Reduced Model of One-Dimensional Unsaturated Flow in Heterogeneous Soils with Spatially Stochastic Soil Hydraulic Conductivities

A reduced model for unsaturated flow in one-dimensional layered soils with local stochastic soil hydraulic conductivity is proposed. The reduced model relies on an improved closure assumption compared with straightforward truncation of moment equations for the statistics (expectation and covariance) of the volumetric water content, whereby certain higher-order moments can be expressed in terms of known quantities. The reduced model was compared numerically with (1) direct numerical simulations using homogenized soil properties and (2) agent-based stochastic direct numerical simulations, with soil hydraulic properties defined at the local (finite-difference cell) level. Numerical results showed that the reduced model successfully captures larger variations in water content of the unsaturated flow in heterogeneous soils compared with the solution resulting from homogenization.