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Contaminant Spill in a Sandbox with Non-Gaussian Conductivities: Simultaneous Identification by the Restart Normal-Score Ensemble Kalman Filter


The joint identification of the parameters defining a contaminant source and the heterogeneous distribution of the hydraulic conductivities of the aquifer where the contamination took place is a difficult task. Previous studies have demonstrated the applicability of the restart normal-score ensemble Kalman filter (rNS-EnKF) in synthetic cases making use of sufficient hydraulic head and concentration data. This study shows an application of the same technique to a non-synthetic case under laboratory conditions and discusses the difficulties found on its application and the avenues taken to solve them. The method is first tested using a synthetic case that mimics the sandbox experiment to establish the minimum number of ensemble members and the best technique to prevent the filter collapsing. The synthetic case shows that among different techniques based on update damping and covariance inflation, the Bauser’s covariance inflation method works best in preventing filter collapse. Its application to the sandbox data shows that the rNS-EnKF can benefit from Bauser’s inflation to reduce the number of ensemble realizations substantially in comparison with a filter without inflation, arriving at a good joint identification of both the contaminant source and the spatial heterogeneity of the conductivities.

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Financial support to carry out this work was received from the Spanish Ministry of Science and Innovation through project PID2019-109131RB-I00, and from the Spanish Ministry of Education through project PRX17/00150. Teng Xu also acknowledges the financial support from the Fundamental Research Funds for the Central Universities (B200201015) and Jiangsu Specially-Appointed Professor Program (B19052). And the authors would like to thank University of Parma for providing the experimental equipment. Part of the work was performed during a stay of the third author at the University of Parma under the TeachinParma initiative, co-funded by Fondazione Cariparma and University of Parma.

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Correspondence to Teng Xu.

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Chen, Z., Xu, T., Gómez-Hernández, J.J. et al. Contaminant Spill in a Sandbox with Non-Gaussian Conductivities: Simultaneous Identification by the Restart Normal-Score Ensemble Kalman Filter. Math Geosci 53, 1587–1615 (2021).

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  • Inverse modeling
  • Forensic hydrogeology
  • Data assimilation
  • Sandbox