Bayesian Monitoring Design And Parameter Inversion For Groundwater Contaminant Source Identification

Groundwater serves as one of the most important drinking water sources due to its reliability and often high quality.However,groundwater system may be polluted by many sources of contaminants due to human activities.Using numerical simulation to predict the fate and transport of contaminants provides a powerful means to better manage and assess groundwater pollution.Nevertheless,direct measurements of some key parameters in groundwater models such as location and strength of the contaminant source,and hydraulic conductivity of the aquifer are difficult and these parameters can only be inferred by solving inverse problems based on the monitoring well measurements.Providing the most informative measurements and efficiently and accurately inferring these unknown parameters are critical in subsurface hydrology.Moreover,since the monitoring well design and parameter estimation usually require tens of thousands of model evaluations,the computational cost is extremely high for solving large scale problems.Thus,the overall objective of this dissertation research was to develop new methods to efficiently and accurately design monitoring wells and estimate unknown parameters in the Bayesian framework.The details are shown as follows:(1)To provide the most informative measurements with respect to the unknown parameters,we implemented the optimal monitoring designs based on the expected relative entropy from the prior to the posterior distribution of model parameters.Then we chose the sampling locations with the largest value of the objective function as the optimal design.With the concentration measurements obtained at the optimal sampling locations,we adopted the Markov chain Monte Carlo(MCMC)algorithm to estimate the unknown model parameters.To avoid repetitive evaluation of the original model of groundwater flow and solute transport and to improve the computational efficiency,we constructed a surrogate with adaptive sparse grid interpolation over the prior distribution of model parameters and used it in the sampling location design and MCMC simulation.To eliminate the bias introduced by the surrogate,we proposed to use a two-stage MCMC simulation,in which we first used the surrogate-based MCMC simulation to sufficiently explore the posterior and then used the original model-based MCMC simulation to accurately sample from the posterior.Numerical case studies showed that the proposed method is capable of efficiently and accurately estimating the unknown model parameters,including the contaminant source and hydraulic conductivity.(2)In the two-stage MCMC simulation,it was required to run the original model many times in the second stage,which posed a high computational cost.To further improve the computational efficiency,we proposed to construct a surrogate over the posterior distribution of model parameters.Here we used Gaussian process(GP)to construct the surrogate and integrated the construction process with MCMC simulation.By adaptively adding new base points close to the posterior distribution,the surrogate was gradually refined.Moreover,due to the elegant property of GP,the surrogate error was considered in the posterior distribution.Illustrated with a numerical case study,we found that constructing a surrogate over the posterior is more efficient and accurate than the one constructed over the prior distribution.(3)In high-dimensional problems,both surrogate construction and MCMC simulation are challenging.To design the optimal sampling locations and infer the unknown parameters in high-dimensional settings,we proposed an ensemble-based method.Here we used data-worth analysis to find the most informative measurement scheme and ensemble smoother to infer the unknown parameters.A case study with 8 parameters for the contaminant source and 3321 parameters for the hydraulic conductivity field showed that the proposed method performed well.With 24 optimal sampling locations designed in 12 steps,we could accurately infer these 3329 unknown parameters using concentration and head measurements.(4)Although ensemble smoother is suitable for high-dimensional problems,it fails when the posterior has multiple modes because it is based on the linear estimation theory.We proposed an algorithm named the iterative local updating ensemble smoother(ILUES)to explore multimodal distributions in high-dimensional problems.In ILUES,instead of directly updating each sample in the ensemble,the local ensembles of each sample were updated to explore the possible multimodal distributions.To achieve satisfactory data matches in nonlinear problems,we adopted a simple form of iteration.Without resorting to cluster analysis,ILUES can accurately identify multimodal distributions.Five numerical case studies involving multimodal prior distribution,multimodal posterior distribution and high-dimensionality were tested to show the performance of the proposed method.All the case studies showed that the proposed method could adequately quantify parametric uncertainties in complex systems.Compared with MCMC,ILUES has an obvious advantage in computational efficiency.(5)As mentioned before,surrogate construction loses its efficiency when the problem is high-dimensional.This greatly restricts the applicability of surrogate-based simulations.To solve this problem,we proposed to integrate the techniques of dimension reduction and surrogate construction,and applied this idea to the failure probability analysis of groundwater pollution.When estimating a small failure probability(i.e.,some environmental response exceeds a predefined threshold),direct Monte Carlo(MC)simulation usually invokes a large number of model evaluations.To relieve the computational burden,it is common practice to use a surrogate in the MC simulation.However,it is rather challenging to construct a surrogate for a high-dimensional model.Moreover,it is inevitable that a significant error is introduced by the surrogate.To solve these problems,we proposed a two-stage MC simulation to accurately and efficiently implement the failure probability analysis.In the first stage,we used Karhunen-Loeve expansion and sliced inverse regression to sufficiently reduce the dimensionality of the parameters for the heterogeneous conductivity field,based on which a surrogate was built with polynomial chaos expansion.With this surrogate,we efficiently simulated the quantity of interest(Qol)on a large number of samples.In the second stage,we re-evaluated these samples that fell near the failure boundary to eliminate the error introduced by the surrogate.In this way,we obtained an accurate estimate of the failure probability,which was well illustrated with a high-dimensional example of groundwater contaminant transport.It showed that,with less than 1%the computational cost,the two-stage MC approach could obtain the same result as the original model-based approach.