Michael Cardiff

A Potential‐Based Inversion of Unconfined Steady‐State Hydraulic Tomography

The importance of estimating spatially variable aquifer parameters such as transmissivity is widely recognized for studies in resource evaluation and contaminant transport. A useful approach for mapping such parameters is inverse modeling of data from series of pumping tests, that is, via hydraulic tomography. This inversion of field hydraulic tomographic data requires development of numerical forward models that can accurately represent test conditions while maintaining computational efficiency. One issue this presents is specification of boundary and initial conditions, whose location, type, and value may be poorly constrained. To circumvent this issue when modeling unconfined steady-state pumping tests, we present a strategy that analyzes field data using a potential difference method and that uses dipole pumping tests as the aquifer stimulation. By using our potential difference approach, which is similar to modeling drawdown in confined settings, we remove the need for specifying poorly known boundary condition values and natural source/sink terms within the problem domain. Dipole pumping tests are complementary to this strategy in that they can be more realistically modeled than single-well tests due to their conservative nature, quick achievement of steady state, and the insensitivity of near-field response to far-field boundary conditions. After developing the mathematical theory, our approach is first validated through a synthetic example. We then apply our method to the inversion of data from a field campaign at the Boise Hydrogeophysical Research Site. Results from inversion of nine pumping tests show expected geologic features, and uncertainty bounds indicate that hydraulic conductivity is well constrained within the central site area.

A field proof‐of‐concept of aquifer imaging using 3‐D transient hydraulic tomography with modular, temporarily‐emplaced equipment

[1] Hydraulic tomography is a field scale aquifer characterization method capable of estimating 3-D heterogeneous parameter distributions, and is directly sensitive to hydraulic conductivity (K), thus providing a useful data source for improving flow and transport models. We present results from a proof-of-concept field and modeling study in which we apply 3-D transient hydraulic tomography (3DTHT) to the relatively high-K and moderately heterogeneous unconfined aquifer at the Boise Hydrogeophysical Research Site. Short-duration (20 min) partially penetrating pumping tests, for which observed responses do not reach steady state, are used as the aquifer stimulation. To collect field data, we utilize a system of temporarily emplaced packer equipment to isolate multiple discrete intervals in boreholes. To analyze the data, we utilize MODFLOW combined with geostatistical inversion code based on the quasilinear approach of Kitanidis (1995). This combination of practical software allows inversion of large datasets (>250 drawdown curves, and almost 1000 individual data points) and estimation of K at >100,000 locations; reasonable runtimes are obtained using a single multicore computer with 12 GB of RAM. The K heterogeneity results from 3DTHT are cross-validated against K characterization from a large set of partially penetrating slug tests, and found to be quite consistent. The use of portable, modular equipment for field implementation means that 3DTHT data collection can be performed (including mobilization/demobilization) within a matter of days. Likewise, use of a practical, efficient and scalable numerical modeling and inversion strategy means that computational effort is drastically reduced, such that 3-D aquifer property distributions can be estimated quickly.

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.

Cost optimization of DNAPL source and plume remediation under uncertainty using a semi-analytic model

Dense non-aqueous phase liquid (DNAPL) spills represent a potential long-term source of aquifer contamination, and successful low-cost remediation may require a combination of both plume management and source treatment. In addition, substantial uncertainty exists in many of the parameters that control field-scale behavior of DNAPL sources and plumes. For these reasons, cost optimization of DNAPL cleanup needs to consider multiple treatment options and their associated costs while also gauging the influence of prediction uncertainty on expected costs. In this paper, we present a management methodology for field-scale DNAPL source and plume management under uncertainty. Using probabilistic methods, historical data and prior information are combined to produce a set of equally likely realizations of true field conditions (i.e., parameter sets). These parameter sets are then used in a simulation-optimization framework to produce DNAPL cleanup solutions that have the lowest possible expected net present value (ENPV) cost and that are suitably cautious in the presence of high uncertainty. For simulation, we utilize a fast-running semi-analytic field-scale model of DNAPL source and plume evolution that also approximates the effects of remedial actions. The degree of model prediction uncertainty is gauged using a restricted maximum likelihood method, which helps to produce suitably cautious remediation strategies. We test our methodology on a synthetic field-scale problem with multiple source architectures, for which source zone thermal treatment and electron donor injection are considered as remedial actions. The lowest cost solution found utilizes a combination of source and plume remediation methods, and is able to successfully meet remediation constraints for a majority of possible scenarios. Comparisons with deterministic optimization results show that not taking into account uncertainty can result in optimization strategies that are not aggressive enough and result in greater overall total cost.

Increasing Confidence in Mass Discharge Estimates Using Geostatistical Methods

Mass discharge is one metric rapidly gaining acceptance for assessing the performance of in situ groundwater remediation systems. Multilevel sampling transects provide the data necessary to make such estimates, often using the Thiessen Polygon method. This method, however, does not provide a direct estimate of uncertainty. We introduce a geostatistical mass discharge estimation approach that involves a rigorous analysis of data spatial variability and selection of an appropriate variogram model. High-resolution interpolation was applied to create a map of measurements across a transect, and the magnitude and uncertainty of mass discharge were quantified by conditional simulation. An important benefit of the approach is quantified uncertainty of the mass discharge estimate. We tested the approach on data from two sites monitored using multilevel transects. We also used the approach to explore the effect of lower spatial monitoring resolution on the accuracy and uncertainty of mass discharge estimates. This process revealed two important findings: (1) appropriate monitoring resolution is that which yielded an estimate comparable with the full dataset value, and (2) high-resolution sampling yields a more representative spatial data structure descriptor, which can then be used via conditional simulation to make subsequent mass discharge estimates from lower resolution sampling of the same transect. The implication of the latter is that a high-resolution multilevel transect needs to be sampled only once to obtain the necessary spatial data descriptor for a contaminant plume exhibiting minor temporal variability, and thereafter less spatially intensely to reduce costs.

Aquifer imaging with pressure waves—Evaluation of low‐impact characterization through sandbox experiments

Understanding the detailed spatial variation of hydraulic properties in the subsurface has been the subject of intensive research over the past three decades. A recently developed approach to characterize subsurface properties is hydraulic tomography, in which a series of pumping tests are jointly inverted using a heterogeneous numerical model. Recently, Cardiff et al. (2013) proposed a modified tomography approach named Oscillatory Hydraulic Tomography (OHT), in which periodic pumping signals of different frequencies serve as the aquifer stimulation, and pressure responses are recorded at observation locations for tomographic analysis. Its key advantages over traditional hydraulic tomography are that: (1) there is no net injection or extraction of water, and (2) the impulse (an oscillatory signal of known frequency) is easily extracted from noisy data. However, OHT has only been evaluated through numerical experiments to date. In this work, we evaluate OHT performance by attempting to image known heterogeneities in a synthetic aquifer. An instrumented laboratory sandbox is filled with material of known hydraulic properties, and we measure aquifer responses due to oscillatory pumping stimulations at periods of 2, 5, 10, and 20 s. Pressure oscillation time series are processed through Fourier Transforms and inverted tomographically to obtain estimates of aquifer heterogeneity, using a fast, steady-periodic groundwater flow model. We show that OHT is able to provide robust estimates of aquifer hydraulic conductivity even in cases where relatively few pumping tests and observation locations are available. The use of multiple stimulation frequencies is also shown to improve imaging results.

The return of groundwater quantity: a mega-scale and interdisciplinary “future of hydrogeology”?

A series of recent papers suggest groundwater quantity may be returning to prominence in hydrogeology research. The unsustainable depletion of groundwater has been documented on both regional (Rodell et al. 2009; Tiwari et al. 2009; Famiglietti et al. 2011) and global scales (Wada et al. 2010; Konikow 2011; Wada et al. 2012) using data synthesis and the GRACE satellite data. Additionally, how groundwater resources will be impacted by global change remains important but uncertain and difficult to predict (Green et al. 2011; Taylor et al. 2013). Recent discussions on groundwater sustainability have suggested applying cutting-edge sustainability concepts such as multigenerational goal setting and adaptive management to groundwater quantity problems (Gleeson et al. 2010, 2012). At its core, groundwater quantity is a water budget question of fluxes and stores. The critical applied questions of groundwater quantity are “how much groundwater is available for sustainable use, and what is the impact of the various uses on interconnected social, economic and environmental systems” From the perspective of the authors, as young and possibly naive early-career hydrogeologists, it is suggested that this overall question is one “future of hydrogeology”, like the other futures of hydrogeology described in the Hydrogeology Journal special edition of 2005 (Voss 2005). In the following, this vast question is tentatively divided into a series of smaller questions. Undoubtedly, other researchers will raise other questions or suggest other angles or avenues of research. The purpose of this essay is to encourage this discussion. The term “return” is used to reflect the historical trends in hydrogeologic research. In Fig. 1, the evolution of hydrogeologic research has been divided into three overlapping phases, based on trends in citations and benchmark papers (Schwartz et al. 2005; Anderson 2008). Prominent research in early quantitative hydrogeology focused on questions of “capacity” or “safe yield” when studying aquifers (Meinzer 1923; Theis 1935, 1940). Over the past ∼30–40 years, the community has been largely focused on issues of groundwater contamination and quality as well as more recently on groundwater/surface-water interactions. This research remains important and can be integrated into a holistic view of groundwater and sustainability. The trajectory of hydrogeology research has been increasing in scope, interdisciplinarity and complexity (Fig. 1). It is suggested that a return to groundwater quantity research at the mega-scale, which addresses long-term issues of sustainability, equity, ecology and economics, may have a high return-oninvestment for science and society. Here, the focus is on groundwater systems at regional (≈10-km length scale) to continental (>1000 km) scales, herein called “mega-scale”. Since the 1970s, hydrogeology has often, but not exclusively, focused on site-scale (<1 km) research to examine important water resource and contamination problems and how groundwater interacts with surface water. Regional-scale groundwater systems were first modeled in the 1960s (Toth 1963; Freeze and Witherspoon 1967; Garven 1995; Person et al. 1996) but the numerical simulation of groundwater systems over entire continents has only been recently possible (Fan et al. 2007; Lemieux et al. 2008). Additionally, continental-scale remote sensing from the GRACE satellites have only recently documented realtime groundwater depletion at the mega-scale. Numerous fundamental questions of the spatio-temporal variability of groundwater fluxes and stores remain, especially at the mega-scale. These questions resemble recurring issues in groundwater science and engineering but with a new large-scale twist:

Graph theory for analyzing pair-wise data: application to geophysical model parameters estimated from interferometric synthetic aperture radar data at Okmok volcano, Alaska

Graph theory is useful for analyzing time-dependent model parameters estimated from interferometric synthetic aperture radar (InSAR) data in the temporal domain. Plotting acquisition dates (epochs) as vertices and pair-wise interferometric combinations as edges defines an incidence graph. The edge-vertex incidence matrix and the normalized edge Laplacian matrix are factors in the covariance matrix for the pair-wise data. Using empirical measures of residual scatter in the pair-wise observations, we estimate the relative variance at each epoch by inverting the covariance of the pair-wise data. We evaluate the rank deficiency of the corresponding least-squares problem via the edge-vertex incidence matrix. We implement our method in a MATLAB software package called GraphTreeTA available on GitHub (https://github.com/feigl/gipht). We apply temporal adjustment to the data set described in Lu et al. (Geophys Res Solid Earth 110, 2005) at Okmok volcano, Alaska, which erupted most recently in 1997 and 2008. The data set contains 44 differential volumetric changes and uncertainties estimated from interferograms between 1997 and 2004. Estimates show that approximately half of the magma volume lost during the 1997 eruption was recovered by the summer of 2003. Between June 2002 and September 2003, the estimated rate of volumetric increase is

Stochastic cost optimization of DNAPL remediation - Field application

(6.2 \, \pm \, 0.6) \times 10^6~\mathrm{m}^3/\mathrm{year}