Flow Recession Models for Sloping Aquifers

Abstract

Recession analysis is a powerful tool for determining the hydraulic properties of a riparian aquifer. The basis of the method relies on analytical solutions of the nonlinear Boussinesq equation in horizontal aquifers. In the present work, the nonlinear Boussinesq equation for groundwater flow in sloping aquifers is tackled analytically via a refinement of its linear solution in a perturbation series framework. The analytical solution is composed of three parts: the representative depth , the linear solution, and the correction term that is derived from the perturbation expansion. It can handle arbitrary initial water table profile, time‐varying stream level at the downstream end, as well as non‐uniform and non‐steady recharge and seepage distributions. The solution is evaluated for specific drainage conditions to obtain explicit equations for the outflow discharge rates and volume for both finite and semi‐infinite aquifers. The approximate solutions reproduce the original nonlinear behavior with high accuracy due to the introduction and proper quantification of the depth parameter . The linear semi‐infinite solution is used as the basis for introducing a recession flow model and formulating a surrogate model that replicates the original nonlinear behavior. An additional model that is based on the quasi‐steady approach is also presented and constitutes a special case of the surrogate model. Explicit equations relating the discharge rate to the outflow volume are obtained for easy implementation in recession flow analysis. Application of the recession models to practical cases demonstrate their effectiveness in the estimation of the basin‐scale hydraulic conductivity and drainable porosity.