Probabilistic solution to soil water evaporated flow equation

A new stochastic model for one-dimensional evaporated soil water flow is proposed with major focus on its probabilistic structure. The newly developed model has the form of the Fokker-Planck equation, and its validity as a model for the probabilistic evolution of the nonlinear stochastic unsaturated flow process is investigated under a stochastic soil-related parameter (i.e., saturated hydraulic conductivity). This model is based on a parabolic type of stochastic partial differential equation, and has the advantage of providing the probabilistic solution in the form of a probability distribution function, from which one can obtain the ensemble average behavior of the flow system. The comparison results with Monte Carlo simulations show that the proposed model can reproduce well the vertically varying soil water wetting front depth. Overall, the ensemble averaging approach using the cumulant expansion method shows good promise for the stochastic modeling of nonlinear hydrologic processes.