Steady-state groundwater recharge in trapezoidal-shaped aquifers: A semi-analytical approach based on variational calculus

- A simple expression for areal recharge in trapezoidal aquifers is proposed.
- The solution exhibits strictly close agreement with Modflow simulation results.
- Isotropic and anisotropic aquifers are modeled.
- The anisotropic case is characterized by comparatively lower water levels.
- The triangular aquifer is regarded as a special case of the present formulation.

SummaryThis study presents a semi-analytical solution for steady groundwater flow in trapezoidal-shaped aquifers in response to an areal diffusive recharge. The aquifer is homogeneous, anisotropic and interacts with four surrounding streams of constant-head. Flow field in this laterally bounded aquifer-system is efficiently constructed by means of variational calculus. This is accomplished by minimizing a properly defined penalty function for the associated boundary value problem. Simple yet demonstrative scenarios are defined to investigate anisotropy effects on the water table variation. Qualitative examination of the resulting equipotential contour maps and velocity vector field illustrates the validity of the method, especially in the vicinity of boundary lines. Extension to the case of triangular-shaped aquifer with or without an impervious boundary line is also demonstrated through a hypothetical example problem. The present solution benefits from an extremely simple mathematical expression and exhibits strictly close agreement with the numerical results obtained from Modflow. Overall, the solution may be used to conduct sensitivity analysis on various hydrogeological parameters that affect water table variation in aquifers defined in trapezoidal or triangular-shaped domains.