Analytical Model of Groundwater Flow in a Rectangular Domain for Spatiotemporally Distributed Recharge

Abstract

This study introduces a reliable analytical solution to the two-dimensional linearised Boussinesq equation, applicable to groundwater flow in an anisotropic rectangular aquifer over an impervious stratum. Validation is performed using a numerical solution based on the finite difference method for the nonlinear Boussinesq equation. Additionally, the proposed two-dimensional analytical model for finite or semi-infinite domains effectively estimates groundwater level changes due to diffuse recharge, with converging simulation results as the finite domain size increases. By incorporating Horton's equation to represent the spatiotemporally varying diffuse recharge, the study provides a more accurate method for estimating groundwater level fluctuations, allowing the model to simulate real-world recharge patterns more effectively than previous analytical models. The analytical simulations for groundwater level estimations in the Zeng Wen river basin agree well with field data and display that the peak groundwater levels shift in the $x$ direction at both observation stations, with a time lag of approximately 2–5 days, demonstrating its applicability in predicting groundwater levels under various hydrological and geological conditions. This suggests that the current model offers advantages over previous analytical methods, such as greater accuracy and efficiency, allowing for quicker assessments and broader applicability to various recharge patterns and aquifer conditions.