Application of Bayesian geostatistics for evaluation of mass discharge uncertainty at contaminated sites

Abstract

[1] Mass discharge estimates are increasingly being used when assessing risks of groundwater contamination and designing remedial systems at contaminated sites. Such estimates are, however, rather uncertain as they integrate uncertain spatial distributions of both concentration and groundwater flow. Here a geostatistical simulation method for quantifying the uncertainty of the mass discharge across a multilevel control plane is presented. The method accounts for (1) heterogeneity of both the flow field and the concentration distribution through Bayesian geostatistics, (2) measurement uncertainty, and (3) uncertain source zone and transport parameters. The method generates conditional realizations of the spatial flow and concentration distribution. An analytical macrodispersive transport solution is employed to simulate the mean concentration distribution, and a geostatistical model of the Box-Cox transformed concentration data is used to simulate observed deviations from this mean solution. By combining the flow and concentration realizations, a mass discharge probability distribution is obtained. The method has the advantage of avoiding the heavy computational burden of three-dimensional numerical flow and transport simulation coupled with geostatistical inversion. It may therefore be of practical relevance to practitioners compared to existing methods that are either too simple or computationally demanding. The method is demonstrated on a field site contaminated with chlorinated ethenes. For this site, we show that including a physically meaningful concentration trend and the cosimulation of hydraulic conductivity and hydraulic gradient across the transect helps constrain the mass discharge uncertainty. The number of sampling points required for accurate mass discharge estimation and the relative influence of different data types on mass discharge uncertainty is discussed.

Screening-level estimates of mass discharge uncertainty from point measurement methods

“…Values of Ĵ are estimated from a given interpolation scheme using measured J, and can include relatively simple approaches such as a Theissen polygon approach (e.g., MacKay et al, 2012) to more complex Bayesian geostatisical approaches (e.g., Troldborg et al, 2012). Eq.…”

“…A number of studies have been completed on pointmeasurement method uncertainty (Béland-Pelletier et al, 2011;Cai et al, 2011Cai et al, , 2012Chen et al, 2014;Klammler et al, 2012;Kübert and Finkel, 2006;Li and Abriola, 2009;Li et al, 2007;MacKay et al, 2012;Schwede and Cirpka, 2010;Troldborg et al, 2010Troldborg et al, , 2012. Two of these studies were based on field trials (Béland-Pelletier et al, 2011;MacKay et al, 2012), two of the studies used flow and transport simulations within Monte Carlo frameworks (Chen et al, 2014;Kübert and Finkel, 2006); two more studies likewise used flow and transport simulations within Monte Carlo frameworks, but simulations were conditioned to field data (Schwede and Cirpka, 2010;Troldborg et al, 2010); and the remaining studies employed various conditional, geostatistical techniques, wherein one or more parameters across the control plane were treated as spatial random variables.…”

“…Other studies that likewise presented methods to estimate ṁ uncertainty using geostatistical simulations of random spatial variables conditioned to field measurements include Cai et al (2011), Cai et al (2012, Klammler et al (2012), and Troldborg et al (2012). In each case, uncertainty was quantified by generating empirical CDFs of ṁ.…”

“…Data from the boxplots was used to calculate a normalized 95% confidence interval (defined as the difference between the 97.5% and 2.5% quantiles, divided by the 50% quantile), which ranged from 35% to 76% for the case studies investigated. Troldborg et al (2012) calculated mass discharge uncertainty through Bayesian conditional simulations, where C and q were treated as independent random spatial variables, but q was generated from a joint conditional simulation of K and I. The method was applied to a field site with σ lnK 2 = 1.4, and using sampling networks with S D = {0.32, 0.05} pts/m 2 , they estimated ṁ = {12, 21} g/d total chlorinated ethenes, respectively.…”

A new approach to spatial data interpolation using higher-order statistics

“…Such ineffectiveness is especially severe in geological or environmental studies, as discussed by , Strebelle (2002) and Tjelmeland and Besag (1998). In the past decade, various techniques have been developed to improve the reliability of characterizing random fields, such as bootstrapping (Kleijnen et al, 2012;Schelin and Luna, 2010;Stein, 2008, 2004;Mukul et al, 2004), copula-based methods (Kazianka, 2013;Pilz et al, 2012;Kazianka andPilz, 2010a, 2010b;Bárdossy and Li, 2008;Bárdossy, 2006), kernel-based methods (Honarkhah and Caers, 2010;Scheidt and Caers, 2010, 2009a, 2009b), Bayesian (Nieto-Barajas and Sinha, 2014Troldborg et al, 2012;Pilz et al, 2012;Kazianka andPilz, 2011, 2012), multi-point simulation methods (De Iaco, 2013;Boucher, 2009;Chugunova and Hu, 2008;Wu et al, 2008;Mirowski et al, 2008;Arpat and Caers, 2007;Zhang et al, 2006;Strebelle, 2002), multi-scale simulations using wavelets (Chatterjee and Dimitrakopoulos, 2012;Dimitrakopoulos, 2009, 2008), and spatial-cumulant-based simulation methods (Goodfellow et al, 2012;MachucaMory and Dimitrakopoulos, 2012;, Dimitrakopoulos et al, 2010.…”