Joint identification of hydraulic conductivity and groundwater pollution sources using unscented Kalman smoother with multiple data assimilation and deep learning

Identification of groundwater pollution sources (IGPSs) is a prerequisite for pollution remediation and pollution risk prediction. Data assimilation approaches have been used extensively in IGPSs field in recent years. A data assimilation approach-unscented Kalman filter is complex to operate due to the need to repeatedly restart the simulation model, and the identification accuracy needs to be improved further for application to IGPSs with strong nonlinear characteristics. Thus, to improve the identification performance and enrich the technology for IGPSs, a novel data assimilation approach called unscented Kalman smoother with multiple data assimilation (UKS-MDA) was applied to identify hydraulic conductivity and GPSs. To assess the identification performance, the identification results (IRs) obtained with UKS-MDA were compared with those produced by the ensemble smoother with multiple data assimilation (ES-MDA) in terms of the identification accuracy and computational efficiency. In addition, given the strong learning ability of deep belief neural network (DBNN) for complex nonlinear systems, this study employs a deep belief neural network (DBNN) as a substitute model for the simulation model to reduce the computational load and loss of computational accuracy caused by iterative calculations. The results indicated that (1) the mean relative error (MRE) between the DBNN substitute model and the simulation model was 0.92 %, and when applied to IGPSs, it could save approximately 99 % of the computation time and load. (2) The MREs between the IRs obtained using UKS-MDA and the true values in scenarios with smaller errors in concentrations and in scenarios with larger errors in concentrations were 0.4 % and 4.16 % lower than that obtained using ES-MDA. (3) Compared to ES-MDA, UKS-MDA could save approximately 12 % of computational efficiency in the execution of IGPSs. The combination of DBNN and UKS-MDA could effectively recognize GPSs, which has guiding significance for the remediation and prediction of groundwater pollution.