Stochastic delineation of capture zones: classical versus Bayesian approach

Feyen, Luc; Ribeiro, Paulo Justiniano; Smedt, Florimond De; Diggle, P.

doi:10.1016/s0022-1694(03)00193-8

Cited by 17 publications

(16 citation statements)

References 26 publications

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“…Discussions regarding to the limitations of MCS have been made in many previous studies (e.g. Neuman, 1999, Kunstmann andKinzelbach, 2000;Zhang, 2002, Feyen et al, 2003aBallio and Guadagnini, 2004;Dagan, 2004;Neuman, 2004;Li et al, 2003, 2004a, b, Ni and Li, 2005.…”

Section: Introductionmentioning

confidence: 97%

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Lin

et al. 2011

Hydrol. Earth Syst. Sci.

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Abstract. This study presents a numerical first-order spectral model to quantify transient flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers. Taking advantages of spectral theories in solving unmodeled small-scale variability in hydraulic conductivity (K), the presented nonstationary spectral method (NSM) can efficiently estimate flow uncertainties, including hydraulic heads and Darcy velocities in r-and z-directions in a cylindrical coordinate system. The velocity uncertainties associated with the particle backward tracking algorithm are then used to estimate stochastic remediation zones for scenarios with partially opened well screens. In this study the flow and remediation zone uncertainties obtained by NSM were first compared with those obtained by Monte Carlo simulations (MCS). A layered aquifer with different geometric mean of K and screen locations was then illustrated with the developed NSM. To compare NSM flow and remediation zone uncertainties with those of MCS, three different small-scale K variances and correlation lengths were considered for illustration purpose. The MCS remediation zones for different degrees of heterogeneity were presented with the uncertainty clouds obtained by 200 equally likely MCS realizations. Results of simulations reveal that the first-order NSM solutions agree well with those of MCS for partially opened wells. The flow uncertainties obtained by using NSM and MCS show identically for aquifers with small ln K variances and correlation lengths. Based on the test examples, the remediation zone uncertainties (bandwidths) are not sensitive to the changes of small-scale ln K correlation lengths. However, the increases of remediation zone uncertainties (i.e. the Correspondence to: C.-F. Ni (nichuenfa@geo.ncu.edu.tw) uncertainty bandwidths) are significant with the increases of small-scale ln K variances. The largest displacement uncertainties may have several meters of differences when the ln K variances increase from 0.1 to 1.0. Such conclusions are also valid for the estimations of remediation zones in layered aquifers.

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Section: Introductionmentioning

confidence: 97%

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Lin

et al. 2011

Hydrol. Earth Syst. Sci.

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“…Hydraulic conductivity, which reflects the characteristics of porous media, is considered to be the most important uncertain input parameter of groundwater flow models ). Its variability in space is considerably higher than that of other hydraulic properties relevant to groundwater flow, and it can vary by orders of magnitude over a few meters (Feyen et al 2003).…”

Section: Introductionmentioning

confidence: 99%

“…To characterize the spatial variability of the hydraulic conductivity, random space function (RSF) is often adopted (Ezzedine and Rubin 1996;Feyen et al 2003;Franssen et al 2003;Kerrou et al 2008;Hassan et al 2009;Liang et al 2009Liang et al , 2010. However, scarcity of measurements leads to generating spatial structure pattern of hydraulic conductivity at a few sampling location, which arouse uncertainty of spatial hydraulic conductivity distribution.…”

Section: Introductionmentioning

confidence: 99%

“…Parameter uncertainty is quantified by a prior probability distribution, which represents historical or expert information before any new data are collected, and a likelihood function, which characterizes the proximity of simulated and observed data. Feyen et al (2003) were the first to pay attention to the uncertainty of the parameters in RSF and apply Bayesian approach to infer them. They found that the predictions of the Bayesian approach was more conservative compared with classical approach.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian approach to quantify parameter uncertainty and impacts on predictive flow and mass transport in heterogeneous aquifer

Liang

Zeng

Shen

et al. 2013

Int. J. Environ. Sci. Technol.

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Groundwater flow and mass transport predictions are subjected to uncertainty due to heterogeneity of hydraulic conductivity, whose variability in space is considerably higher than that of other hydraulic properties relevant to groundwater flow. To characterize the distribution of hydraulic conductivity, random space function (RSF) is often used. The Bayesian approach was applied to quantitatively study the effect of parameter uncertainty in RSF on a hypothetical two-dimensional uniform groundwater flow and mass transport. Specifically, the parameter uncertainty transmitted to macrodispersion in mass transport model was also inferred. The results showed that the posterior probability distributions of parameters were updated after Bayesian inference. The numerical experiments indicated that the overall predictive uncertainty was increased with simulating time along the flow direction. As to the relative contribution of the two types of uncertainty, it indicated that parametric uncertainty was a little more important than stochastic uncertainty for the predictive uncertainty of hydraulic head. When the uncertainty of hydraulic head as well as macrodispersion was transported to mass transport model, a much bigger contribution of stochastic uncertainty was observed. Therefore, parametric uncertainty should not be neglected during the process of subsurface simulation.

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“…Feyen et al (2001) considered the data uncertainties in terms of the spatial correlation uncertainty (or semivariogram uncertainty) and uncertainty propagation to groundwater flow responses and predictions. Feyen et al (2003) examined semivariogram uncertainty for capture zones in a Bayesian framework. Following the work of Ortiz and Deutsch (2002), Rahman et al (2008a, b) studied the semivariogram parameter uncertainty in capture zone modeling and demonstrated the importance of semivariogram model uncertainty compared with fluctuations of a fixed geostatistical model.…”

Section: Introductionmentioning

confidence: 99%

Bayesian model averaging assessment on groundwater management under model structure uncertainty

Tsai

2010

Stoch Environ Res Risk Assess

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This study introduces Bayesian model averaging (BMA) to deal with model structure uncertainty in groundwater management decisions. A robust optimized policy should take into account model parameter uncertainty as well as uncertainty in imprecise model structure. Due to a limited amount of groundwater head data and hydraulic conductivity data, multiple simulation models are developed based on different head boundary condition values and semivariogram models of hydraulic conductivity. Instead of selecting the best simulation model, a variance-window-based BMA method is introduced to the management model to utilize all simulation models to predict chloride concentration. Given different semivariogram models, the spatially correlated hydraulic conductivity distributions are estimated by the generalized parameterization (GP) method that combines the Voronoi zones and the ordinary kriging (OK) estimates. The model weights of BMA are estimated by the Bayesian information criterion (BIC) and the variance window in the maximum likelihood estimation. The simulation models are then weighted to predict chloride concentrations within the constraints of the management model. The methodology is implemented to manage saltwater intrusion in the ''1,500-foot'' sand aquifer in the Baton Rouge area, Louisiana. The management model aims to obtain optimal joint operations of the hydraulic barrier system and the saltwater extraction system to mitigate saltwater intrusion. A genetic algorithm (GA) is used to obtain the optimal injection and extraction policies. Using the BMA predictions, higher injection rates and pumping rates are needed to cover more constraint violations, which do not occur if a single best model is used.

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Stochastic delineation of capture zones: classical versus Bayesian approach

Cited by 17 publications

References 26 publications

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Quantifying flow and remediation zone uncertainties for partially opened wells in heterogeneous aquifers

Bayesian approach to quantify parameter uncertainty and impacts on predictive flow and mass transport in heterogeneous aquifer

Bayesian model averaging assessment on groundwater management under model structure uncertainty

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