A geostatistical approach to contaminant source identification

Snodgrass, M. F.; Kitanidis, Peter K.

doi:10.1029/96wr03753

Cited by 181 publications

(173 citation statements)

References 28 publications

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“…non-detects). These and other difficulties have been documented in Snodgrass and Kitanidis [1997], Walvoort and de Gruijter [2001], and Michalak and Kitanidis [2003], among others. In addition, traditional data transformations are only valid for enforcing a single upper or lower bound that is constant for all estimation times or locations.…”

Section: Constrained Interpolation and Inverse Modelingmentioning

confidence: 99%

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

Michalak

2008

Water Resources Research

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[1] Interpolation and inverse modeling problems are ubiquitous in environmental sciences. In many applications, the parameters being estimated or mapped have physical constraints, such as nonnegativity (e.g. concentration, hydraulic conductivity), solubility limits, censored data (e.g. due to dry wells or detection limits), and other physical boundaries or missing data. Geostatistical interpolation and inverse modeling techniques have often been applied for estimating such parameters, but these methods typically cannot enforce physical constraints. This paper describes a statistically rigorous and computationally efficient Gibbs sampler, a Markov chain Monte Carlo technique, based on an a priori truncated Gaussian distribution model, which allows for multiple and variable physical constraints to be enforced within a geostatistical framework. Sample interpolation and inverse modeling applications confirm that estimates, uncertainty bounds and conditional simulations reflect the specified constraints, leading to conclusions that are more consistent with the underlying conceptual model, and provide a more accurate measure of the posterior uncertainty of the parameters being estimated. In addition, especially in inverse modeling applications, a posteriori confidence bounds are narrower even in areas where constraints are not imposed. The method is applicable in multiple dimensions, for data with or without measurement error, and with any variogram model.

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Section: Constrained Interpolation and Inverse Modelingmentioning

confidence: 99%

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

Michalak

2008

Water Resources Research

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“…The unknown field s is modeled as a random vector with expected value where X s defines known zonation (18) or spatial trends of s (15). For this work, we assume that the attribute value in the sediment has a constant but unknown mean s , and X s therefore becomes an m × 1 vector of ones.…”

Section: Initial Setup For Geostatistical Downscalingmentioning

confidence: 99%

“…Detailed descriptions of linear geostatistical inverse modeling (GIM) are available in Snodgrass and Kitanidis (15) and Michalak et al (20), among others, and only the key equations are reproduced here.…”

Section: Initial Setup For Geostatistical Downscalingmentioning

confidence: 99%

“…Alternately, this paper presents a geostatistical downscaling approach, expressed as a special form of a linear geostatistical inverse problem, which can account for variable resolution in the data. Geostatistical inverse modeling has been widely used in hydrogeology for characterizing contaminant sources (13)(14)(15) and identifying the distribution of hydraulic conductivities or transmissivities in aquifers (16)(17)(18). In this work, geostatistical downscaling is applied to benthic sediment data, through the definition of a sensitivity matrix representing the quantitative relationship between the measured average attribute value and the uniform resolution values to be estimated.…”

Section: Introductionmentioning

confidence: 99%

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Characterizing Attribute Distributions in Water Sediments by Geostatistical Downscaling

Zhou

Michalak

2009

Environ. Sci. Technol.

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Information about attributes such as contaminant concentrations or hydraulic properties in benthic sediments is typically obtained in core sections of varying lengths, and only the average value is measured in each section. However, an estimate of the attribute distribution at a uniform spatial resolution is often required for site characterization and the design of appropriate risk-based remediation alternatives. Because attributes exhibit spatial autocorrelation, geostatistical methods have become an essential tool for estimating their spatial distribution. The purpose of this paper is to optimally infer the spatial distribution of sampled attributes at a uniform resolution from fluvial core sampling data, using a downscaling technique formulated as a geostatistical inverse problem. We compare geostatistical downscaling to the more traditional approach of point-to-point ordinary kriging for a hypothetical case study, and for total organic carbon observations from the Passaic River, New Jersey. Although frequently used to interpolate measurements, ordinary kriging is shown not to be able to estimate the spatial distribution of attributes accurately, because this approach assumes that data are sampled at a uniform resolution. Geostatistical downscaling, on the other hand, is shown to resolve this problem by explicitly accounting for the relationship between the known average measurements and the unknown fine-resolution attribute distribution to be estimated.

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“…Other approach for source identification consists of solving the differential equations backwards in time (inverse problem). The random walk particle method [10,11], the quasi-reversibility technique [12], the minimum relative entropy method [13], the Bayesian theory and geostatistical techniques [14], and genetic algorithm [15,16] are some examples of this approach.…”

Section: Introductionmentioning

confidence: 99%

Application of Simulated Annealing and Adaptive Simulated Annealing in Search for Efficient Optimal Solutions of a Groundwater Contamination related Problem

Amirabdollahian¹,

Datta²

2017

Computational Optimization in Engineering - Paradigms and Applications

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Characterization of groundwater contamination sources is a complex inverse problem. This inverse problem becomes complicated, due to the nonlinear nature of the groundwater flow and transport processes and the associated natural uncertainties. The mathematical challenges arise due to the nonunique characteristics of this problem resulting from the nonunique response of the aquifer system to a set of stresses and the possibility of instead locating only local optimal solutions. The linked simulation-optimization model is an efficient approach to identifying groundwater contamination source characteristics. Efficiency and accuracy of the search for optimum solutions of a linked simulation-optimization depend on the utilized optimization algorithm. This limited study focuses on the application and efficiency of simulated annealing (SA) as the optimization algorithm for solving the source characterization problem. The advantages in using adaptive simulated algorithm (ASA) as an alternative are then evaluated. The possibility of identifying a local optimal solution rather than a global optimal solution when using SA implies failure to solve the source characterization inverse problem. The cost of such inaccurate characterization may be enormous when a remediation strategy is based on the model inferences. ASA is shown to provide a reliable and acceptable alternative for solving this challenging aquifer contamination problem.

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A geostatistical approach to contaminant source identification

Cited by 181 publications

References 28 publications

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

A Gibbs sampler for inequality‐constrained geostatistical interpolation and inverse modeling

Characterizing Attribute Distributions in Water Sediments by Geostatistical Downscaling

Application of Simulated Annealing and Adaptive Simulated Annealing in Search for Efficient Optimal Solutions of a Groundwater Contamination related Problem

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