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 \({K}_{x}/{K}_{y}\) exceeds 10, leading to predominantly \(X\)-direction flow, with the flow rate increasing by 1.3 times compared to the scenario where \({K}_{x}/{K}_{y}=1\) under slope angles \({\theta }_{x}={\theta }_{y}=5^\circ\). This model also aids in predicting groundwater behavior in small watersheds without field data.

本研究提出了一个二维 （2D） 模型，用于模拟倾斜含水层中的地下水位变化，其中降雨是主要补给源。该模型使用 Heaviside 函数来表示时空表面补给，并基于 2D 线性化 Boussinesq 方程。使用积分变换方法得出分析解决方案，从而可以分析含水层特征，例如各向异性、坡度和水力传导率。与假设总降雨量成为补给的研究相比，该模型采用 Horton 渗透方程进行更准确的估计，显示出与现场数据的高度一致性。结果强调了各向异性对地下水流的显著影响，特别是当水力传导率比\（{K}_{x}/{K}_{y}\）超过10时，导致主要是\（X\）方向的流动，与\（{K}_{x}/{K}_{y}=1\）在坡度角\（{\theta }_{x}={\theta }_{y}=5^\circ\）下的情况相比，流速增加了1.3倍.该模型还有助于在没有现场数据的情况下预测小流域中的地下水行为。