Improving joint identification of groundwater contaminant source and non-Gaussian distributed conductivity field using a deep learning-based ensemble smoother

Accurate simulation of groundwater flow and solute transport is crucial for effective risk assessment and targeted pollution remediation. The inherent complexity of groundwater systems, characterized by elusive contamination sources and heterogeneous aquifer structures, introduces significant uncertainty into model simulations and predictions. Given the difficulty in directly measuring these unknown parameters, their estimation often relies on utilizing indirect observational data (e.g., hydraulic head and solute concentration) with data assimilation (DA) techniques. Traditional DA methods such as Markov chain Monte Carlo (MCMC) and ensemble smoother with multiple DA (ESMDA) struggle with high dimensionality and non-Gaussianity issues, leading to suboptimal performance in calibrating complex groundwater models. In this study, we introduce an innovative DA approach that integrates ensemble smoother (ES) with deep learning (DL), termed ESDL, designed for joint identification of contaminant source and heterogeneous conductivity field represented by high-dimensional and non-Gaussian distributed parameters. ESDL leverages DL's robust capabilities in fitting non-linear relationships and discerning complex (including non-Gaussian) features to extract valuable insights from observational data. We systematically evaluate the efficacy of ESDL and ESMDA through three case studies involving 3,329 unknown model parameters with non-Gaussian spatial characteristics (multi-facies and channels, respectively). The impact of biased prior assumptions on identification performance is also investigated. Across these cases, ESDL exhibits superior performance in characterizing non-Gaussian conductivity fields and matching the observations, while ESMDA excels in estimating contaminant source parameters. Both methods demonstrate distinct strengths, underscoring the potential for future research to integrate these approaches for enhanced performance.