Elsevier

Journal of Hydrology

Volume 588, September 2020, 125099
Journal of Hydrology

Research papers
Identification of groundwater basin shape and boundary using hydraulic tomography

https://doi.org/10.1016/j.jhydrol.2020.125099Get rights and content

Highlights

  • Basin shape and boundary condition can be identified by Hydraulic Tomography method.

  • Boundary shape and condition affect the estimated aquifer properties.

  • Prior information of geology can improve the estimated aquifer characteristics.

  • A mean value initial guess yields a better estimation for the incorrect boundary case.

Abstract

Shapes and boundary types of a groundwater basin play essential roles in the analysis of groundwater management and contaminant migration. Hydraulic tomography (HT), a recently developed new approach for high-resolution characterization of aquifers, is not only an inverse method but a logical strategy for collecting non-redundant hydraulic information. In this study, HT was applied to synthetic 2-D aquifers to investigate its feasibility to map the irregular shapes and types of the aquifer boundaries. We first used the forward model of VSAFT2 to simulate hydraulic responses due to HT surveys in the aquifer with irregular geometry and predetermined constant head conditions at some boundaries, and no-flow conditions at others. The SimSLE (Simultaneous Successive Linear Estimator) inverse model in VSAFT2 was then used to interpret the simulated HT data to estimate the spatial distribution of hydraulic properties of the aquifer using a domain with a wrong geometry surrounded by boundaries of a constant head condition. The inverse modeling experiment used steady-state and transient-states data from the HT forward simulations, and it used the same monitoring network as in the aquifer with irregular geometry to assess the ability of HT for detecting types and shapes of the boundary as well as heterogeneity in the aquifer. Results of the experiment show that no-flow boundaries, which were incorrectly treated as constant head boundaries in inverse models, were portrayed as low permeable zones of the aquifer near the boundaries. Overall, the results show that HT could delineate not only the irregular shape of the aquifer in general but also heterogeneity in the aquifer. Improvements of the estimation with prior information of transmissivity and storage coefficient was also investigated. The study shows that using homogeneous initial guess parameters resulted in a slightly better estimate than others. Moreover, this study employs Monte Carlo simulations to ensure statistically meaningful conclusions.

Introduction

Proper management and protection of groundwater resources require detailed aquifer characterization. Over the past few decades, the conventional pumping test analyses, such as methods by Theis (1935) and by Cooper and Jacob (1946), have been widely adopted to estimate the aquifer characteristics. They are parsimonious, but they do not provide sufficient information for a high-resolution understanding and prediction of flow and contaminant transport processes (Wu et al., 2005).

Recently, a new method of aquifer test and analysis (i.e., Hydraulic Tomography, HT) has been developed (see Yeh and Liu, 2000, Zhu and Yeh, 2005, Xiang et al., 2009). It involves successively conducting a pumping test at a well and monitoring aquifer responses at others in a well field until the test is completed at all selected pumping wells. Such test data are then analyzed using a highly parameterized inverse model to estimate detailed spatial distributions of hydraulic parameters of the aquifer. HT, in essence, gathers aquifer responses from a limited number of wells under different flow fields. These responses contain non-redundant information about aquifer heterogeneity such that the inverse modeling of heterogeneity is improved (Wen et al., 2019). Because of this new aquifer characterization approach, Yeh and Lee (2007) championed the time to change our approach to characterize aquifers. Over the past decades, many studies have validated HT’s robustness, for examples, synthetic aquifers (Yeh and Liu, 2000, Zhu and Yeh, 2005, Ni et al., 2009, Bohling and Butler, 2010, Castagna et al., 2011, Tso et al., 2016), laboratory sandboxes (Liu et al., 2002, Liu et al., 2007, Yin and Illman, 2009, Berg and Illman, 2011, Illman et al., 2015, Zhao et al., 2016), and field aquifers (Straface et al., 2007, Wen et al., 2010, Cardiff and Barrash, 2011, Huang et al., 2011, Berg and Illman, 2013, Berg and Illman, 2015, Cardiff et al., 2012, Zha et al., 2016, Zhao and Illman, 2017, Zhao and Illman, 2018).

While HT is useful, efforts to improve it have been proposed. For instance, the geological knowledge is employed as prior information to improve the heterogeneity estimation as discussed by Zhao et al., 2016, Zha et al., 2017, Zhao and Illman, 2017, Zhao and Illman, 2018, Li et al., 2019. Likewise, transient HT has been developed (e.g., Zhu and Yeh, 2005, Xiang et al., 2009), but few studies have investigated the role of storage coefficient (S) or specific storage (Ss) on the aquifer characterization using HT. For instance, Tiedeman and Barrash (2019) mainly focused on hydraulic conductivity (K) estimation. Cardiff and Barrash (2011) combined the knowledge of geological data with HT and investigated the effect of S on the heterogeneity characterization. Cardiff et al. (2011) stated that the spatial variability of Ss would not have a large effect on estimated K as long as the information of Ss is reasonable. However, Castagna et al., 2011, Sun et al., 2013 advocates the impacts of information of S on the estimation of transmissivity (T) and S.

Similarly, geologic features (such as bedrocks, mountains, and faults) often surround or cut through field aquifers, and their locations and hydraulic properties are generally unknown. Previous HT studies used synthetic aquifers or laboratory sandboxes where boundaries are known precisely. Such certainty about boundary conditions likely minimizes the uncertainty in the HT estimation. Few studies have investigated the effects of these unknown boundaries on the HT estimates. For example, Sun et al. (2013) examined the relationship between drawdown and aquifer properties, including the effect of using incorrect boundaries in the synthetic aquifers. They showed that the use of constant head boundaries in the inverse model could yield low permeability zones near the impermeable boundary of the true model. As such, they suggested using a constant head boundary for the unknown boundaries during HT analysis.

On the other hand, the application of HT to field aquifers undoubtedly involves uncertainty. To reduce the effects of the uncertain boundary conditions in field aquifers, previous studies (e.g., Straface et al., 2007, Cardiff et al., 2013, Lu et al., 2012, Illman et al., 2009, Zha et al., 2016) employed a large simulation domain compared to the size of the well-field. They then assigned some assumed boundary conditions to the boundaries.

Nonetheless, unknown geologic boundaries may exist near the well field and impact the HT estimates. Recently, the effects of the incorrect boundary conditions in synthetic aquifers were explored by Sun et al. (2013). They considered a single heterogeneous rectangular domain with a well field far from boundaries. They reported that HT could map the impermeable boundary at far distances. Nevertheless, Wang et al., 2019, emphasized that HT results based on one single realization of synthetic heterogeneous aquifers may not be conclusive. Further, few studies have thoroughly investigated the effects of the irregular boundary shape on the estimation.

In this study, we apply HT to a synthetic heterogeneous aquifer for imaging the geometry of boundary and determine associated basin boundary conditions. We also investigate the effect of incorrectly assigned boundary conditions on the parameter estimates within the aquifer. Moreover, the impact of prior information of the storage coefficient on estimated T and S are examined. We employ Monte Carlo simulations to obtain representative results.

Section snippets

Governing flow equation

This study uses VSAFT2 (Variably Saturated Flow and Transport in two dimensions) (Yeh et al., 1993) to simulate a two-dimensional, horizontal groundwater flow model for saturated, heterogeneous media. The following partial differential equation describes the flow of groundwater,T(x)H+Q(xp)=S(x)Htwhich is dependent on the boundary and initial conditions,H|Γ1=H1,TxHn|Γ2=q,andH|t=0=H0where T(x) is the transmissivity [L2/T], H is the total head [L], Q(xp) is the pumping rate [L3/T] at

Forward reference model setup

In this study, a 2-D synthetic aquifer, representing a buried-valley aquifer with impermeable bedrocks with irregular shapes on the two sides (Fig. 1a), is considered. The aquifer is 200 m long from top to bottom, with a maximum width of 192 m from left to right. We discretize the aquifer into 1815 equal size finite element of a dimension of 4 m × 4 m. The aquifer is assumed to consist of many facies of glacial sedimentation, which is generally considered as highly heterogeneous (Anderson, 1989

Inverse modeling setups

Using the noise-free steady or transient forward simulation data for each realization, we then investigate the ability of HT to identify the heterogeneity, geometry, and boundaries of the reference field in each realization. Afterward, different prior knowledge of basin geometry, boundary condition, and storage coefficient is applied. The spatial statistics (means, variances, and correlation scales) of the heterogeneity of the reference aquifer is assumed to be known and used in some cases of

Performance metrics

We use the performance metrics, R2, L1, L2, slope, and intercept from the linear regression analysis of the relationship between reference and estimated hydraulic properties to evaluate the results of the inverse simulations of all the cases. The following equations define these metrics,R2=Nxix^i-xix^iNxi2-xi2Nx^i2-x^i22L1=1Ni=1Nxi-x^iL2=1Ni=1Nxi-x^i2where N is the total number of elements, i is the element number, xiis the value of T or S at the element i th of the reference field,

Results and discussions

In this section, we discuss the HT inverse results of Cases 1, 2, and 3, with A, B, and C scenarios first. Then, the discussion of the results of Monte Carlo simulation follows.

Contour Maps.

T estimates. The true distribution of the T field and boundary geometry of the synthetic aquifer are depicted in Fig. 2a. Again, Case 1 denotes the situation where the exact aquifer geometry is known. In this case, the contour maps of the estimated T fields using steady-state heads (Case 1A) is illustrated in Fig. 2b. Fig. 2c shows the T estimates, using transient heads and complete knowledge of S field (i.e., Case 1B). The estimated T field using the transient head data with the mean S (i.e.,

Histograms

As another way to evaluate estimated T and S of the aquifer, histogram plots of the true and estimated T values for Cases 1A, B, and C are presented in Fig. 4a. For Cases 2A, B, and C, they are in Fig. 4b, and Cases 3A, B, and C are in Fig. 4c. Histograms of scenarios A, B, and C in these three cases are shown with different color lines along with the actual distribution (solid black line).

According to the figures, while the histograms in Cases 1A, B, and C are similar to the true one, those of

Scatter plots

Scatter plots in Fig. 6, Fig. 7 show the relationships between the estimates and true T and S values, respectively. Colors of scatter plots represent different data accumulation density; the light-yellow color denotes the highest density, while the dark blue color indicates the lowest density, as shown in the color bars on the right side of the figures. These figures also include the values of R2, L1, and L2, in addition to the slope and intercept of the regression line.

According to Fig. 6, we

Summary of results of single realization

The values of R2, L1, L2, slope, and intercept of the linear regression relationship between T and S estimates and the reference ones for all cases and scenarios are summarized as bar charts in Fig. 8, Fig. 9. According to these bar charts, we may conclude that in this one realization, all scenarios in Case 1, when geometry and boundary conditions are known, have the best T estimates among all the cases. In addition, HT using transient data and exact S field (Case 1B) gives the best estimate of

Conclusions

With incorrect guess constant head boundary conditions, HT identifies the impermeable boundaries as lower T zones in the vicinity of the boundary. These estimated low T zones generally outline the irregular shape of the impermeable boundary of the aquifer. Estimated S shows these characteristics of low S zones as well.

The comparison of the estimates inside the aquifer in every case leads to the conclusion that boundary conditions are essential to parameter estimation. The case with correct

CRediT authorship contribution statement

Kwankwai Daranond: Conceptualization, Methodology, Formal analysis, Writing - original draft, Visualization. Tian-Chyi Jim Yeh: Writing - original draft, Writing - review & editing, Supervision. Yonghong Hao: Writing - review & editing. Jet-Chau Wen: Writing - review & editing. Wenke Wang: Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The first author acknowledges the support of the scholarship from the Royal Thai Government and the Department of Groundwater Resources, Thailand. This study is also partially supported by the U.S. NSF grant EAR1931756.

References (44)

  • G. Bohling et al.

    Inherent limitations of hydraulic tomography

    Ground Water

    (2010)
  • M. Cardiff et al.

    Aquifer heterogeneity characterization with oscillatorypumping: sensitivity analysis and imaging potential

    Water Resour. Res.

    (2013)
  • M. Cardiff et al.

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

    Water Resour. Res.

    (2012)
  • M. Cardiff et al.

    3-D transient hydraulic tomography in unconfined aquifers with fast drainage response

    Water Resour. Res.

    (2011)
  • M. Castagna et al.

    Joint estimation of transmissivity and storativity in a bedrock fracture

    Water Resour. Res.

    (2011)
  • H. Cooper et al.

    A generalized graphical method for evaluating formation constants and summarizing well-field history

    Trans. Am. Geophys. Union

    (1946)
  • A.L. Gutjahr

    Fast fourier transforms for random field generation: project report for Los Alamos Grant to New Mexico Tech

    (1989)
  • Heath, R.C., 1983. Basic ground-water hydrology. doi:...
  • S.-Y. Huang et al.

    Robustness of joint interpretation of sequential pumping tests: Numerical and field experiments

    Water Resour. Res.

    (2011)
  • W. Illman et al.

    Should hydraulic tomography data be interpreted using geostatistical inverse modeling? A laboratory sandbox investigation

    Water Resour. Res.

    (2015)
  • W.A. Illman et al.

    Hydraulic tomography in fractured granite: Mizunami Underground Research site, Japan

    Water Resour. Res.

    (2009)
  • Liu, S., Yeh, T. and Gardiner, R. (2002). Effectiveness of hydraulic tomography: Sandbox experiments.Water Resources...
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