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• 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]

Highlights • The continuous adjoint state associated with the transport equation is derived. • Hydraulic conductivity and porosity fields are estimated by inverse modeling. • Concentration data complementing heads slightly improve inverse solutions to flow. Abstract A parameter estimation methodology has been developed on the basis of model inversion using a Quasi–Newton method and adaptive parameterization. The continuous adjoint state equations for both flow and transport in porous media are employed as the tool calculating the gradient components of the objective function with respect to parameters. Solving the continuous form of the adjoint equations can be implemented independently of the code used to solve the forward problem, which renders the technique non-intrusive. The developed methodology is applied to the identification of hydraulic conductivity and porosity fields conditioned by piezometric head data associated with steady-state flow and transient solute concentrations. Synthetic numerical experiments have been undertaken for test cases of increasing complexity, from an almost uniform flow sweeping the modeled domain with a prescribed uniform continuous injection of solute at the inflow boundary, to spatially highly variable flow conditions obtained through source/sink terms within the flow domain and a local stepwise solute injection. The results of inversions are analyzed using criteria based on the comparisons between estimated concentration and reference concentration values as well as comparisons between estimated hydraulic conductivity (and porosity for one test case) and reference hydraulic conductivity fields. The results show that employing a continuous adjoint state technique computed independently of the direct problem is an efficient option for parameter estimation relying jointly upon flow and transport data. In the reported numerical examples that are characterized by the identifiability of the flow problem on the basis of hydraulic head observations, concentration data from solute transport scenarios bring few added value to sought solutions of hydraulic conductivities. The spatial structure of the conductivity fields is slightly improved compared with the reference, but the overall system in terms of head distribution, identification of main flow paths, and solute transit times, only inherits cosmetics. [ABSTRACT FROM AUTHOR]

The porous medium equation (PME) is a generalization of the traditional Boussinesq equation for hydraulic conductivity as a power law function of height. We analyze the horizontal recharge of an initially dry unconfined aquifer of semi-infinite extent, as would be found in an aquifer adjacent a rising river. If the water level can be modeled as a power law function of time, similarity variables can be introduced and the original problem can be reduced to a boundary value problem for a nonlinear ordinary differential equation. The position of the advancing front is not known ahead of time and must be found in the process of solution. We present an analytical solution in the form of a power series, with the coefficients of the series given by a recurrence relation. The analytical solution compares favorably with a highly accurate numerical solution, and only a small number of terms of the series are needed to achieve high accuracy in the scenarios considered here. We also conduct a series of physical experiments in an initially dry wedged Hele-Shaw cell, where flow is modeled by a special form of the PME. Our analytical solution closely matches the hydraulic head profiles in the Hele-Shaw cell experiment. [ABSTRACT FROM AUTHOR]

The paper deals with the crucial problem of the groundwater parameter estimation that is the basis for efficient modeling and reclamation activities. A hierarchical Bayesian approach is developed: it uses the Akaike's Bayesian Information Criteria in order to estimate the hyperparameters (related to the covariance model chosen) and to quantify the unknown noise variance. The transmissivity identification proceeds in two steps: the first, called empirical Bayesian interpolation, uses Y * ( Y  = ln T ) observations to interpolate Y values on a specified grid; the second, called empirical Bayesian update, improve the previous Y estimate through the addition of hydraulic head observations. The relationship between the head and the ln T has been linearized through a perturbative solution of the flow equation. In order to test the proposed approach, synthetic aquifers from literature have been considered. The aquifers in question contain a variety of boundary conditions (both Dirichelet and Neuman type) and scales of heterogeneities ( σ Y 2 = 1.0 and σ Y 2 = 5.3 ). The estimated transmissivity fields were compared to the true one. The joint use of Y * and head measurements improves the estimation of Y considering both degrees of heterogeneity. Even if the variance of the strong transmissivity field can be considered high for the application of the perturbative approach, the results show the same order of approximation of the non-linear methods proposed in literature. The procedure allows to compute the posterior probability distribution of the target quantities and to quantify the uncertainty in the model prediction. Bayesian updating has advantages related both to the Monte-Carlo (MC) and non-MC approaches. In fact, as the MC methods, Bayesian updating allows computing the direct posterior probability distribution of the target quantities and as non-MC methods it has computational times in the order of seconds. [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]

Due to limited availability of surface water, many arid to semi-arid countries rely on their groundwater resources. Despite the quasi-absence of present day replenishment, some of these groundwater bodies contain large amounts of water, which was recharged during pluvial periods of the Late Pleistocene to Early Holocene. These mostly fossil, non-renewable resources require different management schemes compared to those which are usually applied in renewable systems. Fossil groundwater is a finite resource and its withdrawal implies mining of aquifer storage reserves. Although they receive almost no recharge, some of them show notable hydraulic gradients and a flow towards their discharge areas, even without pumping. As a result, these systems have more discharge than recharge and hence are not in steady state, which makes their modelling, in particular the calibration, very challenging. In this study, we introduce a new calibration approach, composed of four steps: (i) estimating the fossil discharge component, (ii) determining the origin of fossil discharge, (iii) fitting the hydraulic conductivity with a pseudo steady-state model, and (iv) fitting the storage capacity with a transient model by reconstructing head drawdown induced by pumping activities. Finally, we test the relevance of our approach and evaluated the effect of considering or ignoring fossil gradients on aquifer parameterization for the Upper Mega Aquifer (UMA) on the Arabian Peninsula. [ABSTRACT FROM AUTHOR]

Many islands consist of limestone sedimentary deposits that are better described as a two-aquifer system consisting of an unconfined aquifer (Quaternary sediments) above a fractured aquifer (fractured limestone) in which groundwater heads are closely regulated by tidal fluctuations on both sides of the islands (dual tides). Propagation of tidal signal, reflected in hydraulic head fluctuation in such a two-aquifer system is significantly different from that in a single aquifer system that is often assumed. The Laplace domain solution of the head fluctuation in such a two-aquifer system subjected to dual tides is obtained first and subsequently inverted to yield real-time solution. Unlike previous solutions, Fourier series with complex variables are avoided and Fourier sine transform is used instead. The solution takes into account an instantaneously drainable water table, hydraulic conductivity anisotropy and arbitrary time-dependent tidal fluctuations. The hydraulic connection of the underlying fractured aquifer and the overlying unconfined aquifer is explored in details. The presented solution can be used to evaluate the head fluctuations and the aquifer parameter estimation of the two-aquifer system underneath a strip-shape island subjected to dual tides. The results can be used to determine the optimum piezometer location to estimate hydraulic parameters of the two-aquifer system using groundwater head fluctuation data. Stream-aquifer interaction is similar to the tidal-aquifer interaction if the chemical difference of the salt water and fresh water is not a concern. The developed solution for tidal-aquifer interaction here can also be used to investigate the aquifer response to stream stage variations in river basin aquifers. [ABSTRACT FROM AUTHOR]

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]

• The ability to verify predicted groundwater discharge patterns at scale is limited. • Discharge zones mapped with thermal infrared are used to evaluate predicted patterns. • Predicted and observed discharge patterns agree well in large but not small streams. • Improved modeling approaches are needed to capture headwater discharge processes. Predicting baseflow dynamics, protecting aquatic habitat, and managing legacy contaminants requires explicit characterization and prediction of groundwater discharge patterns throughout river networks. Using handheld thermal infrared (TIR) cameras, we surveyed 47 km of stream length across the Farmington River watershed (1,570 km2; CT and MA, USA), mapping locations of bank and waterline groundwater discharges based on their thermal signature. Using the observed groundwater discharge locations and predicted groundwater discharge rates from 6 variations of a numerical groundwater-flow model (MODFLOW-NWT), we compared 1) predicted groundwater-discharge rates in areas with and without observed groundwater discharge, 2) spatial patterns of observed and predicted groundwater discharge locations, and 3) density of observed groundwater discharge locations with predicted discharge rates. Five of six models reasonably predicted the spatial patterns of discharge locations along the 5th order mainstem, but fewer models predicted groundwater discharge patterns in smaller streams. Our results highlight 1) the feasibility of using TIR observations to evaluate groundwater models, 2) model parameters that influence discharge prediction accuracy (riverbed sediment and bedrock hydraulic conductivity and river-aquifer connections), and 3) current strengths and future opportunities for improved modeling of groundwater-discharge patterns. [ABSTRACT FROM AUTHOR]

Abstract: We consider common bank filtration systems and develop an explicit analytic solution representing steady, two-dimensional, groundwater flow to a horizontal well near a river in an unconfined aquifer. For the boundary-value problem investigated, we find that a unique solution exists for all negative well discharges. For positive discharges, a maximum value exists which corresponds to the formation of a cusp on the free surface. For positive discharges less than the maximum, the solution is not unique, consisting of two alternate configurations of the free surface. One solution includes a stable free surface on a single-valued physical plane, while the alternate solution includes a looped free surface lying on two sheets of a Riemann surface. Imposing a stability condition on the free surface results in a unique solution to the problem. We use the solution to investigate the behavior of the free surface under varying well discharges to identify stable pumping rates and predict well yield. In particular, we examine the well yield and the stability of the free surface when the head in the horizontal well is maintained at the top of the well screen. This condition is shown to produce a stable free surface for a wide range of well radii; the stability is independent of the hydraulic conductivity of the aquifer, the location of the well, or the presence of a skin resistance at the well. [Copyright &y& Elsevier]

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]

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, ϵN=αϵcotβ (in which β is the beach slope, α is the amplitude parameter and ϵ is the shallow water parameter) and are limited to tan−1(αϵ)≪β⩽π/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as ϵ and α increase, and reaches 7% of the linear solution. [Copyright &y& Elsevier]

• 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]

• A convolutional neural network (CNN) is built to estimate macro-dispersivity from hydraulic conductivity field directly. • The validation of the CNN shows that most estimations fall within ± 20% error range for conductivity fields with moderate heterogeneity. • For a given size of training datasets, the performance of estimating drops with an increase in the heterogeneity of conductivity field. • The CNN trained by conductivity fields with high heterogeneity can achieve superior performance in estimations for fields with less heterogeneity. Building a quantitative relation between the spatial heterogeneity of the hydraulic conductivity fields and the macroscale behavior of solute transport is fundamental for groundwater environment problem. In this work, the deep learning technique is explored to build the functional mapping between the hydraulic conductivity field and the longitudinal macro-dispersivity. We examine the capability of the deep neural network in estimating macro-dispersivities of conductivity fields with different variances. The universality of the trained deep neural network is investigated. Comparisons of the neural network results and the reference values (macro-dispersivities from transport simulation) suggest the promising potential of deep learning technique in porous media with moderate heterogeneity. For a given size of training datasets, the deep neural network produces better macro-dispersivity estimation for the conductivity field with smaller variance. The trained neural network by conductivity fields with larger variance has stronger universality for macro-dispersivity estimation. This study demonstrates that deep neural network can be an effective alternative for estimating macroscale behavior of solute transport by directly interpreting hydraulic conductivity fields. [ABSTRACT FROM AUTHOR]