A robust geostatistical approach to contaminant source identification

Abstract

[1] Estimation under model uncertainty remains a practical concern in many scientific and engineering fields. A commonly encountered example in groundwater remediation is the contaminant source identification problem. Like many other inverse problems, contaminant source identification is inherently ill posed and is sensitive to both data and model uncertainties. Model uncertainties, which may be introduced at virtually any stage of a model building process, can adversely affect estimator performance if they are not accounted for properly. In this paper, a robust geostatistical approach (RGS), which is extended from the geostatistical inversion approach (GS), is used to solve linear estimation problems. The uncertainties in both model and covariance matrices are taken into account in the RGS formulation. The nominal correlation structural parameters are estimated using a structural analysis procedure. The resulting minimax optimization problem is solved using semidefinite programming techniques. The RGS is generic and can be applied to any problem for which the GS is suitable and the upper bound of uncertainty can be quantified. The RGS is illustrated for source release history identification in a two-dimensional aquifer where the model uncertainty is caused by variability in hydraulic conductivity. It is shown that when the model is perfectly known, the RGS solution coincides with that of the GS; when the model has uncertainty, the RGS is robust against unknown variations from a nominal model, and its overall performance is better than that of the GS using the same nominal model.

Contaminant Source Location Identification in River Networks Using Water Quality Monitoring Systems for Exposure Analysis

“…Boano et al (2005) applied a geostatistical approach to determine the release history of a contaminant source at a known location in a river reach. Sun (2007) solved a similar problem in groundwater environment using a robust geostatistical approach.…”

Optimal Dynamic Monitoring Network Design and Identification of Unknown Groundwater Pollution Sources

“…Comprehensive review of source identification methodologies can be found in work by Atmadja and Bagtzoglou (2001b), Michalak and Kitanidis (2004), and Sun et al (2006a). Numerous works related to pollution source identification are available, like least square regression and linear programming with response matrix approach (Gorelick et al 1983), statistical pattern recognition (Datta et al 1989), random walk based backward tracking model (Bagtzoglou et al 1992), nonlinear maximum likelihood estimation (Wagner 1992), nonlinear optimization with embedding technique (Mahar and Datta 1997, 2001, correlation coefficient optimization (Sidauruk et al 1997), backward probabilistic model (Neupauer and Wilson 1999), geostatistical inversion approach (Snodgrass and Kitanidis 1997;Butera and Tanda 2003;Michalak and Kitanidis 2004), Tikhonov regularization (Skaggs and Kabala 1994;Liu and Ball 1999), quasi-reversibility (Skaggs and Kabala 1995;Bagtzoglou and Atmadja 2003), marching-jury backward beam equation (Atmadja and Bagtzoglou 2001a;Bagtzoglou and Atmadja 2003), genetic algorithm based approach (Aral et al 2001;Mahinthakumar and Sayeed 2005;Singh and Datta 2006), artificial neural network approach Datta 2004, 2007;, constrained robust least square approach (Sun et al 2006a, b), robust geostatistical approach (Sun 2007). However, only few studies have incorporated monitoring network within the source identification framework.…”

Identification of unknown groundwater pollution sources using classical optimization with linked simulation

“…That is why, a unique solution does not necessarily exist and the solution may be unstable to small changes in the input data (Liu and Ball, 1999). Over the years different methodologies have been proposed for groundwater pollution source identification, e.g., least square regression and linear programming with response matrix approach (Gorelick et al, 1983), statistical pattern recognition (Datta et al, 1989), random walk based backward tracking model (Bagtzoglou et al, 1992), nonlinear maximum likelihood estimation (Wagner, 1992), minimum relative entropy (Woodbury and Ulrych, 1996;Woodbury et al, 1998), nonlinear optimization with embedding technique (Mahar and Datta, 1997, 2001, correlation coefficient optimization (Sidauruk et al, 1997), backward probabilistic model Wilson, 1999, 2005;Neupauer et al, 2000), geostatistical inversion approach (Snodgrass and Kitanidis, 1997;Butera and Tanda, 2003;Michalak and Kitanidis, 2004a, b), Tikhonov regularization (Skaggs and Kabala, 1994;Liu and Ball, 1999), quasireversibility (Skaggs and Kabala, 1995;Bagtzoglou and Atmadja, 2003), marching-jury backward beam equation (Atmadja and Bagtzoglou, 2001a;Bagtzoglou and Atmadja, 2003;Bagtzoglou and Baun, 2005), genetic algorithm based approach (Aral et al, 2001;Mahinthakumar and Sayeed, 2005;Singh and Datta, 2006), artificial neural network approach Datta, 2004, 2007;, constrained robust least square approach (Sun et al, 2006a, b), classical optimization based approach (Datta et al, 2009a, b), robust geostatistical approach (Sun, 2007), inverse particle tracking approach (Bagtzoglou, 2003;Ababou et al, 2010).…”