An Integrative Approach for Monitoring Water Movement in the Vadose Zone

While ERT surveys are useful, Yeh et al. (2002) showed that uncertainties in tracking moisture movement in the Electrical resistivity tomography (ERT), during the past few years, vadose zone on the basis of ERT surveys alone can has emerged as a potentially cost-effective, noninvasive tool for imaging changes of moisture content in the vadose zone. The accuracy be quite significant. They reported that both inverse of ERT surveys, however, has been the subject of debate because of modeling of the ERT surveys and the spatial variability its nonunique inverse solution and spatial variability in the constitutive of the parameters in the constitutive resistivity–moisture relation between resistivity and moisture content. In this paper, an content relation contribute to the overall uncertainties. integrative inverse approach for ERT, based on a stochastic informaDepending on the number of parameters to be inverted tion fusion concept of Yeh and Šimůnek, was developed to derive the and the quantity of data available (Yeh and Šimůnek, best unbiased estimate of the moisture content distribution. Unlike 2002), the ERT survey inverse problem is often ill posed, classical ERT inversion approaches, this new approach assimilates and may have no unique solution. For ill-posed probprior information about the geological and moisture content structures lems, most ERT inversion approaches employ optimiin a given geological medium, as well as sparse point measurements of zation algorithms with some type of regularization (e.g., the moisture content, electrical resistivity, and electric potential. Using these types of data and considering the spatial variability of the resistiTikhonov, 1963). While the regularization algorithm yields vity–moisture content relation, the new approach directly estimates smooth estimates, there is no guarantee that it will prothree-dimensional moisture content distributions instead of simply duce the best unbiased estimate of the resistivity field, changes in moisture content in the vadose zone. Numerical experiwhich reflects flow processes and underlying geologiments were conducted to investigate the effect of uncertainties in the cal structures. Neither does the regularization provide prior information on the estimate. The effects of spatial variability in a meaningful way to quantify the uncertainty associated the constitutive relation were then examined on the interpretation of with the spatial variability. Additionally, when convertthe change in moisture content, based on the change in electrical ing changes in resistivity to changes in moisture content, resistivity from the ERT survey. Finally, the ability of the integrative it is often assumed that the parameters in the constituapproach was tested by directly estimating moisture distributions in tive relation (e.g., Archie’s Law) are constant across the three-dimensional, heterogeneous vadose zones. Results show that the integrative approach can produce accurate estimates of the moisture entire domain. Recent studies by Baker (2001) and Yeh content distributions and that incorporating some measurements of et al. (2002) reported pronounced spatial variability of the moisture content is essential to improve the estimate. these parameters in the field. Neglecting this spatial variability and using a single resistivity–moisture calibration curve can add to the level of uncertainty in the final inE resistivity surveys are increasingly used terpreted change in moisture content (in an unquantito collect extensive electric current and potential fiable way). data in multiple dimensions to image subsurface electriBesides the uncertainties inherent in the interpretation cal resistivity distribution (Daily et al., 1992; Ellis and of ERT surveys, most current three-dimensional inverse Oldenburg, 1994; Li and Oldenburg, 1994; Zhang et al., models demand significant computational resources to 1995). Recently, ERT surveys have found their way into process the large data sets typically collected during a sursubsurface hydrology applications. This is attributed to vey. Furthermore, a change in moisture content only prothe fact that knowledge of the spatial distribution of the vides qualitative information about water movement in electrical properties of subsurface media can provide the vadose zone. The actual moisture content values at valuable information for characterizing waste sites and each point, which are vital to hydrological investigations monitoring flow and contaminant movement in the vaor hydrological inverse modeling (e.g., Yeh and Šimůdose zone. For example, during an infiltration event, the nek, 2002), remain unknown. For instance, since the unmoisture content of a geological medium is generally saturated hydraulic conductivity is a nonlinear function the only factor that undergoes dramatic changes, and the of moisture content, changes in the moisture content alone changes in resistivity can be related to changes in moisdo not provide enough information to uniquely characture content. Tracking the changes in resistivity through terize the unsaturated hydraulic properties of the vadose time, therefore, has been found to be useful for detecting zone. As a consequence, an inverse approach is needed temporal changes in the moisture content of the vadose that can account for spatial variability of the resistivity– zone (Daily et al., 1992; Zhou et al., 2001). moisture content relation, efficiently process the large number of data sets, and produce detailed moisture content distributions with the least uncertainty. S. Liu, Burgess & Niple, 5025 E. Washington St., Phoenix, AZ 85034; T.-C.J. Yeh, Dep. of Hydrology and Water Resour., John W. HarshWhile the physical process of electric current flow is barger Bldg., The Univ. of Arizona, Tucson, AZ 85721. Received 18 different from that of groundwater flow, the governing July 2003. Original Research Paper. *Corresponding author (yeh@ equation of the electric current and the potential fields hwr.arizona.edu). created during ERT surveys is analogous to that of steady Published in Vadose Zone Journal 3:681–692 (2004).  Soil Science Society of America 677 S. Segoe Rd., Madison, WI 53711 USA Abbreviations: ERT, electrical resistivity tomography.