Tian Chyi J Yeh

Analysis of hydraulic tomography using temporal moments of drawdown recovery data

Received 2 June 2005; revised 30 September 2005; accepted 21 October 2005; published 1 February 2006. [1] Transient hydraulic tomography (THT) is a potentially cost-effective and highresolution technique for mapping spatial distributions of the hydraulic conductivity and specific storage in aquifers. Interpretation of abundant well hydrographs of a THT survey, however, is a computational challenge. We take on this challenge by developing an estimation approach that utilizes the zeroth and first temporal moments of well hydrographs, instead of drawdown itself. The governing equations for the temporal moments are Poisson’s equations. These equations demand less computational resources as opposed to the parabolic equation that governs drawdown evolution. Likewise, the adjoint equations for evaluating sensitivities of the moments for parameter estimation also take the same forms. Therefore a temporal moment approach is expected to expedite the interpretation of THT surveys. On the basis of this premise we extend our sequential successive linear estimator to use the zeroth moment and characteristic time of the drawdown-recovery data generated by THT surveys. We subsequently investigate computational efficiency and accuracy of the moment approach. Results of the investigation show that the temporal moment approach yields results similar to those from the approach that uses transient heads but at significantly less computational costs. Limitations using temporal moments are discussed subsequently.

Stochastic Fusion of Information for Characterizing and Monitoring the Vadose Zone

are still often raised regarding parameter identifiability and their uniqueness for particular methods. Inverse problems for hydrological processes in the vadose zone While various laboratory and field methods for evaluare often perceived as being ill posed and intractable. Consequently, ating soil hydraulic properties are relatively well estabsolutions to the inverse problems are frequently subject to skepticism. In this paper, we examine the necessary and sufficient conditions for lished, several major problems remain. Most laboratory the inverse problems to be well posed and discuss difficulties associ- methods are applied to samples ranging from 100 to ated with solving the inverse problems. We subsequently explain the about 500 cm 3 . The scale of field methods generally does need for a stochastic conceptualization of inverse problems of the not extend beyond a plot of 1 m 2 and depths of one to vadose zone. Principles of geostatistically based inverse approaches, several meters. There is an urgent need to develop methwhich rely on stochastic concepts, are then illustrated, including cok- ods that characterize hydraulic properties of the vadose riging, a sequential linear estimator, and a successive linear estimator. zone on a much larger scale. Recently developed geoWe then discuss applications involved in the approaches to classical physical methods such as electrical resistivity tomogravadose zone inversion problems (using observed pressure heads, mois

Sensitivity and moment analyses of head in variably saturated regimes

A numerical approach for approximating statistical moments of hydraulic heads of variably saturated flows in multi-dimensional porous media is developed. The approximation relies on a first-order Taylor series expansion of a finite element flow model and an adjoint state numerical method for variably saturated flows to evaluate sensitivities. This approach can be employed to analyze uncertainties associated with predictions of head of steady-state or transient flows in variably saturated porous media, with any type of boundary and initial conditions. Limitations of stochastic analytical methods such as spectral/perturbation approaches and the time-consuming Monte Carlo simulation technique are thus alleviated. An example is given to demonstrate the utility of the approach and to investigate the temporal evolution of head variances in a variably saturated flow regime. Results show that the fluctuation of the water table can have significant impacts on the propagation of the head variance.

Hydraulic Tomography for Detecting Fracture Zone Connectivity

Fracture zones and their connectivity in geologic media are of great importance to ground water resources management as well as ground water contamination prevention and remediation. In this paper, we applied a recently developed hydraulic tomography (HT) technique and an analysis algorithm (sequential successive linear estimator) to synthetic fractured media. The application aims to explore the potential utility of the technique and the algorithm for characterizing fracture zone distribution and their connectivity. Results of this investigation showed that using HT with a limited number of wells, the fracture zone distribution and its connectivity (general pattern) can be mapped satisfactorily although estimated hydraulic property fields are smooth. As the number of wells and monitoring ports increases, the fracture zone distribution and connectivity become vivid and the estimated hydraulic properties approach true values. We hope that the success of this application may promote the development and application of the new generations of technology (i.e., hydraulic, tracer, pneumatic tomographic surveys) for mapping fractures and other features in geologic media.

Hydraulic/partitioning tracer tomography for characterization of dense nonaqueous phase liquid source zones

[1] A new technology, hydraulic/partitioning tracer tomography (HPTT), is proposed to survey spatial distributions of hydraulic properties and dense nonaqueous phase liquids (DNAPLs) in the subsurface. HPTT is nothing more than a set of multiple hydraulic/ partitioning tracer tests and synthesis of all the tests to map the spatial distributions. It involves injection of water at one borehole in a source zone to create a steady state forced gradient flow field, then release of conservative/partitioning tracers at the same borehole, and monitoring heads and tracer breakthroughs at the others. The same operation is repeated using different boreholes for the water and the tracer injections. To analyze the head and tracer data obtained from the proposed tomographic survey, a joint stochastic estimator was developed. Numerical experiments were then conducted to evaluate the effectiveness of HPTT as well as the stochastic estimator. Results show that prior knowledge of hydraulic heterogeneity is critical for mapping the distribution of DNAPLs. In addition, the results suggest that the proposed HPTT in conjunction with the stochastic estimator is potentially a viable tool for high-resolution characterization of subsurface heterogeneity and contamination.

An Integrative Approach for Monitoring Water Movement in the Vadose Zone

Electrical resistivity tomography (ERT), during the past few years, has emerged as a potentially cost-effective, noninvasive tool for imaging changes of moisture content in the vadose zone. The accuracy of ERT surveys, however, has been the subject of debate because of its nonunique inverse solution and spatial variability in the constitutive relation between resistivity and moisture content. In this paper, an integrative inverse approach for ERT, based on a stochastic information fusion concept of Yeh and Simůnek, was developed to derive the best unbiased estimate of the moisture content distribution. Unlike classical ERT inversion approaches, this new approach assimilates prior information about the geological and moisture content structures in a given geological medium, as well as sparse point measurements of the moisture content, electrical resistivity, and electric potential. Using these types of data and considering the spatial variability of the resistivity–moisture content relation, the new approach directly estimates three-dimensional moisture content distributions instead of simply changes in moisture content in the vadose zone. Numerical experiments were conducted to investigate the effect of uncertainties in the prior information on the estimate. The effects of spatial variability in the constitutive relation were then examined on the interpretation of the change in moisture content, based on the change in electrical resistivity from the ERT survey. Finally, the ability of the integrative approach was tested by directly estimating moisture distributions in three-dimensional, heterogeneous vadose zones. Results show that the integrative approach can produce accurate estimates of the moisture content distributions and that incorporating some measurements of the moisture content is essential to improve the estimate.

Comparison of Approaches for Predicting Solute Transport: Sandbox Experiments

The main purpose of this paper was to compare three approaches for predicting solute transport. The approaches include: (1) an effective parameter/macrodispersion approach (Gelhar and Axness 1983); (2) a heterogeneous approach using ordinary kriging based on core samples; and (3) a heterogeneous approach based on hydraulic tomography. We conducted our comparison in a heterogeneous sandbox aquifer. The aquifer was first characterized by taking 48 core samples to obtain local-scale hydraulic conductivity (K). The spatial statistics of these K values were then used to calculate the effective parameters. These K values and their statistics were also used for kriging to obtain a heterogeneous K field. In parallel, we performed a hydraulic tomography survey using hydraulic tests conducted in a dipole fashion with the drawdown data analyzed using the sequential successive linear estimator code (Yeh and Liu 2000) to obtain a K distribution (or K tomogram). The effective parameters and the heterogeneous K fields from kriging and hydraulic tomography were used in forward simulations of a dipole conservative tracer test. The simulated and observed breakthrough curves and their temporal moments were compared. Results show an improvement in predictions of drawdown behavior and tracer transport when the K tomogram from hydraulic tomography was used. This suggests that the high-resolution prediction of solute transport is possible without collecting a large number of small-scale samples to estimate flow and transport properties that are costly to obtain at the field scale.

A revisit of drawdown behavior during pumping in unconfined aquifers

Received 16 March 2010; revised 7 February 2011; accepted 7 March 2011; published 6 May 2011. [1] In this study, the S‐shaped log‐log drawdown‐time curve typical of pumping tests in unconfined aquifers is reinvestigated via numerical experiments. Like previous investigations, this study attributes the departure of the S shape from the drawdown‐time behavior of the confined aquifer to the presence of an “additional” source of water. Unlike previous studies,this sourceof water isreinvestigated byexaminingthetemporal and spatial evolution of the rate of change in storage in an unconfined aquifer during pumping. This evolution is then related to the transition of water release mechanisms from the expansion of water and compaction of the porous medium to the drainage of water from the unsaturated zone above the initial water table and initially saturated pores as the water table falls during the pumping of the aquifer. Afterward, the 1‐D vertical drainage process in a soil column is simulated. Results of the simulation show that the transition of the water release mechanisms in the 1‐D vertical flow without an initial unsaturated zone can also yield the S‐shaped drawdown‐time curve as in an unconfined aquifer. We therefore conclude that thetransitionofthewaterreleasemechanismsandverticalflowintheaquiferarethecauseof the S‐shaped drawdown‐time curve observed during pumping in an unconfined aquifer. We also find that the moisture retention characteristics of the aquifer material have greater impact than its relative permeability characteristics on the drawdown‐time curve. Furthermore, influences of the spatial variability of saturated hydraulic conductivity, specific storage, and saturated moisture content on the drawdown curve in the saturated zone are found to be more significant than those of other unsaturated properties. Finally, a cross‐correlation analysis reveals that the drawdown at a location in a heterogeneous unconfined aquifer is mainly affected by local heterogeneity near the pumping and observation wells. Applications of a model assuming homogeneity to the estimation of aquifer parameters as such may require a large number of observation wells to obtain representative parameter values. In conclusion, we advocate that the governing equation for variably saturated flow through heterogeneous media is a more appropriate and realistic model that explains the S‐shaped drawdown‐time curves observed in the field.

River stage tomography: A new approach for characterizing groundwater basins

Received 19 June 2008; revised 16 February 2009; accepted 12 March 2009; published 9 May 2009. [1] Data from tomographic surveys make an inverse problem better posed in comparison to the data from a single excitation source. A tomographic survey provides different coverages and perspectives of subsurface heterogeneity: nonfully redundant information of the subsurface. Fusion of these pieces of information expands and enhances the capability of a conventional survey, provides cross validation of inverse solutions, and constrains inherently ill posed field-scale inverse problems. Basin-scale tomography requires energy sources of great strengths. Spatially and temporally varying natural stimuli are ideal energy sources for this purpose. In this study, we explore the possibility of using river stage variations for basin-scale subsurface tomographic surveys. Specifically, we use numerical models to simulate groundwater level changes in response to temporal and spatial variations of the river stage in a hypothetical groundwater basin. We then exploit the relation between temporal and spatial variations of well hydrographs and river stage to image subsurface heterogeneity of the basin. Results of the numerical exercises are encouraging and provide insights into the proposed river stage tomography. Using naturally recurrent stimuli such as river stage variations for characterizing groundwater basins could be the future of geohydrology. However, it calls for implementation of sensor networks that provide long-term and spatially distributed monitoring of excitation as well as response signals on the land surface and in the subsurface.

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.