Submitted to: Journal of Hydrology
Publication Type: Peer reviewed journal
Publication Acceptance Date: 10/1/1997
Publication Date: N/A
Citation: Interpretive Summary: Water movement in soil determines the fate of agricultural chemicals and water availability to plants. It is important, therefore, that water flow models accurately describe the processes involved. The ability to predict water flow in soils is still imperfect. We have been investigating a new theory to apply to water flow in an attempt to improve water flow models. This theory involves the concept of fractals. As we measure the length, area, and volume of soil at ever finer resolution, we include ever more of its finer features. The length measured at finer resolution will be longer because it includes these finer features. Flow of water 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. Current simulation models of water flow in soils do not account for this process which may limit their ability to predict water movement. The purpose of this research was to incorporate a mathematical description of this process into equations commonly used by soil scientists to describe water flow in soils and to test the results. We developed a fractal model that described the changes in water flow as a function of the features of soil porosity. The modeling results compared favorably with measured data. The results of this study should help us build more accurate models of water flow in soil.
Technical Abstract: Fractal scaling laws of water transport were found for soils. A water transport model is needed to describe this type of transport in soils. We have developed a water transport equation using the physical model of percolation clusters, employing the mass conversion law, and assuming that hydraulic conductivity is a product of a local component dependent on water content and a scaling component depending on the distance traveled. The model predicts scaling of water contents with a variable X/(t^(1/2+beta)) where beta deviates from the zero value characteristic for the Richards equation. An equation for the time and space invariant soil water diffusivity is obtained. Data sets from five published papers were used to test the scaling properties predicted by the model. The value of Beta was significantly greater than zero in almost all data sets and typically was in the range from 0.05 to 0.5. This exponent was found from regression equations that has correlation coefficients from 0.97 to 0.995. In some cases a dependence of Beta on water content was found indicating changes in scaling as the water transport progressed.