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 1 (2+β) where β 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 of β 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 of β on water content was found indicating changes in scaling as the water transport progressed.

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