Water transport in soils as in fractal media

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 conservation 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 v(2dJ) wherefl deviates from the zero value characteristic for the Richards equation. A change in the apparent water diffusivity with the distance is predicted if the apparent diffusivity is calculated using the Richards equation. An equation for the time and space invariant soil water diffusivity is obtained. Published data sets of five authors were used to test the scaling properties predicted by the model. The value offl 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 had correlation coefficients from 0.97 to 0.995. In some cases a dependence offl on water content was found indicating changes in scaling as the water transport progressed.

Unsaturated hydraulic conductivity of disturbed and undisturbed loam soil

“…Nimmo (1997) quantified the influence of soil structure on the water retention curve. Bird et al (1996), Perfect et al (1996), Guerrini and Swartzendruber (1997), and Pachepsky and Timlin (1998) applied fractal theory to the study of soil water retention and soil water diffusivity curves. Using the representation of Brooks-Corey for the soil water retention curve, Chu (1995) determined the effect of the initial water content on the parameters of the Green-Ampt equation.…”

Multiscaling analysis and random cascade modeling of dye infiltration

“…Simple scaling is defined for sets of points and is thus generally restricted to “binary” fields, which can be characterized by a single fractal dimension. Several studies have investigated water retention and transport assuming a simple scaling soil structure [e.g., Tyler and Wheatcraft , 1989; Flury and Flühler , 1995; Pachepsky and Timlin , 1998]. Multiscaling is defined for probability measures and thus accommodates intensity‐varying processes, characterized by a hierarchy of fractal dimensions (multiscaling encompasses simple scaling as a special case).…”

Towards an alternative blueprint for a physically based digitally simulated hydrologic response modelling system

“…There have certainly been some attempts to take account of heterogeneity of porous medium properties, including fractal heterogeneity (e.g. Neuman, 1995;Pachepsky and Timlin, 1998) and to include preferential flows into hillslope and catchment-scale models (e.g. Bronstert and Plate, 1997;Faeh et al, 1997).…”