Stochastic Fusion of Information for Characterizing and Monitoring the Vadose Zone

Abstract

Inverse problems for vadose zone hydrological processes are often being perceived as illposed and intractable. Consequently, solutions to inverse problems are often subject to skepticism. In this paper, using examples, we elucidate difficulties associated with inverse problems and the prerequisites for such problems to be well -posed so that a unique solution exists. We subsequently explain the need of a stochastic conceptualization of the inverse problem and, in turn, the conditional-effective -parameter concept. This concept aims to resolve the ill -posed nature of inverse problems for the vadose zone, for which generally only sparse data are available. Next, the development of inverse methods for the vadose zone, based on a conditional -effective -parameter concept, is explored, including cokriging, the use of a successive linear estimator, and a sequential estimator. Their applications to the vadose zone inverse problems are subsequently examined, which include hydraulic /pneumatic and electrical resistivity tomography surveys, and hydraulic conductivity estimation using observed pressure heads, concentrations, and arrival times. Finally, a stochastic information fusion technology is presented that assimilates information from unsaturated hydraulic tomography and electrical resistivity tomography. This technology offers great promise to effectively characterize heterogeneity, to monitor processes in the vadose zone, and to quantify uncertainty associated with vadose zone characterization and monitoring.

Generalized sequential kriging (GSK) for heterogeneous cell size: property modeling without matrices

“…The inverse problem with SLE has been applied in numerous contexts; e.g., Liu and Yeh [9], Nowak and Cirpka [12], hydraulic tomography applications are in Yeh and Liu [29], Liu et al [8], electrical resistivity tomography is in Yeh et al [30], and data fusion Yeh and Simunek [31]. SQK is a powerful tool and allows for various generalizations.…”

Determining Soil Hydraulic Properties

“…If structure is identified at the scale of interest, it might be sufficient to determine the hydraulic properties of the structural elements in an approximate manner. Stochastic fusion of a variety of moisture-related instrumental information by noninvasive sensoring methods (electrical resistivity tomography, passive microwave, ground-penetrating radar, and others) and its inverse evaluation (Yeh and Simunek, 2001) appears to be a promising direction.…”

Soil Hydraulic Properties

“…This cannot be obtained by point measurements. Therefore, the further development of hydrogeophysical methods, possibly coupled with remote sensing technologies, and the linking of these data with functional hydraulic properties, for example, by stochastic data fusion (Yeh and Simunek, 2001), will play a crucial role in future developments.…”