Theoretical and conceptual models of subsurface hillslope flows

Theoretical and conceptual models for predicting the subsurface flow in a sloping aquifer are presented. One category of models is of the lumped conceptual type that is based on combining the continuity equation with discharge-storage relationships derived from the steady state solutions of the linearized Boussinesq equation. The second categories of models are derived from the linearized unsteady Boussinesq equation using the method of Green's function. The Green's function solution determines the water table profile and the aquifer outflow for nonuniform and nonsteady recharge distribution, arbitrary initial water table profile, and time-varying stream level at the downstream end. The latter theoretical models pertain to a finite domain and to a semi-infinite domain and are of two types depending on the linearization approach. The conceptual and theoretical models are used to derive the outflow and the cumulative outflow expressions for a particular set of conditions, and a comparative analysis is carried out. Semi-infinite aquifer models generate almost the same results as the more complicated finite aquifer models and the quasi-steady state models perform as well as the nonsteady ones for long recharge events. The kinematic wave model is also shown to provide a good approximation of Boussinesq models for steep slopes and high hydraulic conductivity. The application of the various models is also illustrated for three published experimental data. The present models can be easily incorporated in catchments models and can provide a suitable framework for aquifer parameter estimation, base flow separation and recession analysis, and analysis of drainage in landfills.