Ensemble Modeling of the Theis Equation under Uncertain Parameter Conditions

Abstract

The Fokker-Planck equation (FPE) methodology was applied to the transient state confined groundwater flow equation under the initial and boundary conditions leading to the Theis problem. The differential Theis equation was transformed to the FPE form, which describes the evolution of the probability density function of the state variable for this system. Numerical solutions of the FPE were obtained with a hybrid numerical scheme that uses the explicit Lax-Wendroff scheme with a flux limiter for the advective terms and the implicit Euler scheme for the dispersive terms. The results of the FPE methodology were compared with the Monte-Carlo solutions of the analytical Theis solution. The comparison shows a good match in terms of the ensemble mean, variance, and probability density functions in general. The computation times also were improved in the FPE methodology in comparison with the method of Monte-Carlo simulations.