Steady-state flow under surface recharge through unconfined aquifer with depth-decaying hydraulic conductivity: Analytical results

Abstract

This paper presents some analytical results related to groundwater flow through an unconfined horizontal aquifer induced by areal recharge on the top and a decaying hydraulic conductivity. Under steady-state conditions, and in the context of Boussinesq equation, exact analytical solutions describing drainage into one or two penetrating channels at the aquifer boundaries have been derived in closed forms. The analytical expressions have been used to investigate the existence of water divide inside the unconfined aquifer. Based on the derived analytical solutions, a closed-form analytical formula is developed for calculating groundwater transit time within Dupuit-type flow system. The analytical transit time expression is simply expressed in terms of common mathematical functions. Analytical results are verified against a numerical model and show excellent agreements. The analytical transit time is validated against a numerical one obtained from a two-dimensional model representing a rectangular unconfined aquifer. Based on the explicit closed-form solution, a fully analytical inverse problem to estimate the decay parameter is proposed using a least-square objective function. The solution of the inverse problem simply corresponds to the solution of a nonlinear algebraic equation obtained from the definition of the objective function and the form of the analytical solution.