Abstract
A new stochastic model for one-dimensional unsaturated water flow is proposed with focus on its probabilistic structure resulting from random variations in saturated hydraulic conductivity. The newly developed model has the form of a Fokker-Planck equation, and its validity is investigated under different stochastic saturated hydraulic conductivity fields. The point-scale Richards equation for soil water flow, which is a parabolic nonlinear partial differential equation (PDE), is first converted into a simplified ordinary differential equation (ODE) using a depth-integrated scheme. This nonlinear ODE is further converted into a linear PDE using the stochastic Liouville equation. Finally, the upscale conservation equation is obtained using the cumulant expansion method. When compared with Monte Carlo simulations, this model yields good agreements. In particular, this upscale model can reproduce the vertical profile of mean soil-water content very well. Besides, the results from model application show that ...
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.