Unsaturated flow in heterogeneous soils with spatially distributed uncertain hydraulic parameters

Uncertain soil properties are often modeled as random fields. This renders the unsaturated flow equations stochastic. Determining statistics of pressure head is nontrivial, since the Richards equation is highly nonlinear. The prevalent approach is to linearize relative hydraulic conductivity around the ensemble mean pressure head, which often leads to significant errors. Recently, an approach has been proposed to avoid such a linearization for the Gardner model, with the soil parameter a being a random variable. We generalize this approach by allowing the latter to be a random field. This is achieved by means of a partial mean-field approximation. Using two-dimensional infiltration into a heterogeneous soil with uncertain hydraulic parameters as an example, we demonstrate that our predictions of the mean pressure head and its variance remain accurate for moderately variable systems. The robustness of our solutions increases with the correlation length of the Gardner parameter.