Submitted to: Physical and Chemical Processes of Water and Solute Transport
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: July 22, 2000
Publication Date: March 1, 2001
Interpretive Summary: Water movement in soil carries surface applied chemicals and nutrients which can potentially reach the groundwater. Agricultural researchers have been developing simulation models to estimate the movement of chemicals to groundwater. Often there may be errors in predictions because the chemical appears to disperse more with depth. It has been difficult to account for this dispersion using current theory of chemical movement in soil, as the parameters to describe dispersion appears to vary with soil depth. We have been investigating a new theory to apply to chemical transport. This theory involves the concept of fractal. As we measure the length, area, and volume of soil at finer resolution, we include more of its finer features. The length measured at finer resolution will be longer because it includes these finer features. Transport of chemicals in soils may also follow such a fractal path. This means that as water flows in smaller and smaller pores, the travel path it takes will also increase. Dispersion can be linked in this manner to travel distance. The purpose of this research was to incorporate a mathematical description of this process into equations commonly used by soil scientists to describe chemical transport in soils and to test the results. The dispersion with depth is accounted for by the equations and not the parameters. The results of this research will help improve models which describe the fate of chemicals in soils.
Fractal models have been useful in quantifying inherent soil variability and structural hierarchy. Diffusion of solutes in a fractal pore network does not obey Fick's law; anomalous, or non-Fickian diffusion, takes place instead. We explore 1) the extent to which solute dispersion and horizontal water movement exhibit anomalous behavior; 2) the application of some simple fractal-based modeling approaches which accommodate the anomalous transport phenomena. The dispersivity (Ds) in the advective-dispersive equation (ADE) has a power-law dependence Ds=f(Ls^y) on the mean solute transport distance (Ls). The exponent, y, varied between 0.3 and 1.7 in different data sets. The diffusivity (Dw) in the Richards' equation is also scale dependent and has a power-law dependence on the mean distance of horizontal water transport (Lw) in form Dw=f(1/Lw^b). The exponent, b varies between 0.04 and 0.91 in published data. Soil heterogeneity gives rise to scale-dependence of transport parameters. When solute movements are spatially fractal, they can be described by the fractional advective-dispersive equation (FADE). We applied the FADE to two sets of solute breakthrough curves, and found an improvement in accuracy compared with ADE. In the FADE, the scale effects are reflected by the order of the fractional derivative, and the transport coefficient is not scale-dependent. The heavy tails of the breakthrough curves were well modeled by the FADE. The Richards' equation with fractional time derivative has shown promise in simulating the horizontal water transport in soil. The anomalous transport of solutes can be an important phenomenon to consider in estimations of the fate of agricultural chemicals.