Stochastic Fusion of Information for Characterizing and Monitoring the Vadose Zone

are still often raised regarding parameter identifiability and their uniqueness for particular methods. Inverse problems for hydrological processes in the vadose zone While various laboratory and field methods for evaluare often perceived as being ill posed and intractable. Consequently, ating soil hydraulic properties are relatively well estabsolutions to the inverse problems are frequently subject to skepticism. In this paper, we examine the necessary and sufficient conditions for lished, several major problems remain. Most laboratory the inverse problems to be well posed and discuss difficulties associ- methods are applied to samples ranging from 100 to ated with solving the inverse problems. We subsequently explain the about 500 cm 3 . The scale of field methods generally does need for a stochastic conceptualization of inverse problems of the not extend beyond a plot of 1 m 2 and depths of one to vadose zone. Principles of geostatistically based inverse approaches, several meters. There is an urgent need to develop methwhich rely on stochastic concepts, are then illustrated, including cok- ods that characterize hydraulic properties of the vadose riging, a sequential linear estimator, and a successive linear estimator. zone on a much larger scale. Recently developed geoWe then discuss applications involved in the approaches to classical physical methods such as electrical resistivity tomogravadose zone inversion problems (using observed pressure heads, mois