A QUASI-ANALYTICAL SOLUTION FOR GROUNDWATER MOVEMENT IN HILLSLOPES

Several catchment models simplify flow to being a topographically driv en, one-dimensional process. Under certain conditions analytical solut ions to the governing flow equation can be derived. However, for most hillslopes aquifers, the transmissivity varies with topography and, fo r unconfined problems, through time. In addition, recharge rates are a lso functions of time and position. For these conditions analytical so lutions for groundwater flow are difficult to derive. In this article a quasi-analytical solution procedure is presented which offers a numb er of advantages over existing analytical and numerical solutions to g roundwater flow in unconfined, one-dimensional, hillslope aquifers. Th e method is based on dividing the problem domain into elements and ass uming parameter values within the elements are constant. In Laplace tr ansform space a simple analytical solution to a constant coefficient f orm of the governing groundwater flow equation can be derived. This an alytical solution is used as an element ''basis function''; each eleme nt equation coupled together by conditions an mass and dependent varia ble continuity. Time stepping can be introduced to account for transie nt parameter variation. The method is similar in some respects to the Laplace transform/finite analytic procedure, but avoids overlapping el ements and parameter definitions. The developed method is applied to f our hypothetical problems for groundwater movement in a one-dimensiona l 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 c omputational efficiency. (C) 1998 Elsevier Science B.V.