From Percolation to Infiltration: Using Fractal Models in Unsaturated Soils.

Physical models based on percolation theory have recently been developed to predict water and solute movement in soils. These formulations seek to address some of the short-comings of classic approaches, and (for example) move away from the conceptual model of soil pores as clusters of capillary tubes. However, percolation theory has not yet been widely applied to model surface infiltration and runoff.

Here I provide two examples of how percolation theory concepts can be applied to predict the movement of water into and through soils. In the first example, I derive a new percolation-based expression for the matric flux and sorptivity of a soil, which can be used to predict 1D infiltration from both saturated (i.e., ponded) and unsaturated (i.e., tension) sources. For comparison purposes, I present the predictions given by the percolation-based equation alongside those given by a numerical model (HYDRUS-1D). As a second example, I use a simple percolation-based framework to model a network of soil cracks as a stochastic lattice, and use this model to predict the transition between infiltration-dominant and runoff-dominant hydrologic regimes. Taken together, these examples may help to inform and improve our conceptualizations of flow and transport through soils.