Coupling ensemble smoother and deep learning with generative adversarial networks to deal with non-Gaussianity in flow and transport data assimilation

Dynamic data such as hydraulic head and concentration data can be integrated into the groundwater flow and contaminant transport model to improve its predictive ability for groundwater resource management and aquifer remediation. Ensemble Smoother with Multiple Data Assimilation (ES-MDA) has gained popularity for data assimilation in the field of hydrogeology, where aquifer parameters such as hydraulic conductivity are calibrated by conditioning on observed dynamic data. The ES-MDA has an optimal solution if aquifer parameters follow a multi-Gaussian distribution. However, fluvial deposits commonly exhibit a strong heterogeneity with channels (i.e., connectivity). In other words, the hydraulic conductivity does not follow the multi-Gaussian distribution. To deal with data assimilation in channelized aquifers, we propose to couple ES-MDA with deep learning. Specifically, Generative Adversarial Networks (GAN), a deep learning algorithm, are used to re-parameterize the channelized aquifer with a low-dimension latent variable. The ES-MDA is then used to update the latent variable by assimilating dynamic data into the groundwater model. Synthetic studies of groundwater flow and contaminant transport models are used to demonstrate the proposed method. The results illustrate that the coupling of GAN and ES-MDA is able to reconstruct the channel structures and reduce the uncertainty of hydraulic head and contaminant concentration predictions.