[1] Three conceptual models are evaluated for estimating transmissivity (T) fields using data from sequential pumping tests at a field site and data from similar tests simulated in a synthetic aquifer. The three approaches are (1) an equivalent homogeneous approach, (2) a heterogeneous approach based on a single pumping test, and (3) a heterogeneous approach based on joint interpretation of the sequential pumping tests (i.e., hydraulic tomography, HT). They are evaluated on the basis of their abilities to obtain representative estimates of the T field of the aquifer and, more importantly, on the ability of their estimates to predict drawdown distributions in the aquifer induced by independent validation pumping tests. Results show that the first approach yields scenario-dependent T estimates, which vary with the location of the pumping well. Independent validation tests show that the predicted drawdowns in both aquifers are biased and dispersed. While the second approach produces scenario-dependent T spatial distributions capturing the general pattern of the aquifer, the T fields consistently yield better drawdown predictions than those based on the first approach. Lastly, the joint interpretation approach reduces the scenario dependence of the T estimates and improves the quality of the T estimates as more data sets from sequential pumping tests are included. More importantly, the resultant T estimates lead to the best prediction of different flow events. The robustness of the joint interpretation is then elucidated.

[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 source of water is reinvestigated by examining the temporal 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 the transition of the water release mechanisms and vertical flow in the aquifer are the cause of 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.

[1] Using a first-order cross-correlation analysis, this paper investigates the relationship between observed heads and hydraulic properties in the saturated and vadose zones at different times and locations of three-dimensional unconfined aquifers during pumping tests. Cross-correlation analysis is a weighted sensitivity analysis casted into a stochastic framework. It determines the relative impact of each parameter with respect to others in time and space on the observed heads according to uncertainty or spatial variability of each parameter. It reveals the information content in measured drawdowns about heterogeneity during a pumping test in an unconfined aquifer, which is critical for aquifer parameter estimation. Based on a synthetic, numerical example, our cross-correlation analysis reveals that heads in the saturated zone at late times carry the greatest nonsymmetrically weighted information content about the hydraulic conductivity (K S ) distribution within the cone of depression. On the other hand, heads in the saturated zone at early times contain the most information about the specific storage (S S ) heterogeneity in a narrow region between the observation and pumping locations. During intermediate and late times, heads in the saturated zone largely reflect the effects of saturated water content ( S ) and pore-size parameter () in the thin unsaturated region near the water table above the pumping and observation locations. At last, heads in the vadose zone at late times carry the greatest information about S and around the observation point.

[1] In this study, we developed a stochastic estimator for characterizing the hydraulic heterogeneity in both unsaturated and saturated zones of unconfined aquifers using transient drawdown data from sequential pumping tests. This estimator was built upon the successive linear estimator by Yeh et al. (1996), the simultaneous successive linear estimator by Xiang et al. (2009), and the 3-D finite element program for flow and transport through heterogeneous media by Srivastava and Yeh (1992). The estimator was tested afterward using simulated data sets of sequential pumping tests in a synthetic unconfined aquifer where saturated conductivity, specific storage, saturated water content, and pore-size distribution parameter vary spatially in three dimensions. Test results show that the estimator is able to produce parameter fields that capture the overall 3-D pattern of the true heterogeneous parameter fields. We subsequently validated the estimated parameter fields by assessing their ability to predict drawdowns during an independent pumping test, which was not used during the estimation phase. Results of the validation show that the predicted drawdowns based on the estimated heterogeneous parameter fields are in close agreement with the true drawdowns. In addition, predicted drawdowns based on the parameter fields from the joint interpretation are superior to those based on the parameters estimated from the homogeneous conceptual model. Lastly, while many field experiments are necessary to fully assess the robustness of this estimator and sequential pumping tests, results of this study suggest they are a promising characterization technique for unconfined aquifers.

Hydraulic tomography (HT) has become a mature aquifer test technology over the last two decades. It collects nonredundant information of aquifer heterogeneity by sequentially stressing the aquifer at different wells and collecting aquifer responses at other wells during each stress. The collected information is then interpreted by inverse models. Among these models, the geostatistical approaches, built upon the Bayesian framework, first conceptualize hydraulic properties to be estimated as random fields, which are characterized by means and covariance functions. They then use the spatial statistics as prior information with the aquifer response data to estimate the spatial distribution of the hydraulic properties at a site. Since the spatial statistics describe the generic spatial structures of the geologic media at the site rather than site‐specific ones (e.g., known spatial distributions of facies, faults, or paleochannels), the estimates are often not optimal. To improve the estimates, we introduce a general statistical framework, which allows the inclusion of site‐specific spatial patterns of geologic features. Subsequently, we test this approach with synthetic numerical experiments. Results show that this approach, using conditional mean and covariance that reflect site‐specific large‐scale geologic features, indeed improves the HT estimates. Afterward, this approach is applied to HT surveys at a kilometer‐scale‐fractured granite field site with a distinct fault zone. We find that by including fault information from outcrops and boreholes for HT analysis, the estimated hydraulic properties are improved. The improved estimates subsequently lead to better prediction of flow during a different pumping test at the site.