Time to change the way we collect and analyze data for aquifer characterization.

Over the past few decades, enormous effort has been expended on conducting traditional aquifer tests and model calibration for characterizing aquifers. Traditional aquifer tests generally involve pumping at one well and using the observed drawdown data at another well to estimate aquifer hydraulic properties. Analysis of the test is built upon Theis’ or Jacob’s approximate solution. These solutions assume aquifer homogeneity and uniform thickness despite the fact that aquifers are inherently heterogeneous at multiple scales and their thicknesses vary significantly spatially. These solutions at best predict an averaged drawdown over some volume of the aquifer (apples), which is likely different from the actual drawdown observed at a well, i.e., a single point in space (oranges). An application of these solutions to estimation of averaged aquifer properties based on a hydrograph from only one well is tantamount to comparing apples and oranges. Despite this inconsistency and impropriety, traditional aquifer tests continue to be widely adopted because the methods yield results, however questionable. Unfortunately, these results can significantly affect water resources management. For example, a recent study of traditional aquifer tests in heterogeneous aquifers by Wu et al. (2005) shows that the transmissivity estimate is a nonunique average of heterogeneity over the cone of depression, which evolves with time and depends on the location of the observation well. On the other hand, the estimated storage coefficient is mainly influenced by the geology between the pumping and the observation well. These findings suggest that ground water availability may have been either underestimated or overestimated, and our current management strategies of ground water resources as such are subject to great uncertainty. Likewise, calibrating a ground water model with spatially distributed parameters has been known as solving an ill-posed problem, which is often attributed to a lack of data. Despite of this fact, modelers have continued to search for magic algorithms to solve these problems that inherently have nonunique solutions and seldom have emphasized the need for collecting more data. Moreover, both modelers and practitioners rarely attempt to recognize the kinds of data (the necessary and sufficient conditions, see Yeh and Šim _ unek [2002]) that make an inverse problem well posed. As such, designs of laboratory and field experiments or monitoring networks often collect information irrelevant to resolve the ill-posed issue. Instead of collecting data to meet the necessary and sufficient conditions, which can be expensive and prohibitive for many large-scale field problems, a new technology, known as hydraulic tomography (HT), which collects data intelligently and analyzes data smartly, has recently been developed to provide high-resolution aquifer characterization (Gottlieb and Dietrich 1995; Renshaw 1996; Vasco et al. 2000; Yeh and Liu 2000; Bohling et al. 2002; Liu et al. 2002; Brauchler et al. 2003; McDermott et al. 2003; Zhu and Yeh 2005, 2006). In simple terms, HT is a sequential cross-hole hydraulic test followed by inversion of all the data to map the spatial distribution of aquifer hydraulic properties. Specifically, HT involves installation of multiple wells in an aquifer, which are partitioned into several intervals along the depth using packers. A sequential aquifer test at selected intervals is then conducted. During the test, water is injected or withdrawn (i.e., a pressure excitation) at a selected interval in a given well. Pressure responses of the subsurface are then monitored at other intervals at this well and other wells. This test produces a set of pressure excitation/response data of the subsurface. Once a test is completed, the pump is moved to another interval and the test is repeated to collect another set of data. The same procedure is then 1Corresponding author: Department of Hydrology and Water Resources, The University of Arizona, Tucson, AZ 85721; (520) 621-5943; fax (520) 621-1422; [email protected] 2Department of Resources Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China. 3Department of Resources Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China; [email protected]. edu.tw Received November 2006, accepted November 2006. Copyright a 2007 The Author(s) Journal compilationa2007National GroundWaterAssociation. doi: 10.1111/j.1745-6584.2006.00292.x