Low enthalpy geothermal systems exploited with ground source heat pumps or groundwater heat pumps present many advantages within the context of sustainable energy use. Designing, monitoring and controlling such systems requires the measurement of spatially distributed temperature fields and the knowledge of the parameters governing groundwater flow (permeability and specific storage) and heat transport (thermal conductivity and volumetric thermal capacity). Such data are often scarce or not available. In recent years, the ability of electrical resistivity tomography (ERT), self-potential method (SP) and distributed temperature sensing (DTS) to monitor spatially and temporally temperature changes in the subsurface has been investigated. We review the recent advances in using these three methods for this type of shallow applications. A special focus is made regarding the petrophysical relationships and on underlying assumptions generally needed for a quantitative interpretation of these geophysical data. We show that those geophysical methods are mature to be used within the context of temperature monitoring and that a combination of them may be the best choice regarding control and validation issues.

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.

In theory, aquifer thermal energy storage (ATES) systems can recover in winter the heat stored in the aquifer during summer to increase the energy efficiency of the system. In practice, the energy efficiency is often lower than expected from simulations due to spatial heterogeneity of hydraulic properties or non‐favorable hydrogeological conditions. A proper design of ATES systems should therefore consider the uncertainty of the prediction related to those parameters. We use a novel framework called Bayesian Evidential Learning (BEL) to estimate the heat storage capacity of an alluvial aquifer using a heat tracing experiment. BEL is based on two main stages: pre‐ and postfield data acquisition. Before data acquisition, Monte Carlo simulations and global sensitivity analysis are used to assess the information content of the data to reduce the uncertainty of the prediction. After data acquisition, prior falsification and machine learning based on the same Monte Carlo are used to directly assess uncertainty on key prediction variables from observations. The result is a full quantification of the posterior distribution of the prediction conditioned to observed data, without any explicit full model inversion. We demonstrate the methodology in field conditions and validate the framework using independent measurements.

In inverse problems, investigating uncertainty in the posterior distribution of model parameters is as important as matching data. In recent years, most efforts have focused on techniques to sample the posterior distribution with reasonable computational costs. Within a Bayesian context, this posterior depends on the prior distribution. However, most of the studies ignore modeling the prior with realistic geological uncertainty. In this paper, we propose a workflow inspired by a Popper‐Bayes philosophy that data should first be used to falsify models, then only be considered for matching. We propose a workflow consisting of three steps: (1) in defining the prior, we interpret multiple alternative geological scenarios from literature (architecture of facies) and site‐specific data (proportions of facies). Prior spatial uncertainty is modeled using multiple‐point geostatistics, where each scenario is defined using a training image. (2) We validate these prior geological scenarios by simulating electrical resistivity tomography (ERT) data on realizations of each scenario and comparing them to field ERT in a lower dimensional space. In this second step, the idea is to probabilistically falsify scenarios with ERT, meaning that scenarios which are incompatible receive an updated probability of zero while compatible scenarios receive a nonzero updated belief. (3) We constrain the hydrogeological model with hydraulic head and ERT using a stochastic search method. The workflow is applied to a synthetic and a field case studies in an alluvial aquifer. This study highlights the importance of considering and estimating prior uncertainty (without data) through a process of probabilistic falsification.