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  • 1
    Electronic Resource
    Electronic Resource
    An Application of the Holistochastic Human Exposure Methodology to Naturally Occurring Arsenic in Bangladesh Drinking Water (2003)
    350 Main Street , Malden , MA 02148 , USA , and 9600 Garsington Road , Oxford OX4 2DQ , UK . : Blackwell Publishing Inc.
    Risk analysis 23 (2003), S. 0 
    Details
    ISSN: 1539-6924
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Energy, Environment Protection, Nuclear Power Engineering
    Notes: The occurrence of arsenic in drinking water is an issue of considerable interest. In the case of Bangladesh, arsenic concentrations have been closely monitored since the early 1990s through an extensive sampling network. The focus of the present work is methodological. In particular, we propose the application of a holistochastic framework of human exposure to study lifetime population damage due to arsenic exposure across Bangladesh. The Bayesian Maximum Entropy theory is an important component of this framework, which possesses solid theoretical foundations and offers powerful tools to assimilate a variety of knowledge bases (physical, epidemiologic, toxicokinetic, demographic, etc.) and uncertainty sources (soft data, measurement errors, etc.). The holistochastic exposure approach leads to physically meaningful and informative spatial maps of arsenic distribution in Bangladesh drinking water. Global indicators of the adverse health effects on the population are generated, and valuable insight is gained by blending information from different scientific disciplines. The numerical results indicate an increased lifetime bladder cancer probability for the Bangladesh population due to arsenic. The health effect estimates obtained and the associated uncertainty assessments are valuable tools for a broad spectrum of end-users.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/1539-6924.t01-1-00332
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  • 2
    Electronic Resource
    Electronic Resource
    Stochastic perturbation analysis of groundwater flow. Spatially variable soils, semi-infinite domains and large fluctuations (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 213-239 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; perturbation ; random fields ; graph theory
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract As is well known, a complete stochastic solution of the stochastic differential equation governing saturated groundwater flow leads to an infinite hierarchy of equations in terms of higher-order moments. Perturbation techniques are commonly used to close this hierarchy, using power-series expansions. These methods are applied by truncating the series after a finite number of terms, and products of random gradients of conductivity and head potential are neglected. Uncertainty regarding the number or terms required to yield a sufficiently accurate result is a significant drawback with the application of power series-based perturbation methods for such problems. Low-order series truncation may be incapable of representing fundamental characteristics of flow and can lead to physically unreasonable and inaccurate solutions of the stochastic flow equation. To support this argument, one-dimensional, steady-state, saturated groundwater flow is examined, for the case of a spatially distributed hydraulic conductivity field. An ordinary power-series perturbation method is used to approximate the mean head, using second-order statistics to characterize the conductivity field. Then an interactive perturbation approach is introduced, which yields improved results compared to low-order, power-series perturbation methods for situations where strong interactions exist between terms in such approximations. The interactive perturbation concept is further developed using Feynman-type diagrams and graph theory, which reduce the original stochastic flow problem to a closed set of equations for the mean and the covariance functions. Both theoretical and practical advantages of diagrammatic solutions are discussed; these include the study of bounded domains and large fluctuations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01585600
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  • 3
    Electronic Resource
    Electronic Resource
    Norm-dependent covariance permissibility of weakly homogeneous spatial random fields and its consequences in spatial statistics (2000)
    Springer
    Stochastic environmental research and risk assessment 14 (2000), S. 471-478 
    Details
    ISSN: 1436-3259
    Keywords: Key words: Random fields, norm, covariance, permissibility, estimation.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract.  Permissibility of a covariance function (in the sense of Bochner) depends on the norm (or metric) that determines spatial distance in several dimensions. A covariance function that is permissible for one norm may not be so for another. We prove that for a certain class of covariances of weakly homogeneous random fields, the spatial distance can be defined only in terms of the Euclidean norm. This class includes commonly used covariance functions. Functions that do not belong to this class may be permissible covariances for some non-Euclidean metric. Thus, a different class of covariances, for which non-Euclidean norms are valid spatial distances, is also discussed. The choice of a coordinate system and associated norm to describe a physical phenomenon depends on the nature of the properties being described. Norm-dependent permissibility analysis has important consequences in spatial statistics applications (e.g., spatial estimation or mapping), in which one is concerned about the validity of covariance functions associated with a physically meaningful norm (Euclidean or non-Euclidean).
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004770070001
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  • 4
    Electronic Resource
    Electronic Resource
    Stochastic analysis of spatiotemporal solute content measurements using a regression model (1997)
    Springer
    Stochastic environmental research and risk assessment 11 (1997), S. 267-295 
    Details
    ISSN: 1436-3259
    Keywords: Space/time processes ; stochastic analysis ; regression model ; solute contents
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract A regression model is used to study spatiotemporal distributions of solute content ion concentration data (calcium, chloride and nitrate), which provide important water contamination indicators. The model consists of three random and one deterministic components. The random space/time component is assumed to be homogeneous/stationary and to have a separable covariance. The purely spatial and the purely temporal random components are assumed to have homogenous and stationary increments, respectively. The deterministic component represents the space/time mean function. Inferences of the random components involve maximum likelihood and semi-parametric methods under some restrictions on the data configuration. Computational advantages and modelling limitations of the assumptions underlying the regression model are discussed. The regression model leads to simplifications in the space/time kriging and cokriging systems used to obtain space/time estimates at unobservable locations/instants. The application of the regression model in the study of the solute content ions was done at a global scale that covers the entire region of interest. The variability analysis focuses on the calculation of the spatial direct and cross-variograms and the evaluation of correlations between the three solute content ions. The space/time kriging system is developed in terms of the space direct and cross-variograms, and allows the separate estimation of the regression model components. Maps of these components are then obtained for each one of the three ions. Using the estimates of the purely spatial component, spatial dependencies between the ions are studied. Physical causes and consequences of the space/time variability are discussed, and comparisons are made with previous analyses of the solute content dataset.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02427919
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  • 5
    Electronic Resource
    Electronic Resource
    The development of stochastic space transformation and diagrammatic perturbation techniques in subsurface hydrology (1993)
    Springer
    Stochastic environmental research and risk assessment 7 (1993), S. 14-32 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; random fields ; space transformation ; perturbation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper develops concepts and methods to study stochastic hydrologic models. Problems regarding the application of the existing stochastic approaches in the study of groundwater flow are acknowledged, and an attempt is made to develop efficient means for their solution. These problems include: the spatial multi-dimensionality of the differential equation models governing transport-type phenomena; physically unrealistic assumptions and approximations and the inadequacy of the ordinary perturbation techniques. Multi-dimensionality creates serious mathematical and technical difficulties in the stochastic analysis of groundwater flow, due to the need for large mesh sizes and the poorly conditioned matrices arising from numerical approximations. An alternative to the purely computational approach is to simplify the complex partial differential equations analytically. This can be achieved efficiently by means of a space transformation approach, which transforms the original multi-dimensional problem to a much simpler unidimensional space. The space transformation method is applied to stochastic partial differential equations whose coefficients are random functions of space and/or time. Such equations constitute an integral part of groundwater flow and solute transport. Ordinary perturbation methods for studying stochastic flow equations are in many cases physically inadequate and may lead to questionable approximations of the actual flow. To address these problems, a perturbation analysis based on Feynman-diagram expansions is proposed in this paper. This approach incorporates important information on spatial variability and fulfills essential physical requirements, both important advantages over ordinary hydrologic perturbation techniques. Moreover, the diagram-expansion approach reduces the original stochastic flow problem to a closed set of equations for the mean and the covariance function.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581564
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  • 6
    Electronic Resource
    Electronic Resource
    Diagrammatic solutions for hydraulic head moments in 1-D and 2-D bounded domains (1995)
    Springer
    Stochastic environmental research and risk assessment 9 (1995), S. 269-296 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic analysis ; diagrams ; groundwater flow
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract We present a diagrammatic method for solving stochastic 1-D and 2-D steady-state flow equations in bounded domains. The diagrammatic method results in explicit solutions for the moments of the hydraulic head. This avoids certain numerical constraints encountered in realization-based methods. The diagrammatic technique also allows for the consideration of finite domains or large fluctuations, and is not restricted by distributional assumptions. The results of the method for 1-D and 2-D finite domains are compared with those obtained through a realization-based approach. Mean and variance of head are well reproduced for all log-conductivity variances inputted, including those larger than one. The diagrammatic results also compare favorably to hydraulic head moments derived by standard analytic methods requiring a linearized form of the flow equation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01581729
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  • 7
    Electronic Resource
    Electronic Resource
    Modern geostatistics: computational BME analysis in the light of uncertain physical knowledge – the Equus Beds study (1999)
    Springer
    Stochastic environmental research and risk assessment 13 (1999), S. 1-26 
    Details
    ISSN: 1436-3259
    Keywords: Key words: Spatiotemporal ; stochastic ; mapping ; Bayes ; entropy ; computational approach ; physical knowledge bases ; epistemology.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract This paper is concerned with a computational formulation of the Bayesian maximum entropy (BME) mapping method, which can handle rigorously and efficiently spatiotemporal applications of considerable practical importance. BME is a method of modern geostatistics that can integrate and process physical knowledge that belongs to two major bases: general knowledge (i.e., obtained from general principles and laws, summary statistics and background information), and specificatory knowledge (i.e., obtained through experience with the specific situation). BME allows considerable flexibility regarding the choice of an appropriate spatiotemporal map, offers a complete assessment of the mapping uncertainty and contributes to the scientific understanding of the underlying natural phenomenon. Valuable insight is gained by studying a spatiotemporal data set representing water-level elevations at the Equus Beds aquifer (Kansas). Numerical results show that, as was expected in theory, classical geostatistics analysis is obtained as a special case of the considerably more general BME approach. Moreover, modern geostatistical analysis in terms of BME offers more accurate and informative results in practice, by incorporating various sources of physical knowledge that cannot be processed by the classical methods.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004770050029
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  • 8
    Electronic Resource
    Electronic Resource
    Stochastic space transforms in subsurface hydrology — Part 2: Generalized spectral decompositions and plancherel representations (1994)
    Springer
    Stochastic environmental research and risk assessment 8 (1994), S. 117-138 
    Details
    ISSN: 1436-3259
    Keywords: Stochastic hydrology ; random fields ; space transformations ; generalized functions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract In earlier publications, certain applications of space transformation operators in subsurface hydrology were considered. These operators reduce the original multi-dimensional problem to the one-dimensional space, and can be used to study stochastic partial differential equations governing groundwater flow and solute transport processes. In the present work we discuss developments in the theoretical formulation of flow models with space-dependent coefficients in terms of space transformations. The formulation is based on stochastic Radon operator representations of generalized functions. A generalized spectral decomposition of the flow parameters is introduced, which leads to analytically tractable expressions of the space transformed flow equation. A Plancherel representation of the space transformation product of the head potential and the log-conductivity is also obtained. A test problem is first considered in detail and the solutions obtained by means of the proposed approach are compared with the exact solutions obtained by standard partial differential equation methods. Then, solutions of three-dimensional groundwater flow are derived starting from solutions of a one-dimensional model along various directions in space. A step-by-step numerical formulation of the approach to the flow problem is also discussed, which is useful for practical applications. Finally, the space transformation solutions are compared with local solutions obtained by means of series expansions of the log-conductivity gradient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01589893
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  • 9
    Electronic Resource
    Electronic Resource
    Renormalization group analysis of permeability upscaling (1999)
    Springer
    Stochastic environmental research and risk assessment 13 (1999), S. 131-161 
    Details
    ISSN: 1436-3259
    Keywords: Key words: Renormalization ; random fields ; effective ; permeability ; preasymptotic.
    Source: Springer Online Journal Archives 1860-2000
    Topics: Architecture, Civil Engineering, Surveying , Energy, Environment Protection, Nuclear Power Engineering , Geography , Geosciences
    Notes: Abstract The heterogeneity of the subsurface permeability is considered as the most influential factor in determining groundwater flow and the transport of toxic contaminants. Numerical simulators cannot handle the large grids required to represent the small-scale variability of permeability, and thus explicit estimates of the large-scale behavior in terms of coarse-grained parameters are often required. Perturbation formulations of the effective permeability are based on simplifying assumptions that are valid only for certain probability distributions and weak heterogeneity. A generalized perturbation ansatz that involves higher orders has been proposed (Gelhar and Axness, 1983), but to our knowledge its validity has not been rigorously proved before in three dimensions. In this work we propose a general upscaling formulation valid for strong heterogeneity, general permeability distributions, and media with impermeable zones. We show that the effective permeability is determined by the self-energy series of the permeability fluctuations at zero frequency. Using the diagrammatic representation, we obtain a Dyson equation that involves only irreducible diagrams of the proper self-energy series. We develop a renormalization group (RG) analysis for isotropic lognormal media that proves the generalized perturbation ansatz to all orders. We show that the RG result accurately estimates laboratory permeability measurements in limestone (strong heterogeneity) and sandstone (weak heterogeneity). We also propose an explicit RG estimate for the preasymptotic effective permeability. We compare our results with an approach based on a leading order Green's function expansion (Paleologos et al., 1996), which, however, requires intensive numerical computations. Finally, we investigate the relation between the RG expression and the algebraic means used in numerical upscaling.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/s004770050036
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  • 10
    Electronic Resource
    Electronic Resource
    On the functional optimization of a certain class of nonstationary spatial functions (1987)
    Springer
    Journal of optimization theory and applications 52 (1987), S. 191-208 
    Details
    ISSN: 1573-2878
    Keywords: Functional optimization ; spatial functions ; hypothesis of inherentity
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract Procedures are developed in order to obtain optimal estimates of linear functionals for a wide class of nonstationary spatial functions. These procedures rely on well-established constrained minimum-norm criteria, and are applicable to multidimensional phenomena which are characterized by the so-called hypothesis of inherentity. The latter requires elimination of the polynomial, trend-related components of the spatial function leading to stationary quantities, and also it generates some interesting mathematics within the context of modelling and optimization in several dimensions. The arguments are illustrated using various examples, and a case study computed in detail.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00941280
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