On the Performance of Pilot-Point Based Hydraulic Tomography with a Geophysical a Priori Model

We present a novel method to estimate the hydraulic and storage properties of a heterogeneous aquifer system using pilot-point-based hydraulic tomography (HT) inversion in conjunction with a geophysical a priori model. The a priori model involved a soil stratification obtained by combining electrical resistivity tomography inversion and field data from hydrogeological experiments. Pilot-point densities were assigned according to the stratification, which also constrained aquifer parameters during HT inversion. The forward groundwater flow model, HydroGeoSphere, was supplied to the parameter-estimation tool, PEST, to perform HT inversion. The performance of our method was evaluated on a hypothetical, two-dimensional, multi-layered, granitic aquifer system representative of those commonly occurring in the Kandi region in Telangana. Inversion results were compared using two commonly adopted methods of modeling parameter-heterogeneity: (1) using piece-wise zones of property values obtained from geostatistical interpolation of local-scale estimates; and (2) HT inversion starting from a homogeneous parameter field with a uniform distribution of pilot-points. Performances of the inverted models were evaluated by conducting independent pumping tests and statistical analyses (using a Taylor diagram) of the model-to-measurement discrepancies in drawdowns. Our results showed that using the aforementioned geophysical a priori model could improve the parameter-estimation process.     

Basin-scale transmissivity and storativity estimation using hydraulic tomography

While tomographic inversion has been successfully applied to laboratory- and field-scale tests, here we address the new issue of scale that arises when extending the method to a basin. Specifically, we apply the hydraulic tomography (HT) concept to jointly interpret four multiwell aquifer tests in a synthetic basin to illustrate the superiority of this approach to a more traditional Theis analysis of the same tests. Transmissivity and storativity are estimated for each element of a regional numerical model using the geostatistically based sequential successive linear estimator (SSLE) inverse solution method. We find that HT inversion is an effective strategy for incorporating data from potentially disparate aquifer tests into a basin-wide aquifer property estimate. The robustness of the SSLE algorithm is investigated by considering the effects of noisy observations, changing the variance of the true aquifer parameters, and supplying incorrect initial and boundary conditions to the inverse model. Ground water flow velocities and total confined storage are used as metrics to compare true and estimated parameter fields; they quantify the effectiveness of HT and SSLE compared to a Theis solution methodology. We discuss alternative software that can be used for implementing tomography inversion.     

Redundant and Nonredundant Information for Model Calibration or Hydraulic Tomography

Drawdown data from independent pumping tests have widely been used to validate the estimated hydraulic parameters from inverse modeling or hydraulic tomography (HT). Yet, the independent pumping test has not been clearly defined. Therefore, the goal of this paper is to define this independent pumping test concept, based on the redundant or nonredundant information about aquifer heterogeneity embedded in the observed heads during cross-hole pumping tests. The definition of complete, moderate redundancy and high nonredundancy of information are stipulated using cross-correlation analysis of the relationship between the head and heterogeneity. Afterward, data from numerical experiments and field sequential pumping test campaigns reinforce the concept and the definition.     

Reducing Uncertainty in Calibrating Aquifer Flow Model with Multiple Scales of Heterogeneity

Modeling and calibration of natural aquifers with multiple scales of heterogeneity is a challenging task due to limited subsurface access. While computer modeling plays an essential role in aquifer studies, large uncertainty exists in developing a conceptual model of an aquifer and in calibrating the model for decision making. Due to uncertainties such as a lack of understanding of subsurface processes and a lack of techniques to parameterize the subsurface environment (including hydraulic conductivity, source/sink rate, and aquifer boundary conditions), existing aquifer models often suffer nonuniqueness in calibration, leading to poor predictive capability. A robust calibration methodology is needed that can address the simultaneous estimations of aquifer parameters, source/sink, and boundary conditions. In this paper, we propose a multistage and multiscale approach that addresses subsurface heterogeneity at multiple scales, while reducing uncertainty in estimating the model parameters and model boundary conditions. The key to this approach lies in the appropriate development, verification, and synthesis of existing and new techniques of static and dynamic data integration. In particular, based on a given set of observation data, new inversion techniques can be first used to estimate aquifer large‐scale effective parameters and smoothed boundary conditions, based on which parameter and boundary condition estimation can be refined at increasing detail using standard or highly parameterized estimation techniques.     

Combining 3D Hydraulic Tomography with Tracer Tests for Improved Transport Characterization

Hydraulic tomography (HT) is a method for resolving the spatial distribution of hydraulic parameters to some extent, but many details important for solute transport usually remain unresolved. We present a methodology to improve solute transport predictions by combining data from HT with the breakthrough curve (BTC) of a single forced‐gradient tracer test. We estimated the three dimensional (3D) hydraulic‐conductivity field in an alluvial aquifer by inverting tomographic pumping tests performed at the Hydrogeological Research Site Lauswiesen close to Tübingen, Germany, using a regularized pilot‐point method. We compared the estimated parameter field to available profiles of hydraulic‐conductivity variations from direct‐push injection logging (DPIL), and validated the hydraulic‐conductivity field with hydraulic‐head measurements of tests not used in the inversion. After validation, spatially uniform parameters for dual‐domain transport were estimated by fitting tracer data collected during a forced‐gradient tracer test. The dual‐domain assumption was used to parameterize effects of the unresolved heterogeneity of the aquifer and deemed necessary to fit the shape of the BTC using reasonable parameter values. The estimated hydraulic‐conductivity field and transport parameters were subsequently used to successfully predict a second independent tracer test. Our work provides an efficient and practical approach to predict solute transport in heterogeneous aquifers without performing elaborate field tracer tests with a tomographic layout.     

Three-dimensional geostatistical inversion of synthetic tomographic pumping and heat-tracer tests in a nested-cell setup

A main purpose of groundwater inverse modeling lies in estimating the hydraulic conductivity field of an aquifer. Traditionally, hydraulic head measurements, possibly obtained in tomographic setups, are used as data. Because the groundwater flow equation is diffusive, many pumping and observation wells would be necessary to obtain a high resolution of hydraulic conductivity, which is typically not possible. We suggest performing heat tracer tests using the same already installed pumping wells and thermometers in observation planes to amend the hydraulic head data set by the arrival times of the heat signals. For each tomographic combinations of wells, we recommend installing an outer pair of pumping wells, generating artificial ambient flow, and an inner well pair in which the tests are performed. We jointly invert heads and thermal arrival times in 3-D by the quasi-linear geostatistical approach using an efficiently parallelized code running on a mid-range cluster. In the present study, we evaluate the value of heat tracer versus head data in a synthetic test case, where the estimated fields can be compared to the synthetic truth. Because the sensitivity patterns of the thermal arrival times differ from those of head measurements, the resolved variance in the estimated field is 6 to 10 times higher in the joint inversion in comparison to inverting head data only. Also, in contrast to head measurements, reversing the flow field and repeating the heat-tracer test improves the estimate in terms of reducing the estimation variance of the estimate. Based on the synthetic test case, we recommend performing the tests in four principal directions, requiring in total eight pumping wells and four intersecting observation planes for heads and temperature in each direction.     

Constraints on hydraulic parameters and implications for groundwater flux across the upland–estuary interface

Analyses of independent laboratory- and field-scale measurements from two sites on Sapelo Island, Georgia reveal heterogeneity in hydraulic parameters across the upland–estuary interface. Regardless of the method used (short-duration pumping tests, amplitude attenuation of tidal pumping data, sediment grain size distributions, and falling head permeameter tests), we obtain hydraulic conductivity of 10⁻⁴ m s⁻¹ for the fine-grained, well-sorted, clean sands that make up the upland areas. Proximal to the upland–estuary boundary, the tidal pumping analyses and permeameter tests suggest that hydraulic conductivities decrease by more than two orders of magnitude, a result consistent with the presence of a clogging layer. Such a clogging layer may arise due to a variety of physical, chemical, or biological processes. The extent and orientation of the layers of reduced hydraulic conductivity near the upland–estuary boundary influence the nature of the aquifer's response to tidal forcing. Where the lower conductivity layer forms a relatively flat creek bank, tidal pumping produces a primarily mechanical response in the adjacent aquifer. Where the creek bank is nearly vertical, there is a more direct hydraulic connection between the tidal creek and the adjacent aquifer. The clogging layer likely contributes to the development of complicated flow pathways across the upland–estuary boundary. Effective flow paths calculated from tidal pumping data terminate within the marsh, beyond the boundary of the upland aquifer, suggesting a diffuse regime of groundwater discharge in the marsh. We postulate that, in many settings, submarsh flow may be as important as seepage faces for groundwater discharge into the marsh–estuary complex.     

Tensor Hydraulic Conductivity Estimation for Heterogeneous Aquifers under Unknown Boundary Conditions

A physically based inverse method is developed using hybrid formulation and coordinate transform to simultaneously estimate hydraulic conductivity tensors, steady‐state flow field, and boundary conditions for a confined aquifer under ambient flow or pumping condition. Unlike existing indirect inversion techniques, the physically based method does not require forward simulations to assess model‐data misfits. It imposes continuity of hydraulic head and Darcy fluxes in the model domain while incorporating observations (hydraulic heads, Darcy fluxes, or well rates) at measurement locations. Given sufficient measurements, it yields a well‐posed inverse system of equations that can be solved efficiently with coarse grids and nonlinear optimization. When pumping and injection are active, well rates are used as measurements and flux sampling is not needed. The method is successfully tested on synthetic aquifer problems with regular and irregular geometries, different hydrofacies and flow patterns, and increasing conductivity anisotropy ratios. All problems yield stable inverse solutions under increasing head measurement errors. For a given set of observations, inversion accuracy is strongly affected by the conductivity anisotropy ratio. Conductivity estimation is also affected by flow pattern: within a hydrofacies, when Darcy flux component is very small, the corresponding directional conductivity perpendicular to streamlines becomes less identifiable. Finally, inversion is successful even if the location of aquifer boundaries is unknown. In this case, the inversion domain is defined by the location of the measurements.     

Cross-borehole flowmeter tests for transient heads in heterogeneous aquifers

Cross-borehole flowmeter tests have been proposed as an efficient method to investigate preferential flowpaths in heterogeneous aquifers, which is a major task in the characterization of fractured aquifers. Cross-borehole flowmeter tests are based on the idea that changing the pumping conditions in a given aquifer will modify the hydraulic head distribution in large-scale flowpaths, producing measurable changes in the vertical flow profiles in observation boreholes. However, inversion of flow measurements to derive flowpath geometry and connectivity and to characterize their hydraulic properties is still a subject of research. In this study, we propose a framework for cross-borehole flowmeter test interpretation that is based on a two-scale conceptual model: discrete fractures at the borehole scale and zones of interconnected fractures at the aquifer scale. We propose that the two problems may be solved independently. The first inverse problem consists of estimating the hydraulic head variations that drive the transient borehole flow observed in the cross-borehole flowmeter experiments. The second inverse problem is related to estimating the geometry and hydraulic properties of large-scale flowpaths in the region between pumping and observation wells that are compatible with the head variations deduced from the first problem. To solve the borehole-scale problem, we treat the transient flow data as a series of quasi-steady flow conditions and solve for the hydraulic head changes in individual fractures required to produce these data. The consistency of the method is verified using field experiments performed in a fractured-rock aquifer.     

Reconstruction of the Water Table from Self-Potential Data: A Bayesian Approach

Ground water flow associated with pumping and injection tests generates self-potential signals that can be measured at the ground surface and used to estimate the pattern of ground water flow at depth. We propose an inversion of the self-potential signals that accounts for the heterogeneous nature of the aquifer and a relationship between the electrical resistivity and the streaming current coupling coefficient. We recast the inversion of the self-potential data into a Bayesian framework. Synthetic tests are performed showing the advantage in using self-potential signals in addition to in situ measurements of the potentiometric levels to reconstruct the shape of the water table. This methodology is applied to a new data set from a series of coordinated hydraulic tomography, self-potential, and electrical resistivity tomography experiments performed at the Boise Hydrogeophysical Research Site, Idaho. In particular, we examine one of the dipole hydraulic tests and its reciprocal to show the sensitivity of the self-potential signals to variations of the potentiometric levels under steady-state conditions. However, because of the high pumping rate, the response was also influenced by the Reynolds number , especially near the pumping well for a given test. Ground water flow in the inertial laminar flow regime is responsible for nonlinearity that is not yet accounted for in self-potential tomography. Numerical modeling addresses the sensitivity of the self-potential response to this problem.     

Three-dimensional geostatistical inversion of flowmeter and pumping test data

We jointly invert field data of flowmeter and multiple pumping tests in fully screened wells to estimate hydraulic conductivity using a geostatistical method. We use the steady-state drawdowns of pumping tests and the discharge profiles of flowmeter tests as our data in the inference. The discharge profiles need not be converted to absolute hydraulic conductivities. Consequently, we do not need measurements of depth-averaged hydraulic conductivity at well locations. The flowmeter profiles contain information about relative vertical distributions of hydraulic conductivity, while drawdown measurements of pumping tests provide information about horizontal fluctuation of the depth-averaged hydraulic conductivity. We apply the method to data obtained at the Krauthausen test site of the Forschungszentrum Jülich, Germany. The resulting estimate of our joint three-dimensional (3D) geostatistical inversion shows an improved 3D structure in comparison to the inversion of pumping test data only.     

Two-dimensional physical-based inversion of confined and unconfined aquifers under unknown boundary conditions

An inverse method is developed to simultaneously estimate multiple hydraulic conductivities, source/sink strengths, and boundary conditions, for two-dimensional confined and unconfined aquifers under non-pumping or pumping conditions. The method incorporates noisy observed data (hydraulic heads, groundwater fluxes, or well rates) at measurement locations. With a set of hybrid formulations, given sufficient measurement data, the method yields well-posed systems of equations that can be solved efficiently via nonlinear optimization. The solution is stable when measurement errors are increased. The method is successfully tested on problems with regular and irregular geometries, different heterogeneity patterns and variances (maximum K_max/K_min tested is 10,000), and error magnitudes. Under non-pumping conditions, when error-free observed data are used, the estimated conductivities and recharge rates are accurate within 8% of the true values. When data contain increasing errors, the estimated parameters become less accurate, as expected. For problems where the underlying parameter variation is unknown, equivalent conductivities and average recharge rates can be estimated. Under pumping (and/or injection) conditions, a hybrid formulation is developed to address these local source/sink effects, while different types of boundary conditions can also exert significant influences on drawdowns. Local grid refinement near wells is not needed to obtain accurate results, thus inversion is successful with coarse inverse grids, leading to high computation efficiency. Furthermore, flux measurements are not needed for the inversion to succeed; data requirement of the method is thus not much different from that of interpreting classic well tests. Finally, inversion accuracy is not sensitive to the degree of nonlinearity of the flow equations. Performance of the inverse method for confined and unconfined aquifer problems is similar in terms of the accuracy of the estimated parameters, the recovered head fields, and the solver speed.     

A new method for aquifer system identification and parameter estimation

The standard practice for assessing aquifer parameters is to match groundwater drawdown data obtained during pumping tests against theoretical well function curves specific to the aquifer system being tested. The shape of the curve derived from the logarithmic time derivative of the drawdown data is also very frequently used as a diagnostic tool to identify the aquifer system in which the pumping test is being conducted. The present study investigates the incremental area method (IAM) to serve as an alternative diagnostic tool for the aquifer system identification as well as a supplement to the aquifer parameter estimation procedure. The IAM based diagnostic curves for ideal confined, leaky, bounded and unconfined aquifers have been derived as part of this study, and individual features of the plots have been identified. These features were noted to be unique to each aquifer setting, which could be used for rapid evaluation of the aquifer system. The effectiveness of the IAM methodology was investigated by analyzing field data for various aquifer settings including leaky, unconfined, bounded and heterogeneous conditions. The results showed that the proposed approach is a viable method for use as a diagnostic tool to identify the aquifer system characteristics as well as to support the estimation of the hydraulic parameters obtained from standard curve matching procedures. Copyright © 2012 John Wiley & Sons, Ltd.     

Using data assimilation method to calibrate a heterogeneous conductivity field conditioning on transient flow test data

A data assimilation method is developed to calibrate a heterogeneous hydraulic conductivity field conditioning on transient pumping test data. The ensemble Kalman filter (EnKF) approach is used to update model parameters such as hydraulic conductivity and model variables such as hydraulic head using available data. A synthetical two-dimensional flow case is used to assess the capability of the EnKF method to calibrate a heterogeneous conductivity field by assimilating transient flow data from observation wells under different hydraulic boundary conditions. The study results indicate that the EnKF method will significantly improve the estimation of the hydraulic conductivity field by assimilating continuous hydraulic head measurements and the hydraulic boundary condition will significantly affect the simulation results. For our cases, after a few data assimilation steps, the assimilated conductivity field with four Neumann boundaries matches the real field well while the assimilated conductivity field with mixed Dirichlet and Neumann boundaries does not. We found in our cases that the ensemble size should be 300 or larger for the numerical simulation. The number and the locations of the observation wells will significantly affect the hydraulic conductivity field calibration.     

Geophysical Assessment of Groundwater Potential: A Case Study from Mian Channu Area,Pakistan

An integrated study using geophysical method in combination with pumping tests and geochemical method was carried out to delineate groundwater potential zones in Mian Channu area of Pakistan. Vertical electrical soundings (VES) using Schlumberger configuration with maximum current electrode spacing (AB/2 = 200 m) were conducted at 50 stations and 10 pumping tests at borehole sites were performed in close proximity to 10 of the VES stations. The aim of this study is to establish a correlation between the hydraulic parameters obtained from geophysical method and pumping tests so that the aquifer potential can be estimated from the geoelectrical surface measurements where no pumping tests exist. The aquifer parameters, namely, transmissivity and hydraulic conductivity were estimated from Dar Zarrouyk parameters by interpreting the layer parameters such as true resistivities and thicknesses. Geoelectrical succession of five‐layer strata (i.e., topsoil, clay, clay sand, sand, and sand gravel) with sand as a dominant lithology was found in the study area. Physicochemical parameters interpreted by World Health Organization and Food and Agriculture Organization were well correlated with the aquifer parameters obtained by geoelectrical method and pumping tests. The aquifer potential zones identified by modeled resistivity, Dar Zarrouk parameters, pumped aquifer parameters, and physicochemical parameters reveal that sand and gravel sand with high values of transmissivity and hydraulic conductivity are highly promising water bearing layers in northwest of the study area. Strong correlation between estimated and pumped aquifer parameters suggest that, in case of sparse well data, geophysical technique is useful to estimate the hydraulic potential of the aquifer with varying lithology.     

Inversion of interference hydraulic pumping tests in both homogeneous and fractal dual media

This work proposes a complete method for automatic inversion of data from hydraulic interference pumping tests based on both homogeneous and fractal dual-medium approaches. The aim is to seek a new alternative concept able to interpret field data, identify macroscopic hydraulic parameters and therefore enhance the understanding of flow in porous fractured reservoirs. Because of its much contrasted sensitivities to parameters, the dual-medium approach yields an ill-posed inverse problem that requires a specific optimization procedure including the calculation of analytical sensitivities and their possible re-scaling. Once these constraints are fulfilled, the inversion proves accurate, provides unambiguous and reliable results. In the fractal context inverting several drawdown curves from different locations at the same time reveals more accurate. Finally, hydraulic parameters drawn from inversion should be taken into account to improve in various situations the conditioning of up-scaled flow in fractured rocks.     

Practical issues in imaging hydraulic conductivity through hydraulic tomography

Hydraulic tomography has been developed as an alternative to traditional geostatistical methods to delineate heterogeneity patterns in parameters such as hydraulic conductivity (K) and specific storage (S(s)). During hydraulic tomography surveys, a large number of hydraulic head data are collected from a series of cross-hole tests in the subsurface. These head data are then used to interpret the spatial distribution of K and S(s) using inverse modeling. Here, we use the Sequential Successive Linear Estimator (SSLE) of Yeh and Liu (2000) to interpret synthetic pumping test data created through numerical simulations and real data generated in a laboratory sandbox aquifer to obtain the K tomograms. Here, we define "K tomogram" as an image of K distribution of the subsurface (or the inverse results) obtained via hydraulic tomography. We examine the influence of signal-to-noise ratio and biases on results using inverse modeling of synthetic and real cross-hole pumping test data. To accomplish this, we first show that the pumping rate, which affects the signal-to-noise ratio, and the order of data included into the SSLE algorithm both have large impacts on the quality of the K tomograms. We then examine the role of conditioning on the K tomogram and find that conditioning can improve the quality of the K tomogram, but can also impair it, if the data are of poor quality and conditioning data have a larger support volume than the numerical grid used to conduct the inversion. Overall, these results show that the quality of the K tomogram depends on the design of pumping tests, their conduct, the order in which they are included in the inverse code, and the quality as well as the support volume of additional data that are used in its computation.     

Transient flowmeter test: semi-analytic crossflow model

The transient flowmeter test (TFMT) provides more information about the well–aquifer system than the traditional quasi-steady-state flowmeter test (QFMT). The TFMT duration may be much shorter than that of a QFMT, which is desirable at highly contaminated sites where the extracted water has to be treated as hazardous waste. Here we present the TFMT model that accounts for inter-layer crossflow, a thick skin surrounding the well, and wellbore storage. The model is derived under the simplifying assumptions of the pseudo-steady-state inter-layer crossflow and the uniform wellface flux within each layer. The semi-analytic solution is inverted numerically from the Laplace domain to the time domain. Layer and skin parameters are estimated from the TFMT data via the modified Levenberg–Marquardt algorithm. The estimation is robust when the initial parameter guesses are close to their true values. Otherwise, a computationally expensive search among the local minima of the objective function is necessary to find the parameter estimates. The modeling errors and the associated parameter estimation errors are evaluated in a number of synthetic TFMTs and compared to the corresponding results obtained with a general numerical model that relaxes the two simplifying assumptions. The TFMT provides reasonably accurate estimates of hydraulic conductivities for the aquifer layers and the damaged skins and order-of-magnitude estimates of layer specific storativities and hydraulic conductivities for the normal skin. The skin specific storativities should not be estimated from a TFMT. Multi-rate TFMTs with a step-variable pumping rate yield significantly more accurate parameters than constant-pumping-rate TFMTs. The calculated modeling errors may be useful in estimating the magnitude of parameter estimation errors from the TFMT. Our field tests in a coastal aquifer at the Lizzie Site in North Carolina (USA) demonstrate the feasibility of a TFMT for aquifer characterization. The downhole hydraulic conductivity profiles from our field and synthetic TFMTs are consistent with the corresponding profiles from QFMTs.     

Simulation/optimization modeling for robust pumping strategy design

A new simulation/optimization modeling approach is presented for addressing uncertain knowledge of aquifer parameters. The Robustness Enhancing Optimizer (REO) couples genetic algorithm and tabu search as optimizers and incorporates aquifer parameter sensitivity analysis to guide multiple-realization optimization. The REO maximizes strategy robustness for a pumping strategy that is optimal for a primary objective function (OF), such as cost. The more robust a strategy, the more likely it is to achieve management goals in the field, even if the physical system differs from the model. The REO is applied to trinitrotoluene and Royal Demolition Explosive plumes at Umatilla Chemical Depot in Oregon to develop robust least cost strategies. The REO efficiently develops robust pumping strategies while maintaining the optimal value of the primary OF-differing from the common situation in which a primary OF value degrades as strategy reliability increases. The REO is especially valuable where data to develop realistic probability density functions (PDFs) or statistically derived realizations are unavailable. Because they require much less field data, REO-developed strategies might not achieve as high a mathematical reliability as strategies developed using many realizations based upon real aquifer parameter PDFs. REO-developed strategies might or might not yield a better OF value in the field.     

Water Table Uncertainties due to Uncertainties in Structure and Properties of an Unconfined Aquifer

We consider two sources of geology‐related uncertainty in making predictions of the steady‐state water table elevation for an unconfined aquifer. That is the uncertainty in the depth to base of the aquifer and in the hydraulic conductivity distribution within the aquifer. Stochastic approaches to hydrological modeling commonly use geostatistical techniques to account for hydraulic conductivity uncertainty within the aquifer. In the absence of well data allowing derivation of a relationship between geophysical and hydrological parameters, the use of geophysical data is often limited to constraining the structural boundaries. If we recover the base of an unconfined aquifer from an analysis of geophysical data, then the associated uncertainties are a consequence of the geophysical inversion process. In this study, we illustrate this by quantifying water table uncertainties for the unconfined aquifer formed by the paleochannel network around the Kintyre Uranium deposit in Western Australia. The focus of the Bayesian parametric bootstrap approach employed for the inversion of the available airborne electromagnetic data is the recovery of the base of the paleochannel network and the associated uncertainties. This allows us to then quantify the associated influences on the water table in a conceptualized groundwater usage scenario and compare the resulting uncertainties with uncertainties due to an uncertain hydraulic conductivity distribution within the aquifer. Our modeling shows that neither uncertainties in the depth to the base of the aquifer nor hydraulic conductivity uncertainties alone can capture the patterns of uncertainty in the water table that emerge when the two are combined.