Introduction

The hydrologic properties of the vadose zone often exhibit high degrees of spatial variability over a range of scales because of the heterogeneous nature of geologic formations. For laboratory-scale problems (i.e., small cores, soil columns, and sand-boxes), variations in pore size, pore geometry, and tortuosity of pore channels are the major sources of heterogeneity. They are called laboratory-scale heterogeneities. Microstratification, foliation, cracks, and roots are also some possible heterogeneities at this scale. As our problem scale increases to that of a field, stratification or layering in a geologic formation becomes the dominant heterogeneity, often classified as field-scale heterogeneity. At an even larger problem scale, regional-scale heterogeneity consists in variations in geologic formations or facies. Variations among sedimentary basins are then categorized as global-scale heterogeneities.

The fundamental theories for flow and solute transport through porous media have essentially been derived for laboratory-scale heterogeneities. When we attempt to apply these theories to the vadose zone, comprising heterogeneities on many different scales, we encounter a scale issue. That is, these theories, suitable for the laboratory-scale problem, may not be applicable to problems at other scales. To deal with this issue, two approaches have evolved: the systems approach and the physical approach. The systems approach treats the vadose zone as a low-pass filter, and its governing principle is determined by the relationship between its input and output histories (e.g., Jury, Sposito, and White, 1986). The physical approach relies on the upscaling of laboratory-scale theories to the vadose zone.