Analytical Derivation of Steady-State Soil Water Probability Density Function Coupled with Simple Stochastic Point Rainfall Model

Abstract

In this study, a new stochastic model for the propagation analysis of fluctuations in rainfall to soil water dynamics is proposed. Based on a lumped conceptualization of soil water dynamics with rainfall forcings, which are incorporated by a simple stochastic point rainfall model, a model is derived by using cumulant expansion theory from a stochastic differential equation. The advantage of the model is to provide the probabilistic solution in the form of a probability density function (PDF), from which one can find the ensemble average behavior of the system. Steady-state PDF of soil water is analytically obtained and analyzed for different climate, soil, and vegetation conditions. The city of Daegue in Korea, which represents the driest parts of the Korean, Peninsula, is applied for a case study and the result shows that the analytically derived steady-state soil water PDF can make a good agreement to the numerically obtained steady-state PDF from a lumped conceptualization model of soil water dynamics....