A quasi-analytical solution for groundwater movement in hillslopes

Abstract

Abstract Several catchment models simplify flow to being a topographically driven, one-dimensional process. Under certain conditions analytical solutions to the governing flow equation can be derived. However, for most hillslopes aquifers, the transmissivity varies with topography and, for unconfined problems, through time. In addition, recharge rates are also functions of time and position. For these conditions analytical solutions for groundwater flow are difficult to derive. In this article a quasi-analytical solution procedure is presented which offers a number of advantages over existing analytical and numerical solutions to groundwater flow in unconfined, one-dimensional, hillslope aquifers. The method is based on dividing the problem domain into elements and assuming parameter values within the elements are constant. In Laplace transform space a simple analytical solution to a constant coefficient form of the governing groundwater flow equation can be derived. This analytical solution is used as an element “basis function”; each element equation coupled together by conditions on mass and dependent variable continuity. Time stepping can be introduced to account for transient parameter variation. The method is similar in some respects to the Laplace transform/finite analytic procedure, but avoids overlapping elements and parameter definitions. The developed method is applied to four hypothetical problems for groundwater movement in a one-dimensional hillslope and results are compared with finite element analyses. The method is shown to be able to include spatial and temporal variations of parameters in a format that offers highly accurate solutions and computational efficiency.