Analytical study on 2D groundwater flow in a sloping unconfined aquifer under spatiotemporal recharge

Abstract

Abstract This study presents a two-dimensional (2D) model for simulating groundwater level variations in sloping aquifers, where rainfall is the primary recharge source. The model uses Heaviside functions to represent spatiotemporal surface recharges and is based on the 2D linearized Boussinesq equation. Analytical solutions were derived using an integral transformation method, allowing for analysis of aquifer characteristics, such as anisotropy, slope, and hydraulic conductivity. In contrast to studies that assume total rainfall becomes recharge, this model employs Horton’s infiltration equation for more accurate estimates, showing strong alignment with field data. The results highlight the significant impact of anisotropy on groundwater flow, particularly when the hydraulic conductivity ratio $${K}_{x}/{K}_{y}$$ K x / K y exceeds 10, leading to predominantly $$X$$ X -direction flow, with the flow rate increasing by 1.3 times compared to the scenario where $${K}_{x}/{K}_{y}=1$$ K x / K y = 1 under slope angles $${\theta }_{x}={\theta }_{y}=5^\circ$$ θ x = θ y = 5 ∘ . This model also aids in predicting groundwater behavior in small watersheds without field data.

Keywords

• Sloping aquifer
• Integral transformation
• Groundwater
• Anisotropy