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• Exploiting ERT's detailed structural insights to address HT's limitations in aquifer characterization. • Developing a robust methodology to establish the relationship between resistivity and hydraulic parameters. • The efficacy of the proposed approach was corroborated through independent hydraulic and tracer tests. Hydraulic tomography (HT) has been proven effective for characterizing aquifer hydraulic heterogeneity for decades. Many have also proposed using electrical resistivity tomography (ERT) to gain prior information about large-scale layer structures to improve the HT estimates, when the number of pumping tests and drawdown measurements is limited. This study investigates the merits of such proposals via numerical and physical experiments using an actual sandbox. The numerical experiments show that ERT can detect the sandbox's layer structure under fully saturated conditions. Surprisingly, the physical sandbox experiments yielded different results: ERT could not detect the layer structures under saturated conditions. Nevertheless, the surveys in the physical experiments under drained conditions facilitated mapping structures, revealing that electrical conductivity show a stronger correlation with moisture content than porosity. We then used the detected layer structure under unsaturated conditions from the ERT without a definitive resistivity/hydraulic conductivity relationship as the HT prior information to improve HT's saturated hydraulic conductivity (K) estimates. The results of independent pumping and tracer tests in the numerical sandbox experiments demonstrated and validated improvements in K estimation. These findings are significant, questioning the need for accurate local-scale resistivity/hydraulic conductivity relationships. It is a new insight into hydrogeophysics. [ABSTRACT FROM AUTHOR]

• The value of hydraulic tomography with periodic signals is evaluated. • Transient signals with short periods provide better resolution. • Resolution is improved by the right combination of periods. • Optimal periods are linked to hydraulic properties. • The choice of periods is crucial for optimal results. An accurate assessment of the hydraulic properties of aquifers is required to represent groundwater flow and solute transport. This study investigates periodic hydraulic tomography performed between wells to obtain accurate images of hydraulic properties. Tomographic experiments with different period and amplitude of sinusoidal test flow, hydraulic properties and well configurations were simulated with a numerical flow model. An l -curve analysis of the obtained heads and sensitivities identified the optimal parameter resolution and served as a basis for comparing the experiments. The results show that the transient phase of signals with short periods provides the most information about the resolution of the aquifer. The resolution could be further improved if tests with different periods were properly combined in the analysis. The study concludes that periodic tomography provides valuable insight into the spatial resolution of hydraulic conductivity and its vertical anisotropy and specific storage, but the choice of signal characteristics is critical. [ABSTRACT FROM AUTHOR]

Characterizing groundwater flow parameters is crucial for understanding complex aquifer systems, and inverse techniques play a fundamental role in modeling hydrogeological parameters and assessing their uncertainties. Nonetheless, the use of a forward model in these methods can be highly time-consuming, especially with an increasing number of model parameters. To address this issue, we propose a surrogate model based on a U-Net architecture that replaces the transient groundwater flow model, reducing runtime and enabling a fast quantification of uncertainties related to key parameters, including heterogeneous hydraulic conductivity, boundary conditions, specific storage, and pumping rate. The surrogate is trained using limited evaluations of the forward model to learn the physical relationship between hydraulic conductivity fields and transient hydraulic heads measured on-site. The physical principles of the studied problem, including boundary conditions, specific storage, and source terms, are also mapped and introduced as inputs to the model to enhance its understanding of the governing equation of transient groundwater flow. To speed up learning using image–image regression, the previously predicted transient hydraulic heads also serve as an input to predict the transient heads at the current time step. Once the model is trained, we use a spectral geostatistical method to solve the inverse problem, a pumping test of 12 h, using the surrogate model in place of the forward model. Our study demonstrates that the trained U-Net accurately reproduces the state variables corresponding to a specific parameter field, and in terms of computational demand, using U-Net as a surrogate model reduces the required computational time by approximately an order of magnitude for the defined problem. The proposed approach offers an efficient and accurate method for groundwater flow parameter characterization and uncertainty quantification in complex aquifer systems. [Display omitted] • A U-Net surrogate approach is developed for transient groundwater inverse problems. • Uncertainties are rapidly evaluated using a geostatistical spectral method. • Uncertain parameters include log(K), Q, Ss, and boundary conditions • Integrate time into image–image regression for capturing time-varying processes. • The surrogate model significantly reduces computation times for inverse problems. [ABSTRACT FROM AUTHOR]

• The variability of solute transport in heterogeneous confined aquifers of variable thickness is quantified by the variance of solute displacement. • Variability of solute displacement is caused by variability of the hydraulic conductivity and the thickness of the aquifer. • Even if the random fields of hydraulic conductivity and aquifer thickness are second-order stationary, the hydraulic head fields could be nonstationary. • The nonstationary hydraulic head fields lead to nonstationary flow fields and thus to nonstationary solute displacement fields. In this work, the variability of regional-scale transport of inert solutes in heterogeneous confined aquifers of variable thickness is quantified by the variance of the displacement of a solute particle. In the traditional stochastic approach to solute transport at the regional scale, the variability of solute displacement is attributed to the variability of the transmissivity fields. In this work, however, variability in solute displacement is attributed to variability in hydraulic conductivity and aquifer thickness fields. A general stochastic methodology for deriving the variance of the displacement of a solute particle based on the convection velocity of solute particles, developed from the relationship between the two-dimensional depth-averaged solute mass conservation equation and the Fokker-Planck equation, is given. Assuming that the fluctuations in log hydraulic conductivity and log thickness of the confined aquifer are second-order stationary processes, a closed-form expression for the solute displacement variance in the mean flow direction is obtained for the case of advection-dominated solute transport. The results show that variation in hydraulic conductivity and aquifer thickness can lead to nonstationarity in the covariance of flow velocity, making longitudinal macrodispersion anomalous and increasing linearly with travel time at large distances. [ABSTRACT FROM AUTHOR]

• Spatially variable, scale-dependent dispersivities are jointly estimated with hydraulic conductivity. • Joint inversion of tracer and ERT data improves aquifer characterization and transport predictions. • Spatially variable dispersivities outperform uniform dispersivities in transport prediction when adding ERT data. The hydraulic conductivity (K) has been recognized as one of the controlling parameters that significantly impact the transport behavior in groundwater systems. To improve the predictive ability of a transport model, concentration measurements are commonly used in inverse modeling to characterize the K distribution. In addition to K , the spread of the solute plume also depends on dispersion coefficients. The evolution of the plume morphology can only be satisfactorily reproduced with appropriate dispersivities. Dispersivity values or distributions rely on the resolution of the inferred K distribution. Dispersivities were typically treated as spatially uniform in inverse modeling and jointly estimated with K. Although employing spatially variable dispersivities may hold the potential to better capture the solute transport behavior, it may significantly increase the number of unknown parameters for inverse modeling. Solving such an ill-posed inversion problem is challenging, especially when the amount of intrusive borehole-based measurements is limited. As a non-intrusive, cost-effective, and high sampling density method, time-lapse geophysical technique (e.g. , electrical resistivity tomography, ERT) has not yet drawn much attention as a useful source of information for dispersivity estimation. In this study, we developed a joint hydrogeophysical inversion framework to simultaneously estimate spatially variable K and dispersivities by integrating tracer-concentration and ERT-derived potential data. We evaluated the proposed framework by conducting numerical tracer experiments in a highly heterogeneous aquifer. Results show that using limited tracer concentration data alone failed to resolve the fine structure in K field. In this case, there was little difference in the prediction performance of solute transport by considering spatially uniform or variable dispersivities. In contrast, the K distribution was estimated at a significantly higher resolution when integrating tracer-concentration and ERT data, contributing to a remarkable improvement in transport modeling. Powered by the sufficient amount of ERT measurements, jointly estimating spatially variable dispersivities further enhanced the reproduction of tracer plumes and breakthrough curves. [ABSTRACT FROM AUTHOR]

• We solve low-velocity non-Darcian flow to a confined and partially penetrating well in a leaky aquifer system. • An analysis is conducted to examine the temporal and spatial changes in confined groundwater head differences between Darcian and non-Darcian flow conditions. • Non-Darcian flow in the aquitard needs to be considered under small confined aquifer hydraulic conductivity and large threshold pressure gradient of the aquitard. Previous studies on the flow dynamics of leaky aquifer systems have primarily relied on Darcy's law, assuming fully penetrating wells in confined aquifers. However, when dealing with aquitards dominated by clay, the flow behavior often deviates from Darcy's law. Moreover, in the majority of cases, this entails partially penetrating well pumping. This paper introduces a mathematical model for non-Darcian flow in a confined and partially penetrating well system within a leaky aquifer system. The model is based on the low-velocity non-Darcian flow equation, incorporating the threshold pressure gradient. In the confined aquifer, the flow exhibits two-dimensional Darcian flow behavior, while in the aquitard, the flow is characterized by one-dimensional non-Darcian flow in the vertical direction. In the shallow aquifer, the flow is one-dimensional Darcian flow in the radial direction. The mathematical model is solved using the finite difference method, and the obtained results are compared with calculations based on traditional Darcian flow theory. The findings indicate that the confined groundwater head difference, as predicted by the Darcian and non-Darcian flow theories, diminishes radially as the distance from the pumping well increases and vertically as one moves away from the top of the confined aquifer. As pumping progresses, the confined groundwater head difference initially rises and subsequently stabilizes gradually. Moreover, the magnitude of the confined groundwater head difference is more pronounced when the threshold pressure gradient, vertical hydraulic conductivity of the aquitard, pumping rate, hydraulic conductivity and specific yield of shallow aquifer are larger, or when the hydraulic conductivity and specific storage of the confined aquifer are smaller. The effect of well screen length on the confined groundwater head difference is minimal. [ABSTRACT FROM AUTHOR]

Contaminant source and aquifer characterization (CSAC) is critical in groundwater pollution evaluation and remediation. The ensemble smoother with multiple data assimilation (ES-MDA) is utilized to jointly identify contaminant source information and hydraulic conductivities by assimilating time-lapse electrical resistivity tomography (ERT) data. In a synthetic profile with a time-varying release history in a heterogeneous aquifer, we verify the performance of the proposed data assimilation framework. The results show that the CSAC problem could be handled by the proposed approach. The time-varying release history and the high permeability area can be identified with adequate time-lapse ERT measurements. Further reproduction of the evolution of the plume after CSAC also shows consistency with the reference plume. The poor conditioning inversion caused by the filter inbreeding is analyzed by comparing four scenarios with different apparent resistivity measurements. Furthermore, we also evaluate the impact of uncertainties in the petrophysical properties and geophysical observations on our data assimilation framework. The results show that the proposed ES-MDA data assimilation framework could provide a convincing inversion of the time-varying release history and hydraulic conductivities. • We propose a data assimilation framework including the coupling of the simulators of MODFLOW, MT3DS and ResIPy into the Ensemble Smoother with Multiple Data Assimilation (ES-MDA) implementation. • The time-lapse electrical resistivity tomography (ERT) measurements are first employed for the joint identification of contaminant source information and hydraulic conductivities. • We analyze the influence of different bipole–bipole electrode array configurations on the ES-MDA data assimilation framework. [ABSTRACT FROM AUTHOR]

• Dispersion effects on offshore freshwater extent and discharge investigated. • Toe moves seaward monotonically with increased dispersion. • Tip-dispersion relationship is non-monotonic. • Dispersion increases fresh groundwater discharge to the sea. • Dominant control on the interface width at the tip is K:K z contrast. Recent recognition of the widespread occurrence of freshwater beneath the ocean has renewed interest in approaches to understand and predict its extent. The most straightforward methodologies are based on the sharp-interface approximation, which neglects dispersive mechanisms. The understanding of dispersion effects on freshwater extents in coastal aquifers is based almost entirely on onshore aquifer situations. This study explores dispersion in offshore coastal aquifers, in terms of the steady-state freshwater extent, seawater circulation and freshwater discharge, through numerical experimentation. Results show that increasing dispersion causes a seaward shift in the interface toe location, as expected, whereas the interface tip shows a non-monotonic relationship with dispersion that depends on the contrast between aquifer and aquitard hydraulic conductivities. Higher dispersion leads to enhanced seawater recirculation rates and freshwater discharge, as opposed to non-monotonic relationships obtained previously for onshore aquifers. The mixing zone at the toe widens as dispersion increases, similar to onshore cases, whereas the mixing zone at the tip has a surprisingly non-monotonic relationship with dispersion. The dispersion relationships revealed in this study can be explained by counteractions between dispersion, density and advective forces, and refraction across the aquifer-aquitard interface, which in combination produce offshore aquifer behaviour that differs, in some ways, to the manner in which onshore aquifers respond to dispersive processes. Consequently, previous empirical corrections to sharp-interface methods (to account for dispersive effects) applied to onshore coastal aquifers are ineffective in their application to offshore settings. [ABSTRACT FROM AUTHOR]

• A novel approach combining an integrated surface/subsurface model and a groundwater parameter-estimation model, was able to better constrain the model. • The groundwater system may be nearing, if not exceeding, its sustainable groundwater production capacity and the speed of recovery is not indicative of sustainability. • Results from using conventionally-assumed uniform recharge distort calibrated K fields and impacts assessment The quantification of recharge and trans-valley underflow is needed in arid regions to estimate the impacts of new water withdrawals on the water table. However, for mountainous desert areas, such estimates are highly challenging, due to data scarcity, heterogeneous soils, and long residence times. Conventional assessment employs isolated groundwater models configured with simplified uniform estimates of recharge. Here, we employed a data-constrained surface-subsurface process model to provide an ensemble of spatially distributed recharge and underflow estimates using perturbed parameters. Then, the Model-Independent Parameter Estimation and Uncertainty Quantification (PEST) package was used to calibrate the aquifer hydraulic conductivity field in MODFLOW for this ensemble and reject implausible recharge values. This novel dual-model approach, broadly applicable to mountainous arid regions, was designed to maximally exploit available data sources. It can assimilate groundwater head observations, reject unrealistic parameters, and narrow the range of estimated drawdowns due to pumping. We applied this approach to the Chuckwalla basin in California, USA to determine natural recharge. Simulated recharge concentrates along alluvial fans at the mountain fronts and ephemeral washes where run-off water infiltrates. If an evenly distributed recharge was employed as in conventional studies, it would result in regional biases in estimated drawdown and larger uncertainty bounds. We also note that the speed of groundwater recovery does not guarantee sustainability: heavy pumping induces large hydraulic gradients that initially recover quickly when pumping is halted, but the system may not ultimately recover to pre-pumping levels. [ABSTRACT FROM AUTHOR]

The aim of this paper is to analyze the statistical properties of non-reactive solute concentrations in natural aquifers, taking into account the hydraulic conductivity heterogeneity. Quantifying the uncertainty in the evaluation of solute concentrations in aquifers is an important issue for human health and in ecological risk analysis. In particular, the concentration Cumulative Distribution Function (CDF) is a key element, as it informs the decision makers of the probability that the concentration at an environmental target is below a maximum contaminant level. The analysis presented in this paper is performed in a Lagrangian framework. According to the "reverse formulation", the origin of the particle being sampled is sought instead of considering the destination of the injected particles. Based on this formulation, a closed form for the unconditioned concentration CDF is derived. The same procedure is applied to obtain a closed form for the concentration conditioned by measurements at sampling points in an aquifer. [ABSTRACT FROM AUTHOR]

Highlights • Coastal aquifer filters out high-frequency tidal signals and leaves behind low-frequency signals to affect upper saline plume and lower saltwater wedge. • Upper saline plume and lower saltwater wedge are significantly affected by antecedent tidal conditions. • Effect of antecedent tidal conditions was enhanced by increased soil hydraulic conductivity or decreased beach slope. Abstract Subterranean estuary, as a saltwater-freshwater mixing zone in a coastal aquifer, is significantly affected by tides. While many studies have been conducted to examine the effects of tides on groundwater dynamics in subterranean estuaries in relation to submarine groundwater discharge and seawater intrusion, the focus of the investigation, particularly for those based on numerical modelling, has been on tides with few frequencies, e.g., monochromatic tide and spring-neap tides (bichromatic). In this study, we examine numerically effects of measured multi-constituent tides on a coastal unconfined aquifer. With the antecedent tidal conditions accounted for using the Gamma distribution function, we conducted regression analysis and quantified the effects of measured multi-constituent tides on coastal unconfined aquifers in a prolonged and cumulative fashion. The results showed that the response of submarine groundwater discharge to the tidal fluctuation is mostly instantaneous. The coastal aquifer behaved like a low-pass filter that smooths out high-frequency tidal signals and leaves behind low-frequency signals to affect upper saline plume and lower saltwater wedge. The upper saline plume and lower saltwater wedge were significantly affected by antecedent tidal conditions at monthly and yearly time scales, respectively. Sensitivity analysis showed that the low-pass filter capacity can be altered by soil hydraulic conductivity and beach slope. This study revealed the importance of antecedent tidal conditions for seawater intrusion and will help to improve our understanding of hydrological processes in natural coastal unconfined aquifers. [ABSTRACT FROM AUTHOR]

Quantifying the uncertainty in solute mass discharge at an environmentally sensitive location is key to assess the risks due to groundwater contamination. Solute mass fluxes are strongly affected by the spatial variability of hydrogeological properties as well as release conditions at the source zone. This paper provides a methodological framework to investigate the interaction between the ubiquitous heterogeneity of the hydraulic conductivity and the mass release rate at the source zone on the uncertainty of mass discharge. Through the use of perturbation theory, we derive analytical and semi-analytical expressions for the statistics of the solute mass discharge at a control plane in a three-dimensional aquifer while accounting for the solute mass release rates at the source. The derived solutions are limited to aquifers displaying low-to-mild heterogeneity. Results illustrate the significance of the source zone mass release rate in controlling the mass discharge uncertainty. The relative importance of the mass release rate on the mean solute discharge depends on the distance between the source and the control plane. On the other hand, we find that the solute release rate at the source zone has a strong impact on the variance of the mass discharge. Within a risk context, we also compute the peak mean discharge as a function of the parameters governing the spatial heterogeneity of the hydraulic conductivity field and mass release rates at the source zone. The proposed physically-based framework is application-oriented, computationally efficient and capable of propagating uncertainty from different parameters onto risk metrics. Furthermore, it can be used for preliminary screening purposes to guide site managers to perform system-level sensitivity analysis and better allocate resources. [ABSTRACT FROM AUTHOR]

Detecting where and when a contaminant entered an aquifer from observations downgradient of the source is a difficult task; this identification becomes more challenging when the uncertainty about the spatial distribution of hydraulic conductivity is accounted for. In this paper, we have implemented an application of the restart normal-score ensemble Kalman filter (NS-EnKF) for the simultaneous identification of a contaminant source and the spatially variable hydraulic conductivity in an aquifer. The method is capable of providing estimates of the spatial location, initial release time, the duration of the release and the mass load of a point-contamination event, plus the spatial distribution of hydraulic conductivity together with an assessment of the estimation uncertainty of all the parameters. The method has been applied in synthetic aquifers exhibiting both Gaussian and non-Gaussian patterns. The identification is made possible by assimilating in time both piezometric head and concentration observations from an array of observation wells. The method is demonstrated in three different synthetic scenarios that combine hydraulic conductivities with unimodal and bimodal histograms, and releases in high and low conductivity zones. The results prove that the specific implementation of the EnKF is capable of recovering the source parameters with some uncertainty and of recovering the main patterns of heterogeneity of the hydraulic conductivity fields by assimilating a sufficient number of state variable observations. The proposed approach is an important step towards contaminant source identification in real aquifers, which may have logconductivity spatial distributions with either Gaussian or non-Gaussian features, yet, it is still far from practical applications since the transport parameters, the external sinks and sources and the initial and boundary conditions are assumed known. [ABSTRACT FROM AUTHOR]

Geological heterogeneity, i.e. the spatial variability of discrete hydrogeological units, is investigated in an aquifer analog of glacio-fluvial sediments to determine how such a geological structure can be simplified for characterization needs. The aquifer analog consists of ten hydrofacies whereas the scarcity of measurements in typical field studies precludes such detailed spatial models of hydraulic properties. Of particular interest is the role of connectivity of the hydrofacies structure, along with its effect on the connectivity of mass transport, in site characterization for predicting early arrival times. Transport through three realizations of the aquifer analog is modeled with numerical particle tracking to ascertain the fast flow channel through which early arriving particles travel. Three simplification schemes of two-facies models are considered to represent the aquifer analogs, and the velocity within the fast flow channel is used to estimate the apparent hydraulic conductivity of the new facies. The facies models in which the discontinuous patches of high hydraulic conductivity are separated from the rest of the domain yield the closest match in early arrival times compared to the aquifer analog, but assuming a continuous high hydraulic conductivity channel connecting these patches yields underestimated early arrivals times within the range of variability between the realizations, which implies that the three simplification schemes could be advised but pose different implications for field measurement campaigns. Overall, the results suggest that the result of transport connectivity, i.e. early arrival times, within realistic geological heterogeneity can be conserved even when the underlying structural connectivity is modified. [ABSTRACT FROM AUTHOR]

• An analytical model is developed to handle horizontal aquifer/aquitard heterogeneity. • A high- K aquitard window tends to dampen tide-induced aquifer head fluctuations. • Aquifer head fluctuations may be dampened by a large-size high- S s aquitard window. • Sandbox experiments validated the effects of a high- K aquitard window. Low-permeability aquitards are important sedimentary units that protect the underlying confined aquifers from contamination by seawater and anthropogenic sources in coastal leaky aquifer systems. Therefore, the integrity of the aquitard is of crucial importance. However, the aquitard integrity may be vulnerable to horizontal heterogeneities in the form of aquitard windows. In this study, an innovative analytical model was developed to describe groundwater flow in a coastal leaky aquifer system with horizontal heterogeneities in hydraulic properties of either the aquitard or the confined aquifer. Consequently, the effects of aquitard windows, which manifest as horizontally local heterogeneities in hydraulic conductivity and/or specific storage, on the tidal wave propagation can be considered in the analysis. Analytical solutions were derived for tidal-head or constant-flux inland boundary conditions. The derivation process avoided previous methodologies that involved the assembly of large-size matrices. The newly developed analytical model can cover multiple existing analytical models that are associated with the assumptions of homogeneity in hydraulic properties of the aquifer and the aquitard, infinite horizontal extent of the coastal leaky aquifer system, impermeability of the aquitard, or ignorance of aquitard storativity. Analytical investigations revealed that high-permeability aquitard windows acting as preferential-flow conduits tended to dampen the tide-induced head propagation within the underlying confined aquifer. Moreover, an aquitard with a higher storativity (but the same permeability) and of considerable size can result in an apparent propagation bias. The newly developed analytical model in this study was further corroborated through sandbox experiments. Both piezometer measurements and parameter estimates indicated the non-negligible effects of high-permeability aquitard windows on the tidal wave propagation. The sandbox investigation also highlighted the importance of geostatistical inverse modeling in characterizing local heterogeneities within the confined aquifer and in detecting the location and size of aquitard windows, when measurement data of tide-induced aquifer head fluctuations were provided. [ABSTRACT FROM AUTHOR]

A new mathematical model is developed to describe the flow in response to a constant-head pumping (or constant-head test, CHT) in a leaky unconfined aquifer system of infinite lateral extent with considering unsaturated flow. The model consists of an unsaturated zone on the top, an unconfined aquifer in the middle, and a second aquifer (aquitard) at the bottom. The unsaturated flow is described by Richard's equation, and the flows in unconfined aquifer and second layer are governed by the groundwater flow equation. The well partially penetrates the unconfined aquifer with a constant head in the well due to CHT. The governing equations of the model are linearized by the perturbation method and Gardner's exponential model is adopted to describe the soil retention curves. The solution of the model for drawdown distribution is obtained by applying the methods of Laplace transform and Weber transform. Then the solution for the wellbore flowrate is derived from the drawdown solution with Darcy's law. The issue of the equivalence of normalized drawdown predicted by the present solution for constant-head pumping and Tartakovsky and Neuman's (2007) solution for constant-rate pumping is discussed. On the basis of the wellbore flowrate solution, the results of the sensitivity analysis indicate that the wellbore flowrate is very sensitive to the changes in the radial hydraulic conductivity and the thickness of the saturated zone. Moreover, the results predicted from the present wellbore flowrate solution indicate that this new solution can reduce to Chang’s et al. (2010a) solution for homogenous aquifers when the dimensionless unsaturated exponent approaches 100. The unsaturated zone can be considered as infinite extent in the vertical direction if the thickness ratio of the unsaturated zone to the unconfined aquifer is equal to or greater than one. As for the leakage effect, it can be ignored when the vertical hydraulic conductivity ratio (i.e., the vertical hydraulic conductivity of the lower layer over that of the unconfined aquifer) is smaller than 0.1. The present solution is compared with the numerical solution from FEMWATER for validation and the results indicate good match between these two solutions. Finally, the present solution is applied to a set of field drawdown data obtained from a CHT for the estimation of hydrogeologic parameters. [ABSTRACT FROM AUTHOR]

Hydraulic conductivity and its anisotropy are fundamental aquifer properties for groundwater flow and transport modeling. Current in-well or direct-push field measurement techniques allow for relatively quick determination of general conductivity profiles with depth. However, capabilities for identifying local scale conductivities in the horizontal and vertical directions are very limited. Here, we develop the theoretical basis for estimating horizontal and vertical conductivities from different types of steady-state single-well/probe injection tests under saturated conditions and in the absence of a well skin. We explore existing solutions and a recent semi-analytical solution approach to the flow problem under the assumption that the aquifer is locally homogeneous. The methods are based on the collection of an additional piece of information in the form of a second injection (or recirculation) test at a same location, or in the form of an additional head or flow observation along the well/probe. Results are represented in dimensionless charts for partial validation against approximate solutions and for practical application to test interpretation. The charts further allow for optimization of a test configuration to maximize sensitivity to anisotropy ratio. The two methods most sensitive to anisotropy are found to be (1) subsequent injection from a lateral screen and from the bottom of an otherwise cased borehole, and (2) single injection from a lateral screen with an additional head observation along the casing. Results may also be relevant for attributing consistent divergences in conductivity measurements from different testing methods applied at a same site or location to the potential effects of anisotropy. Some practical aspects are discussed and references are made to existing methods, which appear easily compatible with the proposed procedures. [ABSTRACT FROM AUTHOR]

Aquifer heterogeneity presents a primary challenge in predicting the movement of solutes in groundwater systems. The problem is particularly difficult on very large scales, across which permeability, chemical properties, and pumping rates may vary by many orders of magnitude and data are often sparse. An example is the fluvio-deltaic aquifer system of Bangladesh, where naturally-occurring arsenic (As) exists over tens of thousands of square kilometers in shallow groundwater. Millions of people in As-affected regions rely on deep (≥150 m) groundwater as a safe source of drinking water. The sustainability of this resource has been evaluated with models using effective properties appropriate for a basin-scale contamination problem, but the extent to which preferential flow affects the timescale of downward migration of As-contaminated shallow groundwater is unknown. Here we embed detailed, heterogeneous representations of hydraulic conductivity (K), pumping rates, and sorptive properties (K d ) within a basin-scale numerical groundwater flow and solute transport model to evaluate their effects on vulnerability and deviations from simulations with homogeneous representations in two areas with different flow systems. Advective particle tracking shows that heterogeneity in K does not affect average travel times from shallow zones to 150 m depth, but the travel times of the fastest 10% of particles decreases by a factor of ∼2. Pumping distributions do not strongly affect travel times if irrigation remains shallow, but increases in the deep pumping rate substantially reduce travel times. Simulation of advective-dispersive transport with sorption shows that deep groundwater is protected from contamination over a sustainable timeframe (>1000 y) if the spatial distribution of K d is uniform. However, if only low-K sediments sorb As, 30% of the aquifer is not protected. Results indicate that sustainable management strategies in the Bengal Basin should consider impacts of both physical and chemical heterogeneity, as well as their correlation. These insights from Bangladesh show that preferential flow strongly influences breakthrough of both conservative and reactive solutes even at large spatial scales, with implications for predicting water supply vulnerability in contaminated heterogeneous aquifers worldwide. [ABSTRACT FROM AUTHOR]

Estimating spatial distributions of the hydraulic conductivity in heterogeneous aquifers has always been an important and challenging task in hydrology. Generally, the hydraulic conductivity field is determined from hydraulic head or pressure measurements. In the present study, we propose to use temperature data as source of information for characterizing the spatial distributions of the hydraulic conductivity field. In this way, we performed a laboratory sandbox experiment with the aim of imaging the heterogeneities of the hydraulic conductivity field from thermal monitoring. During the laboratory experiment, we injected a hot water pulse, which induces a heat plume motion into the sandbox. The induced plume was followed by a set of thermocouples placed in the sandbox. After the temperature data acquisition, we performed a hydraulic tomography using the stochastic Hybrid Monte Carlo approach, also called the Hamiltonian Monte Carlo (HMC) algorithm to invert the temperature data. This algorithm is based on a combination of the Metropolis Monte Carlo method and the Hamiltonian dynamics approach. The parameterization of the inverse problem was done with the Karhunen-Loève (KL) expansion to reduce the dimensionality of the unknown parameters. Our approach has provided successful reconstruction of the hydraulic conductivity field with low computational effort. [ABSTRACT FROM AUTHOR]

Precise information about the spatial distribution of hydraulic conductivity (K) in an aquifer is essential for the reliable modeling of groundwater flow and transport processes. In this study, we present results of a new inversion procedure for induced polarization (IP) data that incorporates petrophysical relations between electrical and hydraulic parameters, and therefore allows for the direct computation of K. This novel approach was successfully implemented for the Bolstern aquifer analog by performing synthetic IP experiments with a combined surface and cross-borehole setup. From these data, the distribution of K was retrieved with high accuracy and resolution, showing a similar quality compared to images achieved by hydraulic tomography. To further improve the quantitative estimates of K , we use synthetic pumping test data to inform two novel calibration strategies for the IP inversion results. Both calibrations are especially helpful for correcting a possible bias of the IP inversion, e.g., due to resolution limitations and/or to bias in the underlying petrophysical relations. The simulation of tracer experiments on the retrieved tomograms highlights the accuracy of the inversion results, as well as the significant role of the proposed calibrations. • New IP inversion procedure for direct computation of hydraulic conductivity. • IP inversion results have similar quality as hydraulic tomography. • Hydraulic calibration of IP results to improve transport simulations. [ABSTRACT FROM AUTHOR]

Transient hydraulic tomography is used to image the heterogeneous hydraulic conductivity and specific storage fields of shallow aquifers using time series of hydraulic head data. Such ill-posed and non-unique inverse problem can be regularized using some spatial geostatistical characteristic of the two fields. In addition to hydraulic heads changes, the flow of water, during pumping tests, generates an electrical field of electrokinetic nature. These electrical field fluctuations can be passively recorded at the ground surface using a network of non-polarizing electrodes connected to a high impedance (> 10 MOhm) and sensitive (0.1 mV) voltmeter, a method known in geophysics as the self-potential method. We perform a joint inversion of the self-potential and hydraulic head data to image the hydraulic conductivity and specific storage fields. We work on a 3D synthetic confined aquifer and we use the adjoint state method to compute the sensitivities of the hydraulic parameters to the hydraulic head and self-potential data in both steady-state and transient conditions. The inverse problem is solved using the geostatistical quasi-linear algorithm framework of Kitanidis. When the number of piezometers is small, the record of the transient self-potential signals provides useful information to characterize the hydraulic conductivity and specific storage fields. These results show that the self-potential method reveals the heterogeneities of some areas of the aquifer, which could not been captured by the tomography based on the hydraulic heads alone. In our analysis, the improvement on the hydraulic conductivity and specific storage estimations were based on perfect knowledge of electrical resistivity field. This implies that electrical resistivity will need to be jointly inverted with the hydraulic parameters in future studies and the impact of its uncertainty assessed with respect to the final tomograms of the hydraulic parameters. [ABSTRACT FROM AUTHOR]

Assessing the spatial distribution of hydraulic conductivity ( K ) in natural aquifers is fundamental to predict the spatio-temporal evolution of solutes, a process that is mainly controlled by the heterogeneity of K . In sedimentary aquifers, the vertical variations of K are typically more relevant than the horizontal ones in controlling the plume evolution at the local scale; such K vertical distributions can be inferred by combining the Lagrangian formulation of transport with the assimilation of tracer test data via the ensemble Kalman filter (EnKF). In this work, the data for the assimilation procedure are provided by monitoring tracer tests with electrical resistivity tomography (ERT). Our main objective is to show the possibility of directly using ERT data by assimilating the solute travel times, instead of the concentration values, thus avoiding the need for a petrophysical law. The methodology is applied to both a synthetic and a real test case and gives a satisfactory retrieval of the K field distribution, as well as of the solute evolution. [ABSTRACT FROM AUTHOR]

Semi-analytical solutions of flow to a well in an unconfined single porosity aquifer underlain by a fractured double porosity aquifer, both of infinite radial extent, are obtained. The upper aquifer is pumped at a constant rate from a pumping well of infinitesimal radius. The solutions are obtained via Laplace and Hankel transforms and are then numerically inverted to time domain solutions using the de Hoog et al. algorithm and Gaussian quadrature. The results are presented in the form of dimensionless type curves. The solution takes into account the effects of pumping well partial penetration, water table with instantaneous drainage, leakage with storage in the lower aquifer into the upper aquifer, and storativity and hydraulic conductivity of both fractures and matrix blocks. Both spheres and slab-shaped matrix blocks are considered. The effects of the underlying fractured aquifer hydraulic parameters on the dimensionless drawdown produced by the pumping well in the overlying unconfined aquifer are examined. The presented solution can be used to estimate hydraulic parameters of the unconfined and the underlying fractured aquifer by type curve matching techniques or with automated optimization algorithms. Errors arising from ignoring the underlying fractured aquifer in the drawdown distribution in the unconfined aquifer are also investigated. [ABSTRACT FROM AUTHOR]

The knowledge of subsurface heterogeneity is a prerequisite to describe flow and transport in porous media. Of particular interest are the variance and the correlation scale of hydraulic conductivity. In this study, we present how these aquifer parameters can be inferred using empirical steady state pumping test data. We refer to a previously developed analytical solution of “effective well flow” and examine its applicability to pumping test data as under field conditions. It is examined how the accuracy and confidence of parameter estimates of variance and correlation length depend on the number and location of head measurements. Simulations of steady state pumping tests in a confined virtual aquifer are used to systematically reduce sampling size while determining the rating of the estimates at each level of data density. The method was then applied to estimate the statistical parameters of a fluvial heterogeneous aquifer at the test site Horkheimer Insel, Germany. We conclude that the “effective well flow” solution is a simple alternative to laboratory investigations to estimate the statistical heterogeneity parameter using steady state pumping tests. However, the accuracy and uncertainty of the estimates depend on the design of the field study. In this regard, our results can help to improve the conceptual design of pumping tests with regard to the parameter of interest. [ABSTRACT FROM AUTHOR]

Nitrate contamination of aquifers is threatening the sustainability of water resource production around the globe. Denitrification is an ubiquitous process in groundwater systems and needs to be represented in managerial and predictive efforts. Yet, fully understanding the temporal and spatial dynamics of all biogeochemical and physical properties controlling nitrate reduction at the basin scale remains a challenging task. Conceptual simplifications such as homogenization are used, but their implications on model performance are often not well assessed. This paper (1) analyzes the importance of denitrification spatial variability on the fate of non-point source nitrate contamination, and (2) assesses the performance of upscaled denitrification rate coefficient values. Heterogeneity in the hydraulic conductivity of a typical unconsolidated alluvial aquifer system and its associated uncertainty is systematically represented in our 3D numerical simulations of flow and transport. The spatial variability in the nitrate reduction capacities of the aquifer is accounted for by 3 different conceptual models: a positive and a negative correlation with the aquifer hydraulic properties and a uniform random distribution. Our results indicate that heterogeneity in the denitrification rate coefficient – as well as the model describing spatial variability – has a significant impact on concentration statistics observed at a series of extraction wells. However, we also show that, under the modeling setting used in this study (e.g., stationarity of reactivity), upscaled values of denitrification rate coefficients allow a virtually perfect reproduction of nitrate concentration statistics, a promising outcome for employing parameter estimation (calibration) of effective rate coefficients of denitrification: A detailed description of the spatial variability of the nitrate reduction capacity of the alluvial aquifer is not necessary. Yet, these homogeneous, upscaled denitrification rate coefficients result from a complex interaction between the biochemistry and the physics of the aquifer, which makes their direct estimation a challenging task. [Display omitted] • Spatial variability structure of denitrification rate coefficients influence nitrate dynamics. • Upscaled, effective denitrification rate coefficients reproduce well concentration statistics. • Upscaling denitrification rates is complex due to interplays between key processes. [ABSTRACT FROM AUTHOR]

Highlights: [•] A set of hybrid formulations are proposed in a new aquifer inverse method. [•] Simultaneous estimation of hydraulic conductivities, recharge rates, and boundary conditions. [•] Inversion accuracy increases with increasing observed data and grid refinement. [•] Inversion results are stable under increasing measurement errors. [•] The inverse method is able to handle model structure errors in parameterization. [Copyright &y& Elsevier]

Highlights: [•] E. coli transport below freshly-excavated pond receiving latrine effluent modeled. [•] Anisotropy in hydraulic conductivity greatly limited E. coli depth penetration. [•] Reversible and irreversible attachment of E. coli required to match field data. [•] Laboratory-predicted E. coli transport matches field data within factor of two. [•] Kinetic interaction parameters relatively insensitive to scale of measurement. [ABSTRACT FROM AUTHOR]

Highlights: [•] Introduction of a novel hydraulic tomography procedure based on travel-time based inversion and application of pilot points. [•] Reconstruction of the hydraulic conductivity field of a three-dimensional, strongly heterogeneous, aquifer analogue. [•] Encountering the computationally burden by parallel computing and subspace regularization. [Copyright &y& Elsevier]

• New analytical solutions for analysing pumping test near an anisotropic fault. • Fault zone draining aquifers with differing properties. • Unconventional application of the well-image theory. • Satisfactory comparison with numerical modelling in all aquifer compartments. • Useful for analysing pumping tests in fractured media. We present a new set of analytical solutions for analysing pumping tests in a well near a vertical fault zone, dyke or vein. We consider a fault zone with finite width, storativity and hydraulic conductivity, which can be anisotropic, and without limitation of the diffusivity contrast between the three aquifer domains (pumped aquifer, fault zone and opposite-side aquifer). This configuration, not described before, also considers flow transience within the fault zone. Drawdown solutions were developed for the three-aquifer domains based on an unconventional application of the well-image theory. Their comparison with numerical modelling results was very satisfactory. Drawdown behaviour at the pumping well is discussed for contrasted properties between the three-aquifer domains. Original analytical solutions for transient flow along both sides of the fault zone, and net transient flow from the fault itself, are proposed and discussed, with particular attention to flow reversal, from the pumped compartment to the fault zone, which occurs where the fault zone is the most transmissive. Finally, we extend the solutions to the case of a well intersecting and pumping a vertical fracture of finite length located near the same vertical geological discontinuity. [ABSTRACT FROM AUTHOR]

Abstract: The assessment of hydraulic conductivity of heterogeneous aquifers is a difficult task using traditional hydrogeological methods (e.g., steady state or transient pumping tests) due to their low spatial resolution. Geophysical measurements performed at the ground surface and in boreholes provide additional information for increasing the resolution and accuracy of the inverted hydraulic conductivity field. We used a stochastic joint inversion of Direct Current (DC) resistivity and self-potential (SP) data plus in situ measurement of the salinity in a downstream well during a synthetic salt tracer experiment to reconstruct the hydraulic conductivity field between two wells. The pilot point parameterization was used to avoid over-parameterization of the inverse problem. Bounds on the model parameters were used to promote a consistent Markov chain Monte Carlo sampling of the model parameters. To evaluate the effectiveness of the joint inversion process, we compared eight cases in which the geophysical data are coupled or not to the in situ sampling of the salinity to map the hydraulic conductivity. We first tested the effectiveness of the inversion of each type of data alone (concentration sampling, self-potential, and DC resistivity), and then we combined the data two by two. We finally combined all the data together to show the value of each type of geophysical data in the joint inversion process because of their different sensitivity map. We also investigated a case in which the data were contaminated with noise and the variogram unknown and inverted stochastically. The results of the inversion revealed that incorporating the self-potential data improves the estimate of hydraulic conductivity field especially when the self-potential data were combined to the salt concentration measurement in the second well or to the time-lapse cross-well electrical resistivity data. Various tests were also performed to quantify the uncertainty in the inverted hydraulic conductivity field. [Copyright &y& Elsevier]

Abstract: A steady/quasi-steady model is developed for predicting flow into a partially penetrating well with skin zone in a confined aquifer overlying an impervious layer. The model takes into account flow through the bottom of the wellbore, finite skin thickness and finite horizontal and vertical extent of the aquifer. Moreover, the solution can be easily extended to include the mixed-type boundary condition at the well face, where a Dirichlet in the form of a specified hydraulic head and a Neumann in the form of zero flux coexist at the same time at different portions of the well face. The validity of the proposed solution is tested by comparing a few results obtained from the developed model with corresponding results obtained by analytical and numerical means. The study shows that, among other factors remaining constant, both the horizontal and vertical extent of an artesian aquifer, thickness of the skin zone, bottom flow and conductivity contrast of the skin and formation zones, play an important part in deciding flow to a well dug in the aquifer, and hence these factors must be considered while analyzing the problem. The model proposed here can be used to estimate skin thickness as well as hydraulic conductivities of the skin and formation zones of a well with skin zone in an artesian aquifer underlain by an impervious layer by utilizing pumping test data falling in the steady or quasi-steady state of a typical pumping test. As the proposed solution is of a general nature in the sense that it can handle, apart from partial penetration and bottom flow, the finite size skin zone and finite horizontal and vertical extent of an artesian aquifer together with the mixed-type boundary condition at the well face, it is hoped that the predictions coming out of the model will be more realistic than those obtained using solutions developed with more stringent assumptions. [ABSTRACT FROM AUTHOR]

The total travel distance and the hydraulic conductivity in steady-state groundwater flow systems are modeled with asymmetric gamma distribution functions. The ratio of the total travel distance over the hydraulic conductivity, scaled by a factor involving the hydraulic gradient and the aquifer porosity, equals the residence time of groundwater. The residence time measures the period elapsed between recharge and discharge of groundwater from an aquifer flow system. The residence time is a random variable whose probability density function (p.d.f.) is determined by those of the total travel distance and the hydraulic conductivity. The p.d.f. of the residence time was derived and from that, applying basic mass-balance considerations, followed that of the groundwater age. The age is the time elapsed since the recharge of groundwater in transit through an aquifer flow system. It is shown that the p.d.f.s of the residence time and the groundwater age are related by a first-order, linear, differential equation. The cumulative distribution functions of the residence time and the groundwater age and their first and second moments are also derived, and so is the output concentration of a solute that enters a steady-state groundwater flow system dissolved in recharge. A computational example illustrates the advantage of treating the residence time and the groundwater age statistically and constraining them with Darcy''s law and mass-balance principles. Solute output shows a complex structure with stable and radioactive solutes in deceptively simple steady-state groundwater flow regimes. [Copyright &y& Elsevier]

To consider the non-Darcian nature of groundwater flow and the permeability reduction owing to well and aquifer clogging, an Izbash's law-based analytical model with a time-dependent hydraulic conductivity function is proposed for constant-rate recharge and constant-head recharge. By means of linearization approximations, variable substitutions and the Laplace transform, approximate analytical solutions for the model are derived. Comparison of developed approximate analytical solutions with numerical solutions indicates that the approximate solutions are highly accurate except during the short period of initial recharge stage. The proposed model provides a theoretical basis for managed aquifer recharge involving clogging-related permeability reduction and non-Darcian flow. [ABSTRACT FROM AUTHOR]

• A general mathematical model describing non-Darcian flow in a confined aquifer for a single well circulation system was developed. • This study provided an extension of the analytical solution based on Darcy's Law to non-Darcian flow conditions for a single well circulation system. • An approximate analytical solution for non-Darcian flow in the Laplace domain and the steady-state analytical solution in the time domain were obtained. • The characteristics of non-Darcian flow and the influences of different parameters on drawdown were investigated. An analytical model is proposed in this study to describe transient drawdown induced by non-Darcian flow in a confined aquifer with a single well circulation groundwater heat pump system. The Izbash equation and a linearization method are employed to describe non-Darcian flow in the horizontal direction of a confined aquifer and to approximate the nonlinear term in the governing equation, respectively. By applying a combination of the Laplace and Fourier cosine transforms, an approximate analytical solution in the Laplace domain is obtained, which is numerically inverted to obtain transient drawdown in the time domain using the Stehfest algorithm method. The results of the derived analytical solution for the special case of Darcian flow (m = 1) correspond well with the existing solution derived using Darcy's law. The steady-state analytical solution in the time domain is obtained by applying the Fourier cosine transform. Moreover, the sensitivity analysis is performed to investigate the influence of selected parameters, such as the power index m , the radial hydraulic conductivity K r , the aquifer specific storage S , and the length of the sealed section d 2 , on drawdown. The results show that each parameter has its influence period on drawdown, and that drawdown is more sensitive to the power index m compared to other parameters. [ABSTRACT FROM AUTHOR]

Hydraulic barriers using either two or three injection wells are studied analytically to evaluate their performance on improving groundwater extraction in a coastal aquifer under the threat of seawater intrusion. The multiple well system is operated by extracting fresh groundwater through a landward well and partially reinjecting into the aquifer through two or three wells located parallel to the coastline and between the interface toe and the extraction well. We found that with appropriate well locations and pumping rates, the multiple-well system could outperform a single extraction well in terms of net extraction rate, which is up to 90% higher for an aquifer with a thickness of 20 m, hydraulic conductivity of 10 m/d, and freshwater influx of 0.24 m2/d. Sensitivity analyses reveal that the monotonicity of the maximum net extraction rate is determined by the total injection rate. In specific, when the total injection rate is fixed, the maximum net extraction rate is a non-monotonic function of the distance between the injection well and the coastline and the distance between two injection wells, resulting in a global maximum. When the total injection rate is not fixed, by contrast, the maximum net extraction rate depends on the total injection rate, and a larger total injection rate leads to a larger maximum net extraction rate. By using different injection rates for side and middle injection wells of the three-injection-well hydraulic barrier, the maximum net extraction rate could be further improved, depending on the distance between the two injection wells. Analytical analyses can provide initial guidance for the design of a multiple-well system in coastal aquifers with the purpose of obtaining enhanced extraction under the threats of seawater intrusion. [ABSTRACT FROM AUTHOR]

• Heterogeneous aquifers are modeled with log-normal random conductivity fields. • Numerical schemes are tested on two-dimensional benchmark flow problems. • Code verification performed by comparison with analytical manufactured solutions. • Validation done through comparisons between MC statistics and first-order results. • Limited computational feasibility for exponentially correlated log-conductivity. This article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in heterogeneous aquifers. Finite difference, finite element, discontinuous Galerkin, spectral, and random walk methods are tested on two-dimensional benchmark flow problems. Realizations of log-normal hydraulic conductivity fields are generated by Kraichnan algorithms in closed form as finite sums of random periodic modes, which allow direct code verification by comparisons with manufactured reference solutions. The quality of the methods is assessed for increasing number of random modes and for increasing variance of the log-hydraulic conductivity fields with Gaussian and exponential correlation. Experimental orders of convergence are calculated from successive refinements of the grid. The numerical methods are further validated by comparisons between statistical inferences obtained from Monte Carlo ensembles of numerical solutions and theoretical first-order perturbation results. It is found that while for Gaussian correlation of the log-conductivity field all the methods perform well, in the exponential case their accuracy deteriorates and, for large variance and number of modes, the benchmark problems are practically not solvable with reasonably large computing resources, for all the methods considered in this study. [ABSTRACT FROM AUTHOR]

• This setup can describe design of convergent tracer tests or containment systems. • Second-order characterization of K suffices to capture the main features of the BTC. • FOA solution provides a reasonable BTC prediction even for high heterogeneity. This paper studies the impact of the hydraulic conductivity structure on solute transport in a radially convergent heterogeneous flow field, which is generated by a well pumping a confined aquifer. The solute is injected instantaneously in a fully penetrating well at a known distance from the pumping well and the analysis is performed numerically by considering four conductivity structures sharing the same two-point statistics, but displaying widely different higher-order moments and connectivity features. The overall objective of the present work is to assess the impact of three-dimensional hydraulic conductivity structures on the Breakthrough Curve (BTC) at a pumping well as a function of a few structural parameters: the logconductivity variance the integral scales along the horizontal and vertical directions, the local-scale dispersivity and the distance of the injection well. The numerical simulations are also compared with two analytical solutions from literature based on the First Order Approximation and the Self Consistent Approximation, respectively. The results indicate that the principal features of the BTC are weakly dependent on the hydraulic conductivity structure, similar to the findings of Janković (2017) for transport in uniform flow. Also, the simple First-Order solution provides a good approximation of the BTC in most of the scenarios considered, and thus it can be a useful and effective tool for screening purposes in applications dealing with aquifers' contamination. [ABSTRACT FROM AUTHOR]