Modeling groundwater-surface water interactions using the Dupuit approximation

Global errors in head and/or discharge may be introduced when groundwater flow to a stream is modeled using the Dupuit approximation. We consider a simple case of steady groundwater flow in the vertical plane to a horizontal stream bed in direct connection with the aquifer, and compare solutions to the exact problem with Dupuit solutions where common representations of the stream are chosen. In all cases considered, adopting the Dupuit approximation introduces global errors into the mathematical model, and the magnitude of the errors depends on the regional flow conditions. This behavior makes calibration of a model difficult and limits the predictive abilities of the model under conditions of changed regional flow. The global errors and their dependence on flow conditions can be minimized, but not eliminated by treating the resistance of a fictitious leaky stream bed as an effective parameter. We propose an alternate Dupuit model of groundwater-surface water interaction and demonstrate, for the case considered, that adding a second effective parameter allows us to eliminate global errors in head and discharge, and eliminate the dependence of the effective values on the flow field. Explicit expressions are provided to evaluate the two effective properties. We propose that the results be used as a general guideline for modeling groundwater-surface water interaction at streams. (c) 2004 Elsevier Ltd. All rights reserved.