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A new methodology was developed to support contaminant mass discharge (CMD)‐based risk assessment of groundwater contamination downgradient of point source zones. Geoelectrical cross‐borehole induced polarization (IP) data were collected at a site undergoing in situ remediation of chlorinated solvents for determining 2D hydraulic conductivity (K) distributions with an inversion model resolution of 0.15 m (vertically) x 0.50 m (horizontally) in three control planes from 10 to 20 m depth. Additionally, 18 slug tests and 31 grain size distribution analyses (GSA) from the control planes, were used for K‐estimation. The geometric means and variance of the IP, slug test, and GSA derived K‐estimates were consistent with previously studied sandy aquifers. Furthermore, the vertical variation in K between two geological settings, a sandy till and a meltwater sand formation, was clearly identified by the IP K‐estimates. The vertical variation was backed up by hydraulic profiling tool (HPT) measurements. Random realizations of CMD were simulated based on the cross‐borehole IP derived K‐values. For comparison, the CMD was also estimated with a geostatistical conditional simulation approach, using the data from slug tests and GSAs. The high IP resolution captured the small scale variations in K across the transects and led to CMD predictions with a narrow uncertainty interval, whereas slug test and GSA either under‐ or overestimated the magnitude of the areas with the highest CMD. Applying the geophysical cross‐borehole method for estimating K‐distributions in addition to traditional methods would improve CMD‐based risk assessment and evaluation of remediation performance at contaminated sites. Key Points: Cross‐borehole induced polarization (IP) data have successfully been used to infer a high resolution hydraulic conductivity fieldHydraulic conductivity estimates from cross‐borehole IP, slug test, grain size distribution and hydraulic profiling tool compared wellCompared to other hydraulic conductivity estimation methods, application of cross‐borehole IP data enables an improved estimation of contaminant mass discharge [ABSTRACT FROM AUTHOR]

Soil unsaturated hydraulic conductivity (K), which depends on water content (θ) and matric potential (ψ), exhibits a high degree of variability at the field scale. Here we first develop a theoretical hydraulic‐electrical conductivity (σ) relationship under low and high salinity cases based on the capillary bundle model and Waxman and Smits model which can account for the non‐linear behavior of σ at low salinities. Then the K‐σ relationship is converted into a K(θ, ψ) model using the Brooks‐Corey model. The model includes two parameters c and γ. Parameter c accounts for the variation of the term (λ + 2)/(λ + 4) where λ is the pore size distribution parameter in the Brooks‐Corey model, and the term m‐n where m and n are Archie's saturation and cementation exponents, respectively. Parameter γ is the sum of the tortuosity factor accounting for the differences between hydraulic and electrical tortuosity and Archie's saturation exponent. Based on a calibration data set of 150 soils selected from the UNSODA database, the best fitting log(c) and γ values were determined as −2.53 and 1.92, −4.39 and −0.14, −5.01 and −1.34, and −5.79 and −2.27 for four textural groups. The estimated log10(K) values with the new K(θ, ψ) model compared well to the measured values from an independent data set of 49 soils selected from the UNSODA database, with mean error (ME), relative error (RE), root mean square error (RMSE) and coefficient of determination (R2) values of 0.02, 8.8%, 0.80 and 0.73, respectively. A second test of the new K(θ, ψ) model using a data set representing 23 soils reported in the literature also showed good agreement between estimated and measured log10(K) values with ME of −0.01, RE of 9.5%, RMSE of 0.77 and R2 of 0.85. The new K(θ, ψ) model outperformed the Mualem‐van Genuchten model and two recently published pedo‐transfer functions. The new K(θ, ψ) model can be applied for estimating K under field conditions and for hydrologic modeling without need for soil water retention curve data fitting to derive a K function. Key Points: A new unsaturated hydraulic conductivity model was developed in terms of independent θ and ψ valuesBest fitting values of two parameters in the new unsaturated hydraulic conductivity model were determined from 150 soils in the calibration data setThe new model provided reliable estimates of hydraulic conductivity for 72 soils from two independent data sets [ABSTRACT FROM AUTHOR]

We present a finite volume approach for generating doubly‐periodic, 2D heterogeneous groundwater velocity fields, given an arbitrary hydraulic conductivity field discretized on a rectangular lattice. The method conserves mass, allows direct specification of any desired mean flow direction and computes the corresponding field with a single solve operation, and solves for inter‐cell fluxes that may be used directly for particle tracking with the Pollock method without further interpolation. We demonstrate an open‐source Python implementation of the approach that we created. Key Points: A finite volume approach enables generation of periodic groundwater flow fields with arbitrary mean velocities on arbitrary heterogeneous conductivity fieldsThe approach conserves mass and solves for inter‐cell fluxes that can be used directly for particle tracking with the Pollock methodThe approach has been implemented in a freely available Python package [ABSTRACT FROM AUTHOR]

Aquifer storage and recovery (ASR) involves the injection, and later extraction, of freshwater into aquifers, which often contain saline groundwater. Mixing between the fresh injectant and native saltwater often leads to part of the injectant becoming unrecoverable, thereby impacting ASR performance. This study explores freshwater‐saltwater mixing within ASR operations arising from aquifer heterogeneity using Monte Carlo analysis of 2D‐axisymmetric, density‐dependent flow and transport models. Logarithmic hydraulic conductivity (lnK) distributions are generated using either two‐point statistics or higher‐order connectivity features. Results show that higher variance in lnK leads to stronger freshwater‐saltwater mixing, which lowers the recovery efficiency (RE; i.e., ratio of extracted to injected freshwater). On average, the lowest RE values were obtained from lnK fields with connected high‐K features, across all ASR cycles. In contrast, RE values from lnK fields with connected low‐K features were typically the highest, at least where buoyancy was considered. The impact of aquifer heterogeneity on RE reduces with subsequent ASR cycles. Buoyancy was a major factor in lowering RE regardless of the adopted heterogeneity model. Heterogeneity tended to mitigate the adverse impacts of buoyancy, leading to some heterogeneous cases having higher RE values than the corresponding homogeneous case. These results highlight the importance of understanding buoyancy effects and subsurface heterogeneity (including the connectivity of geological structures), and interrelationships thereof when assessing the feasibility of multi‐cycle ASR in heterogeneous saline aquifers. Key Points: Aquifer storage and recovery (ASR) is assessed in heterogeneous, saline aquifers using Monte Carlo simulationsASR performance is influenced by hydraulic conductivity variance, correlation length, anisotropy, number of ASR cycles, and buoyancyConnected high hydraulic conductivity zones lower injectant recovery, highlighting the importance of subsurface characterization [ABSTRACT FROM AUTHOR]

In conventional Bayesian geostatistical inversion, specific values of hyperparameters characterizing the prior distribution of random fields are required. However, these hyperparameters are typically very uncertain in practice. Thus, it is more appropriate to consider the uncertainty of hyperparameters as well. The preconditioned Crank‐Nicolson Markov chain Monte Carlo with parallel tempering (pCN‐PT) has been used to efficiently solve the conventional Bayesian inversion of high‐dimensional multi‐Gaussian random fields. In this study, we extend pCN‐PT to Bayesian inversion with uncertain hyperparameters of multi‐Gaussian fields. To utilize the dimension robustness of the preconditioned Crank‐Nicolson algorithm, we reconstruct the problem by decomposing the random field into hyperparameters and white noise. Then, we apply pCN‐PT with a Gibbs split to this "new" problem to obtain the posterior samples of hyperparameters and white noise, and further recover the posterior samples of spatially distributed model parameters. Finally, we apply the extended pCN‐PT method for estimating a finely resolved multi‐Gaussian log‐hydraulic conductivity field from direct data and from head data to show its effectiveness. Results indicate that the estimation of hyperparameters with hydraulic head data is very challenging and the posterior distributions of hyperparameters are only slightly narrower than the prior distributions. Direct measurements of hydraulic conductivity are needed to narrow more the posterior distribution of hyperparameters. To the best of our knowledge, this is a first accurate and fully linearization free solution to Bayesian multi‐Gaussian geostatistical inversion with uncertain hyperparameters. Key Points: The efficient preconditioned Crank‐Nicolson Markov chain Monte Carlo with parallel tempering method is extended for Bayesian geostatistical inversion with uncertain hyperparameters of multi‐Gaussian fieldsThe model parameters are decomposed into hyperparameters and white noise to utilize the dimension robustness of pCN algorithmHyperparameters cannot be constrained well with head data and direct data are important [ABSTRACT FROM AUTHOR]

In geostatistics, Gaussian random fields are often used to model heterogeneities of soil or subsurface parameters. To give spatial approximations of these random fields, they are discretized. Then, different techniques of geostatistical inversion are used to condition them on measurement data. Among these techniques, Markov chain Monte Carlo (MCMC) techniques stand out, because they yield asymptotically unbiased conditional realizations. However, standard Markov Chain Monte Carlo (MCMC) methods suffer the curse of dimensionality when refining the discretization. This means that their efficiency decreases rapidly with an increasing number of discretization cells. Several MCMC approaches have been developed such that the MCMC efficiency does not depend on the discretization of the random field. The preconditioned Crank Nicolson Markov Chain Monte Carlo (pCN‐MCMC) and the sequential Gibbs (or block‐Gibbs) sampling are two examples. This paper presents a combination of both approaches with the goal to further reduce the computational costs. Our algorithm, the sequential pCN‐MCMC, will depend on two tuning‐parameters: the correlation parameter β of the pCN approach and the block size κ of the sequential Gibbs approach. The original pCN‐MCMC and the Gibbs sampling algorithm are special cases of our method. We present an algorithm that automatically finds the best tuning‐parameter combination (κ and β) during the burn‐in‐phase of the algorithm, thus choosing the best possible hybrid between the two methods. In our test cases, we achieve a speedup factors of 1–5.5 over pCN and of 1–6.5 over Gibbs. Furthermore, we provide the MATLAB implementation of our method as open‐source code. Key Points: A hybrid MCMC between the sequential Gibbs and the pCN‐MCMC approach is presentedThis hybrid MCMC is more efficient than both special casesWe present an adaptive algorithm to optimize the hyper‐parameters of this hybrid MCMC during burn‐in [ABSTRACT FROM AUTHOR]

The widening and narrowing of river‐valley aquifers can cause valley‐scale lateral hyporheic exchange even if the river is straight and its slope is uniform. For the aforementioned system, we derive a semi‐analytical solution describing steady‐state groundwater flow for a simplified two‐dimensional geometry of the aquifer and uniform lateral influx from hillslopes. We use this solution to evaluate the geometry‐driven lateral hyporheic exchange flux between the aquifer and the river. By systematically varying the model parameters, we decipher how this flux and the area of the exchange zone depend on geometric (e.g., minimum and maximum domain width) and hydrogeological parameters (e.g., hydraulic conductivity, ambient hydraulic gradient and lateral influxes). The results suggest pronounced hyporheic flow for cases with distinct widening behavior and small cross‐sectional widths at the floodplain inlet and outlet. Furthermore, we analyze the travel‐time distribution of water flowing through the exchange zone, which approximately follows a beta distribution. We express our findings in terms of simple proxy‐equations that can be used to easily estimate the exchange flux, the area of the exchange zone, and the associated travel‐time distribution for a given geographic/landscape setting. Key Points: We develop a semi‐analytical solution describing lateral exchange between rivers and floodplain aquifers driven by the valley geometryWe investigate how the exchange flux, the area of the hyporheic zone, and travel times depend on geometric and hydraulic propertiesWe derive simplified expressions allowing estimating these quantities as a preliminary step prior to detailed site investigations [ABSTRACT FROM AUTHOR]

The mathematical representation of the soil hydraulic properties is of central importance for modeling water, solute and energy transport in soils. The established models of the water retention and hydraulic conductivity curves account for capillary water retention and conductivity, but neglect water adsorption and water flow in films and pore corners. They are therefore suited for modeling flow and transport processes in the medium to wet moisture range, but are susceptible to failure in dry soil. The model system developed by Peters (2013, https://doi.org/10.1002/wrcr.20548; 2014, https://doi.org/10.1002/2014wr016107) and Iden and Durner (2014, https://doi.org/10.1002/2014wr015937) (PDI in the following) is a simple parametric framework that overcomes these structural shortcomings. However, it requires one additional parameter to scale the hydraulic conductivity curve in the moisture range where non‐capillary flow dominates. Measured conductivity data are required to determine this scaling parameter and to compute the hydraulic conductivity over the complete moisture range. In this contribution, we first show that the original PDI model is in close agreement with a comprehensive model for film conductivity in porous media. We then derive a physically‐based approach to predict the film conductivity from the water retention curve. This improved PDI model has the same number of parameters as established models and provides a complete prediction of the hydraulic conductivity curve including non‐capillary flow if water retention data and the saturated conductivity are known. Application to literature data covering a broad range of textures shows an improvement of the conductivity prediction by the factor five if compared to the van Genuchten/Mualem model. Key Points: Simplified model for non‐capillary conductivity is in good agreement with comprehensive physically‐based modelEasy‐to‐compute, physically‐based prediction of non‐capillary conductivity in the medium to dry moisture rangePrediction of conductivity curve from retention curve parameters shows good agreement with measured data [ABSTRACT FROM AUTHOR]

Geostatistical inversion with quantified uncertainty for nonlinear problems requires techniques for providing conditional realizations of the random field of interest. Many first‐order second‐moment methods are being developed in this field, yet almost impossible to critically test them against high‐accuracy reference solutions in high‐dimensional and nonlinear problems. Our goal is to provide a high‐accuracy reference solution algorithm. Preconditioned Crank‐Nicolson Markov chain Monte Carlo (pCN‐MCMC) has been proven to be more efficient in the inversion of multi‐Gaussian random fields than traditional MCMC methods; however, it still has to take a long chain to converge to the stationary target distribution. Parallel tempering aims to sample by communicating between multiple parallel Markov chains at different temperatures. In this paper, we develop a new algorithm called pCN‐PT. It combines the parallel tempering technique with pCN‐MCMC to make the sampling more efficient, and hence converge to a stationary distribution faster. To demonstrate the high‐accuracy reference character, we test the accuracy and efficiency of pCN‐PT for estimating a multi‐Gaussian log‐hydraulic conductivity field with a relative high variance in three different problems: (1) in a high‐dimensional, linear problem; (2) in a high‐dimensional, nonlinear problem and with only few measurements; and (3) in a high‐dimensional, nonlinear problem with sufficient measurements. This allows testing against (1) analytical solutions (kriging), (2) rejection sampling, and (3) pCN‐MCMC in multiple, independent runs, respectively. The results demonstrate that pCN‐PT is an asymptotically exact conditional sampler and is more efficient than pCN‐MCMC in geostatistical inversion problems. Key Points: We proposed an efficient MCMC method called pCN‐PT for Bayesian inversion of multi‐Gaussian log‐hydraulic conductivity fieldsWe demonstrated that pCN‐PT can estimate and conditionally sample multi‐Gaussian random fields in high‐dimensional linear and nonlinear problemsParallel tempering can improve the performance of pCN‐MCMC [ABSTRACT FROM AUTHOR]

High‐resolution characterization of hydraulic properties and dense nonaqueous phase liquid (DNAPL) contaminant source is crucial to develop efficient remediation strategies. However, DNAPL characterization suffers from a limited number of borehole data in the field, resulting in a low‐resolution estimation. Moreover, high‐resolution DNAPL characterization requires a large number of unknowns to be estimated, presenting a computational bottleneck. In this paper, a low‐cost geophysical approach, the self‐potential method, is used as additional information for hydraulic properties characterization. Joint inversion of hydraulic head and self‐potential measurements is proposed to improve hydraulic conductivity estimation, which is then used to characterize the DNAPL saturation distribution by inverting partitioning tracer measurements. The computational barrier is overcome by (a) solving the inversion by the principal component geostatistical approach, in which the covariance matrix is replaced by a low‐rank approximation, thus reducing the number of forward model runs; (b) using temporal moments of concentrations instead of individual concentration data points for faster forward simulations. To assess the ability of the proposed approach, numerical experiments are conducted in a 3‐D aquifer with 104 unknown hydraulic conductivities and DNAPL saturations. Results show that with realistic DNAPL sources and a limited number of hydraulic heads, the traditional hydraulic/partitioning tracer tomography roughly reconstructs subsurface heterogeneity but fails to resolve the DNAPL distribution. By adding self‐potential data, the error is reduced by 24% in hydraulic conductivity estimation and 68% in DNAPL saturation characterization. The proposed sequential inversion framework utilizes the complementary information from multi‐source hydrogeophysical data sets, and can provide high‐resolution characterizations for realistic DNAPL sources. Key Points: The low‐cost self‐potential (SP) method improves the results of effective hydraulic conductivity (Keff) estimationUsing a sequential strategy, the improved Keff estimation from SP can increase the accuracy of DNAPL mappingThe sequential inversion framework helps in reducing significantly the computational effort for DNAPL inversion [ABSTRACT FROM AUTHOR]

Heterogeneity of the hydraulic properties is one of the main causes of the seemingly random distribution of solute concentration observed in contaminated aquifers, with macrodispersivity providing a global measure of spreading. Earlier studies on transport of solutes in heterogeneous formations, either theoretical or numerical, expressed dispersivity as a function of the geostatistical properties of the hydraulic conductivity K. In most cases, K follows a second-order statistical characterization, which may not be adequate when heterogeneity is high. In this work, we adopt the Multi-Indicator Model-Self Consistent Approach (MIMSCA) to compute the longitudinal and transverse macrodispersivity. This methodology enables to model the K field by using geological inclusions of different shapes and orientation (defined here as the microstructure), while replicating the heterogeneous macrostructure obtained by the second-order statistics. The above scheme attempts to reproduce the effect on macrodispersion of different distribution and orientation of local facies, and for instance it may represent the orientation and spatial features of the layers that are often observed in aquifers. The relevant impact of the microstructure on effective conductivity, longitudinal and transverse macrodispersivities is analyzed and discussed, for both binary and lognormally distributed K fields. [ABSTRACT FROM AUTHOR]

Stochastic realizations of lithofacies assemblage based on lithological data from a relatively small number of boreholes were used to simulate solute transport at the well-known Macrodispersion Experiment (MADE) site in Mississippi (USA). With sharp vertical contrasts and lateral connectivity explicitly accounted for in the corresponding hydraulic conductivity fields, experimental results from a large-scale tracer experiment were adequately reproduced with a relatively simple model based on advection and local dispersion. The geologically based model of physical heterogeneity shows that one well-interconnected lithofacies, with a significantly higher hydraulic conductivity and accounting for 12% of the total aquifer volume, may be responsible for the observed non-Fickian transport behavior indicated by the asymmetric shape of the plumes and by variations of the dispersion rate in both space and time. This analysis provides a lithological basis to the hypothesis that transport at MADE site is controlled by a network of high-conductivity sediments embedded in a less permeable matrix. It also explains the calibrated value of the ratio of mobile to total porosities used in previous modeling studies based on the dual-domain mass transfer approach. The results of this study underscore the importance of geologically plausible conceptualizations of the subsurface for making accurate predictions of the fate and transport of contaminants in highly heterogeneous aquifers. These conceptualizations may be developed through integration of raw geological data with expert knowledge, interpretation, and appropriate geostatistical methods. [ABSTRACT FROM AUTHOR]

Hydraulic redistribution, a process by which vegetation roots redistribute soil moisture, has been recognized as an important mechanism impacting several processes that regulate plant water uptake, energy and water partitioning, and biogeochemical cycling. We analyze how the magnitude of hydraulic redistribution varies across ecosystems that are exposed to different climates and seasonal patterns of incoming shortwave radiation and precipitation. Numerical simulation studies are performed over 10 Ameriflux sites, which show that hydraulic redistribution predictions are significantly influenced by the specified root hydraulic conductivities. We performed sensitivity analyses by considering expected ranges of root conductivities based on previous experimental studies, and found contrasting patterns in energy-limited and water-limited ecosystems. In energy-limited ecosystems, there is a threshold above which high root conductivities enhance hydraulic redistribution with no increase in transpiration, while in water-limited ecosystems increase in root conductivities was always associated with enhancements in both transpiration and hydraulic redistribution. Further we found differences in the magnitude and seasonality of hydraulic redistribution and transpiration across different climates, regulated by interplay between precipitation and transpiration. The annual hydraulic redistribution to transpiration flux ratio (HR/Tr) was significant in Mediterranean climates (HR/Tr ≈ 30%), and in the tropical humid climates (HR/Tr ≈ 15%). However, in the continental climates hydraulic redistribution occurs only during sporadic precipitation events throughout the summer resulting in lower annual magnitudes (HR/Tr < 5%). These results provide more insights for suitable implementation of numerical models to capture belowground processes in eco-hydrology, and enhance our understanding about the variability of hydraulic redistribution across different climates. [ABSTRACT FROM AUTHOR]

Recent advances in geophysical methods have been increasingly exploited as inverse modeling tools in groundwater hydrology. In particular, several attempts to constrain the hydrogeophysical inverse problem to reduce inversion errors have been made using time-lapse geophysical measurements through both coupled and uncoupled (also known as sequential) inversion approaches. Despite the appeal and popularity of coupled inversion approaches, their superiority over uncoupled methods has not been proved conclusively; the goal of this work is to provide an objective comparison between the two approaches within a specific inversion modeling framework based on the ensemble Kalman filter (EnKF). Using EnKF and a model of Lagrangian transport, we compare the performance of a fully coupled and uncoupled inversion method for the reconstruction of heterogeneous saturated hydraulic conductivity fields through the assimilation of ERT-monitored tracer test data. The two inversion approaches are tested in a number of different scenarios, including isotropic and anisotropic synthetic aquifers, where we change the geostatistical parameters used to generate the prior ensemble of hydraulic conductivity fields. Our results show that the coupled approach outperforms the uncoupled when the prior statistics are close to the ones used to generate the true field. Otherwise, the coupled approach is heavily affected by 'filter inbreeding' (an undesired effect of variance underestimation typical of EnKF), while the uncoupled approach is more robust, being able to correct biased prior information, thanks to its capability of capturing the solute travel times even in presence of inversion artifacts such as the violation of mass balance. Furthermore, the coupled approach is more computationally intensive than the uncoupled, due to the much larger number of forward runs required by the electrical model. Overall, we conclude that the relative merit of the coupled versus the uncoupled approach cannot be assumed a priori and should be assessed case by case. [ABSTRACT FROM AUTHOR]

Inverse sequential simulation (iSS) is a new inverse modeling approach for the characterization of hydraulic conductivity fields based on sequential simulation. It is described and demonstrated in a synthetic aquifer with non-Gaussian spatial features, and compared against the normal-score ensemble Kalman filter (NS-EnKF). The new approach uses the sequential simulation paradigm to generate realizations borrowing from the ensemble Kalman filter the idea of using the experimental nonstationary cross-covariance between conductivities and piezometric heads computed on an ensemble of realizations. The resulting approach is fully capable of retrieving the non-Gaussian patterns of the reference field after conditioning on the piezometric heads with results comparable of those obtained by the NS-EnKF. [ABSTRACT FROM AUTHOR]

Hydraulic conductivity is one of the most critical and at the same time one of the most uncertain parameters in many groundwater models. One problem commonly faced is that the data are usually not collected at the same scale as the discretized elements used in a numerical model. Moreover, it is common that different types of hydraulic conductivity measurements, corresponding to different spatial scales, coexist in a studied domain, which have to be integrated simultaneously. Here we address this issue in the context of Image Quilting, one of the recently developed multiple-point geostatistics methods. Based on a training image that represents fine-scale spatial variability, we use the simplified renormalization upscaling method to obtain a series of upscaled training images that correspond to the different scales at which measurements are available. We then apply Image Quilting with such a multiscale training image to be able to incorporate simultaneously conditioning data at several spatial scales of heterogeneity. The realizations obtained satisfy the conditioning data exactly across all scales, but it can come at the expense of a small approximation in the representation of the physical scale relationships. In order to mitigate this approximation, we iteratively apply a kriging-based correction to the finest scale that ensures local conditioning at the coarsest scales. The method is tested on a series of synthetic examples where it gives good results and shows potential for the integration of different measurement methods in real-case hydrogeological models. [ABSTRACT FROM AUTHOR]

The commonly used hydraulic models only account for capillary water retention and conductivity. Adsorptive water retention and film conductivity is neglected. This leads to erroneous description of hydraulic properties in the dry range. The few existing models, which account for film conductivity and adsorptive retention are either difficult to use or physically inconsistent. A new set of empirical hydraulic models for an effective description of water dynamics from full saturation to complete dryness is introduced. The models allow a clear partitioning between capillary and adsorptive water retention as well as between capillary and film conductivity. The number of adjustable parameters for the new retention model is not increased compared to the commonly used models, whereas only one extra parameter for quantifying the contribution of film conductivity is required for the new conductivity model. Both models are mathematically simple and thus easy to use in simulation studies. The new liquid conductivity model is coupled with an existing vapor conductivity model to describe conductivity in the complete moisture range. The new models were successfully applied to literature data, which all reach the dry to very dry range and cannot be well described with the classic capillary models. The investigated soils range from pure sands to clay loams. A simulation study with steady-state water transport scenarios shows that neglecting either film or vapor conductivity or both can lead to significant underestimation of water transport at low water contents. [ABSTRACT FROM AUTHOR]

Hydraulic conductivity ( K) fields are used to parameterize groundwater flow and transport models. Numerical simulations require a detailed representation of the K field, synthesized to interpolate between available data. Several recent studies introduced high-resolution K data (HRK) at the Macro Dispersion Experiment (MADE) site, and used ground-penetrating radar (GPR) to delineate the main structural features of the aquifer. This paper describes a statistical analysis of these data, and the implications for K field modeling in alluvial aquifers. Two striking observations have emerged from this analysis. The first is that a simple fractional difference filter can have a profound effect on data histograms, organizing non-Gaussian ln K data into a coherent distribution. The second is that using GPR facies allows us to reproduce the significantly non-Gaussian shape seen in real HRK data profiles, using a simulated Gaussian ln K field in each facies. This illuminates a current controversy in the literature, between those who favor Gaussian ln K models, and those who observe non-Gaussian ln K fields. Both camps are correct, but at different scales. [ABSTRACT FROM AUTHOR]

Because of the extensive computational burden and perhaps a lack of awareness of existing methods, rigorous uncertainty analyses are rarely conducted for variable-density flow and transport models. For this reason, a recently developed null-space Monte Carlo (NSMC) method for quantifying prediction uncertainty was tested for a synthetic saltwater intrusion model patterned after the Henry problem. Saltwater intrusion caused by a reduction in fresh groundwater discharge was simulated for 1000 randomly generated hydraulic conductivity distributions, representing a mildly heterogeneous aquifer. From these 1000 simulations, the hydraulic conductivity distribution giving rise to the most extreme case of saltwater intrusion was selected and was assumed to represent the 'true' system. Head and salinity values from this true model were then extracted and used as observations for subsequent model calibration. Random noise was added to the observations to approximate realistic field conditions. The NSMC method was used to calculate 1000 calibration-constrained parameter fields. If the dimensionality of the solution space was set appropriately, the estimated uncertainty range from the NSMC analysis encompassed the truth. Several variants of the method were implemented to investigate their effect on the efficiency of the NSMC method. Reducing the dimensionality of the null-space for the processing of the random parameter sets did not result in any significant gains in efficiency and compromised the ability of the NSMC method to encompass the true prediction value. The addition of intrapilot point heterogeneity to the NSMC process was also tested. According to a variogram comparison, this provided the same scale of heterogeneity that was used to generate the truth. However, incorporation of intrapilot point variability did not make a noticeable difference to the uncertainty of the prediction. With this higher level of heterogeneity, however, the computational burden of generating calibration-constrained parameter fields approximately doubled. Predictive uncertainty variance computed through the NSMC method was compared with that computed through linear analysis. The results were in good agreement, with the NSMC method estimate showing a slightly smaller range of prediction uncertainty than was calculated by the linear method. [ABSTRACT FROM AUTHOR]

Inverse modeling has been widely used in subsurface problems, where direct measurements of parameters are expensive and sometimes impossible. Subsurface media are inherently heterogeneous in complex ways, which implies that the number of unknowns is usually large. Furthermore, technologies such as hydraulic tomography and electric resistivity tomography allow the collection of more indirect measurements, and at the same time, there is an increased appreciation of the value of detailed characterization of the subsurface media in, for example, remediation projects. Hence, we need efficient inverse methods that can assimilate a large volume of measurements to estimate even larger numbers of parameters, i.e., large-scale inverse modeling. In this paper, we present a Bayesian method that employs a sparse formulation, and we applied this method to a laboratory hydraulic tomography problem, where we successfully estimated half a million unknowns that represent the hydraulic conductivity field of the sandbox at a fine scale. The inversion took about 2 h with a single core. [ABSTRACT FROM AUTHOR]

Urban groundwater is frequently contaminated, and the exact location of the pollution spots is often unknown. Intelligent monitoring of the temporal variations in groundwater flow in such an area assists in selectively extracting groundwater of drinking water quality. Here an example from the city of Zurich (Switzerland) is shown. The monitoring strategy consists of using the ensemble Kalman filter (EnKF) for optimally combining online observations and online models for the real-time characterization of groundwater flow. We conducted numerical simulation experiments for the period January 2004 to December 2007 with a 3-D finite element model for variably saturated groundwater flow. It was found that the daily assimilation of piezometric head data with EnKF results in a better characterization of piezometric heads than does a model which is inversely calibrated with historical data but not updated in real time. The positive impact of model updating with observations can still be observed 10 days after the update. These simulations also suggest that parameters (hydraulic conductivity and leakage) are successfully updated: 1 and 10 day piezometric head predictions are better with than without updating of parameters. Additional experiments with a synthetic model for the same site, in which the only difference is that certain parameter values are selected as the unknown 'true' conditions, show that EnKF also successfully updates unknown parameters. However, this is only the case if spatially distributed hydraulic conductivities and leakage coefficients are jointly updated and if a damping parameter is used. The mean absolute error of estimated log leakage coefficients decreased by up to 63%; for log hydraulic conductivity a decrease of up to 27% was observed. From January 2009 the method has been operational at the Water Works Zurich and showed a remarkable performance until present (October 2010). [ABSTRACT FROM AUTHOR]

Numerical groundwater models, frequently used to enhance understanding of the hydrologic and chemical processes in local or regional aquifers, are often hindered by an incomplete representation of the parameters which characterize these processes. In this study, we present the use of a data assimilation algorithm that incorporates all past model results and data measurements, an ensemble smoother (ES) to provide enhanced estimates of aquifer hydraulic conductivity ( K) through assimilation of hydraulic head ( H) and groundwater return flow volume ( RFV) measurements into groundwater model simulation results. On the basis of the Kalman filter methodology, residuals between forecasted model results and measurements, together with covariances between model results at measurement locations and nonmeasurement locations, are used to correct model results. Parameter estimation is achieved by incorporating model parameters into the algorithm, thus allowing the correlation between H, RFV, and K to correct the K fields. The applicability of the ES is demonstrated using a synthetic two-dimensional transient groundwater modeling simulation. Sensitivity analyses are carried out to show the performance of the ES in regard to measurement error, number of measurements, number of assimilation times, correlation length of the K fields, and the number of stream gage locations. Results show that the departure of the K fields from a reference K field is greatly reduced through data assimilation and demonstrate that the ES scheme is a promising alternative to other inverse modeling techniques because of low computational burden and the ability to run the algorithm entirely independent of the groundwater model simulation. [ABSTRACT FROM AUTHOR]

Measurements are often unable to uniquely characterize the subsurface at a desired modeling resolution. In particular, inverse problems involving the characterization of hydraulic properties are typically ill-posed since they generally present more unknowns than data. In a Bayesian context, solutions to such problems consist of a posterior ensemble of models that fit the data (up to a certain precision specified by a likelihood function) and that are a subset of a prior distribution. Two possible approaches for this problem are Markov chain Monte Carlo (McMC) techniques and optimization (calibration) methods. Both frameworks rely on a perturbation mechanism to steer the search for solutions. When the model parameters are spatially dependent variable fields obtained using geostatistical realizations, such as hydraulic conductivity or porosity, it is not trivial to incur perturbations that respect the prior spatial model. To overcome this problem, we propose a general transition kernel (iterative spatial resampling, ISR) that preserves any spatial model produced by conditional simulation. We also present a stochastic stopping criterion for the optimizations inspired from importance sampling. In the studied cases, this yields posterior distributions reasonably close to the ones obtained by a rejection sampler, but with a greatly reduced number of forward model runs. The technique is general in the sense that it can be used with any conditional geostatistical simulation method, whether it generates continuous or discrete variables. Therefore it allows sampling of different priors and conditioning to a variety of data types. Several examples are provided based on either multi-Gaussian or multiple-point statistics. [ABSTRACT FROM AUTHOR]

In recent years, a project of anthropogenic Venice uplift caused by seawater injection into a 600-850 m deep brackish aquifer underlying the lagoon has been advanced. While an extensive data set based on marker measurements from a number of gas-producing wells of the northern Adriatic is available for a realistic evaluation of the geomechanical properties of the injected geologic formation, permeability data are very scarce and sparse throughout the area. Previous finite element (FE) predictions relying on a uniform hydraulic conductivity K as derived from pumping tests suggest that a flat uplift of the city is produced over 10 years from the inception of injection. However, it is well-known and widely recognized that in natural porous media very seldom K exhibits an even spatial distribution. In this study, a random distribution is then assumed to address the influence of a variable K on the uniformity of the city uplift. To limit the otherwise prohibitive computational burden, the study is performed relative to the pilot project designed to raise a reduced area at the margin of the lagoon. Monte Carlo groundwater flow simulations are performed using a FE discretization of the injected aquifer system based upon a hydraulic conductivity distribution characterized by a lognormal, stationary random process. The resulting pore overpressure is then implemented into a deterministic FE geomechanical model. A sensitivity analysis is performed to account for the uncertainty on the stochastic process, reflected by both the log K variance σ2 and the correlation length λ over the ranges 0.2-1.0 and 20-1000 m, respectively, which are quite plausible for normally consolidated sedimentary formations such as the Northern Adriatic basin. The cumulative distribution function (CDF) of the ground surface uplift, u z, and its horizontal gradient, ρ z, are computed and used to evaluate the probability for ρ z to be larger than a few significant threshold values as discussed later. It is shown that, even within the most pessimistic scenario (i.e., σ2 = 1.0 and λ = 1000 m), the maximum ρ z is comparable, namely of the same order, with the one obtained from the deterministic case and (1) 2-3 times smaller than the ρ z caused in the city by groundwater withdrawal in the nearby industrial area over the 1960s (10 × 10−5), (2) 1 order of magnitude less than the maximum bound as indicated in the literature for the safety of multifloor masonry buildings (50 × 10−5), and (3) about 20 times smaller than the maximum ρ z values that the city is currently experiencing (100 × 10−5). The results highlight the strong effect exerted by the overburden in smoothing the uneven expansion of the injected heterogeneous formation. [ABSTRACT FROM AUTHOR]

We developed a new model of aquifer heterogeneity to analyze data from a single-well injection-withdrawal tracer test conducted at the Macrodispersion Experiment (MADE) site on the Columbus Air Force Base in Mississippi (USA). The physical heterogeneity model is a hybrid that combines 3-D lithofacies to represent submeter scale, highly connected channels within a background matrix based on a correlated multivariate Gaussian hydraulic conductivity field. The modeled aquifer architecture is informed by a variety of field data, including geologic core sampling. Geostatistical properties of this hybrid heterogeneity model are consistent with the statistics of the hydraulic conductivity data set based on extensive borehole flowmeter testing at the MADE site. The representation of detailed, small-scale geologic heterogeneity allows for explicit simulation of local preferential flow and slow advection, processes that explain the complex tracer response from the injection-withdrawal test. Based on the new heterogeneity model, advective-dispersive transport reproduces key characteristics of the observed tracer recovery curve, including a delayed concentration peak and a low-concentration tail. Importantly, our results suggest that intrafacies heterogeneity is responsible for local-scale mass transfer. [ABSTRACT FROM AUTHOR]

Connectivity constraints and measurements of state variables contain valuable information on aquifer architecture. Multiple-point (MP) geostatistics allow one to simulate aquifer architectures, presenting a predefined degree of global connectivity. In this context, connectivity data are often disregarded. The conditioning to state variables is usually carried out by minimizing a suitable objective function (i.e., solving an inverse problem). However, the discontinuous nature of lithofacies distributions and of the corresponding objective function discourages the use of traditional sensitivity-based inversion techniques. This work presents the Blocking Moving Window algorithm (BMW), aimed at overcoming these limitations by conditioning MP simulations to hydrogeological data such as connectivity and heads. The BMW evolves iteratively until convergence: (1) MP simulation of lithofacies from geological/geophysical data and connectivity constraints, where only a random portion of the domain is simulated at every iteration (i.e., the blocking moving window, whose size is user-defined); (2) population of hydraulic properties at the intrafacies; (3) simulation of state variables; and (4) acceptance or rejection of the MP simulation depending on the quality of the fit of measured state variables. The outcome is a stack of MP simulations that (1) resemble a prior geological model depicted by a training image, (2) honor lithological data and connectivity constraints, (3) correlate with geophysical data, and (4) fit available measurements of state variables well. We analyze the performance of the algorithm on a 2-D synthetic example. Results show that (1) the size of the blocking moving window controls the behavior of the BMW, (2) conditioning to state variable data enhances dramatically the initial simulation (which accounts for geological/geophysical data only), and (3) connectivity constraints speed up the convergence but do not enhance the stack if the number of iterations is large. [ABSTRACT FROM AUTHOR]

We present a method for the calibration of multimodal hydraulic conductivity distributions and apply this method to the particular case of confining layers with a complex geological architecture. The basis of our technique is the transformation of the original multimodal conductivity distribution to the standard normal distribution, thus fulfilling the condition of normality which is required by the used representer-based inverse algorithm (Valstar et al., 2004). Using this transformation, a calibration that starts from a homogeneous prior field is shown to radically improve the estimation of the protective properties of the confining layer compared to a unimodal approach to the calibration. The method is also used for the calibration of multimodal heterogeneous prior fields. The inevitable distortion of the original parameter covariances in the posterior fields that results from the transformation process is absorbed by an iterative postprocessing procedure, in which lithologic information obtained from the distorted calibrated fields is used to condition the generation of a new multimodal field that complies again with the original geostatistics. After transformation, this new field can be calibrated again, and this process is repeated until the newly generated field agrees with the measurement information sufficiently well. Then, the lithologic distribution of this new field is fixed, and the intrafacies conductivity distributions are calibrated. This approach is shown to preserve the original geostatistics, both of the lithology field and of the intralithology hydraulic conductivity distributions. [ABSTRACT FROM AUTHOR]