Approximate Solutions for Horizontal Unconfined Aquifers during pure Drainage Phase

We introduce and analyze conceptual approximations of the Boussinesq equation for horizontal unconfined aquifers during the pure drainage phase, without any reharge and zero-inflow conditions. We employ a variety of methods, which include wave solution, variable separation and series expansion to constract a new model and explore its behavior and performance against the Boussinesq equation and its exact (non-closed form) solution, at early and later times. The modeled non-linear forms are finally linearized concluding with explicit analytical expressions that incorporate most of the basic characteristics regarding the evolution of the water table and the outflow from the exact Boussinesq equation under different initial conditions. The endeavors of this work might be useful for theoretical and modeling purposes related to this problem.