Comparison of Analytical Solutions to Evaluate Aquifer Response to Arbitrary Stream Stage

Abstract

Groundwater table response to arbitrarily varied stream stage is a practical engineering issue related to stream-aquifer interaction processes. A one-dimensional (1D) linear Boussinesq equation is invariably used in the interpretation. Previous studies have emphasized the employment of convolution integration and pulse or function fitting methods to solve this problem. Consequently, complicated mathematical derivations and numerical calculations are involved during an analysis. In this paper, we transformed the previously published solutions into an easily solved formation to investigate this problem. Then the solution is solved based on the trapezoidal method and applied in cases. The solution fits favorably with the previous classic solutions in the simulations of groundwater table responses to sinusoidal, linear, and unit step rise varied stream stages. This approach was also applied to interpret groundwater table fluctuations induced by typical flood waves and field measured stream stage fluctuations. The developed approach performs well compared with those solved numerically by function fitting methods and modular finite-difference flow model (MODFLOW). This analytical solution potentially provides a rapid and simple way to estimate aquifer responses to any type of stream stage variation.