Characterizing the interactions between streams and aquifers is a major challenge in hydrology. Electrical self-potential (SP) is sensitive to groundwater flow through the electrokinetic effect, which is proportional to Darcy velocity. SP surveys have been extensively used for the characterization of seepage flow in a variety of contexts. But to our knowledge, a model coupling SP and groundwater flow has never been implemented for the study of stream-aquifer interactions. To address the issue, we first implemented a two-dimensional model to a synthetic stream-aquifer cross section. Results underline the very distinct nature of SP profiles in gaining or losing stream conditions. Second, we presented a field application in a transect crossing a stream in losing conditions. The coupled model successfully reproduced the observed SP profile. This inverse modeling of the SP signal provides quantitative data on hydrodynamic parameters (hydraulic conductivity, hydraulic heads) and geophysical parameters (coupling coefficient). Nevertheless, all relevant parameters cannot be uniquely estimated without precise prior information on at least some of these parameters. Our results confirm the potential of SP surveys on the characterization of stream-aquifer exchanges. Recommendations on the collection of high-quality data are also provided, along with a description of the contexts in which the methodology is likely to perform well.

Most groundwater models simulate stream-aquifer interactions with a head-dependent flux boundary condition based on a river conductance (CRIV). CRIV is usually calibrated with other parameters by history matching. However, the inverse problem of groundwater models is often ill-posed and individual model parameters are likely to be poorly constrained. Ill-posedness can be addressed by Tikhonov regularization with prior knowledge on parameter values. The difficulty with a lumped parameter like CRIV, which cannot be measured in the field, is to find suitable initial and regularization values. Several formulations have been proposed for the estimation of CRIV from physical parameters. However, these methods are either too simple to provide a reliable estimate of CRIV, or too complex to be easily implemented by groundwater modelers. This paper addresses the issue with a flexible and operational tool based on a 2D numerical model in a local vertical cross section, where the river conductance is computed from selected geometric and hydrodynamic parameters. Contrary to other approaches, the grid size of the regional model and the anisotropy of the aquifer hydraulic conductivity are also taken into account. A global sensitivity analysis indicates the strong sensitivity of CRIV to these parameters. This enhancement for the prior estimation of CRIV is a step forward for the calibration and uncertainty analysis of surface-subsurface models. It is especially useful for modeling objectives that require CRIV to be well known such as conjunctive surface water-groundwater use.

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