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

Model-Based Geostatistics for Prevalence Mapping in Low-Resource Settings

In low-resource settings, prevalence mapping relies on empirical prevalence data from a finite, often spatially sparse, set of surveys of communities within the region of interest, possibly supplemented by remotely sensed images that can act as proxies for environmental risk factors. A standard geostatistical model for data of this kind is a generalized linear mixed model with binomial error distribution, logistic link and a combination of explanatory variables and a Gaussian spatial stochastic process in the linear predictor. In this paper, we first review statistical methods and software associated with this standard model, then consider several methodological extensions whose development has been motivated by the requirements of specific applications. These include: methods for combining randomised survey data with data from non-randomised, and therefore potentially biased, surveys; spatio-temporal extensions; spatially structured zero-inflation. Throughout, we illustrate the methods with disease mapping applications that have arisen through our involvement with a range of African public health programmes.Comment: Submitte

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

History Matching Using Principal Component Analysis

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A pairwise likelihood approach for the empirical estimation of the underlyingvariograms in the plurigaussian models

The plurigaussian model is particularly suited to describe categorical regionalized variables. Starting from a simple principle, the thresh-olding of one or several Gaussian random fields (GRFs) to obtain categories, the plurigaussian model is well adapted for a wide range ofsituations. By acting on the form of the thresholding rule and/or the threshold values (which can vary along space) and the variograms ofthe underlying GRFs, one can generate many spatial configurations for the categorical variables. One difficulty is to choose variogrammodel for the underlying GRFs. Indeed, these latter are hidden by the truncation and we only observe the simple and cross-variogramsof the category indicators. In this paper, we propose a semiparametric method based on the pairwise likelihood to estimate the empiricalvariogram of the GRFs. It provides an exploratory tool in order to choose a suitable model for each GRF and later to estimate its param-eters. We illustrate the efficiency of the method with a Monte-Carlo simulation study .The method presented in this paper is implemented in the R packageRGeostats.Comment: To be submitted to Spatial Statistic