systems are also becoming increasingly commonly available. However, currently there seems to be little interest in exploiting this extra processing power within the context of geostatistics. In this paper we review the existing parallel approaches for geostatistics. By recognising that diffeerent natural parallelisms exist and can be exploited depending on whether the dataset is sparsely or densely sampled with respect to the range of variation, we introduce two contrasting novel implementations of parallel algorithms based on approximating the data likelihood extending the methods of Vecchia [1988] and Tresp [2000]. Using parallel maximum likelihood variogram estimation and parallel prediction algorithms we show that computational time can be significantly reduced. We demonstrate this with both sparsely sampled data and densely sampled data on a variety of architectures ranging from the common dual core processor, found in many modern desktop computers, to large multi-node super computers. To highlight the strengths and weaknesses of the diffeerent methods we employ synthetic data sets and go on to show how the methods allow maximum likelihood based inference on the exhaustive Walker Lake data set.

Sequential, Bayesian geostatistics:a principled method for large data sets

The principled statistical application of Gaussian random field models used in geostatistics has historically been limited to data sets of a small size. This limitation is imposed by the requirement to store and invert the covariance matrix of all the samples to obtain a predictive distribution at unsampled locations, or to use likelihood-based covariance estimation. Various ad hoc approaches to solve this problem have been adopted, such as selecting a neighborhood region and/or a small number of observations to use in the kriging process, but these have no sound theoretical basis and it is unclear what information is being lost. In this article, we present a Bayesian method for estimating the posterior mean and covariance structures of a Gaussian random field using a sequential estimation algorithm. By imposing sparsity in a well-defined framework, the algorithm retains a subset of “basis vectors” that best represent the “true” posterior Gaussian random field model in the relative entropy sense. This allows a principled treatment of Gaussian random field models on very large data sets. The method is particularly appropriate when the Gaussian random field model is regarded as a latent variable model, which may be nonlinearly related to the observations. We show the application of the sequential, sparse Bayesian estimation in Gaussian random field models and discuss its merits and drawbacks.

Pragmatic algorithms for implementing geostatistics with large datasets

With the ability to collect and store increasingly large datasets on modern computers comes the need to be able to process the data in a way that can be useful to a Geostatistician or application scientist. Although the storage requirements only scale linearly with the number of observations in the dataset, the computational complexity in terms of memory and speed, scale quadratically and cubically respectively for likelihood-based Geostatistics. Various methods have been proposed and are extensively used in an attempt to overcome these complexity issues. This thesis introduces a number of principled techniques for treating large datasets with an emphasis on three main areas: reduced complexity covariance matrices, sparsity in the covariance matrix and parallel algorithms for distributed computation. These techniques are presented individually, but it is also shown how they can be combined to produce techniques for further improving computational efficiency.

Stochastic simulation of time-series models combined with geostatistics to predict water-table scenarios in a Guarani Aquifer System outcrop area, Brazil

Stochastic methods based on time-series modeling combined with geostatistics can be useful tools to describe the variability of water-table levels in time and space and to account for uncertainty. Monitoring water-level networks can give information about the dynamic of the aquifer domain in both dimensions. Time-series modeling is an elegant way to treat monitoring data without the complexity of physical mechanistic models. Time-series model predictions can be interpolated spatially, with the spatial differences in water-table dynamics determined by the spatial variation in the system properties and the temporal variation driven by the dynamics of the inputs into the system. An integration of stochastic methods is presented, based on time-series modeling and geostatistics as a framework to predict water levels for decision making in groundwater management and land-use planning. The methodology is applied in a case study in a Guarani Aquifer System (GAS) outcrop area located in the southeastern part of Brazil. Communication of results in a clear and understandable form, via simulated scenarios, is discussed as an alternative, when translating scientific knowledge into applications of stochastic hydrogeology in large aquifers with limited monitoring network coverage like the GAS.

Amostragem e variabilidade espacial de atributos químicos do solo em área de vegetação natural em regeneração

The objectives of this work was to estimate the number of soil subsamples considering the classical statistics and geostatistics and determine the spatial variability of soil fertility attributes of an Ultisol, with clay texture, in an area of regenerating natural vegetation in Alegre - ES. Soil samples were collected in a depth of 0.0-0.2 m, at the crossing points of a regular grid, comprising a total of 64 points located at 10 m-intervals. The area presented low fertility soil. Considering a variation of 5% around the mean in the classic statistics, it is necessary a larger number of samples in relation to geostatistics. All the chemical attributes showed moderate to high spatial dependence, except for the effective cation exchange capacity (CECe), which showed pure nugget effect. The spherical semivariogram model gave the best fit to the data. Isoline maps allowed visualizing the differentiated spatial distribution of the contents of soil chemical attributes.