Scale issues of heterogeneity in vadose zone hydrology and practical solutions

Abstract

Hydrological properties of the vadose zone often exhibit a high degree of spatial variability at various scales due to the heterogeneous nature of geological formations. For laboratory scale problems (i.e., small cores, soil columns, and sand boxes), variation in pore size, pore geometry, and tortuosity of pore channels are the major source of heterogeneity. They are called laboratory-scale heterogeneity. Microstratification, foliation, cracks, and roots are also some possible heterogeneities at this scale. As our observation scale increases to a field, stratification or layering in a geologic formation becomes the dominant heterogeneity, which is often classified as field-scale heterogeneity. At an even larger observation scale, the regional-scale heterogeneity represents the variation of geologic formations or facies. Variations among sedimentary basins are then categorized as the global-scale heterogeneity. Fundamental theories for flow and solute transport through porous media are essentially derived for the laboratory-scale heterogeneity. When we attempt to apply these theories to the vadose zone, comprising heterogeneities of many different scales, we encounter the scale problem. To resolve this problem two approaches have evolved in the past: the system approach and the physical approach. The former 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 et al., 1986). The latter approach however relies on upscaling the laboratory-scale theories to the vadose zone. While the system approach has been widely used by soil scientists, it is often criticized for its empiricism and the lack of physical principles. Besides, it is known to be limited to nonpoint source problems or those related to the integrated behavior of a system (for example, the average concentration of nitrate in the irrigation return flow at irrigation drains or their breakthrough at the water table beneath an irrigation field). Since this approach requires the knowledge of input and output histories and model calibrations, flow and tracer experiments must be carried out at a given site prior to prediction. Further, a calibrated system model for the vadose zone at a given depth under a given condition is often found unsuitable for different depths and conditions (e.g., Butters et al., 1989; Butters and Jury, 1989; Roth et al., 1991). While such system approaches are practical tools for predicting water flow and pollutant transport through thin vadose zones to the water table or to irrigation drains at agricultural fields, their utility for general hydrogeological problems is limited. Hydrogeological problems involve vadose zones of tens and hundreds of meters in thickness. Input sources to these vadose zones are small compared with the scale of hydrogeological settings. Yet, groundwater hydrologists have to focus on the spatial and temporal evolution of flow and spread of solutes over the vadose zone and regional aquifers (Stephens, 1996). Because of these above- mentioned reasons, the following discussion will concentrate on the physical approach that has been widely used by groundwater hydrologists. Moreover, the discussion will present only the author's point of view about the scale issue and approaches to the heterogeneity in the vadose zone.