A fractal analysis of the water retention curve

The dependence of the soil water content ϑ upon the matric potential ψ is studied within a fractal approach that regards the water retention curve as a sequence of well defined fractal regimes. Each of such regimes accounts for a given functional dependence ϑ≡ϑ(ψ), which in turn is characterized by a fractal dimension. The difference between the double fractal (observed into sandy soils) and multifractal (observed into clay soils) regime is explained by recalling that, for a sandy soil, the transition from saturated to dry conditions is driven by a steep reduction of ψ. To the contrary, for a clay (where the change from the highest water contents to the smallest ones is characterized by a large range of the matric potential), the multifractal behaviour is observed. These results are also confirmed by the analysis of experimental data. In particular, we show that the intermediate regime, generally accounting for the fractal multimodality, is due to the sandy nature of the soil at stake, practically immaterial. Finally, we demonstrate that our model can be also regarded as the straightforward generalization of that of Millán and González-Posada (2005).