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REVIEW OF MODELING OF WATER FLOW AND SOLUTE TRANSPORT IN THE VADOSE ZONE: Stochastic ApproachesYeh, T.-C. Jim; McCord, J. T.; Department of Hydrology & Water Resources, The University of Arizona (Department of Hydrology and Water Resources, University of Arizona (Tucson, AZ), 1994-11-10)Hydrologic properties of the vadose zone are heterogeneous at many different scales. An accurate prediction of water flow and solute transport in the vadose zone requires detailed information about spatial distributions of the properties. Collecting such detailed spatial distribution of hydrologic properties of geological formations is a formidable task. As a result, hydrologic modelers face a difficult challenge: to make the best prediction with little information. During the past few decades many approaches and theories based on stochastic concepts have been developed in an attempt to overcome this difficulty. These stochastic approaches and theories provide ways not only to predict flow and transport processes in large -scale, heterogeneous vadose zones, but also to assess uncertainties in our predictions. One widely -investigated stochastic approach involves the use of effective flow and transport properties. The effective property approach essentially represents a generalization of the well -known equivalent homogeneous media approach discussed in most hydrology textbooks (e.g., using the arithmetic mean conductivity and harmonic mean conductivity for flow parallel to and normal to stratification, respectively, in layered media). This approach is a valuable tool in many practical situations but it predicts the ensemble behavior of a system which can be quite different from reality. To obtain predictions at higher resolutions than the effective property approach, many heterogeneous approaches have also been developed. This paper presents an overview of the stochastic theories related to both equivalent homogeneous media and heterogeneous approaches, it highlights their applications, and it discusses some of their deficiencies.