Assimilation of Contamination Data for the Hydrogeological Characterization of a Heterogeneous Aquifer

Abstract:

Knowledge of hydraulic conductivity (K) fields is of primary importance to ensure optimal groundwater management. Ensemble Kalman filters are increasingly used to infer the hydraulic conductivity field and to assess its uncertainty through indirect and direct data assimilation. Time-varying variables, linearly or non-linearly related to K such as pressure head or concentration data are often accessible to hydrogeologists and can therefore be used to estimate the hydraulic conductivity of a heterogeneous aquifer. Kalman filters (KF) allow to take into consideration the dynamics of the system, thus improving the estimation through time-dependent data. The ensemble kalman filter (EnKF) is an extension of the KF for non-linear forward models, such as the groundwater flow model but at the cost of requiring the computation of several forward models.. Since many groundwater variables, such as concentration or pressure head, do not follow a Gaussian distribution and are computationally expensive to have high numbers of ensembles members, various modifications have been applied to the EnKF. These modifications include variable transformations to adjust to gaussianity and transformations on the covariance matrix, such as covariance localization or covariance inflation, to compensate for the small ensemble size.

The present study aims to assimilate tracer concentration data through direct measurements and electrical resistivity tomography in order to infer a heterogeneous K field through the use of EnKF. A 2D synthetic case is studied to evaluate the effect of the number of ensembles and a technique to optimize the ensemble number is proposed. In addition, different parameters such as variable gaussian transformation, localization and covariance inflation are tested. The effect of the time step on the non-linearity of the problem is also evaluated. Coupled hydrogeophysical assimilation is compared to uncoupled assimilation. The final aim of the study is to define an optimal parameter setting for the use of Ensemble Kalman filters in groundwater transport.