Inverse problems for hydrological processes in the vadose zone are often perceived as being ill posed and intractable. Consequently, solutions to the inverse problems are frequently subject to skepticism. In this paper, we examine the necessary and sufficient conditions for the inverse problems to be well posed and discuss difficulties associated with solving the inverse problems. We subsequently explain the need for a stochastic conceptualization of inverse problems of the vadose zone. Principles of geostatistically based inverse approaches, which rely on stochastic concepts, are then illustrated, including cokriging, a sequential linear estimator, and a successive linear estimator. We then discuss applications involved in the approaches to classical vadose zone inversion problems (using observed pressure heads, moisture contents, concentrations, and arrival times), hydraulic tomography, and electrical resistivity tomography for vadose zone characterization and monitoring. Finally, we present a stochastic information fusion technology that assimilates information from both unsaturated hydraulic tomography and electrical resistivity tomography. Preliminary results suggest that this fusion technology is a promising tool for effectively characterizing heterogeneity, monitoring processes in the vadose zone, and quantifying uncertainties associated with vadose zone characterization and monitoring.

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