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Quantitative estimates of hydrological state variables using electrical or electromagnetic geophysical methods are systematically biased by overlooked heterogeneity below the spatial scale resolved by the method. We generalize the high‐salinity asymptotic limit of electrical conduction in porous media at the continuous (e.g., Darcy) scale, by introducing a new petrophysical parameter, the mixing factor M, which accounts for the effect of fluid conductivity heterogeneity on the equivalent electrical conductivity tensor; it is expressed in terms of the volume‐average of the product of mean‐removed fluid conductivity and electric fields. We investigate the behavior of M for static and evolving fluid conductivity scenarios. Considering 2‐D ergodic log‐normal random fields of fluid conductivity, we demonstrate, in absence of surface conductivity, that observing the components of the M‐tensor allows univocally determining the variance and anisotropy of the field. Further, time‐series of the M‐tensor under diffusion‐limited mixing allows distinguishing between different characteristic temporal scales of diffusion, which are directly related to the initial integral scales of the salinity field. Under advective‐diffusive transport and for a pulse injection, the time‐series of M have a strong dependence on the Péclet number. Since M is defined in the absence of surface conductivity, we investigate how to correct measurements for surface conductivity effects. The parameter M provides conceptual understanding about the impact of saline heterogeneity on electrical measurements. Further work will investigate how it can be incorporated into hydrogeophysical inverse formulations and interpretative frameworks. Plain Language Summary Electrical and electromagnetic geophysical methods provide information about the spatio‐temporal distribution of average electrical conductivity of porous media. This property is affected by the transport of electrically conductive solutes, which unfolds over a wide range of spatial scales. However, when translating electrical data into solute concentration, almost all studies to date have ignored solute heterogeneity below the averaging volume inherent to geophysical measurements or modeling, leading to unphysical results. We introduce the mixing factor M, an electrical parameter that links small‐scale solute heterogeneity and average electrical conductivity, via a closed‐form expression depending on the small‐scale features of electric and solute concentration fields. We show that observation of the M‐tensor allows recovering the variance and anisotropy of the solute field in a time‐static setting. For diffusion‐limited transport, the time‐series of M help distinguishing the initial length scales of the fields, whereas for advective‐diffusive transport, these data help distinguishing the Peclet number. The presented framework helps to decode information about solute heterogeneity that is contained in geoelectrical measurements, while also avoid making biased hydrological estimates. Future venues of research will investigate how to incorporate M in available (hydro)geophysical modeling workflows. Key Points Petrophysical parameter generalizing the high‐salinity limit of electrical conduction for heterogeneous fluid conductivity in porous media Formal expression for M provides framework to interpret impact of small‐scale fluid conductivity heterogeneity on electrical measurements The mixing factor M depends on geostatistical properties of solute concentration fields and thus on transport characteristics

Essentially all hydrogeological processes are strongly influenced by the subsurface spatial heterogeneity and the temporal variation of environmental conditions, hydraulic properties, and solute concentrations. This spatial and temporal variability generally leads to effective behaviors and emerging phenomena that cannot be predicted from conventional approaches based on homogeneous assumptions and models. However, it is not always clear when, why, how, and at what scale the 4D (3D + time) nature of the subsurface needs to be considered in hydrogeological monitoring, modeling, and applications. In this paper, we discuss the interest and potential for the monitoring and characterization of spatial and temporal variability, including 4D imaging, in a series of hydrogeological processes: (1) groundwater fluxes, (2) solute transport and reaction, (3) vadose zone dynamics, and (4) surface–subsurface water interactions. We first identify the main challenges related to the coupling of spatial and temporal fluctuations for these processes. We then highlight recent innovations that have led to significant breakthroughs in high-resolution space–time imaging and modeling the characterization, monitoring, and modeling of these spatial and temporal fluctuations. We finally propose a classification of processes and applications at different scales according to their need and potential for high-resolution space–time imaging. We thus advocate a more systematic characterization of the dynamic and 3D nature of the subsurface for a series of critical processes and emerging applications. This calls for the validation of 4D imaging techniques at highly instrumented observatories and the harmonization of open databases to share hydrogeological data sets in their 4D components.

We investigate how diffusion-limited mixing of a layered solute concentration distribution within a porous medium impacts bulk electrical conductivity. To do so, we perform a milli-fluidic tracer test by injecting a fluorescent and electrically conductive tracer in a quasi two-dimensional (2D) water-saturated porous medium. High resolution optical- and geoelectrical monitoring of the tracer is achieved by using a fluorimetry technique and equipping the flow cell with a resistivity meter, respectively. We find that optical and geoelectrical outputs can be related by a temporal re-scaling that accounts for the different diffusion rates of the optical and electrical tracers. Mixing-driven perturbations of the electrical equipotential field lines cause apparent electrical conductivity time-series, measured perpendicularly to the layering, to peak at times that are in agreement with the diffusion transport time-scale associated with the layer width. Numerical simulations highlight high sensitivity of such electrical data to the layers’ degree of mixing and their distance to the injection electrodes. Furthermore, the electrical data correlate well with time-series of two commonly used solute mixing descriptors: the concentration variance and the scalar dissipation rate.

Essentially all hydrogeological processes are strongly influenced by the subsurface spatial heterogeneity and the temporal variation of environmental conditions, hydraulic properties, and solute concentrations. This spatial and temporal variability needs to be considered when studying hydrogeological processes in order to employ adequate mechanistic models or perform upscaling. The scale at which a hydrogeological system should be characterized in terms of its spatial heterogeneity and temporal dynamics depends on the studied process and it is not always necessary to consider the full complexity. In this paper, we identify a series of hydrogeological processes for which an approach coupling the monitoring of spatial and temporal variability, including 4D imaging, is often necessary: (1) groundwater fluxes that control (2) solute transport, mixing and reaction processes, (3) vadose zone dynamics, and (4) surface-subsurface water interaction occurring at the interface between different subsurface compartments. We first identify the main challenges related to the coupling of spatial and temporal fluctuations for these processes. Then, we highlight some recent innovations that have led to significant breakthroughs in this domain. We finally discuss how spatial and temporal fluctuations affect our ability to accurately model them and predict their behavior. We thus advocate a more systematic characterization of the dynamic nature of subsurface processes, and the harmonization of open databases to store hydrogeological data sets in their four-dimensional components, for answering emerging scientific question and addressing key societal issues.