Comparative analysis between analytical approximations and numerical solutions describing recession flow in unconfined hillslope aquifers

Recession flow of aquifers from a hillslope can be described by the non-linear Boussinesq equation. Under strong assumptions and for specific conceptual formulations, different authors derived analytical approximations or linearized versions to this partial differential equation. A comparative analysis between some analytical approximations of the Boussinesq equation and the numerical solution of the recession flow of an unconfined homogeneous aquifer (horizontal, inclined and concave aquifer floor) was carried out. The objective was to define the range where the analytical solutions approximate the numerical solution. The latter was considered in this study as the reference method, because it requires fewer assumptions. From the considered analytical approximations, exponential decay relationships were found to be mainly valid for fine domain materials when horizontal, mild slopes (less than 2%) and concave aquifer floors were considered, but failed to reproduce coarse aquifer numerical model outflows, in contrast to the quadratic decay relationship, which better reproduce outflows in such domains. On the basis of the comparative analysis, it has been found that recession flows obtained with the considered analytical approximations yield similar values only for certain ranges of aquifer properties and geometries.