Contaminant source reconstruction by empirical Bayes and Akaike's Bayesian Information Criterion

Reconstructing the release history of a contaminant source with different precision via the ensemble smoother with multiple data assimilation

Identifying a contaminant time-varying release history is an ill-posed problem but crucial for groundwater contamination issues. A precise inversed release history offers a promising estimation of contaminant movement and is of great importance for environmental monitoring and further management. In this paper, a recent emerging data assimilation method, the ensemble smoother with multiple data assimilation (ES-MDA) is employed to handle this conundrum. The study starts with some synthetic cases in which several factors are analyzed, such as the observation data frequency, covariance inflation schemes, iteration numbers used in the ES-MDA for the purpose of identifying a time-varying contaminant injection event with different precision. The results show that the ES-MDA performs well in recovering the release history when the injection is discretized into 50 or 100-time steps but encounters fluctuation problems in the cases with 300-time steps. Further comparison reveals that the observation data frequency is a very influential factor, while the number of iterations or the kind of covariance inflation used has a lesser effect. Nevertheless, this is a first test in a non-synthetic environment, in which the ES-MDA has proven its ability to recover the release history in two close-to-reality sandbox experiments. The outcome shows that the ES-MDA with Rafiee's inflation scheme has the ability to capture the main pattern of the release history. But in order to move one more step to field cases, a more detailed description of uncertainties or elaborated parameterization of the time functions is paramount.

Simultaneous identification of groundwater contamination source and aquifer parameters with a new weighted-average wavelet variable-threshold denoising method

This paper first proposed a parallel heuristic search strategy for simultaneous identification of groundwater contamination source and aquifer parameters. As identification results are influenced by many factors, such as noisy contamination concentration data, data denoising is necessary. The existing wavelet threshold denoising method has unavoidable shortcomings; therefore, this paper first proposed a new weighted-average wavelet variable-threshold denoising (WWVD) method to improve the denoising effect for concentration data, which further enhanced the subsequent identification accuracy. However, frequent calls to the simulation model could produce high computational cost during likelihood calculation. Hence, single surrogate model of the simulation model was developed to reduce cost; however, it presented limitation. Thus, this paper first developed a differential evolution-tabu search (DE-TS) hybrid algorithm to construct an optimal ensemble surrogate model, which assembled Gaussian process, kernel extreme learning machine, and support vector regression. The first proposed DE-TS algorithm also improved the approximation accuracy of surrogate model to simulation model. This paper first proposed and implemented a parallel heuristic search iterative process for simultaneous identification, and the identification results were obtained when the iteration process terminated. The accuracy and efficiency of these newly proposed approaches were tested through a hypothetical case. Results showed that the WWVD method not only improved the denoising effect for concentration data but also enhanced the subsequent identification accuracy. The OES model using DE-TS hybrid algorithm improved the approximation accuracy of surrogate model to simulation model, and the parallel heuristic search strategy is helpful for simultaneous identification of groundwater contamination source and aquifer parameters.

Parallel heuristic search strategy based on a Bayesian approach for simultaneous recognition of contaminant sources and aquifer parameters at DNAPL-contaminated sites

In this study, we develop a parallel heuristic search strategy based on a Bayesian approach for simultaneously recognizing groundwater contaminant sources and aquifer parameters (unknown variables) at sites contaminated with dense non-aqueous phase liquids (DNAPLs). The parallel search strategy is time-consuming because thousands of simulation models must run in order to calculate the likelihood. Various stand-alone surrogate systems for the simulation models have been established, but they also have unavoidable limitations. Thus, we develop an optimal combined surrogate system by combining Gaussian process, kernel extreme learning machine, and support vector regression methods using a differential evolution algorithm with a variable mutation rate based on the rand-to-best/1/bin strategy, thereby improving the approximation accuracy of the surrogate system to the simulation model and significantly decreasing the high computational cost. Utilizing the optimal combined surrogate system reduced the CPU time by more than 400 times. In the iterative parallel heuristic search process, each round of iteration involves determining the candidate points and state transitions. The Monte Carlo approach is used widely for selecting candidate point, but this approach does not readily converge to the posterior distribution for unknown variables when the probability density function types are complex with weak search ergodicity. In order to improve the search ergodicity, we develop a particle swarm optimization algorithm with a non-linear decreasing inertia weight and Metropolis criterion, which is more suitable for unknown variables with complex probability density functions. The recognition results are obtained simultaneously when the iterative process terminates. We assess our proposed approaches based on a hypothetical case study at a three-dimensional site contaminated with DNAPLs. The results demonstrate that the parallel heuristic search strategy is helpful for the simultaneous recognition of DNAPL contaminant sources in groundwater and aquifer parameters.

Solving Inverse Problems of Unknown Contaminant Source in Groundwater-River Integrated Systems Using a Surrogate Transport Model Based Optimization

The paper presents a new approach to identify the unknown characteristics (release history and location) of contaminant sources in groundwater, starting from a few concentration observations at monitoring points. An inverse method that combines the forward model and an optimization algorithm is presented. To speed up the computation, the transfer function theory is applied to create a surrogate transport forward model. The performance of the developed approach is evaluated on two case studies (literature and a new one) under different scenarios and measurement error conditions. The literature case study regards a heterogeneous confined aquifer, while the proposed case study was never investigated before, it involves an aquifer-river integrated flow and transport system. In this case, the groundwater contaminant originated from a damaged tank, migrates to a river through the aquifer. The approach, starting from few concentration observations monitored at a downstream river cross-section, accurately estimates the release history at a groundwater contaminant source, even in presence of noise on observations. Moreover, the results show that the methodology is very fast, and can solve the inverse problem in much less computation time in comparison with other existing approaches.

Identification of immiscible NAPL contaminant sources in aquifers by a modified two-level saturation based imperialist competitive algorithm

A simulation-optimization model is proposed for identifying the characteristics of local immiscible NAPL contaminant sources inside aquifers. This model employs the UTCHEM 9.0 software as its simulator for solving the governing equations associated with the multi-phase flow in porous media. As the optimization model, a novel two-level saturation based Imperialist Competitive Algorithm (ICA) is proposed to estimate the parameters of contaminant sources. The first level consists of three parallel independent ICAs and plays as a pre-conditioner for the second level which is a single modified ICA. The ICA in the second level is modified by dividing each country into a number of provinces (smaller parts). Similar to countries in the classical ICA, these provinces are optimized by the assimilation, competition, and revolution steps in the ICA. To increase the diversity of populations, a new approach named knock the base method is proposed. The performance and accuracy of the simulation-optimization model is assessed by solving a set of two and three-dimensional problems considering the effects of different parameters such as the grid size, rock heterogeneity and designated monitoring networks. The obtained numerical results indicate that using this simulation-optimization model provides accurate results at a less number of iterations when compared with the model employing the classical one-level ICA.