21,282 research outputs found
High-Dimensional Bayesian Geostatistics
With the growing capabilities of Geographic Information Systems (GIS) and
user-friendly software, statisticians today routinely encounter geographically
referenced data containing observations from a large number of spatial
locations and time points. Over the last decade, hierarchical spatiotemporal
process models have become widely deployed statistical tools for researchers to
better understand the complex nature of spatial and temporal variability.
However, fitting hierarchical spatiotemporal models often involves expensive
matrix computations with complexity increasing in cubic order for the number of
spatial locations and temporal points. This renders such models unfeasible for
large data sets. This article offers a focused review of two methods for
constructing well-defined highly scalable spatiotemporal stochastic processes.
Both these processes can be used as "priors" for spatiotemporal random fields.
The first approach constructs a low-rank process operating on a
lower-dimensional subspace. The second approach constructs a Nearest-Neighbor
Gaussian Process (NNGP) that ensures sparse precision matrices for its finite
realizations. Both processes can be exploited as a scalable prior embedded
within a rich hierarchical modeling framework to deliver full Bayesian
inference. These approaches can be described as model-based solutions for big
spatiotemporal datasets. The models ensure that the algorithmic complexity has
floating point operations (flops), where the number of spatial
locations (per iteration). We compare these methods and provide some insight
into their methodological underpinnings
Identification of high-permeability subsurface structures with multiple point geostatistics and normal score ensemble Kalman filter
Alluvial aquifers are often characterized by the presence of braided high-permeable paleo-riverbeds, which constitute an interconnected preferential flow network whose localization is of fundamental importance to predict flow and transport dynamics. Classic geostatistical approaches based on two-point correlation (i.e., the variogram) cannot describe such particular shapes. In contrast, multiple point geostatistics can describe almost any kind of shape using the empirical probability distribution derived from a training image. However, even with a correct training image the exact positions of the channels are uncertain. State information like groundwater levels can constrain the channel positions using inverse modeling or data assimilation, but the method should be able to handle non-Gaussianity of the parameter distribution. Here the normal score ensemble Kalman filter (NS-EnKF) was chosen as the inverse conditioning algorithm to tackle this issue. Multiple point geostatistics and NS-EnKF have already been tested in synthetic examples, but in this study they are used for the first time in a real-world casestudy. The test site is an alluvial unconfined aquifer in northeastern Italy with an extension of approximately 3 km2. A satellite training image showing the braid shapes of the nearby river and electrical resistivity tomography (ERT) images were used as conditioning data to provide information on channel shape, size, and position. Measured groundwater levels were assimilated with the NS-EnKF to update the spatially distributed groundwater parameters (hydraulic conductivity and storage coefficients). Results from the study show that the inversion based on multiple point geostatistics does not outperform the one with a multiGaussian model and that the information from the ERT images did not improve site characterization. These results were further evaluated with a synthetic study that mimics the experimental site. The synthetic results showed that only for a much larger number of conditioning piezometric heads, multiple point geostatistics and ERT could improve aquifer characterization. This shows that state of the art stochastic methods need to be supported by abundant and high-quality subsurface data
Spatial variability of soil properties and soil erodibility in the Alqueva reservoir watershed
The aim of this work is to investigate how the spatial variability of soil properties and soil erodibility (K factor) were affected by the changes in land use allowed by irrigation with water from a reservoir in a semiarid area. To this end, three areas representative of different land uses (agroforestry grassland, lucerne crop and olive orchard) were studied within a 900 ha farm. The interrelationships between variables were analyzed by multivariate techniques and extrapolated using geostatistics. The results confirmed differences between land uses for all properties analyzed, which was explained mainly by the existence of diverse management practices (tillage, fertilization and irrigation), vegetation cover and local soil characteristics. Soil organic matter, clay and nitrogen content decreased significantly, while the K factor increased with intensive cultivation. The HJ-Biplot methodology was used to represent the variation of soil erodibility properties grouped in land uses. Native grassland was the least correlated with the other land uses. The K factor demonstrated high correlation mainly with very fine sand and silt. The maps produced with geostatistics were crucial to understand the current spatial variability in the Alqueva region. Facing the intensification of land-use conversion, a sustainable management is needed to introduce protective measures to control soil erosion
Analysing spatial data via geostatistical methods
Faculty of Science
School of Statistics snd Acturial Science
9907894x
[email protected] dissertation presents a detailed study of geostatistics. Included in this work
are details of the development of geostatistics and its usefulness both in and
outside of the mining industry, a comprehensive presentation of the theory of
geostatistics, and a discussion of the application of this theory to practical
situations. A published debate over the validity of geostatistics is also examined.
The ultimate goal of this dissertation is to provide a thorough investigation of
geostatistics from both a theoretical and a practical perspective. The theory
presented in this dissertation is thus tested on various spatial data sets, and from
these tests it is concluded that geostatistics can be effectively used in practice
provided that the practitioner fully understands the theory of geostatistics and the
spatial data being analyzed. A particularly interesting conclusion to come out of
this dissertation is the importance of using additive regionalized variables in all
geostatistical analyses
Modelling of radionuclide migration through the geosphere with radial basis function method and geostatistics
The modelling of radionuclide transport through the geosphere is necessary in the safety assessment of repositories for radioactive waste. A number of key geosphere processes need to be considered when predicting the movement of radionuclides through the geosphere. The most important input data are obtained from field measurements, which are not available for all regions of interest. For example, the hydraulic conductivity, as input parameter, varies from place to place. In such cases geostatistical science offers a variety of spatial estimation procedures. To assess the a long term safety of a radioactive waste disposal system, mathematical models are used to describe the complicated groundwater flow, chemistry and potential radionuclide migration through geological formations. The numerical solution of partial differential equations (PDEs) has usually been obtained by finite difference methods (FDM), finite element methods (FEM), or finite volume methods (FVM). Kansa introduced the concept of solving PDEs using radial basis functions (RBFs) for hyperbolic, parabolic and elliptic PDEs. The aim of this study was to present a relatively new approach to the modelling of radionuclide migration through the geosphere using radial basis functions methods and to determine the average and sample variance of radionuclide concentration with regard to spatial variability of hydraulic conductivity modelled by a geostatistical approach. We will also explore residual errors and their influence on optimal shape parameters
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