Is fully coupled hydrogeophysical inversion really better than uncoupled? A comparison study using ensemble Kalman filter assimilation of ERT-monitored tracer test data.

Recent advances in geophysical methods have been increasingly exploited as inverse modeling tools in groundwater hydrology. In particular, several attempts to constrain the hydrogeophysical inverse problem to reduce inversion error have been made using time-lapse geophysical measurements through both coupled and uncoupled inversion approaches. On one hand, the main advantage of coupled approaches is that the numerical models for the geophysical and hydrological processes are linked together such that the geophysical data are inverted directly for the hydrological properties of interest, avoiding artifacts related to the classical geophysical inversions. On the other hand, uncoupled approaches, relying upon a geophysical inversion that is carried out before estimating the hydrological variable of interest, could reveal something about the process that is not accounted for in a model, i.e., they are not constrained by the conceptualization of the hydrological model. In spite of the appeal and popularity of fully coupled inversion approaches, their superiority over more traditional uncoupled methods still needs to be objectively proven; the aim of this work is to shed some light on this debate. An approach based on the Lagrangian formulation of transport and the ensemble Kalman filter (EnKF) is here applied to assess the spatial distribution of hydraulic conductivity (K) by assimilating time-lapse cross-hole electrical resistivity tomography (ERT) data generated for a synthetic tracer test in a heterogeneous aquifer. In the coupled version of the proposed inverse modeling approach, the K distribution is retrieved by assimilating raw ERT resistance data without the need for a preliminary geoelectrical inversion. In the uncoupled version, K is estimated by assimilating electrical conductivity data derived from a previously performed classical geophysical inversion of the same resistance dataset. We compare the performance of the two approaches in a number of simulation scenarios and evaluate the impact on the inversions of the choice of the prior statistics of K. Our results show that the fully coupled approach outperforms the uncoupled when the prior statistics used to generate the initial guess of the hydraulic conductivity fields are close to the ones used to generate the true field. Otherwise, the coupled approach is heavily affected by the filter “inbreeding” (a well known effect of variance underestimation typical of EnKF), while the uncoupled approach is more robust due to the larger uncertainty characterizing the electrical conductivity data. Furthermore, in our study the coupled approach is more computationally intensive than the uncoupled, due to the much larger number of forward runs required by the electrical model.