Simulating groundwater flow to surface water features with leaky beds using analytic elements

A new analytic element approach is presented for simulating the steady-state interaction between groundwater and surface water features with leaky beds. Surface water features (lakes, streams or polders) are modeled as semi-confined areas with fixed but spatially varying water levels that are separated from the aquifer by a leaky layer. Each semi-confined area is modeled locally as a two-aquifer system by adding an additional layer of high transmissivity on top of the aquifer. A theoretical analysis is presented to develop guidelines for the selection of the transmissivity of the additional layer for modeling applications. The analytic element solution allows for the analytic computation of head and flow in the aquifer, and of the vertical leakage through the leaky bed. The approach requires a discretization of the boundary of the surface water feature only. Conditions of continuity of head and normal flow are met exactly at collocation points on the boundary of each semi-confined area; the comprehensive discharge is continuous everywhere. Results of the analytic element approach compare well with an exact solution for flow to a circular lake; either the lake level or the net lake flux may be specified. Good agreement was also obtained with a high-resolution finite-difference model for a case where the surface water boundary coincides exactly with the numerical grid. A model of a meandering river with a variable water table is presented as a practical application.