Ensemble Modeling of Hydrologic and Hydraulic Processes at One Shot: Application to Kinematic Open-Channel Flow under Uncertain Channel Properties by the Stochastic Method of Characteristics

Abstract

A stochastic kinematic wave model for open-channel flow under uncertain channel properties is developed. The Fokker-Planck equation (FPE) of the kinematic open-channel flow process under uncertain channel properties is developed by using the method of characteristics. Every stochastic partial differential equation has a one-to-one relationship with a nonlocal Lagrangian-Eulerian FPE (LEFPE). As such, one can develop an LEFPE for the governing equation of any hydrologic or hydraulic process as the physically based stochastic model of the particular process. A linear, deterministic, differential equation in Eulerian-Lagrangian form, LEFPE provides a quantitative description of the evolution of the probability density functions of the state variables of the process at one shot to describe the ensemble behavior of the process instead of the commonly used many Monte Carlo simulations to quantify the same ensemble behavior. Under certain assumptions, the nonlocal LEFPE reduces to the classical local FPE, which is more convenient in practical applications. The numerical solutions of the resulting FPE are validated by Monte Carlo simulations under varying channel conditions. The validation results demonstrated that the developed FPE can express the ensemble behavior of the kinematic wave process under uncertain channel properties adequately.