Abstract
We study the dynamics of soil moisture in the presence of precipitation, evapotranspiration and leakage. This study utilizes a probabilistic framework, and considers the evolution of the probability density function of soil moisture. Our main objective is to assess when the stationary solution is a physically realizable state of the system. Mathematically, this is equivalent to analyzing when the stationary solutions are stable. We show the following main results: For a general rainfall and evapotranspiration model, in a multiple plant framework, the stationary solution is a stable attractor in L 1. However, the stationary solution is at best conditionally stable in L ∞. This has important implications in terms of (1) the validity of moment analysis of the transient problem, (2) the physical importance of transient solutions, and (3) the numerical solution of the stationary problem as a late time solution of the transient problem.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
